Size of the electron?

[Perpetual Student]

The electron is considered to be a point particle, i. e., it has no extent in space. From Wiki: "In fact, modern particle physics experiments indicate that the electron is a point particle, i.e. it has no size and its radius is zero." My question is: How do we know that? What are the experiments mentioned here? If the electron were extremely small, say, on the order of one or a few Planck lengths, would we be able to detect that? If so, what experiments have done so? And finally, if the electron were one or two Planck lengths in size would it matter?

[Vorpal]

Some scattering experiment--probably Bhabha (electron/positron) scattering. I don't know of the particular experiments that wiki might have in mind, but whatever the current experimental upper limit is, I'm certain it's at least a dozen orders of magnitude higher than the scale you're considering here.

An electron size on the order of a few Planck length won't matter except at ludicrously high energies (for particles). In general, if you look at an electron closely enough to tell apart some level of detail Δx, then the momentum uncertainty would be on the order of hbar/Δx, which for Planck-scale is about 1 Ns, corresponding to an energy that can easily blow up your house.

[MRC_Hans]

Isn't talking about size of electrons really taking the particle analogy too far. The idea of the electron as a particle (some tiny ball of something) is really something we use to try to wrap our minds around something that cannot really be explained in everyday terms.

An electron is really a charge and some energy which moves at some speed below c, which is why we can say it has a position, but to extend it to say it has a size is probably stretching it.

Hans

[sol invictus]

The electron is considered to be a point particle, i. e., it has no extent in space. From Wiki: "In fact, modern particle physics experiments indicate that the electron is a point particle, i.e. it has no size and its radius is zero." My question is: How do we know that? What are the experiments mentioned here?

Every experiment in particle physics going back to Rutherford. The best modern data on that probably comes from LEP.

If the electron were extremely small, say, on the order of one or a few Planck lengths, would we be able to detect that?

No. To probe small sizes you need high energy (that's the uncertainty principle). Given the maximum energy E of a collision at a collider, hc/E is the shortest distance it can probe.

And finally, if the electron were one or two Planck lengths in size would it matter?

It might, but in an indirect way. Physics is a tight structure.

Isn't talking about size of electrons really taking the particle analogy too far. The idea of the electron as a particle (some tiny ball of something) is really something we use to try to wrap our minds around something that cannot really be explained in everyday terms.

An electron is really a charge and some energy which moves at some speed below c, which is why we can say it has a position, but to extend it to say it has a size is probably stretching it.

In modern physics an electron is a quantum of a Dirac spinor field. Its "size" is its Compton wavelength, h/(mp), which goes to zero when p gets large. More importantly the electron has no substructure - just a (fixed) spin and a charge and a mass. If it had a finite size it would have additional degrees of freedom, like rotational angular momentum or vibrational modes.

[Cuddles]

More importantly the electron has no substructure - just a (fixed) spin and a charge and a mass. If it had a finite size it would have additional degrees of freedom, like rotational angular momentum or vibrational modes.

Well, the word "probably" should be included there. See, for example, this paper (http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=PRLTAO000097000003030802000001&idtype=cvips&gifs=yes) (may require a subscription). Theory and measurement of g (electron magnetic moment) only rules out absolutely an electron size and structure > 10-18m, although if it really were that large it should have been noticed at LEP. More sensible possible models of electron structure would put it's size at < 10-24m, which is a few orders of magnitude smaller than anything we can see at the moment. We assume that the electron has no size or internal structure, and we've ruled out it having structure at the sizes we can currently measure, but we certainly haven't ruled it out entirely.

[sol invictus]

Well, the word "probably" should be included there. See, for example, this paper (http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=PRLTAO000097000003030802000001&idtype=cvips&gifs=yes) (may require a subscription). Theory and measurement of g (electron magnetic moment) only rules out absolutely an electron size and structure > 10-18m, although if it really were that large it should have been noticed at LEP. More sensible possible models of electron structure would put it's size at < 10-24m, which is a few orders of magnitude smaller than anything we can see at the moment. We assume that the electron has no size or internal structure, and we've ruled out it having structure at the sizes we can currently measure, but we certainly haven't ruled it out entirely.

I suggest you re-read my post - you've simply repeated my comments with a few details added.

I repeat: in the modern and "standard" model of particle physics, the electron has no substructure. If in reality it does have one its size must be below the scale probed by accelerators.

Incidentally, string theory is a good example of a theory where the electron is not a point particle.

[Cuddles]

you've simply repeated my comments with a few details added.

Of course I have, that's exactly what I intended to do. You know, you don't have to treat every reply to your posts as if it is claiming you are wrong or a personal attack.

[sol invictus]

You know, you don't have to treat every reply to your posts as if it is claiming you are wