Theory of Everything?

[dogjones]

http://www.newscientist.com/article/mg19626303.900

Check this out - very cool (you have to subscribe I'm afraid).

(snip)

Finally, he filled in most of the 248 points of the E8 pattern, using various "identities" of the 40 known particles and forces. For example, some particles can have quantum spin values that are either up or down, and each of these identities would sit on a different point. He filled the remaining 20 gaps with notional particles, for example those that some physicists predict to be associated with gravity.


(snip)


So far, all the interactions predicted by the complex geometrical relationships inside E8 match with observations in the real world. "As far as I have been able to tell, it's a perfect match of tens of thousands of interactions," says Lisi. "How cool is that?"

(snip)

The crucial test of Lisi's work will come only when he has made testable predictions. Lisi himself accepts this, saying that although his theory is beautiful to him, "nature may disagree". To fill E8 entirely will require more than 20 new particles not envisaged by the standard model. Lisi is now calculating the masses that these particles should have, in the hope that they may be spotted when the Large Hadron Collider - being built at CERN, near Geneva in Switzerland - starts up next year.


Hope that's snipped enough for the mods!

[This Guy]

Interesting, but confusing to my simple mind :boggled:

For those interested, you can view or download Lisi's..whatever at this link (http://www.arxiv.org/abs/0711.0770). I DL'd the PDF file, and glanced at. I was quickly able to determine that I had no freaking clue what he was going on about :D

[dogjones]

I liked the pretty diagrams though.

[sol invictus]

This is a forum for skeptics, so I won't pull any punches: this "theory" is nonsense. He doesn't seem to even understand the meaning of the terms he uses - or at best, he means something else by them than anyone else.

Now, I understand that non-physicists might not be able to tell that by looking at his paper. But when you see a story like that, ask yourself this question - how many times in the history of science has someone come along and suddenly invented a brand-new theory that explained everything? Hint - the answer is a non-negative integer less than 1.

You might also ask how many times the New Scientist has trumpeted a major advance of this type, only to have it fade gently away into the mists on quackery. Answer: an integer of the order of the number of issues of the New Scientist magazine.

[dogjones]

That was quite vehement, well done! Which terms does he not understand then?

[INRM]

1.) If this theory of everything is right -- does this mean that there are no new discoveries to be made in the area of physics -- is everything known? Or are there still new discoveries to be made?

2.) If this theory is nonsense -- How so?


INRM

[This Guy]

1.) If this theory of everything is right -- does this mean that there are no new discoveries to be made in the area of physics -- is everything known? Or are there still new discoveries to be made?

2.) If this theory is nonsense -- How so?


INRM

As for 1.) I hope not! As I understand it, once the theory of everything is discovered, it's game over :eek:

OK, actually it sounds like we need to discover another.. 20(?) elements or something or other to fill in the remaining blanks. But I don't know.

As for 2.) Beats me :D

[dogjones]

As for 1.) I hope not! As I understand it, once the theory of everything is discovered, it's game over :eek:



1) Are you saying it will be a ToE-tal loss?

[ben m]

I'm an experimentalist, not a theorist, so I can't judge the details of this paper. I would point out:

1) It looks like he's just cramming the Standard Model into a higher group representation---that's what all of those tables of numbers are. This is a totally standard technique---he's using E8, well-known unification attempts used SO(5) and SO(10); E8 comes up in string theory a lot. I am not qualified to tell whether he's doing it right. The normal questions about higher unification groups is "do they predict proton decay" and "do they reduce to the SM at low energies". I don't see where he addresses these in a quick scan.

2) He makes assertions about how gravity fits in, but since he doesn't use inline citations it's hard to tell whether these assertions are supported.

3) He's written four other papers on the ArXiV, generally quite little-cited.

4) Follow the "trackbacks" from the ArXiV page. Lubos Motl (a smart guy, but not necessarily an unbiased source) says it's a joke, John Baez and Backreaction (both, again, very smart) think it's interesting. Unless Baez and Bee are speaking with tongue in cheek and I'm not picking it up, that tells me he's not a crackpot.

5) If all he's done is to find a way to represent all of the SM particles in a group, color me unexcited. SO(5) and SO(10) can already do that. The question is whether the group structure is reflected in the physics, or whether he's simply found a desk with approximately the right number of pigeonholes.

[sol invictus]

That was quite vehement, well done! Which terms does he not understand then?

There are many. The one that jumped out at me first is that he seems to think gravity in 4 dimensions is a gauge theory.

[Schneibster]

If Baez ain't calling him a crackpot, I'll wait to see what others have to say. Baez is, after all, the inventor of the crackpot index.

It was suggested (not by me) on a thread on a different forum that waiting to see what Witten has to say is a good idea. I think that's good advice.

[H3LL]

I liked this bit.

Some aspects of this theory are not yet completely understood, and until they are it should be treated with appropriate skepticism. However, the current match to the standard model and gravity is very good. Future work will either strengthen the correlation to known physics and produce successful predictions for the LHC, or the theory will encounter a fatal contradiction with nature.

Other than that I've not any skill to comment.

I just love seeing a statement like this...compared to any woo "theory".

.

[sol invictus]

It was suggested (not by me) on a thread on a different forum that waiting to see what Witten has to say is a good idea. I think that's good advice.

I doubt very much he is going to comment on this, so you're probably going to have to make your own judgment.

[dogjones]

I liked this bit.



Other than that I've not any skill to comment.

I just love seeing a statement like this...compared to any woo "theory".

.

Agreed. In the article I also like this bit:

"Being poor sucks," Lisi says. "It's hard to figure out the secrets of the universe when you're trying to figure out where you and your girlfriend are going to sleep next month."

Nothing to do with the theory of course, but I find it pleasing!

[Cuddles]

I think his comment at the end of the NS article sums it up nicely:
"This is an all-or-nothing kind of theory - it's either going to be exactly right, or spectacularly wrong," says Lisi. "I'm the first to admit this is a long shot. But it ain't over till the LHC sings."

This isn't some crackpot claiming to have magically solved everything. It's someone trained in the relevant field coming up with a new theory that he admits could be completely wrong and needs testing. Hooray for science.

[becomingagodo]

This isn't some crackpot claiming to have magically solved everything. It's someone trained in the relevant field coming up with a new theory that he admits could be completely wrong and needs testing. Hooray for science.

http://www.telegraph.co.uk/earth/main.jhtml?xml=/earth/2007/11/14/scisurf114.xml&CMP=ILC-mostviewedbox

Some more details about the person. Did someone say Einstein?

I kind of like the idear
You know that reality is this
http://www.math.lsa.umich.edu/~jrs/data/coxplanes/E8plane.jpg

Yeah, so he is not so crazy person making the claim.
"For comparison, I think the chances are higher that LHC will see some of these particles than it is that the LHC will see superparticles, extra dimensions, or micro black holes as predicted by string theory. I hope to get more (and different) predictions, with more confidence, out of this E8 Theory over the next year, before the LHC comes online."
Compared to all the other TOE's this seems to be better. Aleast when we start the E8 religion we have a nice picture.

[sol invictus]

This isn't some crackpot claiming to have magically solved everything. It's someone trained in the relevant field coming up with a new theory that he admits could be completely wrong and needs testing.

I beg to differ, but perhaps my definition of "crackpot" is less pejorative than most people's. To me, a crackpot is someone who thinks everything that came before her/him is wrong (as opposed to a curmudgeon, who thinks everything that came after is wrong). Every scientist falls somewhere on that spectrum, and this guy is on the extreme crackpot end.

It's not that his theory needs experimental testing - as far as I can tell from taking a quick look, it's not even logically consistent at the most basic level.

[Darth Rotor]

You know that reality is this
http://www.math.lsa.umich.edu/~jrs/data/coxplanes/E8plane.jpg
Reality is a spirograph drawing? :confused:
Compared to all the other TOE's this seems to be better. Aleast when we start the E8 religion we have a nice picture.
Who is this "we," kemo sabe? Do you intend to be a founding member of the Church of E8?

The paper: too much of the mathematics I'll have to look up. It is tempting to cordon off a weekend over Christmas vacation time with this paper, and some resources, and see how well I can grasp what he's on about.

I had a wise crack about sacred geometry ready after looking at the diagrams, but I'll hold off. Needs more understanding.

DR

[becomingagodo]

Reality is a spirograph drawing?
Yes

It's not that his theory needs experimental testing - as far as I can tell from taking a quick look, it's not even logically consistent at the most basic level.
You can say that about any theory, atleast this one is trying to make predictions unlike string theory. Quantum mechanics was that seen as logically consistent when it was first proposed?

Saying that the person is really poor, maybe he is trying to get money.

[sol invictus]

You can say that about any theory

No, you can't.

atleast this one is trying to make predictions unlike string theory. Quantum mechanics was that seen as logically consistent when it was first proposed?

People are also trying to get predictions out of string theory, and in fact there are many - such as general relativity - with lots of experimental verification. What there isn't is a result that distinguishes string theory from some putative other theory of quantum gravity (not that one exists).

Most people saw problems with QM, yes. It survived only because it works very very well explaining data which there is otherwise no way to understand. Lisi's "theory" doesn't work, can't make predictions (because it doesn't make sense), and doesn't explain any anomalies in the data. Not a good comparison.

[Pidge]

Lisi's "theory" doesn't work, can't make predictions (because it doesn't make sense), and doesn't explain any anomalies in the data.

Can you actually follow the math, or are you repeating someone else's informed opinion?

For the former, hats off to you, if the latter, cite please?

[sol invictus]

Can you actually follow the math, or are you repeating someone else's informed opinion?

For the former, hats off to you, if the latter, cite please?

The former. Although I'll admit that I didn't pay much attention to it after the first few equations I looked at turned out to be nonsensical.

[Yoink]

The former. Although I'll admit that I didn't pay much attention to it after the first few equations I looked at turned out to be nonsensical.
I haven't a hope in hell of understanding the equations. I'm puzzled, though, that some perfectly respectable scientists seem to be willing to say "this is interesting" if it's actually nonsense, as you allege. Are you just a lot smarter than them, or are they saying "well, something along these lines might be fruitful, even if details of this are unreliable" or what?

I mean, I would have thought that if it were as absurd as you say that they wouldn't have been able to find a single "real" physicist who would say anything other than "it's nonsense."

[sol invictus]

I mean, I would have thought that if it were as absurd as you say that they wouldn't have been able to find a single "real" physicist who would say anything other than "it's nonsense."

Who are the real physicists that say it's interesting?

[ben m]

Who are the real physicists that say it's interesting?

John Baez and Sabine Hossenfelder ("Bee"). Also, the people who scheduled Lisi for the seminar at http://relativity.phys.lsu.edu/ilqgs/.

Plugging gravity into a gauge theory is a perfectly OK thing to do, believe it or not, as long as it's an effective theory which cuts off at some scale---my understanding is that people are reasonably happy to label any plausible massless spin-2 boson a "graviton" and worry about the cutoff later. Plugging the whole Standard Model into an arbitrary symmetry group is also a perfectly OK thing to do. Mixing fermions and bosons? Sounds weird to me, but QFT was never my strong suit, and the author (read his posts at physicsforums.com) claims that he's being careful with the appropriate no-go theorems.

My impression: if it's wrong, it's wrong in a way that's worth writing a paper about on the ArXiV.

(It's also worth noting the contrast with Terence Witt. I don't get the impression that Lisi *sought* the publicity he's now getting, just that the media sort of latched on.)

[sol invictus]

John Baez and Sabine Hossenfelder ("Bee"). Also, the people who scheduled Lisi for the seminar at http://relativity.phys.lsu.edu/ilqgs/.

Baez isn't exactly a physicist, and the only comment I found on his blog was one he posted last summer (long before this paper appeared) after a conversation with Lisi. It's mostly about E8, not this theory. I don't know Hossenfelder - what did she say? Scheduling someone for a seminar does not constitute an endorsement of their work.

Plugging gravity into a gauge theory is a perfectly OK thing to do, believe it or not, as long as it's an effective theory which cuts off at some scale---my understanding is that people are reasonably happy to label any plausible massless spin-2 boson a "graviton" and worry about the cutoff later.

Whoa there. It's probably true that every theory with a massless spin two boson is gravity, but that does not imply that gravity is a gauge theory - and it's just not. Gauge bosons are spin 1, not spin 2, and there is no way to write the Einstein-Hilbert action in d=4 as a gauge theory, despite many failed attempts over the years. It is possible to do in d=3, incidentally, where you can use the Chern-Simons action.

Plugging the whole Standard Model into an arbitrary symmetry group is also a perfectly OK thing to do. Mixing fermions and bosons? Sounds weird to me, but QFT was never my strong suit, and the author (read his posts at physicsforums.com) claims that he's being careful with the appropriate no-go theorems.

This is a good point - equation 1.1 of the paper appears to be utter nonsense. Not only does it add fermions to bosons, which is nonsensical (can you add a vector to a scalar?), it also adds fields with different gauge transformations.

My impression: if it's wrong, it's wrong in a way that's worth writing a paper about on the ArXiV.

I don't agree.

(It's also worth noting the contrast with Terence Witt. I don't get the impression that Lisi *sought* the publicity he's now getting, just that the media sort of latched on.)

Being less of a crackpot than a really big crackpot isn't saying much.

[baron]

This is a forum for skeptics, so I won't pull any punches: this "theory" is nonsense. He doesn't seem to even understand the meaning of the terms he uses - or at best, he means something else by them than anyone else.

Now, I understand that non-physicists might not be able to tell that by looking at his paper. But when you see a story like that, ask yourself this question - how many times in the history of science has someone come along and suddenly invented a brand-new theory that explained everything? Hint - the answer is a non-negative integer less than 1.

You might also ask how many times the New Scientist has trumpeted a major advance of this type, only to have it fade gently away into the mists on quackery. Answer: an integer of the order of the number of issues of the New Scientist magazine. So, because nobody has had any success in the past then every proposition should be discounted? That's a really scientific approach you have there. My suggestion would be that you write a paper refuting this guy's theory (it would only take you a few minutes if, as you say, the entire paper is nonsense). Then you would be in the news and this guy could get back to his surfing. Saying that the person is really poor, maybe he is trying to get money. Like that pesky upstart Einstein. (And everyone knows that the best way to "get money" is to submit a theory concerning one of the most impenetrable areas of science)

(And why does this ******* "WYSIWYG" editor not work anymore?)

[sol invictus]

So, because nobody has had any success in the past then every proposition should be discounted? That's a really scientific approach you have there.

Let's see - I read the paper and concluded that the theory is nonsense. Then I pointed out that someone who doesn't have the background to do that might still be skeptical based on the fact that nothing like this has every happened before, but crackpots with false claims to a theory of everything come along all the time.

Could you point out the non-scientific part of that again?

My suggestion would be that you write a paper refuting this guy's theory (it would only take you a few minutes if, as you say, the entire paper is nonsense). Then you would be in the news and this guy could get back to his surfing.

It most certainly wouldn't be in the news. Physicists already know it's nonsense, and science journalists aren't going to write a story about how a crackpot, marginal theory that no one believed in has been shown to be false. Particularly not one they got suckered into trumpeting as a great advance.

It's understandable - they want to write about something exciting - but it leads to extremely skewed reactions, like this one. A paper like this would ordinarily have been totally ignored along with all the others like it, but it somehow got into the press.

[Schneibster]

Bee thinks the entire point of the first half of the paper is to justify the exact thing you're having a fit about, sol. According to Bee, Lisi claims (and it appears to be true) that the exceptional Lie groups "... have the remarkable property that the adjoint action of a subgroup is the fundamental subgroup action on other parts of the group. This then offers the possibility to arrange both, the fermions as well as the gauge fields, in the Lie algebra and root diagram of a single group." (Bee wrote that here (http://backreaction.blogspot.com/2007/11/theoretically-simple-exception-of.html).) Is this your "adding fermions to bosons?" If so, it appears you may be unfamiliar with this property of the exceptional Lie groups and their algebras.

Bee thinks the problem isn't "adding fermions to bosons;" that's the part she likes. I agree. It's cool, because it's unexpected, but can be demonstrated; and it surprisingly emerges smoothly and naturally from the character of the algebra of the E8 Lie group, or any of the exceptional Lie groups, although the lower-order ones aren't complex enough to serve up the SM. What she doesn't like is the assumptions Lisi has to make to write down an action that breaks the symmetry between Lorentz transformations and gauge transformations; it sounds to me like she thinks it's arbitrary, rather than emerging smoothly from the original idea or from other fundamental considerations.

I've already seen one theoretical physicist whose opinion I respect change that opinion from "it's another crackpot theory" to "hmmm, maybe there's more to this than I thought;" that's the person who suggested that what Witten has to say about it may be interesting. I think it merits further study.

[baron]

Let's see - I read the paper and concluded that the theory is nonsense. Then I pointed out that someone who doesn't have the background to do that might still be skeptical based on the fact that nothing like this has every happened before, but crackpots with false claims to a theory of everything come along all the time.

Could you point out the non-scientific part of that again?

Yep, it's this part ~

I read the paper and concluded that the theory is nonsense. Then I pointed out that someone who doesn't have the background to do that might still be skeptical based on the fact that nothing like this has every happened before, but crackpots with false claims to a theory of everything come along all the time.

You have provided absolutely no scientific rebuttals to back up your argument, nor do I believe you have any. You took a "quick look" at the PDF and stated, "It's nonsense." That's as far from scientific as you can get.

It most certainly wouldn't be in the news.

Nope, because you can't provide it.

I don't understand the majority of the paper and I'm not afraid to say so. Based on the feedback from people who are verifiably more knowledgable in this area than me, I am prepared to accept that it's very unlikely the theory will amount to anything. What I decline to take on board are the views of some random person who glances at the paper for 5 minutes and dismisses it for no reason.

[sol invictus]

Bee thinks the entire point of the first half of the paper is to justify the exact thing you're having a fit about, sol. According to Bee, Lisi claims (and it appears to be true) that the exceptional Lie groups "... have the remarkable property that the adjoint action of a subgroup is the fundamental subgroup action on other parts of the group. This then offers the possibility to arrange both, the fermions as well as the gauge fields, in the Lie algebra and root diagram of a single group." (Bee wrote that here (http://backreaction.blogspot.com/2007/11/theoretically-simple-exception-of.html).) Is this your "adding fermions to bosons?" If so, it appears you may be unfamiliar with this property of the exceptional Lie groups and their algebras.

No no no - that's yet another problem. You're confusing gauge transformations with Lorentz transformations.

In the standard model, the fermions transform in the fundamentatal representation of various gauge symmetries. Gauge bosons transform in the adjoint. It is not possible to combine them into a single representation of a larger gauge group, no matter what properties the subgroups of that group have, because gauge transformations in the larger group will always mix them. So that by itself kills this idea.

However that's not what I was talking about. In the very first equation of his paper, he adds fermions to bosons. Never mind the gauge transformations - those are fields with different transformation properties under the Lorentz group, and with different statistics. You simply cannot add fields with different spin. It makes as much sense as adding fish to spoon. You can combine them into a multiplet (which is not what he is doing), but only if the group is NOT a Lie group - it must be a supergroup, meaning that the raising operators are fermions. E8 does not have that property.

Incidentally, there is a mathematical theorem, called the Coleman-Mandula theorem, which proves rigourously what I am saying here. The only exception to that theorem is when the symmetry group is a supergroup, so that the generators are fermions. That's what happens in supersymmetry, but there is no supergroup here.

[sol invictus]

You have provided absolutely no scientific rebuttals to back up your argument, nor do I believe you have any.


Yes I did. You just didn't both to read them. There is more detail in my post above.

The paper is utter nonsense. The very first equation (which defines the model) is not even wrong. I'm not going to waste my time reading the rest of it carefully (although I did have a look out of curiousity).

[Schneibster]

No no no - that's yet another problem. You're confusing gauge transformations with Lorentz transformations.I thought that was the second part. And I distinctly recall you stating you couldn't add fermions to bosons, and looking below, I see you said it again- and I'm still not convinced that's what he's doing (at least not as a whole symmetry).

Also, your statement that I'm confusing Lorentz transformations with gauge transformations has no basis I can see; as far as I know, I was only talking about your statement that he is "adding fermions and bosons;" and about Bee's assertion that the fermions and bosons can indeed be combined in this way, and (although neither she nor I explicitly stated it) that this is not technically "adding fermions and bosons" in the sense you seem to mean it. Have you forgotten that he's implying that there is some spontaneously broken symmetry between these topologically distinct elements?

And I don't see where Lorentz transforms come into that, except tangentially as part of the representation of spin. Given that the fermions appear as the elements of the algebra, and the bosons as the operations (i.e., gauge transforms) of the fundamental group that algebra represents, I'm afraid I neither see why you say he's "adding fermions and bosons," nor what the Lorentz transforms have to do with the matter at this early stage of the development of his argument.

Perhaps you should specify which particular equation you claim is "adding fermions and bosons."

In the standard model, the fermions transform in the fundamentatal representation of various gauge symmetries. Gauge bosons transform in the adjoint. So far, so good; that's my understanding too.

It is not possible to combine them into a single representation of a larger gauge group, no matter what properties the subgroups of that group have, because gauge transformations in the larger group will always mix them. So that by itself kills this idea.I don't follow that. I can only make sense of it if I assume that you have forgotten spontaneously broken symmetries.

However that's not what I was talking about. See, this is totally incomprehensible to me; it seems to me it was precisely what you were talking about, because you said, "adding fermions to bosons."

In the very first equation of his paper, he adds fermions to bosons. Please specify which "first equation" you are talking about. The first equation I see is,
(spin connection) (element of) so(3,1) [which is equivalent to] Cl2(3,1)
and this is merely a statement of the equivalence of the spin group to the Clifford bivector form of (what I think is) the same group.

Again, perhaps you'd better be a bit more specific about which "first equation" you're talking about. I don't see anything inherently wrong with that one, and I don't see what it's got to do with "adding fermions to bosons."

Never mind the gauge transformations - those are fields with different transformation properties under the Lorentz group, and with different statistics. You simply cannot add fields with different spin. It makes as much sense as adding fish to spoon. You can combine them into a multiplet (which is not what he is doing), but only if the group is NOT a Lie group - it must be a supergroup, meaning that the raising operators are fermions. E8 does not have that property.I'm obviously missing something here. Yes, yes, I know you can't add fermions to bosons; the laws of spin and statistics for fermions dictate the exclusion principle, whereas the laws of spin and statistics for bosons dictate an "inclusion principle," in which identical bosons are [I]more likely to be found in identical states than different ones; this is the reason for coherence in a laser beam, or for the curious behavior of BECs. What I don't see is why you state so definitively that that is what he's doing. Again, I can only make sense of this if I assume you have forgotten spontaneous symmetry breaking.

Incidentally, there is a mathematical theorem, called the Coleman-Mandula theorem, which proves rigourously what I am saying here. The only exception to that theorem is when the symmetry group is a supergroup, so that the generators are fermions. That's what happens in supersymmetry, but there is no supergroup here.Again, yes, of course I know why fermions and bosons are topologically distinct and cannot be continuously transformed into one another; I don't need to be told even of the existence of the Coleman-Mandula theorem. That's not the issue. The issue is, you're claiming he's doing something that violates it, and I don't see proof of that.

But since you've brought it up, the Coleman-Mandula theorem explicitly does not constrain spontaneously broken symmetries; and it has to be obvious that any symmetry proposed for topologically distinct fermions and bosons would have to be spontaneously broken, and either at extremely high energies, because otherwise our universe would not contain differentiable matter and energy, or we would be able to create a non-diffentiable state in particle accelerators of only moderate energy; or that it would be broken by a phase transition from a very different state of affairs than obtains in our universe. Perhaps it's this limitation on the theorem that you've missed; and that's consistent with my assumption above. Then again, perhaps I've completely misunderstood your argument.

I will confess that I do not have the math to really fully comprehend this paper; and this post may be gobbledegook as a result. If it is, take pity on me and explain it without all the leaps of logic that I'm missing; I'm sure that will be valuable for most others here too. But keep the point about spontaneously broken symmetries in mind; I suspect that's something you might have missed.

[sol invictus]

Sorry if my previous post wasn't very clear. I don't have a lot of practice explaining physics in this format.

Let start with the first equation of the paper, eq. 1.1:

A = 2 ω + 4 eφ + B + W + g + ( .ν e + .e + .u + .d) + ( .ν μ + .μ + .c + .s) + ( .ν τ + .τ + .t + .b)

In this equation (sorry about the crappy formatting) everything inside () is a fermionic field, and everything before the first () is a bosonic field. For example, u is the field that creates an up quark (which is a spin 1/2 Dirac fermion), and g is the gluon field (a spin 1 gauge boson). Shortly after equation 1.1 he writes:


In this connection the bosonic fields, such as the strong g = dx_i g^{A i} T_A, are Lie algebra valued 1-forms, and the fermionic fields, such as u = u^A T_A, are Lie algebra valued Grassmann numbers.

Let me explain what this "means". "Lie-algrebra valued" refers to the fact that everything is multipled by T_A, where T_A are a set of matrices that generate some representation of E_8. In the equation for g, dx_i is evidently an infinitesimal displacement, and the "i" index is a spin 1 (4-vector) index, which is contracted with the spin 1 index on the gauge field A. So A is a 1-form, a vector field, as it should be.

Unfortunately for Lisi, u is a dirac fermion. It must be a Grassmann (anti-commuting) field, and it must have a spin 1/2 Lorentz index - which is contracted with what? Either (as he says) u really doesn't have a spinor index, in which case it's a Grassmann scalar or 1-form (in which case it's a ghost, a field that violates spin-statistics and unitarity, and also isn't a quark), or it's a Grassmann fermion and he forgot to write the index, in which case there's a mismatch in the Lorentz transformation properties between those two terms. Either way it's nonsense.

You cannot add a field that transforms in the spin 1 rep. of the Lorentz group to a field that transforms in the spin 1/2 rep.

The other problem (the one Bee seemed to be addressing and I mentioned above) is the one related to the standard model gauge transformations of these fields.

As for this issue of spontaneous breaking, I took a look at the rest of the paper to see if that's mentioned. I found equations 3.7 and 3.8, which for some reason I can't paste here. You'll have to look at them yourself. In 3.7 he writes down his action, which is some arbitrary thing with a Lagrange multiplier field B he's pulled out from somewhere, which EXPLICITLY (not spontaneously) breaks E_8. After integrating out B he gets the action in 3.8, which again manifestly breaks E_8 explicitly.

Not to be hyperbolic, but this is even stupider. You cannot break a gauge invariance explicitly - by definition. A gauge invariance is a redundancy in your description - it's not a real symmetry. If it's explicitly broken it wasn't a gauge invariance.

In that vein I can write down my own theory of everything. It has an SU(70293424) "gauge" invariance, but it's explicitly broken down to SU(3)X(SU(2)XU(1) plus gravity. You can find the action for my theory in any field theory book. It's extremely successful - it explains almost everything!

Yet another problem (very minor compared to the others) I see in eq. 3.8 is that the gravitational part (\phi^2 R - \phi^4) is almost certainly ruled out by equivalence principle tests.

Anyway, I'm sorry to be perhaps overly vehement, but as far as I can tell this guy simply doesn't understand even the basic definitions of the things he's writing. I'm not going to waste any more of my time looking at this piece of junk.

[Schneibster]

Sorry if my previous post wasn't very clear. I don't have a lot of practice explaining physics in this format.That's OK. But I hope that you will continue in this thread for a bit longer; I have a few observations and questions.

Let start with the first equation of the paper, eq. 1.1:

A = 2 ω + 4 eφ + B + W + g + ( .ν e + .e + .u + .d) + ( .ν μ + .μ + .c + .s) + ( .ν τ + .τ + .t + .b)

In this equation (sorry about the crappy formatting) everything inside () is a fermionic field, and everything before the first () is a bosonic field. OK, we're good. I see that what's inside the ()s is a field of "fermionness" partially differentiated wrt time, for each of the fermions.

For example, u is the field that creates an up quark (which is a spin 1/2 Dirac fermion), Well, I guess in more traditional terms I'd say that's the squared wave equation over some dimension (which might or might not be a physical dimension- it might be a charge, say, or a rotation, or a quantum number), representing the probability that there will be an up quark at that "location" (whatever "location" might mean in this context). Right?

As far as it having to be a fermion, i.e. a spin 1/2 particle that obeys Fermi-Dirac statistics, yes, I can see why that has to be so; it could not otherwise be the generator (that is, the conserved quantity, or charge) of the "upness field" because an up is a fermion.

and g is the gluon field (a spin 1 gauge boson). OK, I'm cool with that too. Same arguments apply, boson substituted for fermion, except that the color charge that a gluon generator represents isn't physically a piece of matter, but a force, and must therefore be a boson as well.

Shortly after equation 1.1 he writes:

<snip>

Let me explain what this "means". "Lie-algrebra valued" refers to the fact that everything is multipled by T_A, where T_A are a set of matrices that generate some representation of E_8. Right, OK, I understand you so far. T_A (I'll stick with your notation) has to be the generator of the representation of E_8 from the "direction" the gauge is fixed in. But stop right there- do you see where this leads? Think about it a moment- we've fixed a gauge. That's implicit in the fact that the representation requires that this matrix T_A multiply the field. I know what you're going to say: "Yes, but you can't fix the same gauge for a fermion and a boson." As it turns out, that's correct, but only if the Poincare symmetry applies. Should the Poincare symmetry not apply, then there are conditions under which a gauge could be fixed that applies to both bosons and fermions. I'll refer to that again shortly.

In the equation for g, dx_i is evidently an infinitesimal displacement, and the "i" index is a spin 1 (4-vector) index, which is contracted with the spin 1 index on the gauge field A. So A is a 1-form, a vector field, as it should be.

Unfortunately for Lisi, u is a dirac fermion. It must be a Grassmann (anti-commuting) field, and it must have a spin 1/2 Lorentz index - which is contracted with what? Either (as he says) u really doesn't have a spinor index, in which case it's a Grassmann scalar or 1-form (in which case it's a ghost, a field that violates spin-statistics and unitarity, and also isn't a quark), or it's a Grassmann fermion and he forgot to write the index, in which case there's a mismatch in the Lorentz transformation properties between those two terms. Either way it's nonsense.This is where we start to go in different directions, as a result of the difference above. There are always possible ways to fix the gauge so that this is true- but there are also circumstances under which there are possible ways to fix it so it is not; so that the same gauge fixing applies to both fermions and bosons. And that's only true if Poincare symmetry does not apply. And again I'll defer justification of that statement. Don't worry, I'll get to it.

You cannot add a field that transforms in the spin 1 rep. of the Lorentz group to a field that transforms in the spin 1/2 rep. This is the right place. Here I will note that this is proven by the Coleman-Mandula theorem, as you have already stated. However, it turns out that there is a loophole in the Coleman-Mandula theorem: it assumes that the background space in which it is applied exhibits Poincare symmetry. And apparently, Lisi asserts that his theory does not have a background space that exhibits Poincare symmetry. I'm not sure yet, but I think he recovers Poincare symmetry from the theory; it's not a background symmetry. I'll tell you this, my eyes just about rolled up into my head when I saw him say that, and if the Poincare symmetry isn't demonstrably recoverable from this theory, I'm going to give up and agree with you, and assert it's just not physical. He says it's a de Sitter space, whatever the hell he means by that (that's some pretty old relativity yer cookin' up there, pardner, sure it's still good to eat?).

Now, I'll say this: I searched that paper, and he doesn't mention the Lorentz or Poincare symmetries or groups once, anywhere. He keeps talking about the "spin connection." He talks about spinors. But he doesn't actually speak of spin until he recovers it as a quantum number of the fermions from the theory. Now, the quantum number, spin, is the representation of the quantum in the rotation group; and the rotation group is one of the two subgroups of the Lorentz group, and one of three of the Poincare group; translations are a normal subgroup of only the Poincare group, and boosts are a subgroup of both, like rotations; hyperbolically speaking, boosts are rotations in the three "invisible" planes, x-t, y-t, z-t and are non-abelian just as the ordinary rotations are, which is why the Lorentz group is made up of the rotation group and the boost group; it's the group of possible rotations in spacetime. And if he's recovering the spins of the fermions from this theory, then he might recover the boosts and the translations as well, and if that's true, then suddenly we're talking about a theory whose background space is not our spacetime, but a completely different set of "dimensions."

Now, I got no idea what that means. I think I want to see what "dimensions" this E_8 group exists in, number one urgent. But I'll say this: the last time I know of that anybody came up with anything like this was when Theodor Kaluza walked into Einstein's study.

The other problem (the one Bee seemed to be addressing and I mentioned above) is the one related to the standard model gauge transformations of these fields.OK. I've already got enough to chew on. I'm going to hit the sites and read some more. Let's put this part off.

As for this issue of spontaneous breaking, I took a look at the rest of the paper to see if that's mentioned. I found equations 3.7 and 3.8, which for some reason I can't paste here. You'll have to look at them yourself. In 3.7 he writes down his action, which is some arbitrary thing with a Lagrange multiplier field B he's pulled out from somewhere, which EXPLICITLY (not spontaneously) breaks E_8. After integrating out B he gets the action in 3.8, which again manifestly breaks E_8 explicitly.

Not to be hyperbolic, but this is even stupider. You cannot break a gauge invariance explicitly - by definition. A gauge invariance is a redundancy in your description - it's not a real symmetry. If it's explicitly broken it wasn't a gauge invariance. I got some problems with this. I'm thinking about the Goldstone and the Higgs, and the electroweak breaking resulting in fermions acquiring rest mass. And I'm thinking about the fact that electroweak symmetry is a gauge symmetry; that is, a gauge invariance under which EM and the weak force are equivalent. It appears to me, and I could be wrong but this is how I understand it, that this is a gauge invariance, that it's a real symmetry, and that it's broken. It appears to be explicitly broken, and it appears it breaks spontaneously when the temperature gets low enough- at high enough energy, so goes the theory, it is restored. The Higgs and Goldstone become indistinguishable, mass disappears, and the photon, W, and Z become indistinguishable. Do I have that right? And if so, how does that relate to your statement above? What's the catch?

And here's another point about this theory: what the heck is the electroweak symmetry breaking doing creating mass, the charge of the gravity field? I been thinkin' about that a LONG time; never said anything about it, either. But here's this guy talking about graviweak. Hmmmm.

[In that vein I can write down my own theory of everything. It has an SU(70293424) "gauge" invariance, but it's explicitly broken down to SU(3)X(SU(2)XU(1) plus gravity. You can find the action for my theory in any field theory book. It's extremely successful - it explains almost everything!LOL, no doubt. I hear you, but I think there might still be something to this.

Yet another problem (very minor compared to the others) I see in eq. 3.8 is that the gravitational part (\phi^2 R - \phi^4) is almost certainly ruled out by equivalence principle tests. This one also I'll leave out- I'll just say preliminarily that I'm not sure the equivalence principle applies in a "space" that isn't made up of the four ordinary spacetime dimensions.

Anyway, I'm sorry to be perhaps overly vehement, but as far as I can tell this guy simply doesn't understand even the basic definitions of the things he's writing. I'm not going to waste any more of my time looking at this piece of junk.I hope you'll not consider it a waste of time to at least explain some of the above matters to us all. If this is going to get the kind of airplay that it seems to be acquiring, it would be awesome to know whether it's garbage or not. Quite frankly, right or wrong, I certainly stand to learn a great deal from you, if you'll humor me.

[Schneibster]

We're up to four threads in 24 hours now. Interest is high.

I made it to the bottom of the Backreaction thread. Lisi is starting to get hammered with email and calls from the press. He has stated:

Sorry I haven't been able to comment in a while -- the media is... well, being the media. And my inbox exploded. I expect to have more time in a few days when the attention simmers down. However, if there are SHORT (one or two sentence) questions posted, that are CONSTRUCTIVE (i.e. will help clarify matters) I will come back and do my best to answer them. Long posts, and anything posted by people who have been mean in this thread, will be ignored. I'm hoping to help explain the math here, which will be familiar to some but not others. The theory might turn out to be wrong about nature, but the math does make sense.That seems to be the word on that. It sounds like he's finally tired of Motl and that ilk.

A commenter I have occasionally encountered in the past says, paraphrasing, "Rather than make 3000 word posts criticizing someone's stuff, why don't you go make a theory of your own? A troll with a PhD is still a troll." I found that amusing.

He's still not maintaining it's physical; not yet. I think it's pretty clear he's no woo. This is the real deal, as far as being mathematically viable. It's also incomplete; the symmetry breaking and the action are hand-chosen. All this shows is that it's possible to construct a theory that unifies gravity and the SM this way, not how to do it yet. To do that, the action would need to emerge naturally and gracefully, and the symmetry would have to be broken by a provable mechanism.

I was only partially correct about whether Poincare symmetry emerges, and I have seen no statement directly asserting that either Lorentz or Poincare symmetry are recovered; all arguments along the lines of the one I was responding to in my previous post boil down to, "This is how it is done in BRST. It works." This guy is not doing something totally new in that respect. And he's not the only one saying so.

I'm still not quite clear on how the dimensions that underlie this theory are constructed, but there is apparently at least some contact with a relativistic spacetime; I'm not absolutely convinced he's absolutely clear on that. BRST seems to me to do some pretty wild stuff with these "ghosts." They aren't supposed to be physical particles; they're a computational mechanism, according to the Wikipedia article, and are not permitted to have external lines in a Feynman diagram. They can only be used as virtual particles, IOW. They are therefore permitted to violate the spin-statistics theorem (which I often call the Laws of Spin and Statistics, for those who have read what I have posted in the past). It appears that adding them to either bosons or fermions is therefore permitted in BRST.

What it appears he is doing is recovering spinors from some of these additions, and those spinors are apparently capable of being physical particles and having external lines in a Feynman diagram. He is saying that this, also, is an accepted procedure in BRST, and I've found nothing to deny it (although I'm still looking for substantiation).

Bottom line: it's been through a small part of the mill, has been shown to be based quite properly on foregoing work by both Lisi and others, has survived attack by trolls, and is still ticking. It is not, as Bee quite properly points out, a ToE other than in hyperbole (and apparently in the popular press, no surprise there). It is, however, a promising approach, and an innovative one. Garrett Lisi has made quite a splash, and I suspect we'll be hearing more about this as time goes on. Now the hard work starts (for everyone but Garrett Lisi- he's been doing hard work on it from the word "go").

[sol invictus]

This is the right place. Here I will note that this is proven by the Coleman-Mandula theorem, as you have already stated.

The Coleman-Mandula theorem proves something much more powerful. What I said is simply a consequence of Lorentz invariance.

De Sitter space has nothing to do with this. Any non-singular space (including dS) is locally Minkowski, and one of the few things we know extremely well about physics is that it is Lorentz invariant - that is, that it obeys Einstein's postulates for special relativity (physics doesn't depend on absolute motion or on absolute direction). It's Lorentz invariance that allows us to classify particles as spin 0, spin 1/2, spin 1, etc., which is what we see in nature. And therefore you cannot add fields representing two such particles. It's exactly like adding a number to a vector - it means nothing.

Even if you don't follow that fully, ask yourself the following question - if we do an experiment involving particles which are around 10^{-15} meters in size, interacting in a tiny fraction of a second and detected a meter away, should it matter that the observable universe is 13 billion lightyears across? Because that's what you said when you said changing to de Sitter space (not a terrible approximation to the universe on large scales) would fix this problem.

Of course it doesn't matter, and representations of the Lorentz group are extremely accurate approximations to the true states of the exact theory desribing particles. We know that both experimentally and theoretically, and adding fields of different spin violates that maximally.

To reiterate - either his u field has integer spin, in which case he has no spin 1/2 particles in this theory and therefore can't describe any of the particles that consitute matter (and it's also a ghost and the theory will contain negative probabilities), or it has a spin index, in which case his theory violates Lorentz invariance maximally and is ruled out by some incredible number of orders of magnitude by just about every experiment in physics. That almost makes the problem sound less trivial than it is, but there you have it.


I got some problems with this. I'm thinking about the Goldstone and the Higgs, and the electroweak breaking resulting in fermions acquiring rest mass. And I'm thinking about the fact that electroweak symmetry is a gauge symmetry; that is, a gauge invariance under which EM and the weak force are equivalent. It appears to me, and I could be wrong but this is how I understand it, that this is a gauge invariance, that it's a real symmetry, and that it's broken. It appears to be explicitly broken, and it appears it breaks spontaneously when the temperature gets low enough- at high enough energy, so goes the theory, it is restored. The Higgs and Goldstone become indistinguishable, mass disappears, and the photon, W, and Z become indistinguishable. Do I have that right? And if so, how does that relate to your statement above? What's the catch?

When we say a theory has a symmetry, we mean that the defining equations for it are invariant under some transformation. For example, a part of Lorentz invariance is rotation invariance - your experimental apparatus will give you the same results regardless of whether its front end is pointed towards Chicago or New York, right? So that's a consequence of the symmetry of rotation invariance. However that does not mean that a given solution must be rotation invariant - in fact almost all solutions spontaneously break the symmetry (for example the room you're sitiing in now, which is unlilkely to be rotation invariant). What the symmetry does tell you is that if you take that solution and rotate it, the result will also be a solution. Your apparatus once was oriented towards New York, but now towards Chicago, and those are two different solutions - you can tell them apart if you know where New York is - but both are (obviously) valid solutions. So the symmetry is still there, but the particular solution breaks it.

On the other hand if you write down a theory in which the equations do not respect the symmetry from the very beginning, that's what's called explicit symmetry breaking. What it really means is that the symmetry was never there at all, so you might ask why there's even a term for it: it's because sometimes the symmetry is only broken by a little bit and it's still useful to think about it.

Gauge invariances are a special case because they are not really symmetries. I told you above that when you have a symmetry, acting on a solution with the symmetry gives you a new, physical solution. That's not the case with gauge invariances - changing the gauge gives you exactly the same solution you started with. That's because when we use gauge fields to describe a problem we're using bad, redundant variables - more than one choice of variables describes the same physical solution. Tha redundancy leads to all sorts of annoying complications, but it's worth it for the convenience of using the gauge field formalism.

Spontaneous breaking of gauge invariance doesn't mean that gauge invariance is really broken, anymore than it did in my example above, and a gauge transformation will still give you back the same state you started in (unlike the example of rotations above). Spontaneous breaking does have implications for the particle content - generally, the gauge bosons acquire a mass. One example of that (we think) is the electroweak phase transition you mentioned, another is a superconductor.

In any case, an explicitly broken gauge invariance is a contradiction in terms. Either gauge transformations are redundancies in the description, in which case all equations and physical quantifies must be gauge invariant, or they are not, in which case they were not gauge invariances (or symmetries at all).

[Thabiguy]

(Do not mean to interrupt your discussion, Schneibster and sol invictus; do carry on, I follow the debate with great interest.)

Based on what I've read so far, I conclude that at this moment it is best to postpone judgement on the value of the paper, pending further analysis by experts in the field.

But regardless of whether it's agreed that the paper is nonsensical, or whether it makes sense but not physical sense, or whether it is a coherent hypothesis but falsified or unsupported by evidence, or whether it turns out to be a valid physical theory (which would arguably be one of the most surprising and extraordinary events in the history of physics), I'm fairly certain of one thing that will happen next and I'll even make a prediction here:

Before long, we shall be blessed with genuine, unambiguously crackpot claims and pseudotheories referring to, or patched together using terms taken from this paper. Before long, we shall encounter the vertex-edge graph of the E8 polytope, rendered in sundry colors, in paranormal and "alternative science" publications of all sorts, and incorporated in design of various esoteric merchandise.

[Schneibster]

http://science.slashdot.org/comments.pl?sid=362251&cid=21373093 <- a pretty fair non-technical overview of the basic idea. Best I could find quickly.

[sol invictus]

Bottom line: it's been through a small part of the mill, has been shown to be based quite properly on foregoing work by both Lisi and others, has survived attack by trolls, and is still ticking. It is not, as Bee quite properly points out, a ToE other than in hyperbole (and apparently in the popular press, no surprise there). It is, however, a promising approach, and an innovative one. Garrett Lisi has made quite a splash, and I suspect we'll be hearing more about this as time goes on. Now the hard work starts (for everyone but Garrett Lisi- he's been doing hard work on it from the word "go").

What actually happened in that thread is that the people asking reasonable questions never got answers and gave up, leaving the crackpots to talk amongst themselves. You'll notice that even Bee cooled off considerably as she wasn't able to understand the (nonsensical and contradictory) answers Lisi was giving. At this point I imagine she's pretty embarrassed.

BRST is a formal procedure for dealing with gauge fixing (this is part of the annoying complications of gauge invariance I mentioned in my post above). It contains no physics whatsoever; it's just one of several ways to get rid of the redundancy. The BRST charge Q in a bosonic theory (such as Lisi's) is a scalar - it has spin 0 - but it has fermionic statistics. It seems (from some comments he posted in that thread, not from the paper) that Lisi thinks his quark fields can be created by Q. If so he has exhibited yet another basic misunderstanding of the terms and formalisms he's using.

First of all, physical statea are those annihilated by Q. (Or a little more precisely, two states are physically identical if their difference can be written as Q acting on something.) So anything you get by acting with Q is unphysical. If you try to keep those states you'll get negative probabilities, among other problems.

Secondly, as I already mentioned above Q does not have 1/2 integer spin in this theory, so even if you could somehow use it the theory would still not have any matter in it (which we know has spin 1/2).

To reiterate, ghosts cannot appear in the action if the theory is to make sense, and yet Lisi has them in his. His ghosts have integer spin, even though he seems to think otherwise (presumably because he failed to comprehend the difference between fermionic statistics and spin).

This theory is the product of someone with a tenuous grasp of some physics concepts, lots of buzzwords, a talent for language, and enough charisma to temporarily fool a set of people who are pre-disposed to be friendly to crazy ideas - which are many people at the Perimeter Institute, FQXI, the foundation that gave him his grant, and all science journalists. (FYI, FQXI is a branch of the Templeton foundation, the goal of which is to promote connections between religion and science.)

It's deeply embarassing that this story has gotten so much play in the press, and even more so that an established and supposedly responsible physicist - Lee Smolin - seems to have endorsed it. I'm ashamed for the field. I'd be ashamed for Smolin if I had any sympathy for him, but I think he has brought this on himself. He will trumpet anything that looks like an alternative to string theory, because he's staked out an extreme - and extremely rigid - political (not scientific) position, and now he can't back off without losing even more face.

[sol invictus]

A commenter I have occasionally encountered in the past says, paraphrasing, "Rather than make 3000 word posts criticizing someone's stuff, why don't you go make a theory of your own? A troll with a PhD is still a troll." I found that amusing.


By the way this little snide comment really irritates me. In case you've forgotten, it was you that asked me to please keep posting about this and not give up on this topic:


I hope you'll not consider it a waste of time to at least explain some of the above matters to us all. If this is going to get the kind of airplay that it seems to be acquiring, it would be awesome to know whether it's garbage or not. Quite frankly, right or wrong, I certainly stand to learn a great deal from you, if you'll humor me.

So which is it, Schneibster - should physicists keep working, ignore crackpots like this and let nonsense spread freely, or should they post in public forums and try to clarify what's really going on?

Make up your mind.

[Schneibster]

The Coleman-Mandula theorem proves something much more powerful. What I said is simply a consequence of Lorentz invariance.

De Sitter space has nothing to do with this. It has everything to do with it, according to the author (and other credible sources agree). One of the underlying assumptions of the CM theorem is Poincare symmetric space, and that is a loophole; and Lisi is not the first to exploit it.

Any non-singular space (including dS) is locally Minkowski, and one of the few things we know extremely well about physics is that it is Lorentz invariant - that is, that it obeys Einstein's postulates for special relativity (physics doesn't depend on absolute motion or on absolute direction). It's Lorentz invariance that allows us to classify particles as spin 0, spin 1/2, spin 1, etc., which is what we see in nature. And therefore you cannot add fields representing two such particles. It's exactly like adding a number to a vector - it means nothing.You're still assuming that the space in which this theory is defined is Poincare symmetric and that's not necessarily the case. First of all, it's an 8-dimensional space- that's what the 8 in E_8 means. We have only four. Second, you're completely ignoring the fact that the paper does not mention either Lorentz or Poincare symmetry at any point. Third, you're completely ignoring the fact that the spins of the particles are recovered, apparently from the product of the addition; according to what the author has written on Backreaction, after the symmetry is broken. Fourth, you're ignoring that the mathematical formalism involved stems directly from BRST, and BRST has been peer-reviewed and proven. Your arguments would apply just as strongly to BRST as they do to this theory. And that means you're not just arguing against surfer dude, you're arguing against peer-reviewed successful mathematics.

To illuminate this further for those following this debate, BRST uses so-called "ghost" particles that exist only as internal exchanges within Feynman diagrams- virtual particles- as a computational mechanism. These particles need not follow the spin-statistics theorem, because they never emerge from an interaction as real particles. The physical meaning of these ghost particles is a matter of debate in the mathematical physics community. The E_8 theory we are discussing here proposes (if I'm interpreting it correctly, and I know much more today than I did last night) that these ghost particles add with other elements of the theory and that the results are real particle states that we can observe. It is therefore, IMHO, immaterial whether these ghost particles obey constraints that are imposed only on real particles; those constraints need not apply in particles that do not have real physical existence. The underlying concept is very much the same sort of thing as we see in Heisenberg uncertainty; conservation laws and causality can be violated, as long as this violation can never be observed directly.

Even if you don't follow that fully, ask yourself the following question - if we do an experiment involving particles which are around 10^{-15} meters in size, interacting in a tiny fraction of a second and detected a meter away, should it matter that the observable universe is 13 billion lightyears across? Because that's what you said when you said changing to de Sitter space (not a terrible approximation to the universe on large scales) would fix this problem.That's not a valid criticism. You have yet to show that the underlying space in which this theory is enacted is a direct representation of our four-dimensional spacetime. You are arguing that since a rule applies to our four-dimensional spacetime, it must exist in spaces that are formed from dimensions of charge, spin, or other quantum numbers that have nothing directly to do with spacetime physics. This is a non-sequitur. You can easily show that these constraints apply in ordinary four-dimensional spacetime; you have so far not shown that there is either any reason to believe that this theory exists in ordinary four-dimensional spacetime, or that those constraints apply in the dimensionality this theory exists in.

To illuminate further for those following this debate, the point here is that at least one of the underlying symmetries of the Lorentz (and by derivation the Poincare) symmetry is recovered from this theory as a derived quantity, not a basic characteristic. That symmetry is the symmetry of spin; that is, ordinary non-abelian rotational symmetry in four-dimensional spacetime. It is not clear to me, as a result of this, that the underlying space of this theory is even partially our ordinary four-dimensional spacetime. It may have novel characteristics, and the characteristics of our ordinary four-dimensional spacetime may emerge as derived quantities from this theory. It is therefore, IMHO, a non-sequitur to insist that constraints that apply to the derived quantities must apply to that from which they are derived.

Of course it doesn't matter, and representations of the Lorentz group are extremely accurate approximations to the true states of the exact theory desribing particles. We know that both experimentally and theoretically, and adding fields of different spin violates that maximally.Still no sign of connecting the space in which this theory exists to our spacetime, and therefore still a non-sequitur. It does not follow.

To reiterate - either his u field has integer spin, in which case he has no spin 1/2 particles in this theory and therefore can't describe any of the particles that consitute matter (and it's also a ghost and the theory will contain negative probabilities), or it has a spin index, in which case his theory violates Lorentz invariance maximally and is ruled out by some incredible number of orders of magnitude by just about every experiment in physics. That almost makes the problem sound less trivial than it is, but there you have it.You are arguing that he somehow cannot do what BRST already does- recover spinful particles from interactions that do not obey the laws of spin and statistics. Again, your argument is against the constituents on the basis that they must follow the constraints on the result. It does not follow, and in fact it has been shown pretty conclusively that these constraints need not apply to constituents that already do produce results that follow those constraints- in BRST.

When we say a theory has a symmetry, we mean that the defining equations for it are invariant under some transformation. For those following this debate, "symmetry" means much the same thing, but on a far more comprehensive basis, as it means in ordinary conversation. An object that is symmetric can be rotated in certain ways and will appear unchanged. The simplest example is a vase thrown on a pottery wheel; rotate it how you like, it is still the same shape no matter which way you turn it. Symmetries in physics are far deeper in many cases, and indicate that things remain unchanged under far more challenging circumstances; furthermore, there is a theorem, called Noether's Theorem, that states that for every continuous symmetry of physics, there is a corresponding conservation law, and physicists often refer to these symmetries with that well-proven result in mind. Whenever a physicist speaks of a symmetry, not only should the much deeper types of operations under which it might remain unchanged be considered, but also this inherent connection with conservation laws (like conservation of energy or momentum) should be kept carefully in mind. Note also that this connection applies only if the operation is continuous; it must be capable of producing changes incrementally, not discretely; that is, rotations can be any number of degrees, even fractions as far down as we care to take it, but in cases where there are only a limited number of alternatives, for example electric charge which can only be positive or negative, or spin which can only be up or down, Noether's Theorem does not apply and there is no connected conservation law.

For example, a part of Lorentz invariance is rotation invariance - your experimental apparatus will give you the same results regardless of whether its front end is pointed towards Chicago or New York, right? So that's a consequence of the symmetry of rotation invariance. A good example.

However that does not mean that a given solution must be rotation invariant - in fact almost all solutions spontaneously break the symmetry (for example the room you're sitiing in now, which is unlilkely to be rotation invariant). And another good example, in this case of how a symmetry can be broken. One could think of a vase with handles added after it has been thrown- now, there are only two positions that are indistinguishable, not an infinite number; there may be an infinite number of pairs, but each pair is distinguishable from all others. The symmetry of the vase is broken by the asymmetry of the handles.

What the symmetry does tell you is that if you take that solution and rotate it, the result will also be a solution. Your apparatus once was oriented towards New York, but now towards Chicago, and those are two different solutions - you can tell them apart if you know where New York is - but both are (obviously) valid solutions. So the symmetry is still there, but the particular solution breaks it.And yet another good example. The reader will no doubt get a good idea of how a symmetry can be broken by fixing a gauge- and how this doesn't necessarily break the validity of the results, it only changes what particular results you'll get when you look at it from this direction. What is not yet obvious is that the "direction" might not be a matter of physical direction as we ordinarily think of it- it might be a matter of what charge the place we're looking from has, or what color it is, or whether we're suspended from the ceiling or not, rather than anything to do with the thing we're observing- and when we talk about theories as complicated as the one under discussion here is, those definitions of "direction" can be far more esoteric.

On the other hand if you write down a theory in which the equations do not respect the symmetry from the very beginning, that's what's called explicit symmetry breaking. What it really means is that the symmetry was never there at all, so you might ask why there's even a term for it: it's because sometimes the symmetry is only broken by a little bit and it's still useful to think about it.

Gauge invariances are a special case because they are not really symmetries. I told you above that when you have a symmetry, acting on a solution with the symmetry gives you a new, physical solution. That's not the case with gauge invariances - changing the gauge gives you exactly the same solution you started with. That's because when we use gauge fields to describe a problem we're using bad, redundant variables - more than one choice of variables describes the same physical solution. Tha redundancy leads to all sorts of annoying complications, but it's worth it for the convenience of using the gauge field formalism.

Spontaneous breaking of gauge invariance doesn't mean that gauge invariance is really broken, anymore than it did in my example above, and a gauge transformation will still give you back the same state you started in (unlike the example of rotations above). Spontaneous breaking does have implications for the particle content - generally, the gauge bosons acquire a mass. One example of that (we think) is the electroweak phase transition you mentioned, another is a superconductor.

In any case, an explicitly broken gauge invariance is a contradiction in terms. Either gauge transformations are redundancies in the description, in which case all equations and physical quantifies must be gauge invariant, or they are not, in which case they were not gauge invariances (or symmetries at all).This is a point I have not seen addressed elsewhere, and I have to do some research to respond. I'm also going to need to go back to your original statement of it and my original objection to see whether you've properly responded to it, and quite frankly, it's football day and I want to watch some. So I'll get back to you later on this point.

[sol invictus]

You're still assuming that the space in which this theory is defined is Poincare symmetric and that's not necessarily the case. First of all, it's an 8-dimensional space- that's what the 8 in E_8 means.

I'll just address that, which is wrong. The 8 in E_8 refers to the rank of the group (the rank is the maximal number of commuting generators), not to the dimension. The dimension of E_8 is 248. Neither of those numbers have much of anything to do with the dimension of spacetime.

There are many other incorrect statements in your post, but I simply don't have the time or the inclination to respond to them point by point. I'm especially unmotivated to do so given your attitude (which seems to be to argue forcefully about things you don't understand, witness the above), as well as the lack of evidence that anyone else is getting anything out of this thread.

So bye for now, and enjoy your football.

[Schneibster]

By the way this little snide comment really irritates me. In case you've forgotten, it was you that asked me to please keep posting about this and not give up on this topic:The comment was not directed at you, and I am sorry that you took it so. It was directed at Motl, who I have noticed long before now has seriously compromised his credibility by such excursions from properly constructed debate tactics.

So which is it, Schneibster - should physicists keep working, ignore crackpots like this and let nonsense spread freely, or should they post in public forums and try to clarify what's really going on?

Make up your mind.It's made up. I think that ideas like this one, constructed from well-founded prior work, apparently both internally and externally consistent, and exploring an area that is not yet well-explored, need to be aired, and need to be criticized, and for that to happen properly the term "crackpot" needs to be avoided; it's pejorative, unproductive, and stifles constructive discussion. I have seen much the same arguments used against string theory, and if you want my personal opinion on what Motl is doing, it's a reaction against precisely this type of pejorative, unproductive, stifling BS. I don't endorse or agree with what Motl does, but I certainly understand why he does it, and I think it might not be happening, and Motl might be following a far more productive course of action, had it not started elsewhere. That's where science goes when terms like "crackpot" start getting thrown around with regard to well-founded work. I don't like it, and the fact that you're doing it isn't recommending your arguments to me; furthermore, the fact that when your assumptions are challenged, this is where you go, rather than answer those challenges directly, tells me more than I suspect you are going to be entirely comfortable with, and I don't think anyone else reading this has missed that either. You've simply re-asserted rather than answer. We observe that kind of behavior here quite a lot. It's not generally a recommendation of the arguments presented.

I'll be frank; because of your initial use of the term crackpot for an apparently well-founded idea, I've been watching quite closely to see whether you actually know what you're talking about in physics or not. I remain quite concerned that you have asserted that John Baez is not a physicist; he states on the first lin of the home page of his web site (http://math.ucr.edu/home/baez/), "I'm a mathematical physicist." I also remain quite concerned that you have asserted that a degreed physicist publishing a paper in a forum that is intended for pre-publication comment is a crackpot, particularly when the paper is in an area of mathematical physics that is not well explored.

Adding after re-reviewing this thread and seeing your latest post: I note that you fasten onto a single error in order to avoid discussing the rest. My bad; you're correct, the 8 in E_8 doesn't refer to the dimensionality, it refers to the rank; however, it is not incorrect to state that it exists in eight dimensions, and you still have not addressed the objection to your assumptions I brought up. Nor, at this point, do you appear likely to. I'm content to wait until it gets thoroughly reviewed by someone with more credibility than you.

[Yllanes]

My opinion on this paper is roughly that of Sean Carroll in Cosmic Variance (http://cosmicvariance.com/2007/11/16/garrett-lisis-theory-of-everything/).

[Schneibster]

http://www.telegraph.co.uk/connected/main.jhtml?xml=/connected/2007/03/19/ecpattern19.xml <- more on E8, for your delectation.

[sol invictus]

I'm sure I'm going to regret this, but this comment has successfully trolled me back into this for at least one more post. Congratulations.

The comment was not directed at you, and I am sorry that you took it so. It was directed at Motl, who I have noticed long before now has seriously compromised his credibility by such excursions from properly constructed debate tactics.

Lubos has some personality problems, and he doesn't know very well how to relate to people or how to argue convincingly in an online forum (which isn't easy at all even when you are correct and have every possible advantage of facts and expertise - witness this thread). Nonetheless he remains an extremely good physicist, and his comments on physics are almost always spot on if you can get past the insulting tone and crazy beliefs on other subjects.

It's made up. I think that ideas like this one, constructed from well-founded prior work, apparently both internally and externally consistent, and exploring an area that is not yet well-explored, need to be aired, and need to be criticized, and for that to happen properly the term "crackpot" needs to be avoided; it's pejorative, unproductive, and stifles constructive discussion. I have seen much the same arguments used against string theory, and if you want my personal opinion on what Motl is doing, it's a reaction against precisely this type of pejorative, unproductive, stifling BS. I don't endorse or agree with what Motl does, but I certainly understand why he does it, and I think it might not be happening, and Motl might be following a far more productive course of action, had it not started elsewhere. That's where science goes when terms like "crackpot" start getting thrown around with regard to well-founded work.

Fair enough.

In my informed opinion this theory isn't logically consistent and has no relation to the world we live in (or even one we don't). It appears to have been created by someone with a poor understanding of the concepts involved. I don't think it deserves the attention it's getting, it will not pass peer-review, and it will be ignored by mainstream researchers.

Is that better?

I don't like it, and the fact that you're doing it isn't recommending your arguments to me; furthermore, the fact that when your assumptions are challenged, this is where you go, rather than answer those challenges directly, tells me more than I suspect you are going to be entirely comfortable with, and I don't think anyone else reading this has missed that either. You've simply re-asserted rather than answer. We observe that kind of behavior here quite a lot. It's not generally a recommendation of the arguments presented.

I'm sorry, but you have that exactly backwards. I started from the assertion that the theory is crackpot, and I've now explained as clearly as I can precisely why.

I'll be frank; because of your initial use of the term crackpot for an apparently well-founded idea, I've been watching quite closely to see whether you actually know what you're talking about in physics or not. I remain quite concerned that you have asserted that John Baez is not a physicist; he states on the first lin of the home page of his web site (http://math.ucr.edu/home/baez/), "I'm a mathematical physicist."

Let's see - you're quite concerned that I may not know what I'm talking about because I said that Baez "isn't exactly a physicist", but he says he's "a mathematical physicist"?

Whatever.

I also remain quite concerned that you have asserted that a degreed physicist publishing a paper in a forum that is intended for pre-publication comment is a crackpot, particularly when the paper is in an area of mathematical physics that is not well explored.

Anybody can put a paper there (it's not publishing), and there are many crackpots with degrees.

Adding after re-reviewing this thread and seeing your latest post: I note that you fasten onto a single error in order to avoid discussing the rest. My bad; you're correct, the 8 in E_8 doesn't refer to the dimensionality, it refers to the rank; however, it is not incorrect to state that it exists in eight dimensions,

I'm sorry, but it is incorrect. And the reason I didn't respond to the rest is to avoid wasting even more of my time, which unfortunately has happened anyway. Such is life.

and you still have not addressed the objection to your assumptions I brought up. Nor, at this point, do you appear likely to. I'm content to wait until it gets thoroughly reviewed by someone with more credibility than you.

OK, here goes.

You're still assuming that the space in which this theory is defined is Poincare symmetric and that's not necessarily the case. First of all, it's an 8-dimensional space- that's what the 8 in E_8 means. We have only four.

Wrong. See above.

Second, you're completely ignoring the fact that the paper does not mention either Lorentz or Poincare symmetry at any point.

You regard that as a good thing? You do believe in conservation of energy and linear and angular momentum, right? Did you realize those are the result of microscopic Poincare invariance? And why have you ignored what I pointed out: that Lorentz/Poincare invariance is one of the best tested facts in all of science? It's an incredibly strong constraint on theories, but that won't stop Lisi.

Third, you're completely ignoring the fact that the spins of the particles are recovered, apparently from the product of the addition; according to what the author has written on Backreaction, after the symmetry is broken.

Gauge symmetries cannot be explicitly broken, as I already explained. Furthermore there is nothing in the paper, or in those comments, that explains where spin 1/2 particles come from no matter what breaking there is.

Fourth, you're ignoring that the mathematical formalism involved stems directly from BRST, and BRST has been peer-reviewed and proven. Your arguments would apply just as strongly to BRST as they do to this theory. And that means you're not just arguing against surfer dude, you're arguing against peer-reviewed successful mathematics.

I already addressed that above, and you ignored my post. Apparently hypocrisy wasn't enough to stop you from accusing me of doing that to you.

BRST is a perfectly valid way to gauge fix. The references Lisi gave in his comments on that other thread were to papers on conventional BRST - which I understand quite well. Lisi is using BRST nonsensically, and I explained in detail how and why above.

Finally, I'll expand on my previous comment about de Sitter, as that seems to be one of the key points causing confusion here. It is true that Coleman-Mandula doesn't apply to dS, but as I already said my objection is more basic. We do physics by making approximations. One of the approximations we make in particle physics is that space is flat Minkowski space, with an exact Poincare invariance. That is not exactly true - the universe is expanding and contains matter, and therefore is not exactly flat. However it is an incredibly good approximation on the scales relevant to elementary particles. This is because any space is smooth and flat when you look very closely at it (just as it's not obvious the earth is round when you're a human standing on it). Not only is this true theoretically, we have massive confirmation of it from all sorts of experiments (look up constraints on Lorentz violation).

Now, it's fine for Lisi's theory to exist in de Sitter if he wants it to, but there are then two options.

One is that the dS curvature is close to consistent with cosmological data, in which case - for particle physics experiments - we can assume the space is flat to an incredibly good approximation. Then classifying particles by representations of the Poincare group is a good idea, and (as I've explained four times now) Lisi's theory isn't consistent with that.

The other option is that the dS curvature in his theory is extremely high (actually if his theory made sense this would certainly be the case, since he claims not to have any parameters in his theory, and the natural scale for the curvature is very very high - that's called the cosmological constant problem). In that case the size of particles (more precisely, their Compton wavelength), could be of order the curvature radius, and then it's true that representations of the Poincare group would no longer mean much. However in such a theory there would be an event horizon with a radius of about 1 fermi surrounding every point, and all larger structures would be instantly torn to pieces. I'll let you decide for yourself if that's a good theory.

[Schneibster]

I'm sure I'm going to regret this, but this comment has successfully trolled me back into this for at least one more post. Congratulations.You're probably right, it probably was a mistake.

Lubos has some personality problems, and he doesn't know very well how to relate to people or how to argue convincingly in an online forum (which isn't easy at all even when you are correct and have every possible advantage of facts and expertise - witness this thread). Nonetheless he remains an extremely good physicist, and his comments on physics are almost always spot on if you can get past the insulting tone and crazy beliefs on other subjects.I don't question any of this. Still, the tone is there, and he is attacking based on these "crazy beliefs on other subjects," whether exclusively or in addition to problems in the physics gets pretty difficult to determine.

Fair enough.

In my informed opinion this theory isn't logically consistent and has no relation to the world we live in (or even one we don't). It appears to have been created by someone with a poor understanding of the concepts involved. I don't think it deserves the attention it's getting, it will not pass peer-review, and it will be ignored by mainstream researchers.

Is that better?It's an opinion. I have not formed an opinion yet, other than that it needs more investigation. I'll point out that E8 (I'll go with the standard typography from now on) was only thoroughly investigated earlier this year; it's been around a long time. I think it's early times to be making definitive statements about physics theories based on it. I'm still waiting for any evidence that I consider conclusive. You haven't done anything in this post (and yes, I read it all before starting this reply) to convince me otherwise.

I'm sorry, but you have that exactly backwards. I started from the assertion that the theory is crackpot, and I've now explained as clearly as I can precisely why. I was referring to the fact that you have repeatedly ignored my assertions that you haven't shown that your objections are connected to the premises of the theory. You still haven't.

Let's see - you're quite concerned that I may not know what I'm talking about because I said that Baez "isn't exactly a physicist", but he says he's "a mathematical physicist"?

Whatever. It's kind of like saying that I am concerned that you don't know what you're talking about because you say a Rottweiler isn't a dog, and you responding "it's not a dog, it's a Rottweiler."

As you say, whatever.

Anybody can put a paper there (it's not publishing), and there are many crackpots with degrees.So? It doesn't rate very high on the crackpot index, I'll wait to see what people who demonstrate more ability to understand the math have to say; meanwhile, I think I'm going to have to acquire some more expertise myself. I suspect that the people who DO have the expertise haven't weighed in yet because they need more time to examine it. I think that the fact that I don't see any people whose prior work HAS demonstrated that kind of expertise weighing in yet means that anyone dismissing it as crackpot at this early a point has just added some points on their own crackpot index.

I'm sorry, but it is incorrect. How many references do you need me to produce from my google of, "E8 symmetry eight dimensions?" We can start with Wikipedia (http://en.wikipedia.org/wiki/E8_(mathematics)): "The vectors of the root system are in eight dimensions..." and move on from there, if you like. You need to read more carefully, and you don't show apparent underlying knowledge of E8, which it's pretty obvious is required in order to properly evaluate this theory, further damaging your credibility.

And the reason I didn't respond to the rest is to avoid wasting even more of my time, which unfortunately has happened anyway. Such is life.Cry me a river. You're commenting on a theory you've just demonstrated you haven't the basic mathematical expertise to comment on, and calling the person who wrote it a crackpot. Sorry, this just looks like more ad hom to me. The only obvious waste of time appears to be ours in reading what you are writing.

OK, here goes.

Wrong. See above.Right. See above.

You regard that as a good thing? You do believe in conservation of energy and linear and angular momentum, right? Did you realize those are the result of microscopic Poincare invariance? And why have you ignored what I pointed out: that Lorentz/Poincare invariance is one of the best tested facts in all of science? It's an incredibly strong constraint on theories, but that won't stop Lisi.Neato. Now prove it applies to this theory. You still haven't. It doesn't matter how many times you re-assert it. We all know what it means when you don't address objections to your assumptions, and just keep saying the same thing over and over.

Gauge symmetries cannot be explicitly broken, as I already explained. Furthermore there is nothing in the paper, or in those comments, that explains where spin 1/2 particles come from no matter what breaking there is.Once the first generation of fermions, with correct charges and spins, are assigned to elements of e8, this T rotates them to the second and third generations. The second and third generations only have the correct spins and charges when considered as equivalent under this T. When considered as independent fields with E8 quantum numbers, irrespective of this triality relationship, the second and third generation of fields do not have correct charges and spins.Pardon me? I see your mouth moving, and your lips and tongue seem to be attempting to form words, but all I hear is "foona foona foona."

I already addressed that above, and you ignored my post. Apparently hypocrisy wasn't enough to stop you from accusing me of doing that to you.Actually, I didn't. I reviewed the last post on the previous page, and discovered that you had not addressed the objection you are purporting to respond to here there, either. That's why I left it stand. I'll be happy to respond to it in detail if you like, but it seems that all I have to do is copy material from the Backreaction thread to do so. I'm still not convinced, and this post has done little to change that and much to reinforce it.

BRST is a perfectly valid way to gauge fix. The references Lisi gave in his comments on that other thread were to papers on conventional BRST - which I understand quite well. Lisi is using BRST nonsensically, and I explained in detail how and why above. Uh huh. Pull the other one. It looks valid to me; I guess I'll be taking his word for it over yours, considering you don't seem to think that his paper is even worth considering, despite it being interesting to people who seem to know more about that specific area of physics than you do, and considering your assertion that John Baez is not a physicist.

Finally, I'll expand on my previous comment about de Sitter, as that seems to be one of the key points causing confusion here. It is true that Coleman-Mandula doesn't apply to dS, Stop right there. De Sitter space has nothing to do with this. Any non-singular space (including dS) is locally Minkowski, and one of the few things we know extremely well about physics is that it is Lorentz invariant - that is, that it obeys Einstein's postulates for special relativity (physics doesn't depend on absolute motion or on absolute direction). Oops.

but as I already said my objection is more basic. We do physics by making approximations. One of the approximations we make in particle physics is that space is flat Minkowski space, with an exact Poincare invariance. That is not exactly true - the universe is expanding and contains matter, and therefore is not exactly flat. However it is an incredibly good approximation on the scales relevant to elementary particles. This is because any space is smooth and flat when you look very closely at it (just as it's not obvious the earth is round when you're a human standing on it). Not only is this true theoretically, we have massive confirmation of it from all sorts of experiments (look up constraints on Lorentz violation).Again, you STILL have not shown that the space in which this applies is the space in which this theory applies, and above you attempted to deny against all provable fact that the dimensionality native to this theory has a different number than the space in which your assertion DOES apply.

Now, it's fine for Lisi's theory to exist in de Sitter if he wants it to, but there are then two options. No, there are more than that. You're ignoring the option I have now presented no less than three times, and which you have not responded to at any point.

One is that the dS curvature is close to consistent with cosmological data, in which case - for particle physics experiments - we can assume the space is flat to an incredibly good approximation. Then classifying particles by representations of the Poincare group is a good idea, and (as I've explained four times now) Lisi's theory isn't consistent with that.

The other option is that the dS curvature in his theory is extremely high (actually if his theory made sense this would certainly be the case, since he claims not to have any parameters in his theory, and the natural scale for the curvature is very very high - that's called the cosmological constant problem). In that case the size of particles (more precisely, their Compton wavelength), could be of order the curvature radius, and then it's true that representations of the Poincare group would no longer mean much. However in such a theory there would be an event horizon with a radius of about 1 fermi surrounding every point, and all larger structures would be instantly torn to pieces. I'll let you decide for yourself if that's a good theory.Again, you STILL have not shown that the space in which this theory is defined conforms to this constraint, or must.

Since you make an issue of it, I'll respond to the last post on the previous page here as well.

What actually happened in that thread is that the people asking reasonable questions never got answers and gave up, leaving the crackpots to talk amongst themselves. You'll notice that even Bee cooled off considerably as she wasn't able to understand the (nonsensical and contradictory) answers Lisi was giving. At this point I imagine she's pretty embarrassed.First, she closed the thread because it was being trolled. Second, she expressed confusion and concern at one point, and Lisi responded, and she was satisfied with that response. Third, her series of assertions regarding the current state of this theory- that it's unproven, that it contains hand-rolled items that need to be derived if it is to claim to be a ToE, and so forth- were exactly the same ones that appeared in her blog entry; she made that statement in response to the trolls. In contrast to you, I would say that she can be proud of demonstrating integrity and proper skepticism in the face of provocation. Her blog remains the best overview of the subject I can find, and I've been looking for many hours- and my google-fu ain't bad, if I may be permitted a bit of arrogance.

BRST is a formal procedure for dealing with gauge fixing (this is part of the annoying complications of gauge invariance I mentioned in my post above). It contains no physics whatsoever; it's just one of several ways to get rid of the redundancy. BRST formalism begins: "In theoretical physics, the BRST formalism..." An alternative article, BRST quantization, begins, "In theoretical physics, BRST quantization is a relatively rigorous mathematical approach to quantizing a field theory with a gauge symmetry." So, is a Rottweiler still not a dog? Seriously, I'm really getting the impression either that you don't know what you're talking about, or that you have such different definitions of what constitutes "physics" that you might as well be talking Swahili.

The BRST charge Q in a bosonic theory (such as Lisi's) is a scalar - it has spin 0 - but it has fermionic statistics. It seems (from some comments he posted in that thread, not from the paper) that Lisi thinks his quark fields can be created by Q. If so he has exhibited yet another basic misunderstanding of the terms and formalisms he's using.As you correctly point out, the C on page 70 of van Holten is a Lie algebra valued Grassmann number, C = C^A T_A. This is formally added to a Lie algebra valued 1-form, H = H^A T_A, to create what I am referring to as a BRST extended connection, A = H + C.

So, how can I be crazy enough to call C a fermion, which (as a spinor) should algebraically be in the fundamental representation space? That is a beautiful thing about the exceptional Lie algebras -- some of their basis Lie algebra elements, T_A, behave algebraically as basis elements of a fundamental representation space! The spinors we need are built into the Lie algebra structure of the exceptional groups! This is explained on page five, and used throughout the rest of the paper. It's a key idea that unlocks everything. Sadly, I was not the first to realize E8 has this structure -- I got the idea from He Who Shall Not Be Named, and it's been known to mathematicians for a very long time.He Who Shall Not Be Named is a reference to Harold Scott MacDonald Coxeter, who promptly appears on the thread after being Not Named. ;) Lisi proceeds to apparently satisfy the querent, or else Bee's chastisement and answer are either sufficient to satisfy hir, or prevent hir from continuing what was actually a rather combative and dismissive posting style.

The elements of the response address your concerns equally well, but I don't see you acknowledging they even exist. Instead I see you saying the same thing over and over and failing to acknowledge counter-arguments that challenge the assumptions you have to make in order to even make the argument.

As you correctly point out, the C on page 70 of van Holten is a Lie algebra valued Grassmann number, C = C^A T_A. This is formally added to a Lie algebra valued 1-form, H = H^A T_A, to create what I am referring to as a BRST extended connection, A = H + C.

So, how can I be crazy enough to call C a fermion, which (as a spinor) should algebraically be in the fundamental representation space? That is a beautiful thing about the exceptional Lie algebras -- some of their basis Lie algebra elements, T_A, behave algebraically as basis elements of a fundamental representation space! The spinors we need are built into the Lie algebra structure of the exceptional groups! This is explained on page five, and used throughout the rest of the paper. It's a key idea that unlocks everything. Sadly, I was not the first to realize E8 has this structure -- I got the idea from He Who Shall Not Be Named, and it's been known to mathematicians for a very long time.

First of all, physical statea are those annihilated by Q. (Or a little more precisely, two states are physically identical if their difference can be written as Q acting on something.) So anything you get by acting with Q is unphysical. If you try to keep those states you'll get negative probabilities, among other problems.I see no reason to believe that Dr. Lisi is doing so. (Let's give him his proper title, he has earned it by defending more than one thesis, and by dissertation.) I see, instead, what appears to be full acknowledgment that this is indeed the case; specifically, he states, the usual ghosts in QFT are Lie algebra valued Grassmann number fields that compensate for gauge degrees of freedom in the Lie algebra valued 1-form connection fields. They are not spinor fields, algebraically, but Lie algebra valued fields, and they can't have external lines in Feynman diagrams -- which means they aren't measured as physical particles, but only figure in to the calculations. He then goes on to state, Now, if we're working with one of the exceptional Lie groups as our gauge group, and we build a certain action, some of the ghost parts ARE, algebraically, spinor field multiplets with respect to some subgroups of the exceptional group. This means, mathematically, they are fermions -- spinor multiplets of Grassmann numbers. Using the same mathematical construction as in BRST, these can be formally added with the rest of the connection in a superconnection, as I have done in the paper.I think your argument lacks merit. Finally, he says, If you don't like the physics of this construction, that's arguable. But the math is correct, as it's lifted straight from standard BRST techniques, with no alterations.Note here that you're just rehashing things that have already been answered. Worse, you're raising them in a forum where there isn't any obvious way for Dr. Lisi to respond, with a person who is far less qualified (but apparently capable of finding the correct answers) than Dr. Lisi. I wonder precisely what I'm looking at here, and I suggest others reading this do the same. I think it's questionable.

Secondly, as I already mentioned above Q does not have 1/2 integer spin in this theory, so even if you could somehow use it the theory would still not have any matter in it (which we know has spin 1/2).Answered in the quotes produced above.

To reiterate, ghosts cannot appear in the action if the theory is to make sense, and yet Lisi has them in his. His ghosts have integer spin, even though he seems to think otherwise (presumably because he failed to comprehend the difference between fermionic statistics and spin). And yet again, answered in the quotes produced above. You have no argument here.

This theory is the product of someone with a tenuous grasp of some physics concepts, lots of buzzwords, a talent for language, and enough charisma to temporarily fool a set of people who are pre-disposed to be friendly to crazy ideas - which are many people at the Perimeter Institute, FQXI, the foundation that gave him his grant, and all science journalists. (FYI, FQXI is a branch of the Templeton foundation, the goal of which is to promote connections between religion and science.)All that was needed to complete the portrait was this image of you poisoning the well. It's not the first time you've done it on this thread, either. This example is sufficient, I think, to lead anyone who is interested to see the others if they are so motivated. I see no point in going beyond the one example; it's enough to prove the point.

This is how woos proceed, sol invictus. We have gone so far as to actually compose the rudiments of a classification system for them on this site, a fact you seem unaware of or at least unwary of.

It's deeply embarassing that this story has gotten so much play in the press, and even more so that an established and supposedly responsible physicist - Lee Smolin - seems to have endorsed it. I'm ashamed for the field. I'd be ashamed for Smolin if I had any sympathy for him, but I think he has brought this on himself. He will trumpet anything that looks like an alternative to string theory, because he's staked out an extreme - and extremely rigid - political (not scientific) position, and now he can't back off without losing even more face.And another example.

I don't see a great deal of value to be added by continuing this conversation. You've taken it in a direction that I dislike, and are just repeating the same things over and over, distracting attention from that by introducing extraneous subjects, and not addressing the objections to those things. You could change that by addressing them, but not by ignoring them and pretending you're not by adding extraneous material.

Straight, simple, and direct: what I object to is not your assertion it MAY be wrong. I agree; it may be. What I object to is your assertion that it's not worth looking into further. Over and over and over again, I see such assertions; when I find significant reason to believe they are correct, I can identify a reason I think so. The author shows no particular expertise in the area in question; the author has confounded concepts that are not related in a way that popular literature might lead someone who's not very knowledgable to do; the author has seriously claimed it's all over with and s/he's right. I can't identify any of those reasons in this case, or any of the others that are similar. I find that when someone asserts that in the absence of those factors, there is invariably an underlying reason that has nothing to do with the subject at hand. Most people call that a hidden agenda. I don't think hidden agendas have any place in science. I'll wait for a more credible source to confirm or deny, and meanwhile attempt to confirm or deny on my own.

[Yllanes]

How many references do you need me to produce from my google of, "E8 symmetry eight dimensions?" We can start with Wikipedia (http://en.wikipedia.org/wiki/E8_(mathematics)): "The vectors of the root system are in eight dimensions..." and move on from there, if you like. You need to read more carefully, and you don't show apparent underlying knowledge of E8, which it's pretty obvious is required in order to properly evaluate this theory, further damaging your credibility.

Schneibster, the vectors of the root system of su(3) span a two dimensional Euclidean space. This is the group used in the Standard Model to classify hadrons (the famous 'Eightfold Way'), yet the Standard Model doesn't imply a two dimensional spacetime. I think this is what sol invictus was saying.

[sol invictus]

I was referring to the fact that you have repeatedly ignored my assertions that you haven't shown that your objections are connected to the premises of the theory. You still haven't.

Total gibberish.

My objections are based on reality. One key aspect of reality is that particles are classified by representations of the Poincare group.


How many references do you need me to produce from my google of, "E8 symmetry eight dimensions?" We can start with Wikipedia (http://en.wikipedia.org/wiki/E8_(mathematics)): "The vectors of the root system are in eight dimensions..."

Now you're just making yourself look stupid. You're arguing by google search?

The vectors of the root system are in eight dimensions because E_8 is rank 8, not because the group manifold or any of its representations is dimension 8. Group theory 101.

Neato. Now prove it applies to this theory. You still haven't. It doesn't matter how many times you re-assert it. We all know what it means when you don't address objections to your assumptions, and just keep saying the same thing over and over.

It applies to reality. If it doesn't apply to this theory, this theory doesn't describe reality.

Pardon me? I see your mouth moving, and your lips and tongue seem to be attempting to form words, but all I hear is "foona foona foona."

Compelling argument.

Worse, you're raising them in a forum where there isn't any obvious way for Dr. Lisi to respond, with a person who is far less qualified (but apparently capable of finding the correct answers) than Dr. Lisi. I wonder precisely what I'm looking at here, and I suggest others reading this do the same. I think it's questionable.


I hope you'll not consider it a waste of time to at least explain some of the above matters to us all. If this is going to get the kind of airplay that it seems to be acquiring, it would be awesome to know whether it's garbage or not. Quite frankly, right or wrong, I certainly stand to learn a great deal from you, if you'll humor me.

No comment necessary.

I don't see a great deal of value to be added by continuing this conversation.

Great!

Straight, simple, and direct: what I object to is not your assertion it MAY be wrong. I agree; it may be. What I object to is your assertion that it's not worth looking into further.

It's not an assertion, it's a decision.

[INRM]

Okay time for me to ask some questions...

What's spontaneous symmetry breaking?
What's background space / poincaire symmetry?

Heisenberg uncertainty; conservation laws and causality can be violated, as long as this violation can never be observed directly

Huh? I always thought that even if one particle disappears, another one would have to appear in it's space to be compliant with the conservation laws. Your saying particles can just disappear and appear as long as nobody actually sees it? Does this just occur at the small scale, or at large scale too?


Also... this theory...
-1 Dimension of Space = What does that mean actually (I know it sounds retarted, but I've heard cases where there were two)?

-According to this theory, are there other "Universes" or are we the only one?

-The Big Bang, how does the theory explain it?


INRM

[Schneibster]

Total gibberish. Ad hom.

My objections are based on reality. One key aspect of reality is that particles are classified by representations of the Poincare group. And another is that E8 keeps popping up in physics. And yet another is that you don't seem able to keep up with the conversation; care to comment on the fact that you just ad hommed two degreed physicists, one by calling him a crackpot, and the other by claiming he's not a physicist?

Now you're just making yourself look stupid. You're arguing by google search? LOL, that's all you've got to say? Try again. It seems that the 240 roots of E8 are vectors in... wait for it... eight dimensions. I believe you stated categorically that was untrue. I don't believe that there's another interpretation to put on your statements, though I'm sure you'll try to wriggle out of it.

The vectors of the root system are in eight dimensions because E_8 is rank 8, not because the group manifold or any of its representations is dimension 8. Group theory 101. Uh huh. My goodness, look at that, he says precisely what I said and this is supposed to be proof I'm "wrong."

And those 240 vectors are (according to this theory we're discussing) each a different particle (or, to get a bit more detailed, a different variant of a particle- I think that, for example, the red, blue, and green up quarks each get their own point). My point was, you're trying to argue that a mathematical structure that contains a wide variety of different dimensions has to comply, in every representation of it among those dimensions, with Poincare symmetry- and whether this particular argument stands or fails, there's another one right behind it, which is that I've shown that at least one of the symmetries that is a component of the Poincare symmetry appears to be derived in this theory. That renders your point moot. And instead of addressing that point, your strategy is to attack this one. You may know more group theory than I do, but I can smell a woo a mile away. And you're a woo, at least on this subject. I don't know what your agenda is, but it's obvious to anyone who's paying attention you've got one, and it's got nothing to do with science.

It applies to reality. If it doesn't apply to this theory, this theory doesn't describe reality. You keep trying, but you're not even answering Dr. Lisi's points, much less mine.

Compelling argument.Nice, go ahead, ignore the real argument, to which you obviously cannot respond, and ad hom some more. Perhaps no one will notice the man behind the curtain.

No comment necessary.I had hoped for a different outcome; that one did not obtain isn't my fault. I tried to be nice. What I got in response was to be **** upon. Unfortunately for you, I **** back.

Great!Oh, I neglected to mention that if you continue to mess with me, I will continue to point out you're a woo. It's easy to do. There are simple means of dealing with this:
1. Walk away.
2. Stop being a woo.

It's not an assertion, it's a decision.And one you advocate to everyone; which appears to be one of the clues to the hidden agenda that everyone has to be aware of now that you've converted someone who would have conversed politely into an enemy. Sorry, you're welcome to your "decision;" I am now more convinced than ever that there is something to this, and I'll wait and see what it is. I've heard too much of exactly the same type of argumentation from the anti-string theory woos not to know exactly what I'm looking at.

[Schneibster]

Okay time for me to ask some questions...

What's spontaneous symmetry breaking? Look carefully above; disagree as I might with sol, s/he did well explaining this concept. I amplified it, so you'll have two viewpoints to compare. The basic idea is, a pencil balanced on its point is very symmetric- and very unstable. The stable solution is the asymmetric one of the pencil lying on its side after it fell over.

What's background space / poincaire symmetry? Two different concepts. Background space is the natural spacetime in which a theory of physics exists; in most cases, this includes our ordinary four dimensional spacetime, but there are theories in which this is not the "default" background, but is a derived thing that appears as a result of an underlying thing. This theory appears to be one of those.

Poincare symmetry is the symmetry of spacetime over three types of changes:
1. Translation- in which the location of your frame of reference changes.
2. Rotation- in which the orientation (the direction you're looking) changes.
3. Rapidity- in which your velocity changes. Technically, this is also a rotation for reasons I have elaborated upon elsewhere on this forum; you can use that as a search term to find them.

Huh? I always thought that even if one particle disappears, another one would have to appear in it's space to be compliant with the conservation laws. Your saying particles can just disappear and appear as long as nobody actually sees it? Does this just occur at the small scale, or at large scale too?Well, it's more complicated than that- they can appear, but they have to disappear before they can be detected. Physicists believe that this happens all the time in empty space, and it's been proven by the existence of the Casimir effect. Uncertainty gives rise to a lot of interesting things.

Also... this theory...
-1 Dimension of Space = What does that mean actually (I know it sounds retarted, but I've heard cases where there were two)?I'm unclear on what you're referring to.

-According to this theory, are there other "Universes" or are we the only one?This theory doesn't make any statement about that.

-The Big Bang, how does the theory explain it? It doesn't. Nobody knows what the potential consequences of it might be to the Big Bang theory, but since it doesn't contradict the Standard Model, there might not be many.

[Yllanes]

LOL, that's all you've got to say? Try again. It seems that the 240 roots of E8 are vectors in... wait for it... eight dimensions. I believe you stated categorically that was untrue. I don't believe that there's another interpretation to put on your statements, though I'm sure you'll try to wriggle out of it.
Schneibster, you are wrong about this whole E8 thing. He said quite clearly that the fact that E8 has rank 8 doesn't mean spacetime has 8 dimensions. This is true. I don't know why you keep arguing about this, when it seems you didn't even know what E8 (or a root system in general) was until this thread started. You said:


You're still assuming that the space in which this theory is defined is Poincare symmetric and that's not necessarily the case. First of all, it's an 8-dimensional space- that's what the 8 in E_8 means.

Again, in QCD Popincaré invariance is obviously included (without Poincaré symmetry we don't even know what a particle is!), while su(3) has rank 2.

[Schneibster]

Schneibster, the vectors of the root system of su(3) span a two dimensional Euclidean space. This is the group used in the Standard Model to classify hadrons (the famous 'Eightfold Way'), yet the Standard Model doesn't imply a two dimensional spacetime. I think this is what sol invictus was saying.While this is true enough, the point was, the dimensions of the Eightfold Way are charge and hypercharge, which have nothing to do with the dimensionality of spacetime; and this was a convenient way for sol to avoid addressing the actual issue.

Thanks for the explanation, Yllanes. I've got a lot to learn about group theory.

[sol invictus]

My point was, you're trying to argue that a mathematical structure that contains a wide variety of different dimensions has to comply, in every representation of it among those dimensions, with Poincare symmetry- and whether this particular argument stands or fails, there's another one right behind it, which is that I've shown that at least one of the symmetries that is a component of the Poincare symmetry appears to be derived in this theory.

It is evident that you have little idea what you're talking about. You appear to be trying to learn these things (which are, after all, rather advanced topics that one typically studies in the later stages on a Ph.D. in theoretical physics) from blogs and google, and - while you're clearly an intelligent person - that's damn hard to do. Particularly in one weekend.

I bear you no ill-will, and I'm deeply tired of this pissing match and can't sustain it any longer. I wrote a response in kind to your post, but I've just deleted almost all of it.

I've noticed you have a rare gift for explaining things you understand - I hope you will take this opportunity to learn something and pass it on better than I seem to be capable of. Moreover I sincerely apologize if I created or contributed to an atmosphere in this thread that led to this impasse. It wasn't my intent. Perhaps it would have been better had I identified myself or my credentials on this topic at the beginning, but I hate the idea of arguing by appeal to credentials - particularly in this case, where Lisi is being promoted by the media as a rebel against the establishment.


And one you advocate to everyone; which appears to be one of the clues to the hidden agenda that everyone has to be aware of now that you've converted someone who would have conversed politely into an enemy. Sorry, you're welcome to your "decision;" I am now more convinced than ever that there is something to this, and I'll wait and see what it is.

I would be very happy if this "theory" inspires someone to go out and learn enough physics to be able to judge it for themselves. I can't imagine a better outcome. Please don't take my word for it.

[Schneibster]

Schneibster, you are wrong about this whole E8 thing. He said quite clearly that the fact that E8 has rank 8 doesn't mean spacetime has 8 dimensions. This is true. I don't know why you keep arguing about this, when it seems you didn't even know what E8 (or a root system in general) was until this thread started. You said:Hmmm, now I never said spacetime has eight dimensions. I said this theory is defined in eight dimensions, and I deliberately did NOT say what they were.

To get into detail on this, if I've got things right the spacetime of this particular theory is so(4,1) or so(3,1), neither of which (whichever it is) necessarily has to have Poincare symmetry directly. Whichever one it is is(have I got the terminology right here?) a subalgebra of the algebra of the E8 base theory. Lisi is claiming that this is a way that previous ideas have been based upon the loophole that the CM theorem only applies in Poincare-symmetric spacetimes, and that the spacetime of his theory isn't Poincare symmetric and the CM theorem therefore doesn't apply. He's also claiming that the math to do this is lifted directly from a previously successful foray into this area, BRST. Some other folks who have dealt with this in the past in published literature are agreeing with him that this is a valid way to proceed. Are you telling me differently?

[Schneibster]

It is evident that you have little idea what you're talking about. You appear to be trying to learn these things (which are, after all, rather advanced topics that one typically studies in the later stages on a Ph.D. in theoretical physics) from blogs and google, and - while you're clearly an intelligent person - that's damn hard to do. Particularly in one weekend.You're correct in every regard.

I bear you no ill-will, and I'm deeply tired of this pissing match and can't sustain it any longer. I wrote a response in kind to your post, but I've just deleted almost all of it. An excellent move, and this post is another. I will harbor no ill-will on my part, after this post. I could hardly ask for a more reasonable response, nor one more calculated to play upon my sense of fairness.

I've noticed you have a rare gift for explaining things you understand - I hope you will take this opportunity to learn something and pass it on better than I seem to be capable of. I intend precisely that, and was very disappointed when the conversation took the turn it did. In case it's not clear, I had hoped that you would provide some of the material that would help me do that, and exercise my gift for the benefit of others here. I still hold out hope that that will be the case.

Moreover I sincerely apologize if I created or contributed to an atmosphere in this thread that led to this impasse. It wasn't my intent. I could hardly ask for a more sincere and reasonable statement. For my part, I apologize as well, for all offenses. It was not my intent either. I'd like to propose that we continue in a less combative vein, but I will not take it as an insult if you do not choose to. You cannot have had a good day here. And I apologize for that, as well as regret it.

Perhaps it would have been better had I identified myself or my credentials on this topic at the beginning, but I hate the idea of arguing by appeal to credentials - particularly in this case, where Lisi is being promoted by the media as a rebel against the establishment.It wouldn't have made much difference. It's probably better that you didn't. I don't, and I don't advise it. Here, we are both public in our statements, and private in our personal details- and one's arguments stand or fall on their own merits. That is how it should be. Things that happen here have little or no repercussions in the real worlds of our work and lives, and that also is how it should be.

I would be very happy if this "theory" inspires someone to go out and learn enough physics to be able to judge it for themselves. I can't imagine a better outcome. Please don't take my word for it.A statement of integrity, and one I heartily echo. If the theory is total rubbish, but inspires one individual to go study physics, it was nevertheless worthwhile. If it is not, that is a bonus.

[Yllanes]

Hmmm, now I never said spacetime has eight dimensions. I said this theory is defined in eight dimensions, and I deliberately did NOT say what they were.

To get into detail on this, if I've got things right the spacetime of this particular theory is so(4,1) or so(3,1), neither of which (whichever it is) necessarily has to have Poincare symmetry directly. Whichever one it is is(have I got the terminology right here?) a subalgebra of the algebra of the E8 base theory. Lisi is claiming that this is a way that previous ideas have been based upon the loophole that the CM theorem only applies in Poincare-symmetric spacetimes, and that the spacetime of his theory isn't Poincare symmetric and the CM theorem therefore doesn't apply. He's also claiming that the math to do this is lifted directly from a previously successful foray into this area, BRST. Some other folks who have dealt with this in the past in published literature are agreeing with him that this is a valid way to proceed. Are you telling me differently?
I haven't read the paper, so I won't comment on what Lisi is saying. I just read your exchange about E8. For a casual reader who knows group theory and particle physics it seemed as if you were saying that classifying the particles through E8 meant that spacetime had to be 8 dimensional. I know see that this is probably not what you were saying, but you had some confusion there with Lie algebra terminology that made it look that way.

And anyway, SO(3,1) is the Lorentz group, so I'm not sure I understand your last post either.

[sol invictus]

I could hardly ask for a more sincere and reasonable statement. For my part, I apologize as well, for all offenses. It was not my intent either. I'd like to propose that we continue in a less combative vein, but I will not take it as an insult if you do not choose to. You cannot have had a good day here. And I apologize for that, as well as regret it.

Accepted and agreed.

Now I'd like to try to state part of my objection to Dr. Lisi's theory. There are many aspects of it I find incomprehensible, starting from the very first equation, but here I'll focus on the Coleman-Mandula theorem and the alleged loophole in it. This is actually an interesting topic for me for other reasons, so it's a little more fun to write about than the rest. I didn't want to discuss this earlier because I think there are much more basic problems and I usually think it's better not to swat flies with sledgehammers, but OK.

First of all, what is the Coleman-Mandula theorem? It states that if a theory has a symmetry group that contains the Poincare group then the group must have a direct product structure (the P. group times something else). (There is a loophole that allows supersymmetry, but since E_8 is bosonic it doesn't apply here, and furthermore there's another theorem that proves supersymmetry is the only such exception.)

Now (as Schneibster nicely explained above) the P. group is the group of isometries of flat space. If you know a little about general relativity, you know that if there is any matter or energy of any form, space is curved. Such a lumpy space has in general no isometries at all, and certainly not the full P group. Of course we live in a space with stuff in it - just look around you - an expanding universe full of matter and energy, which is definitely not flat space. So why should we care about the C-M theorem if the space we live in isn't Poincare invariant?

Furthermore the C-M theorem applies to a mathematical object called the S-matrix which almost certainly doesn't exist in any kind of cosmological spacetime. So naively it really seems irrelevant to the real world.

However something should bother you at this point. In the standard model of particle physics we always do all our calculations assuming space is perfectly flat. Throwing caution to the winds we blithely compute S-matrix elements, and when we compare them to experimental data we find they agree to an accuracy unprecedented in the history of science (at least 10 significant figures for some quantities). How can that be, given that we are ignoring the curvature of spacetime and computing something that doesn't even exist in our world?

The answer comes from the size of the effects of that curvature on particle physics experiments. They are of order (H/E)^2, where H is the Hubble scale of the universe (which in turn is related to its energy density) and E is the typical energy of the particles involved in the experiment. Now, how big is that? Generally, around 10^{-60}, give or take a few orders of magnitude. But our calculations (for other reasons having nothing to do with this) are accurate only to about 10^{-10}, so this effect is utterly negligible. And therefore even though Coleman-Mandula may not apply quite precisely, the mistake we are making in using it is far too small to care about.

Let's come back to Dr. Lisi's theory of everything. According to him his theory produces the standard model plus gravity, but not in flat space - instead, in de Sitter (dS) space. We're asking whether his theory has a chance of describing the real world. What dS is exactly isn't relevant: it's a space with curvature, and let me simply tell you that if we are indeed in a dS space the curvature had better be smaller than, or of order of, the observed curvature in the universe today. Any larger and his theory would be ruled out by large-scale physics (cosmology, solar system tests, solar physics, etc.). Now how his theory (which has no parameters in it) manages to produce a solution with a characteristic curvature scale 30 orders of magnitude below that of the standard model (not even mentioning the 19 parameters of the standard model itself) is but one of the host of problems confronting it, but let's give him all that and proceed.

So what's the problem? Well, it's that if Dr. Lisi were correct, he'd have a theory in a de Sitter space that's within a 10^{-60} error of a theory that violates the C-M theorem (because his theory certainly does not have a symmetry group that's a direct product of the gravity sector with the SM - indeed, that's the whole point of it from the beginning). Put another way, I could approximate his theory to an incredible degree of accuracy with something that we know by C-M is mathematically inconsistent. But if that were possible (it's not) C-M wouldn't mean a thing, because you could always evade it by adding an infinitesimal energy to your theory. Not only that, but all of the constraints and consequences of Poincare invariance (which include some of those 10-digit predictions) would be in the trash.

So that is an abstract - but very general - reason to be extremely skeptical of the existence of this theory.

[Schneibster]

Accepted and agreed.This deserves separate recognition. Rarely do I meet someone with the strength of mind and will to continue such a conversation, and eliminate bad feeling from it. You are exceptional. I will attempt to meet your standard.

[Schneibster]

Now I'd like to try to state part of my objection to Dr. Lisi's theory. There are many aspects of it I find incomprehensible, starting from the very first equation, but here I'll focus on the Coleman-Mandula theorem and the alleged loophole in it. This is actually an interesting topic for me for other reasons, so it's a little more fun to write about than the rest. I didn't want to discuss this earlier because I think there are much more basic problems and I usually think it's better not to swat flies with sledgehammers, but OK.

First of all, what is the Coleman-Mandula theorem? It states that if a theory has a symmetry group that contains the Poincare group then the group must have a direct product structure (the P. group times something else). (There is a loophole that allows supersymmetry, but since E_8 is bosonic it doesn't apply here, and furthermore there's another theorem that proves supersymmetry is the only such exception.)Before we go further, for the sake of others who may not be aware of the difference between a theory and a theorem, I'll point out that a theorem is a provable fact of mathematics. There is a formal process of proof in mathematics that allows mathematicians (and everyone else) to be certain that, given the assumptions of mathematics (and it's definitely worth your time to be sure what specifically the particular assumptions are of the branch of math that the theorem concerns- in this case, it's group theory) a particular statement is true or false. sol's statement here is that there is a full proof from first principles that what he has asserted is true, in the mathematical sense. It's also important to know that a proof that a certain set of phenomena, and I mean "proof" in the more colloquial sense that one might use sitting on a jury and evaluating evidence, would always conform to that mathematics would therefore be a proof of how that system can behave; it would do so according to that theorem.

What's been asserted here first is that a particular theorem states that any theory (which in this case means a system of mathematics that purports to be the representation of a set of physical phenomena) that has a symmetry group (which is a group that not only describes some operations and some entities to which those operations can be applied, but also has the property that those operations do not fundamentally change the entities or their characteristics) that contains the Poincare group (which means that the Poincare group of symmetry operations, which are rotation in both space and spacetime, and translation in space, are subgroups of any group that is part of the theory) then that symmetry group must be constructed of the Poincare group operating upon the other subgroups of that group, or those subgroups operating on the Poincare group. (It's important to mention it both ways, because the group may not be commutative- that is, the operation of another subgroup upon the Poincare group may be different from the operation of the Poincare group upon that other subgroup. If it is different, then the group in question is non-abelian; if it makes no difference, then the group is abelian. One of the interesting things about spacetime symmetries is that translations are abelian- if you move so far in x, then so far in y, that is the same as moving so far in y then so far in x. But rotations are non-abelian; if you turn a die 90 degrees left then 90 degrees over, that's going to give a different result than if you turn it 90 degrees over then 90 degrees left. Take a die and try it for yourself.)

While this is true, not all of the assumptions it is based on are either members of the set of axioms of group theory, or are explicitly stated above. I'll get back to that in a few paragraphs.

Now (as Schneibster nicely explained above) the P. group is the group of isometries of flat space. If you know a little about general relativity, you know that if there is any matter or energy of any form, space is curved. Such a lumpy space has in general no isometries at all, and certainly not the full P group. Of course we live in a space with stuff in it - just look around you - an expanding universe full of matter and energy, which is definitely not flat space. So why should we care about the C-M theorem if the space we live in isn't Poincare invariant?

Furthermore the C-M theorem applies to a mathematical object called the S-matrix which almost certainly doesn't exist in any kind of cosmological spacetime. So naively it really seems irrelevant to the real world.

However something should bother you at this point. In the standard model of particle physics we always do all our calculations assuming space is perfectly flat. So far, we're on track. It's important to interrupt at this point and make it clear that flat space is Special Relativity; the description of the curvature of space is General Relativity. (This is technically an oversimplification, but it's accurate enough for this conversation.) The implication of this is that SR is a part of the Standard Model; and indeed, that also is true. The standard model explicitly contains SR, and explicitly does not contain GR- and because curvature of space is gravity, this means that the SM cannot handle gravity. This is often stated as an inability to handle quantized gravity. While that is true, it's more complicated than that, as you can see. Furthermore, it is important to note that the Poincare symmetry is a symmetry of any SR-containing theory. And the Standard Model of particle physics is such a theory.

Throwing caution to the winds we blithely compute S-matrix elements, and when we compare them to experimental data we find they agree to an accuracy unprecedented in the history of science (at least 10 significant figures for some quantities). How can that be, given that we are ignoring the curvature of spacetime and computing something that doesn't even exist in our world?

The answer comes from the size of the effects of that curvature on particle physics experiments. They are of order (H/E)^2, where H is the Hubble scale of the universe (which in turn is related to its energy density) and E is the typical energy of the particles involved in the experiment. Now, how big is that? Generally, around 10^{-60}, give or take a few orders of magnitude. But our calculations (for other reasons having nothing to do with this) are accurate only to about 10^{-10}, so this effect is utterly negligible. And therefore even though Coleman-Mandula may not apply quite precisely, the mistake we are making in using it is far too small to care about.Technically speaking, over a space the size of the LHC, calculations have shown that the particles will fall a significant amount of distance under the influence of gravity; it's enough that they have to tune the system for it. And the real question isn't the curvature of all of space; it's the curvature of the space we're doing the experiment in. However, despite this, that curvature is so small on the scale of the collision of particles at the crossover point that it's not worth talking about; it's on the close order of 10^-20 away from being flat, which is as sol points out beyond the about 10^-10 we generally bother to calculate.

Going back to the S-matrix, this is the scattering matrix- the math that describes the scattering functions of the quantum field theory. These define what happens- what can happen- when particles collide with one another. It describes each possible outcome and assigns a probability to it. sol's point here is that these probabilities are calculated to incredibly precise degrees. The precision and accuracy of these probabilities is the highest of any theory ever in the history of science. For certain specific interactions, they have been calculated to seventeen decimal places- 10^-17 precision, and verified in the lab. The 10^-10 above is the normal figure, because you have to spend a lot of computer time getting to higher precisions. A few interactions were calculated to that level of precision represented by the level of accuracy of our instruments to measure what's happening. This was done to validate the method of finding the probabilities. We haven't bothered to go that far for most calculations; we now know that we can, and it's not yet important for the results of any theory of physics we have.

Let's come back to Dr. Lisi's theory of everything. According to him his theory produces the standard model plus gravity, but not in flat space - instead, in de Sitter (dS) space. We're asking whether his theory has a chance of describing the real world. What dS is exactly isn't relevant: it's a space with curvature, and let me simply tell you that if we are indeed in a dS space the curvature had better be smaller than, or of order of, the observed curvature in the universe today. Any larger and his theory would be ruled out by large-scale physics (cosmology, solar system tests, solar physics, etc.). Now how his theory (which has no parameters in it) manages to produce a solution with a characteristic curvature scale 30 orders of magnitude below that of the standard model (not even mentioning the 19 parameters of the standard model itself) is but one of the host of problems confronting it, but let's give him all that and proceed.One of the assumptions of the CM theorem that I mentioned above is that the space it applies in is subject to the Poincare symmetries. Technically, these symmetries only exactly apply in a flat spacetime. sol apparently believes that that is the only objection Lisi applies to this, but the real meaning of his statement that the background spacetime of his theory is de Sitter space is not that it has curvature. The real meaning is, his theory does not contain a group isomorphic to the Poincare group- instead, it contains the group SO(4,1). This is the de Sitter group; that's why spaces that have it as a symmetry are called de Sitter spaces. The really interesting thing about such spaces is that they actually are a better representation of our space than the flat Minkowski spacetime in which the Poincare symmetry applies; this is because our universe is expanding, and de Sitter spaces do that, but Minkowski spaces do not. The implication of this expansion is that spacetime in our universe is curved. And in fact, we do observe that spacetime in our universe is in fact curved, and that our universe is in fact expanding.

But there's another subtlety here as well. Lisi's theory is an exactly symmetric one. Now, that's not unusual. As a matter of fact, there is another exactly symmetric theory of physics, called the electroweak theory. This theory was developed in 1967 by Steven Weinberg and Abdus Salam, following up on a lead originally developed in about 1960 by Sheldon Glashow. The thing about this theory is, its perfect symmetry breaks- and this happens when the temperature gets too low. And by too low, I mean enormously high by our standards. The last time the temperature was this high in our universe was only seconds after the Big Bang. And Lisi's theory also is a broken symmetry- the exact symmetry only applies under certain conditions. This must be so at minimum for it to accomodate the Weinberg-Salam electroweak theory, as it does. The thing about these very early times in the universe is, the curvature of space was very much higher than it is now. So the curvature of the universe now isn't important- it's the curvature of the universe before this symmetry was broken that's important; because after that, it's no longer an exact symmetry. It's a broken one, and will manifest very differently than it did when it was not. Electroweak, for example, proposes that the weak nuclear force and the ordinary electromagnetic force are actually two different aspects of the same underlying electroweak force; before the symmetry broke, they were actually physically the same force. After the symmetry broke, we have the massless photon of the electromagnetic force, and the massive W and Z bosons of the weak nuclear force. A further consequence of this symmetry breaking was the acquisition of mass by the fermions, through the Higgs mechanism, but we're getting rather far afield here, so I'll move on.

Thus, the issues of the symmetry breaking, and the violation of the CM theorem, are tied together; and the curvature of space that must apply after the symmetry is broken need not be the curvature of space when the symmetry is exact. This is the reason it is so important where precisely this symmetry breaking event comes from. Currently, Dr. Lisi has "hand entered" it; in other words, he doesn't account for it as a physical phenomenon, he just adds it in when the Standard Model says there should be some, without a physical justification for it. This must change for this theory to be physical- that is, for it to properly represent the state of affairs in the real universe we see around us. Dr. Lisi acknowledges this, but like many another theorist, he is putting off dealing with it until he gets other parts of his theory he thinks are more important, and that he has clear ideas about, completed.

The point is that the statement below that the theory must apply in our current spacetime, exactly as it is written, is incorrect. This is because first, this theory has a broken symmetry, after which the theory does not precisely apply any more; and second, the times in our universe when this symmetry was unbroken were times when the space of our universe was highly curved, and very different both from how it is now and from Minkowski spacetime. During these times, the CM theorem very much did not apply, because our universe was vary far from being like the perfectly flat Minkowski spacetime that is a requirement for the CM theorem to apply.

Drs. Glashow, Salam, and Weinberg won the 1979 Nobel Prize in physics for their broken symmetry theory. Dr. Lisi's theory is nowhere near as complete and developed as theirs was even then, and is a very far cry from its state now. By no means should anyone think that I am saying the Dr. Lisi deserves a Nobel prize; his theory is incomplete, and may prove impossible to complete. Certainly string theory has proven intractable for twenty years or more. Nevertheless, Dr. Lisi's theory shares two important characteristics with their theory:
1. It only applies exactly when the universe is very young.
2. It invokes the breaking of an exact symmetry that is not currently apparent in our universe, and that breaking creates the state of affairs we observe around us.

In the case of electroweak theory, the breaking of the symmetry occurs below a certain very high temperature. Dr. Lisi has not yet specified under what circumstances symmetry breaks in his theory. However, if his theory correctly describes electroweak theory (and it purports to, and its area of competence includes that area of physics), then that symmetry breaking must occur. In addition, Dr. Lisi's theory contains the unbroken Weinberg-Salam electroweak theory- witness the B boson, a boson that ceases to exist when the electroweak symmetry is broken, which appears in the lower left corner of the diagram on page 2. Furthermore, physicists have long speculated that the symmetry between the eight colored gluons and six quarks must have broken away from electroweak at a much higher temperature; and there has even been speculation that this might also be true of a symmetry between gravity and the rest of the forces. So Dr. Lisi's idea is neither unprecedented, nor even particularly surprising from this viewpoint.

There is a further subtlety again, that I picked up while going over the paper for the third time in 24 hours, and this may explain some other apparently anomalous aspects of the theory. I am still working this out, but if I have things right, Dr. Lisi is proposing that gravity is still symmetric with electroweak at a time when the color force is not. This flies in the face of quite a bit of assumption that has been made due to the natural scale of gravity being extremely small; very small areas correspond to very high temperatures, so the assumption has always been that the symmetry between gravity and the other forces must have broken first as the Big Bang progressed, followed by the color-electroweak breaking, finally followed by the electroweak breaking. I am still not entirely certain I have this right, but several things I have seen Dr. Lisi say both in his paper and in responses on various blogs and fora indicate that this may be the case. I'll update later as I come to further understanding of precisely what the meaning is of the things I have seen.

So what's the problem? Well, it's that if Dr. Lisi were correct, he'd have a theory in a de Sitter space that's within a 10^{-60} error of a theory that violates the C-M theorem (because his theory certainly does not have a symmetry group that's a direct product of the gravity sector with the SM - indeed, that's the whole point of it from the beginning). Put another way, I could approximate his theory to an incredible degree of accuracy with something that we know by C-M is mathematically inconsistent. But if that were possible (it's not) C-M wouldn't mean a thing, because you could always evade it by adding an infinitesimal energy to your theory. Not only that, but all of the constraints and consequences of Poincare invariance (which include some of those 10-digit predictions) would be in the trash.That is only true now. Furthermore, Dr. Lisi is not making any apparent claim that this theory applies in its fully symmetric form in a space that is so close to Minkowski space; instead, he breaks the symmetry at a time when the space is highly curved. And if space is highly curved, then the CM theorem is very far from being true; it is only in our very nearly flat spacetime that the CM theorem is nearly true, and in fact, it is not strictly true even now, though as sol points out, it very nearly is.

So that is an abstract - but very general - reason to be extremely skeptical of the existence of this theory.And I have added some reasons to be skeptical of this objection.

Now for a last big twist. I said above that the Higgs mechanism gave mass to all the fermions. There is a problem reconciling that with the fact that gravity fell out of symmetry with the other forces first. Gravity is the force whose charge is mass. So how can gravity exist if mass does not? This has long seemed to me to be a problem with this state of affairs, but I was seduced by the same thing everyone else was- the Planck scale. The Planck scale is the smallest scale of spacetime we know of. It is the natural scale of gravity, and it is the smallest of the scales of any of the forces. For a very long time, physicists have assumed that this meant that gravity must have fallen out of symmetry with the other forces first. Lisi may have challenged this assumption (and he may not be the first- a pair of Italian physicists may already have proposed it, having invented the term "graviweak"). As I said above, I am still investigating this. However, if this is correct, then the implications are profound- the point at which matter acquires mass, and the point at which gravity becomes a separate force, may be much closer than physicists had assumed must be the case until now.

These are interesting times we live in.

[Schneibster]

I haven't read the paper, so I won't comment on what Lisi is saying. I just read your exchange about E8. For a casual reader who knows group theory and particle physics it seemed as if you were saying that classifying the particles through E8 meant that spacetime had to be 8 dimensional. I know see that this is probably not what you were saying, but you had some confusion there with Lie algebra terminology that made it look that way.I probably screwed it up. I haven't had to deal with it much to understand what I wanted to know until now.

And anyway, SO(3,1) is the Lorentz group, so I'm not sure I understand your last post either.It turns out that the natural background spacetime in Lisi's theory is SO(4,1). It also looks like just about everyone hasn't said a thing about the degree of curvature of spacetime in the early universe, or about the fact that the symmetry of this theory cannot be whole. I believe these tidbits may be salient to the theory.

[sol invictus]

That is only true now. Furthermore, Dr. Lisi is not making any apparent claim that this theory applies in its fully symmetric form in a space that is so close to Minkowski space; instead, he breaks the symmetry at a time when the space is highly curved. And if space is highly curved, then the CM theorem is very far from being true; it is only in our very nearly flat spacetime that the CM theorem is nearly true, and in fact, it is not strictly true even now, though as sol points out, it very nearly is.

And I have added some reasons to be skeptical of this objection.


Schneibster, I don't have time (and probably won't today) to make a detailed reply to this. However you're not quite on track with your summary when you get to the part about spontaneously broken symmetries. C-M applies to any theory that has the P. group as a subgroup of the symmetries of its S-matrix. Spontaneously broken symmetries don't appear as symmetries of the S-matrix, so C-M says nothing about them. However in the Weinberg-Salam model (let's just call it the standard model) there are other symmetries which are unbroken, and C-M applies perfectly well to them. It says that the total symmetry group must be a direct product of the P. group with the others.

The temperature has nothing much to do with this - either the S-matrix has a symmetry or it doesn't. What you could say is that it has an approximate symmetry at high energies, and try to apply C-M to that approximate symmetry, but it's not necessary here.

We can apply C-M today, yesterday, tomorrow, or in the early universe - it's up to us. I want to apply it now, because (among other things) this theory is supposed to describe physics now. So I have a set of unbroken symmetries in the standard model, and I have those associated with gravity, which in this theory is the dS group. However note that the particular representation of the dS group which is relevant here is one that must be "within" 10^{-60} of the P. group, in the way I described above. If that doesn't make sense to you, imagine the surface of a sphere (that's what dS is, essentially) of extremely large radius. A sphere has a different set of isometries than a plane, but as it gets bigger and bigger, it's symmetries get closer and close to those of a plane. Eventually it gets so big that no experiment we can do locally can distinguish them. That's the case we know we're in here, today.

In other words Lisi's cosmological constant must be very very very small. It doesn't mean anything at all for particle physics (even less than the grav. effects you mentioned which LHC had to take into account, which would come from the gravity of the earth, not this tiny CC that can only be detected in cosmology). In fact the effects of the earth and the sun etc. on our local spacetime are MUCH larger than the effects of this CC (so Lisi's theory is NOT in dS, not even close, on the scales relevant to particle physics), and so if putting a theory in dS evaded the C-M theorem, so does the existence of the sun nearby. That's the point I was trying to make.

Just think about that last point: if Dr. Lisi is correct, his theory is consistent by virtue of a parameter that's much much much too small to be detected in any experiment in particle physics. So he can evade all these mathematical constraints by adding a parameter that has no effect on any of the theories or experiments in question?


I will attempt to meet your standard.

And I'll attempt to meet yours...

[sol invictus]

By the way, one more quick comment - what you may have in mind is that Lisi's theory spontaneously breaks to SO(4,1)Xinternal symmetries at some relatively high scale (like the electro-weak scale). But then, as I'm trying to point out, the curvature of that de Sitter space will also be much higher than is allowed by experiment. And the other problem is that, if you look at eqs. 3.7 and 3.8, you see that the breaking is not spontaneous - it's explicit. That's nonsensical for a gauge symmetry (one of the more basic problems I referred to earlier) and does away with that possibility.

[Cuddles]

To me, a crackpot is someone who thinks everything that came before her/him is wrong.

As you say, that covers all scientist, which makes it an utterly pointless definition of the word. A much more sensible definition would be "a person who is eccentric, unrealistic, or fanatical." (from dictionary.com). Which doesn't cover this at all. When it comes down to it, we know for a fact that everyone so far has been wrong. Copernicus was wrong. Galileo was wrong. Newton was wrong. Einstein was wrong. We don't know what the right answer is, but people who admit this aren't certainly aren't crackpots, unless you dilute the word so much it no longer has any meaning.

The fact is, this is a theory. It could very well be wrong, and the author admits this. It has been published in an appropriate place and time will tell what actually comes of it. Being wrong does not make one a crackpot, it simply makes one wrong.

[Schneibster]

Schneibster, I don't have time (and probably won't today) to make a detailed reply to this. You and me both; if you even did, I probably wouldn't have time to reply. I do, however, have some comments and a bit of time to make them.

However you're not quite on track with your summary when you get to the part about spontaneously broken symmetries. C-M applies to any theory that has the P. group as a subgroup of the symmetries of its S-matrix. And here's the problem: this theory does NOT have the Poincare group as a subgroup, and for that matter does not produce an S-matrix. Lisi states that it is only capable of providing an approximation to the S-matrix, and that only at low energy.

Quite a few people over at physics forums are being very direct about this issue, on a thread that was started to discuss Lisi's theory. He is a member there, as am I (though I rarely post there), and was posting on the thread up through yesterday. I also found an absolutely fascinating discussion dated this past summer (July through late August) on Cartan geometries that he had with Baez, who is also a member there. This discussion hints that Lisi was figuring out his theory right there and asking the best authority he could get ahold of on Cartan geometry, Lie algebras, Lie groups, and other intimate details of his theory questions the answers to which appear in his paper. I am in no way surprised to see Baez' name in the acknowledgements section of the paper; he provided major material assistance to Lisi in developing the theory.

The consensus statement regarding the CM theorem appears to be, "Sorry, this theory does not contain the Poincare symmetry, does not make precise S-matrices, and does not have symmetry generators that take 1-particle
states into 1-particle states and act on multiparticle states as the direct sum of their action on 1-particle states (the "1-particle" states here are the usual momentum/spin unirreps of Poincare- which doesn't apply)." This 1-particle state to 1-particle state symmetry appears to be the reason for the requirement for not merely very close but exact Poincare symmetry, as well as the requirement that the theory it applies to produce an exact S-matrix. Without these features, CM simply doesn't apply, no matter how close the space may be to one in which it does.

Based on the explanations you have provided, I conclude you're contending that the real world is arbitrarily close to one in which the CM theorem applies; however, you acknowledge that in fact, it cannot apply to the real world. I have been able to find hints that at least some theorists believe (and apparently have good reason to) that the S-matrix is only an approximation of what we observe in the real world, no matter how precise it may be. Baez states at one point in the discussion on Cartan geometry (and the title of the thread, suggestively, is "De Sitter group SO(4,1) intro") that de Sitter space resembles our world more than Minkowski space does. Apparently this requirement for an exact S-matrix and exact Poincare symmetry has much less flexibility than you have assumed; it is not a sliding scale, but an absolute requirement for the proof of the theorem, and ANY violation of it renders the theorem completely unprovable, due to the dependence upon these 1-particle to 1-particle symmetry generators which cannot exist except in the presence of exact Poincare symmetry.

Various slightly off-color comments ("read my lips, CM does not apply" is a good example) were made concerning how the LQG guys, specifically Abhay Ashtekar, got the point of the de Sitter group immediately, but everyone else appeared to be floundering; if you find these offensive, I apologize in advance for bringing them to your attention, and do not endorse them.

That's all I have time for right now. I'll try to make more later.

And I'll attempt to meet yours...We're certainly doing much better.

[sol invictus]

The fact is, this is a theory. It could very well be wrong, and the author admits this. It has been published in an appropriate place and time will tell what actually comes of it. Being wrong does not make one a crackpot, it simply makes one wrong.

It hasn't been published. I agree that being wrong doesn't make you a crackpot - that's more like being not even wrong.

Anyway, my crackpot-curmudgeon spectrum is tongue-in-cheek, of course. Although it actually seems to work pretty well...

[sol invictus]

And here's the problem: this theory does NOT have the Poincare group as a subgroup, and for that matter does not produce an S-matrix. Lisi states that it is only capable of providing an approximation to the S-matrix, and that only at low energy.

I agree with that, although I think you meant to say it has an approximate S-matrix at high energy.

Quite a few people over at physics forums are being very direct about this issue, on a thread that was started to discuss Lisi's theory.

I didn't know about those forums - thanks.

Without these features, CM simply doesn't apply, no matter how close the space may be to one in which it does.

Again, while this is technically true, it isn't relevant until we can measure things to 60 significant digits. It is equally true that C-M fails to apply to all the more conventional theories in the real world, because our space isn't flat, and because we don't measure the S-matrix.

Based on the explanations you have provided, I conclude you're contending that the real world is arbitrarily close to one in which the CM theorem applies; however, you acknowledge that in fact, it cannot apply to the real world.

Precisely.

I have been able to find hints that at least some theorists believe (and apparently have good reason to) that the S-matrix is only an approximation of what we observe in the real world, no matter how precise it may be.

That's not just a belief, it's true by definition. The S-matrix acts on asymptotic scattering states - essentially that means particles which, after an infinite time, are infinitely far away from each other. Obviously we can't measure that, but the characteristic distances (meters inside a particle detector) are so much larger than the Compton wavelength of particles in an accelerator (typically 10^{-15} meters or smaller) that this is an incredibly good approximation - and not the one that limits our precision.

Baez states at one point in the discussion on Cartan geometry (and the title of the thread, suggestively, is "De Sitter group SO(4,1) intro") that de Sitter space resembles our world more than Minkowski space does.

That's true only if the de Sitter curvature is the Hubble scale or smaller. De Sitter with large curvature is an extremely bad description of the world.

Apparently this requirement for an exact S-matrix and exact Poincare symmetry has much less flexibility than you have assumed; it is not a sliding scale, but an absolute requirement for the proof of the theorem, and ANY violation of it renders the theorem completely unprovable, due to the dependence upon these 1-particle to 1-particle symmetry generators which cannot exist except in the presence of exact Poincare symmetry.

It renders the theorem unprovable, but it does not render its conclusions meaningless, as I've tried to explain. Once again: if that weren't true C-M would be utterly meaningless in all interesting situations, since we do not live in flat space. So would all the other results of particle physics derived in the flat space approximation.

Various slightly off-color comments ("read my lips, CM does not apply" is a good example) were made concerning how the LQG guys, specifically Abhay Ashtekar, got the point of the de Sitter group immediately, but everyone else appeared to be floundering; if you find these offensive, I apologize in advance for bringing them to your attention, and do not endorse them.

Don't worry - theoretical physicists are an arrogant and intellectually tough bunch, in general. It's not easy to offend me that way.

[Schneibster]

I agree with that, although I think you meant to say it has an approximate S-matrix at high energy.No, I was able to find where Dr. Lisi had referred to both high and low energy limits; in the ultraviolet limit, the theory has a high cosmological constant and is, as he puts it, "all E8." In the low energy limit, it approximates the S-matrix, and looks like the SM with separate gravity. You can use a text search on Bee's blog and look for "high energy" and "low energy" to find the comments I'm referring to.

I didn't know about those forums - thanks.Sure. They're heavily moderated, and a fair number of professional physicists hang out there. There's a sizeable string contingent, and a sizeable LQG/alternative contingent as well as some "curmudgeons." It's a good idea to find out who you're dealing with before you post.

Again, while this is technically true, it isn't relevant until we can measure things to 60 significant digits. It is equally true that C-M fails to apply to all the more conventional theories in the real world, because our space isn't flat, and because we don't measure the S-matrix.Apparently it nearly holds in the low energy limit, as I said above; again, there's more detail on Bee's blog. A search on the Physics Forums is probably also a good idea.

Precisely.I'm glad I understood you. To my mind it's important to understand what you're arguing against, often as much as what you're arguing for.

That's not just a belief, it's true by definition. The S-matrix acts on asymptotic scattering states - essentially that means particles which, after an infinite time, are infinitely far away from each other. Obviously we can't measure that, but the characteristic distances (meters inside a particle detector) are so much larger than the Compton wavelength of particles in an accelerator (typically 10^{-15} meters or smaller) that this is an incredibly good approximation - and not the one that limits our precision.That sounds about right to me.

That's true only if the de Sitter curvature is the Hubble scale or smaller. De Sitter with large curvature is an extremely bad description of the world.True enough- now. In the early universe it's an extremely good one. It's also possible that it's a good one for very short distances and very high energies; but that remains to be seen. He hasn't developed it far enough to derive that yet.

It renders the theorem unprovable, but it does not render its conclusions meaningless, as I've tried to explain. Once again: if that weren't true C-M would be utterly meaningless in all interesting situations, since we do not live in flat space. So would all the other results of particle physics derived in the flat space approximation.Sure, but as I've pointed out, it reduces to an approximation of the S-matrix in the low-energy limit, and goes to the high-CC E8 symmetric behavior in the high energy limit.

I also have to point out that a lot of people are looking at this and they're saying they see why and how it would avoid the CM theorem's constraints. These aren't joe blow, they're pros. And they include some pretty well-known names. I mean, we can argue here forever, but if a physicist looks at it and goes, "OK, I can see that," they're a hell of a lot better qualified to make that call than I am. Maybe not you; you appear to be a pro too. But in that case, what we're talking about is a professional disagreement, and I'm not qualified to do anything but repeat their remarks.

Seriously, my opinion here is, you're entitled to your opinion, you have what you see as good reasons for it, and time will tell. It appears to be a qualified opinion, but it's at variance with other opinions that look just as well qualified from my viewpoint as an amateur. I am by no means qualified to tell you you're wrong. I am not sure there's a person on the planet who, qualified or not, has enough information to do so; furthermore, I'm pretty sure Lisi won't tell you you are.

Don't worry - theoretical physicists are an arrogant and intellectually tough bunch, in general. It's not easy to offend me that way.Good; we had enough trouble I think for both of us. Just being careful not to offend.

[sol invictus]

No, I was able to find where Dr. Lisi had referred to both high and low energy limits; in the ultraviolet limit, the theory has a high cosmological constant and is, as he puts it, "all E8." In the low energy limit, it approximates the S-matrix, and looks like the SM with separate gravity. You can use a text search on Bee's blog and look for "high energy" and "low energy" to find the comments I'm referring to.

Well, just FYI, it's impossible for a theory in dS to look like an S-matrix theory at low energies. Once the momentum of the particles becomes of order the curvature scale, they can't be regarded as particles anymore... in fact the modes of the field stop fluctuating at those scales. It wouldn't make any sense to discuss scattering.

De Sitter is a space with an event horizon surrounding every point at a distance set by the radius of curvature. If you want you can think of it as an expanding space; at a point far enough away, the space is expanding faster than the speed of light, and therefore no signal can ever reach you from there. As you probably know, the wave-packets we call particles have a size inversely proportional to their momentum (their Compton wavelength). Once that size becomes of order or larger than the horizon radius, the different parts of the wavepacket can't communicate with each other, and the whole thing ceases to look anything like a wave (or particle) and falls apart.

Sure. They're heavily moderated, and a fair number of professional physicists hang out there. There's a sizeable string contingent, and a sizeable LQG/alternative contingent as well as some "curmudgeons." It's a good idea to find out who you're dealing with before you post.

Took a look, but I think I'll pass. There seems to be a very high density of, well, err, c***kp**s.


True enough- now. In the early universe it's an extremely good one.

Only during inflation.

Sure, but as I've pointed out, it reduces to an approximation of the S-matrix in the low-energy limit, and goes to the high-CC E8 symmetric behavior in the high energy limit.

The high energy part might make sense if the E8 was broken spontaneously at some scale. Unfortunately it's not - it's broken explicitly by the Lagrange multiplier field B that appears in eq. 3.7.

I also have to point out that a lot of people are looking at this and they're saying they see why and how it would avoid the CM theorem's constraints. These aren't joe blow, they're pros. And they include some pretty well-known names. I mean, we can argue here forever, but if a physicist looks at it and goes, "OK, I can see that," they're a hell of a lot better qualified to make that call than I am. Maybe not you; you appear to be a pro too. But in that case, what we're talking about is a professional disagreement, and I'm not qualified to do anything but repeat their remarks.


Fair enough.

[Schneibster]

Well, just FYI, it's impossible for a theory in dS to look like an S-matrix theory at low energies. Once the momentum of the particles becomes of order the curvature scale, they can't be regarded as particles anymore... in fact the modes of the field stop fluctuating at those scales. It wouldn't make any sense to discuss scattering.We may be talking at cross purposes. Are you saying that de Sitter space has high curvature at low energy?

De Sitter is a space with an event horizon surrounding every point at a distance set by the radius of curvature. If you want you can think of it as an expanding space; at a point far enough away, the space is expanding faster than the speed of light, and therefore no signal can ever reach you from there. Sounds like our universe. If the curvature is very low.

As you probably know, the wave-packets we call particles have a size inversely proportional to their momentum (their Compton wavelength). Once that size becomes of order or larger than the horizon radius, the different parts of the wavepacket can't communicate with each other, and the whole thing ceases to look anything like a wave (or particle) and falls apart.This makes some sense.

I'm going to wait for your answer to the question above. Depending on the answer, I might do a little speculating.

Took a look, but I think I'll pass. There seems to be a very high density of, well, err, c***kp**s.LOL

The high energy part might make sense if the E8 was broken spontaneously at some scale. Unfortunately it's not - it's broken explicitly by the Lagrange multiplier field B that appears in eq. 3.7.He's already said he hand-entered the symmetry breaking to make it fit the SM- and that he needs to find a justification for that. As a matter of fact, he says it at the end of the paper in the discussion section.

[sol invictus]

We may be talking at cross purposes. Are you saying that de Sitter space has high curvature at low energy?

You've said something like this a few times... I think you might have some kind of misconception here. The curvature of a spacetime is a geometrical quantity - it doesn't depend on the energy, at least not in classical physics. It's part of the definition of the background. Even in a quantum theory it doesn't depend very strongly on the energy as long as quantum gravity is not a very important effect. Now we know that QG isn't important in any experiment we've ever done, and it's certainly not important at lower energies, so we can forget about it for now.

Then the radius of curvature is just some length, which we can measure, and it's fixed. The energy I was talking about is the energy of some particles we might want to scatter, and the relevant dimensionless (in natural units) parameter is the product of their energy with the radius of curvature.


Sounds like our universe. If the curvature is very low.

Like our universe now, yes, if the curvature is many, many orders of magnitude below particle physics scales.


He's already said he hand-entered the symmetry breaking to make it fit the SM- and that he needs to find a justification for that. As a matter of fact, he says it at the end of the paper in the discussion section.

That's fine to say, but it alone makes the theory totally uninteresting (even if it made sense, which I have not changed my opinion on at all). The entire paper could have been one sentence long: the de Sitter group and some symmetries of the standard model are subgroups of E8. It's like my earlier comment - here's my unified theory of SU(4593532419384), broken down to SU(3)XSU(2)XU(1) by hand.

Essentially of the physics of unified theories is in the symmetry breaking. That's the whole point of them - they are interesting because there is some non-trivial physics them, which makes some predictions about what we can see at low energies.

[kjkent1]

Damn, you guys are smart. I can't even remember how to do an integral!

Hey, but I can carve a turkey pretty dern goood...so I got dat goin "fermi."

[sol invictus]

Essentially of the physics of unified theories is in the symmetry breaking.

Essentially all of the physics...

Pre-coffee posting = bad.

[INRM]

Schneibster,

Not sure if I read what you wrote right, but...

So Lisi's theory basically states that the properties of our universe are the results of something underlying it?

On Casimir effect... so if a particle disappears, it has to re-appear faster than it can be detected in the same way that if it appears, it has to disappear before being detected? How do you know there's not another universe that particle's going to?

Regarding the number of dimensions of spacetime, what would 2 dimensions of spacetime be like, or 3 dimensions of space time, or 1. What would the diffferences be?


INRM

[Schneibster]

You've said something like this a few times... I think you might have some kind of misconception here. The curvature of a spacetime is a geometrical quantity - it doesn't depend on the energy, at least not in classical physics. It's part of the definition of the background. Even in a quantum theory it doesn't depend very strongly on the energy as long as quantum gravity is not a very important effect. Now we know that QG isn't important in any experiment we've ever done, and it's certainly not important at lower energies, so we can forget about it for now.OK, the conversation has changed, I haven't noted it, and that's my fault. I'm going to explain it for everyone else, and in the meantime you'll get an idea of how I'm thinking and what I'm saying. A subtext got introduced, because these matters are all twined up with one another in my thinking, and you apparently didn't notice it. Not your problem; it's my responsibility to explicate my arguments more fully to avoid situations like this, which I will now proceed to do.

Most of you will be familiar with the Big Bang theory, but there are some subtleties you might not be aware of, and these subtleties deal with curvature, and symmetry breaking, and some other things that are worth knowing whether you're following the argument or not.

The basic idea of the Big Bang is, the universe is expanding; so if we look backward in time, what we should see is the universe contracting and everything getting closer together. If you take this far enough back, what you get is an extremely hot, extremely dense state of the universe. Cosmologists call this the "Big Bang."

Because of this high density, physicists think that the curvature of the universe was very high back then. The reason is relatively obvious; if mass makes gravity (and don't forget, energy has mass too, according to relativity), then relativity says that that gravity is curvature of space, and so we have another parameter besides hot and dense, which is highly curved.

Furthermore, we have a theory of the electromagnetic and weak forces called "electroweak theory" that says that if things get hot enough, you can't tell electromagnetism from the weak force. When you can't tell things that are otherwise different from one another, physicists call that a "symmetry," as has been discussed elsewhere in this thread. The Big Bang was certainly hot enough that this was true; so when it cooled down, this symmetry broke; that is, it became possible to tell electromagnetism from the weak force. It's the current general consensus (by no means universal, but a consensus nevertheless) that this was not the only symmetry breaking that took place during the early evolution of the universe. Physicists think that the strong force (technically, this is the color force, the strong force is a residual force of the color force, so you'll see me call it the color force pretty much most of the time) and gravity both fell out of symmetry with electroweak at earlier times and higher temperatures.

So the general idea is, at the beginning of the Big Bang, the universe was very hot, very dense, very curved, and highly symmetric. There was only one force, a combined color-gravi-electroweak force. As it cooled down and expanded, the symmetries were broken at various temperatures, the density fell, and the curvature declined. This is all pretty much standard Big Bang theory, and that's the current consensus of how our universe looked during the first second or so of its existence. At no time since have conditions been so hot, so dense, or so curved, with the possible exception of black holes and the conditions from which they might form (and even those extreme conditions would be less than what physicists think the first microsecond or so was like in our universe).

So basically what I've been saying to sol is, the universe was hot, dense, and highly curved when it was young. We continue to see it expanding to this day, and recent evidence says that expansion is increasing (the subtext here is the "dark energy" hypothesis recently advanced to explain the increasing expansion- or, more properly, the evidence which that hypothesis has been advanced to explain). Decreasing temperature explains the symmetry breakings; so far as we know now, there's no reason a theory of physics shouldn't have a symmetry breaking at any convenient point, as long as we find some explanation for it later, and as long as the electroweak symmetry breaking happens at the correct point (because we already know a lot about that) everything is still in accord with the available evidence. Decreasing density explains the decreasing curvature, and that's already a known fact; furthermore, we see increasing curvature again today, so we know the curvature can change, and we might even know that it can change for unknown reasons (dark energy is only a hypothesis at this point). And finally, since we know we live in a curved space, not a flat one, and since de Sitter space is a curved space, why is it unreasonable to postulate that we live in a de Sitter space, and if we do, why is it unreasonable to postulate that the early universe was a highly curved de Sitter space, as this theory postulates? There is no hard evidence to deny this at this time.

It's also important to note that Einstein once said that his only mistake in GR was the introduction of a "cosmological constant" to account for the fact that the exact solutions to his original gravity field equations produces a de Sitter space. At the time, cosmological theories favored a "steady state" universe; so when de Sitter pointed out these exact solutions, Einstein introduced this idea of a "cosmological constant" into the theory to account for that. That's important, because it shows that de Sitter space follows naturally from GR, which is a very well-tested theory; anything that denies GR is immediately questionable on the grounds that it does so.

Another very important point is that de Sitter space reduces to Minkowski space in the limit of low curvature. Therefore arguing about whether our universe today is closer to a de Sitter space or a Minkowski space may be totally meaningless; they may be indistinguishable (and the math says they just about are, and choosing to measure the curvature over a very small area makes that pretty certain).

Then the radius of curvature is just some length, which we can measure, and it's fixed. The energy I was talking about is the energy of some particles we might want to scatter, and the relevant dimensionless (in natural units) parameter is the product of their energy with the radius of curvature. My argument here is, no, the radius of curvature is NOT fixed and we have good evidence to show that it has changed in two important and different ways during the evolution of the universe: it decreased from the Big Bang, and then started to increase again. No one knows why. The mainstream hypothesis for an explanation for this is called dark energy, but it's not the only contender.

The energy I was talking about is the high temperatures of the early universe. The E8 theory postulates a very high degree of symmetry among the forces and among matter particles; it's obvious that this situation does not obtain today. It's therefore obvious (to me at least- YMMV) that conditions when these symmetries are unbroken are going to be very different than they are today. Today, we have a cold, diffuse, low-curvature, asymmetic universe; the S-matrix we measure today need not be the same as it would be for those earlier hot, dense, highly curved, highly symmetric times. It's not even a problem to say that during those times, the S-matrix breaks down and stops working; we don't have any experimental data to deny it. We know that the S-matrix is very precise and very accurate today; we don't know that about very hot, very dense, highly curved, highly symmetric times, because we can't reproduce the conditions of those times in the laboratory.

Therefore, as I said earlier, the theory reducing to the S-matrix in the limit of low energy is no barrier to it being true; by "low" I mean as high as anything we can get in current particle accelerators. Energy levels in the very early universe were almost certainly far higher than that.

Like our universe now, yes, if the curvature is many, many orders of magnitude below particle physics scales.Sure, but that doesn't mean they always had to be like that.

That's fine to say, but it alone makes the theory totally uninteresting (even if it made sense, which I have not changed my opinion on at all). The entire paper could have been one sentence long: the de Sitter group and some symmetries of the standard model are subgroups of E8. It's like my earlier comment - here's my unified theory of SU(4593532419384), broken down to SU(3)XSU(2)XU(1) by hand.But SU(4593532419384) isn't a Lie group with a special exceptional Lie algebra, nor does it reproduce the quantum numbers of the particles we think we observe. The theorist in this case has chosen to work on reproducing the particles we observe first, and figure out how the symmetry broke later; you're criticizing the theory on the grounds it's not complete, and that amounts to an obfuscation of the fact that it DOES reproduce what looks an awful lot like what we see, in the respects it has so far been crafted to.

It furthermore unifies gravity, which is the main program in physics right now, and finally it does so in a different way than has been tried in a long time, since string physics and LQG and twistors and so forth came on the scene, and it might even be compatible with LQG (it shares some conceptual lineage with it) and builds upon recent papers in the field and on a mathematical structure (E8) that we have only recently come to fully understand.

It's topical, it's so far consistent in the ways it has been crafted to be, it promises to be testable in short order, and it's a very ingenious use of a hot piece of mathematics. It is, in short, interesting. And nothing I've seen makes it seem nearly as improbable as you appear to be making it out to be.

Essentially of the physics of unified theories is in the symmetry breaking. That's the whole point of them - they are interesting because there is some non-trivial physics them, which makes some predictions about what we can see at low energies.Right, but first you have to find theories that are worth figuring out the symmetry breaking for. Nobody's come up with a new one in a long time, and nobody's figured out how to properly break the ones we have. Let's see if it has defects in other places first, and figure out what it says, before we start throwing it in the circular file. Even if it doesn't work as-is, it's a new approach. And that may ultimately turn out to be more important than whether it's right or wrong. You're arguing that it's a sterile approach, and on this we strongly disagree. Your grounds are that it doesn't answer the question you think is most important, which is, how and why does the symmetry break? But that ignores that it does answer some other questions, which others (and I am among them) think are at least equally important, and no one has yet successfully produced a theory that details color or gravity symmetry breaking anyway.

So let's wait and see. Give the guy a chance to work down his own line of reasoning; just because it's not reasoned the way you're used to doesn't mean it's wrong.

[sol invictus]

Schneibster, there's absolutely no reason to bring in the big bang or the early universe. Cosmology constrains the theory even more, but it's irrelevant if the theory doesn't pass even basic consistency checks right now. So while you gave a nice description of cosmological phase transitions, they don't have any relevance to what I was discussing.

And finally, since we know we live in a curved space, not a flat one, and since de Sitter space is a curved space, why is it unreasonable to postulate that we live in a de Sitter space, and if we do, why is it unreasonable to postulate that the early universe was a highly curved de Sitter space, as this theory postulates? There is no hard evidence to deny this at this time.

The question is, what does the theory predict right now. Once we know that, we can worry about cosmology.

Another very important point is that de Sitter space reduces to Minkowski space in the limit of low curvature. Therefore arguing about whether our universe today is closer to a de Sitter space or a Minkowski space may be totally meaningless; they may be indistinguishable (and the math says they just about are, and choosing to measure the curvature over a very small area makes that pretty certain).

Correct.

My argument here is, no, the radius of curvature is NOT fixed and we have good evidence to show that it has changed in two important and different ways during the evolution of the universe: it decreased from the Big Bang, and then started to increase again. No one knows why. The mainstream hypothesis for an explanation for this is called dark energy, but it's not the only contender.

You're talking about changes with time now. Before, you were talking about changes with energy. Perhaps you meant the background energy in cosmology, but again, that's totally unimportant to particle physics today.

Today, we have a cold, diffuse, low-curvature, asymmetic universe; the S-matrix we measure today need not be the same as it would be for those earlier hot, dense, highly curved, highly symmetric times. It's not even a problem to say that during those times, the S-matrix breaks down and stops working; we don't have any experimental data to deny it. We know that the S-matrix is very precise and very accurate today; we don't know that about very hot, very dense, highly curved, highly symmetric times, because we can't reproduce the conditions of those times in the laboratory.

Right.

Therefore, as I said earlier, the theory reducing to the S-matrix in the limit of low energy is no barrier to it being true; by "low" I mean as high as anything we can get in current particle accelerators. Energy levels in the very early universe were almost certainly far higher than that.

All I said is that the statement that a theory in a de Sitter background reduces to an S-matrix theory at low energies is false, and I explained why. That's logically independent from anything to do with cosmology or the universe.

But SU(4593532419384) isn't a Lie group with a special exceptional Lie algebra, nor does it reproduce the quantum numbers of the particles we think we observe.

Actually it does. It's not an exceptional Lie group (exceptional is just a technical term describing 5 specific Lie groups), but nonetheless it contains SU(3)XSU(2)XU(1) (the gauge group of the standard model) as a subgroup, as well as plenty of other subgroups to use for things like flavor.

The theorist in this case has chosen to work on reproducing the particles we observe first, and figure out how the symmetry broke later; you're criticizing the theory on the grounds it's not complete, and that amounts to an obfuscation of the fact that it DOES reproduce what looks an awful lot like what we see, in the respects it has so far been crafted to.

That part is trivial, as I've just shown. What's hard is finding a mechanism to break the symmetry spontaneously, which he hasn't done.

It furthermore unifies gravity, which is the main program in physics right now, and finally it does so in a different way than has been tried in a long time, since string physics and LQG and twistors and so forth came on the scene, and it might even be compatible with LQG (it shares some conceptual lineage with it) and builds upon recent papers in the field and on a mathematical structure (E8) that we have only recently come to fully understand.

Except it doesn't do any of that. It doesn't contain any spin 1/2 particles, and it does contain ghosts which render it inconsistent.

It's topical, it's so far consistent in the ways it has been crafted to be, it promises to be testable in short order, and it's a very ingenious use of a hot piece of mathematics. It is, in short, interesting. And nothing I've seen makes it seem nearly as improbable as you appear to be making it out to be.

Well, I've done my best to explain the problems. Maybe I'll post a numbered list of them later.

So let's wait and see. Give the guy a chance to work down his own line of reasoning; just because it's not reasoned the way you're used to doesn't mean it's wrong.

He has all the time in the world.

[Ron_Tomkins]

A theory of everything?

Sure, why not.


A Law of everything?

I'm not so sure about that

[Schneibster]

Schneibster, there's absolutely no reason to bring in the big bang or the early universe. Cosmology constrains the theory even more, but it's irrelevant if the theory doesn't pass even basic consistency checks right now. So while you gave a nice description of cosmological phase transitions, they don't have any relevance to what I was discussing.Then in my opinion, what you're discussing is not this theory.

The question is, what does the theory predict right now. Once we know that, we can worry about cosmology.We're talking here about a theory that makes predictions that have a high degree of symmetry, and we know for a fact that those symmetries do not make themselves obvious at energies up to the TeV level. So, what is it you want to do right now? Have you got a 10 TeV accelerator in your back pocket? That might not even be enough.

Does this theory make predictions of the current SM in the limit of low energy? The answer appears to be "yes." Every objection you've made applies at energies far beyond any we've ever been able to test, yet you're apparently blithely applying those predictions to current conditions; conditions that look nothing like the conditions this theory appears to be effective under. Let's look at your main objection again:

You say, this theory mixes fermions and bosons. I say, that mixture happens only when a symmetry is evident that this theory does not predict is whole at energies below 10 TeV if even that low; if you want my guesstimate, the symmetries this theory predicts may not manifest below an order of magnitude above that, 100 TeV or more. The LHC will only reach 14 TeV.

It doesn't matter, you say. It's based on the Poincare symmetry. I point out that we have never seen a universe in which the Poincare symmetry applies exactly. You say, well, it approximately applies in current particle physics. I say, current particle physics does not take place at energy levels above 10 TeV. The last time in this universe that particle physics did take place at such levels, the geometry of spacetime was highly curved, just like a de Sitter space; and the background geometry of this theory IS de Sitter space. You say, the Big Bang has nothing to do with this. I say, how not? That's the only place this theory applies. In the limit of low energy, it reduces to the SM. It had better; if it doesn't, it's not going to describe reality. And the difference NOW between de Sitter space and Minkowski space, where the Poincare symmetry applies, is negligable- but NOT NON-EXISTENT.

You beginning to follow this? You aren't making me feel confident that what you're talking about is this theory. You're taking portions of it that apply at high energies and claiming it doesn't work because they don't apply at normal energies. Of course they don't; it's like claiming electroweak doesn't apply because the symmetry isn't visible in ordinary physics. And every time I tell you this, you claim I don't know what I'm talking about. It's frustrating.

You're talking about changes with time now. Before, you were talking about changes with energy. Perhaps you meant the background energy in cosmology, but again, that's totally unimportant to particle physics today. The particle physics this theory predicts today is the SM. Again, it had better if it's to be accurate.

All I said is that the statement that a theory in a de Sitter background reduces to an S-matrix theory at low energies is false, and I explained why. That's logically independent from anything to do with cosmology or the universe. I'm sorry, you claimed it, but you haven't proved it to my satisfaction, and I'm very leery when I hear claims that high-energy behavior doesn't manifest now; now isn't high-energy. Others who seem to know as much about S-matrices and de Sitter spaces as you do claim otherwise; they see no problem with it.

I know enough on my own to be relatively certain that the S-matrix applies in low curvature de Sitter space just as well as in Minkowski space, and to know that our universe is far closer to being de Sitter space than Minkowski space simply because it is expanding. I also know enough to know that de Sitter space emerges smoothly and naturally from the field equations of General Relativity, and that de Sitter space approximates Minkowski space in the limit of low curvature, so that a claim that the S-matrix doesn't apply in a de Sitter space at low curvature is basically a claim that it doesn't apply in our universe. I'm very skeptical of this claim. Finally, I know that the S-matrix is based on Special Relativity, and that SR excludes direct description of spatial curvature as in a de Sitter space, so when curvature is high, it's my expectation that the S-matrix will not work.

Your claims are not matching up with well-known theories of physics. I need far more substantiation than you have given so far to be convinced of them.

Actually it does. It's not an exceptional Lie group (exceptional is just a technical term describing 5 specific Lie groups), but nonetheless it contains SU(3)XSU(2)XU(1) (the gauge group of the standard model) as a subgroup, as well as plenty of other subgroups to use for things like flavor.But the nature of exceptional Lie groups is specifically that their subalgebras form representations that interconnect in ways that do not occur in non-exceptional Lie groups. These interconnections will not exist in your SO(somelargenumberorother) group, because it is not an exceptional group. Without those interconnections, mappings of subgroups to other entities within the theory is difficult or impossible. Exceptional is a technical term, certainly, but it is applied to 5 specific Lie groups that have special characteristics that make them good candidates as representations of physics in our universe, and other groups not so good.

That part is trivial, as I've just shown. What's hard is finding a mechanism to break the symmetry spontaneously, which he hasn't done.It doesn't appear to be trivial to me; the string physics guys have been trying for a couple decades, a bunch of them, and haven't done it, and this guy appears to have done it in years, if that, not decades, all by himself. I don't see where you showed it is. What I see you claiming is that any old theory has enough connections to do this, and that doesn't appear to be the case. That says this is a powerful approach, and an effective one. Furthermore, you don't take just any old symmetry group and come up with a close match not only to the number of particles, but to the right number of connections and the right number of subgroups to represent their quantum numbers, and a good match to estimates of how many extra quantum numbers we'll need to get the symmetries we need to bring in QCD and gravity. That says this particular mathematical theory is a decent match to what we know of particle physics. Such things don't grow on trees.

I do not question whether it is hard to find a spontaneous symmetry-breaking mechanism. That's not the point. The point is, he hasn't done that yet; what he's done is show that it's worth looking for for this model. The string physics guys have a symmetry-breaking mechanism; but they don't have a theory that makes contact with real physics. And they're not likely to have one soon. Should they stop looking? I certainly don't think so, and I've been less than friendly to some folks who said they should, right here on this forum. As a matter of fact, I've also said that they're developing some very interesting and useful mathematics that whether they found anything else or not would likely come in handy later, and this guy appears to be using some of that math.

Except it doesn't do any of that. It doesn't contain any spin 1/2 particles, and it does contain ghosts which render it inconsistent.The author claims to have found a way to make those ghosts make contact with real particles, and that way appears to be consistent with recent work in the same field.

Well, I've done my best to explain the problems. Maybe I'll post a numbered list of them later.Unless they're better supported than the ones I've seen so far, I'm unlikely to find them convincing.

He has all the time in the world.He also has an innovative approach, and this is the first hack at it.

[sol invictus]

You say, this theory mixes fermions and bosons.

I didn't say that - I said it doesn't have fermions. Or to be more precise, it doesn't have particles with spin 1/2, and instead it has particles with spin 0 but which obey Fermi-Dirac statistics. Those are called ghosts, and they destroy the consistency of a theory at any energy. They make probabilities negative and screw up causality. They are not very friendly.

I say, that mixture happens only when a symmetry is evident that this theory does not predict is whole at energies below 10 TeV if even that low; if you want my guesstimate, the symmetries this theory predicts may not manifest below an order of magnitude above that, 100 TeV or more. The LHC will only reach 14 TeV.

Nope. It doesn't make any difference what the mass of a ghost is - it's always bad. And anyway these ghosts are supposed to be the fermions of the Standard model, such as the electron (which is very light).

It doesn't matter, you say. It's based on the Poincare symmetry. I point out that we have never seen a universe in which the Poincare symmetry applies exactly. You say, well, it approximately applies in current particle physics.

Correct - and the approximation is incredibly good. Much better than our experimental precision. And one of the many implications of that is that we have spin 1/2 representations of the Poincare group in our world.

You say, the Big Bang has nothing to do with this. I say, how not? That's the only place this theory applies. In the limit of low energy, it reduces to the SM.

No it doesn't.

It had better; if it doesn't, it's not going to describe reality.

Exactly!

You aren't making me feel confident that what you're talking about is this theory. You're taking portions of it that apply at high energies and claiming it doesn't work because they don't apply at normal energies. Of course they don't; it's like claiming electroweak doesn't apply because the symmetry isn't visible in ordinary physics. And every time I tell you this, you claim I don't know what I'm talking about. It's frustrating.

I'm talking about the theory that's in that paper.

The particle physics this theory predicts today is the SM. Again, it had better if it's to be accurate.

Right - and it's not. Not even close.

Others who seem to know as much about S-matrices and de Sitter spaces as you do claim otherwise; they see no problem with it.

I think it's safe to say that I know as much about de Sitter space as anyone in the world. But de Sitter really has little or nothing to do with this theory and its problems.

I know enough on my own to be relatively certain that the S-matrix applies in low curvature de Sitter space just as well as in Minkowski space, and to know that our universe is far closer to being de Sitter space than Minkowski space simply because it is expanding.

Again, if the particle energies are low compared to the de Sitter curvature scale all bets are off. Of course if we're talking about a de Sitter with curvature consistent with cosmology today, those are energies far below any we could possible detect, so (as I keep saying) that's totally irrelevant to particle physics. Nonetheless, in the limit of low energy the S-matrix (and Poincare invariance) would cease to be any kind of good approximation.

That's not a controversial statement.

Your claims are not matching up with well-known theories of physics. I need far more substantiation than you have given so far to be convinced of them.

OK.

But the nature of exceptional Lie groups is specifically that their subalgebras form representations that interconnect in ways that do not occur in non-exceptional Lie groups. These interconnections will not exist in your SO(somelargenumberorother) group, because it is not an exceptional group. Without those interconnections, mappings of subgroups to other entities within the theory is difficult or impossible. Exceptional is a technical term, certainly, but it is applied to 5 specific Lie groups that have special characteristics that make them good candidates as representations of physics in our universe, and other groups not so good.

That's certainly not true. Both SO(10) and SU(5) were candidates for unified theories (of particle physics, not Coleman-Mandula violating theories including gravity), and in the case of SU(5) it was only recently that it was ruled out.

And by the way, SU(5) was ruled out by an extremely careful analysis of the running of couplings, the stability of the proton, and several other very precise calculations. That was SU(5) spontaneously broken at the GUT scale - something like 10^13 TeV, 13 orders of magnitude above the energy we can probe directly with the biggest accelerators. And yet despite that, the theory is experimentally ruled out. Why? Because we have incredibly precise data and clever theorists.

It's really, really, really hard to extend the standard model without running afoul of experimental constraints. No one that hasn't worked on it can really appreciate how hard.

That says this is a powerful approach, and an effective one. Furthermore, you don't take just any old symmetry group and come up with a close match not only to the number of particles, but to the right number of connections and the right number of subgroups to represent their quantum numbers, and a good match to estimates of how many extra quantum numbers we'll need to get the symmetries we need to bring in QCD and gravity. That says this particular mathematical theory is a decent match to what we know of particle physics. Such things don't grow on trees.

Nope - he does all of that by hand. It's completely trivial to make a unified theory (at this level of non-detail) if you simply explicitly break the symmetry by hand, according to whatever pattern you want. Again, SU(anything 5 or greater) will work just fine at that level.

[kjkent1]

Lenny?

[Schneibster]

I didn't say that - I said it doesn't have fermions. Or to be more precise, it doesn't have particles with spin 1/2, and instead it has particles with spin 0 but which obey Fermi-Dirac statistics. Those are called ghosts, and they destroy the consistency of a theory at any energy. They make probabilities negative and screw up causality. They are not very friendly.This is a good point - equation 1.1 of the paper appears to be utter nonsense. Not only does it add fermions to bosons, which is nonsensical (can you add a vector to a scalar?), it also adds fields with different gauge transformations.First you said there were fermions added to bosons, then you said there weren't any fermions. I'm having trouble reconciling these two statements.

Nope. It doesn't make any difference what the mass of a ghost is - it's always bad. And anyway these ghosts are supposed to be the fermions of the Standard model, such as the electron (which is very light).Spin 0, by the way, is a boson. Higgs bosons have spin 0.

Now you're saying they're ghost particles.

What Lisi says is, "The fermions are represented as Grassmann valued spinor fields..."

Now, a Grassmann number is an element of an algebra that anticommutes with generators, but commutes with ordinary numbers. Grassman numbers are used to define the path integrals of fermionic fields; they are the classical analogs of anticommuting operators.

Spinors were first used in physics to define the properties of the spins of the electron and other fermions.

But there are, according to you, no fermions in the theory.

I'm having trouble reconciling these statements too.

What you're saying isn't agreeing with what he's saying, and he's saying it in seminar after seminar filled with working, famous, prize-winning physicists who are applauding after he says it. They are reading his paper. If he's faking it, they're going to know. There's no way out of that.

We have a problem here. I need you to explain these discrepancies.

Correct - and the approximation is incredibly good. Much better than our experimental precision. And one of the many implications of that is that we have spin 1/2 representations of the Poincare group in our world.No, we don't. And we've already covered that. You're fighting with relativity, and I'm sorry, but Albert is going to win that fight. We have very good approximations of representations of the Poincare group. At least, they're very good approximations at the current level of curvature, and at the energies we can access.

No it doesn't.Yes, actually, it does. Lisi is saying so in front of a bunch of people who are absolutely going to know if he's lying, right then and there, and laugh him off the podium and out of the room in disgrace. And they're all applauding.

Something is not right. You need to fix whatever it is. Do that now.

[dogjones]

Thanks for carrying on this debate Sol/Scheib, I'm finding it most stimulating - many thanks also Scheibster for your post #77, which gave me at least a modest glimmer of understanding from then on.

Cheers
Dog

[sol invictus]

Spinors were first used in physics to define the properties of the spins of the electron and other fermions.

But there are, according to you, no fermions in the theory.

I'm having trouble reconciling these statements too.

Because Lisi has ghosts in his action there is a confusion of terminology here - although I have been careful to keep mine consistent in this thread.

In the real world, the statistics of particles can be either Bose-Einstein or Fermi-Dirac. B-E means that the quantum wavefunction is even under exchange of two of the particles. One implication is that arbitrary numbers of particles can occupy the same state (for example in a Bose-Einstein condensate). F-D means the wavefunction is odd under exchange. An implication is that only one particle can be in a given state. This is the Pauli exclusion principle, and is an absolutely essential fact about the world. All known matter is fermionic (as opposed to the force-carrying gauge bosons), and if that weren't the case there would be no such thing as chemistry (because all the electrons could fall down and occupy the lowest orbital). Particles that obey B-E statistics are called bosons, and particles that obey F-D statistics are called fermions.

Again in the real world, we know that exact Poincare invariance is an extremely accurate description of fundamental physics. Indeed this is what we mean by particle - a particle is a state with (almost) definite momentum and energy and spin, which are numbers associated to representations of the Poincare algebra. The algebra tells us that spin must be an integer or half-integer.

There is a connection between statistics and the spin of the particle. A priori there is no reason they should be connected - spin is a number determined by the representation of the Poincare group the particle transforms under, and statistics are a statement about the quantum
wavefunction. However there is a theorem, called the spin-statistics theorem, which proves that all fermions have 1/2 integer spin, and all bosons have integer spin.

A particle which does not obey that theorem is unphysical and is termed a ghost. Such particles, if they are present in the spectrum of the theory, destroy its consistency in several ways. It is true that they do appear in the intermediate steps of formal procedures for gauge fixing such as BRST, but the physical states in BRST are by definition those without ghosts (the ghosts are merely a formal way to remove the unphysical degrees of freedom associated with the gauge redundancy).

What you're saying isn't agreeing with what he's saying, and he's saying it in seminar after seminar filled with working, famous, prize-winning physicists who are applauding after he says it. They are reading his paper. If he's faking it, they're going to know. There's no way out of that.

That's a highly questionable statement for many reasons.

You're fighting with relativity, and I'm sorry, but Albert is going to win that fight.

How am I doing that?

We have very good approximations of representations of the Poincare group. At least, they're very good approximations at the current level of curvature, and at the energies we can access.

Yes, that's what I said.

[Schneibster]

That wasn't it. Try again. I don't believe I'll ask again.

[sol invictus]

That wasn't it. Try again. I don't believe I'll ask again.

??

[shadron]

This is a forum for skeptics, so I won't pull any punches: this "theory" is nonsense. He doesn't seem to even understand the meaning of the terms he uses - or at best, he means something else by them than anyone else.

Now, I understand that non-physicists might not be able to tell that by looking at his paper. But when you see a story like that, ask yourself this question - how many times in the history of science has someone come along and suddenly invented a brand-new theory that explained everything? Hint - the answer is a non-negative integer less than 1.

You might also ask how many times the New Scientist has trumpeted a major advance of this type, only to have it fade gently away into the mists on quackery. Answer: an integer of the order of the number of issues of the New Scientist magazine.

Well, dang. And here I was dreaming that we could all go on a diet of lotus next week, since everything would be known.

So, we are to determine for ourselves that this guy's theory is dumb simply because (by definition) it has never been accomplished before? What kind of proof, or even conviction, is that? Personally, I have problems with a theory that springs from a mathematical model for which there is no theoretical underpinning, but even that is not any kind of proof, only a feeling. Maybe the poor guy just lucked into something real; perhaps not. The term "Theory of Everything" is half-way ironic, in any case. I'm sure that Einstein's Special Relativity, coming as it did from a very young patent clerk, struck many in the same way that this theory is now strinking physicists. If, as you seem to believe, the search for such is futile, then a lot of physicists should be lookiing into McDonald's job listings.

This being a skeptical forum, I would prefer, in my gentle non-physicist, but generalist way, to hear evidence that refutes his theory. Presumably that won't be too hard; the relationships should make all sorts of predictions about the particles that are currently known, and that are unknown. If it does all hang together, then the main question to ask is, "Why?"

(Ah, darn, I was led to believe, by my failing eyes, that I was near the beginning of a neat rant, but find I am way back in the pack. Most of what I said here has been said by others, so just let it rest.)

[sol invictus]

This being a skeptical forum, I would prefer, in my gentle non-physicist, but generalist way, to hear evidence that refutes his theory. Presumably that won't be too hard; the relationships should make all sorts of predictions about the particles that are currently known, and that are unknown.

That's what most of this thread has been about. But the problem is that the theory is not even logically consistent, so it's hard to point out a prediction that's wrong - it doesn't make any!

I guess I can say the following - according to this theory there are no spin 1/2 particles, but there are spin 0 and spin 1 fermions. Both of those are in maximal contradiction to just about every experimental result in all of science, from chemistry (which would not exist - there'd be no chemical reactions) to biology (no such thing as life in such a theory) to physics, which measures those properties with extreme precision.

[sol invictus]

Here's an extremely clear blog post where Jacques Distler (a professor of physics at UT Austin) carefully explains one of the reasons why Lisi's theory is nonsense. It's probably not the most basic or fundamental of the many problems, but it was the most hyped aspect of the paper and the only part of it that might have been interesting.

http://golem.ph.utexas.edu/~distler/blog/archives/001505.html#more

Lisi (who doesn't seem unreasonable, actually) comments and acknowledges that Distler is correct. So much for that.

I wonder whether the media will ever follow up on this story. Somehow I doubt it... but at the very least it seriously damages what little credibility Woit and Smolin might have had. See the comment by "Can We Turn The Tide?" and the responses below.

[newolder]

That blog is a hoot, dontcha think?

eclipse2006.bikerman.info/rdffeb2008addule-gmphysics.htm#sym


sums it up well enough too, imho. ed. :cool:

[fuelair]

As for 1.) I hope not! As I understand it, once the theory of everything is discovered, it's game over :eek:

OK, actually it sounds like we need to discover another.. 20(?) elements or something or other to fill in the remaining blanks. But I don't know.

As for 2.) Beats me :D
Actually, we do not discover new elements anymore, we make them- they will all have vanishingly small lifes very, very small fractions of a second before they decay. We pile protons on (simplification, but...) and if enough stick for a long enough time (as noted) we have MADE the new element and immediately no longer have the new element. It is gigantically unlikely any new element will be discovered in anything approaching normal matter. - and if we capture a UFO that really is an alien craft, it will be made of the elements we know already.

[arthwollipot]

And what's more, potential "theories of everything" usually postulate new subatomic particles, not new elements.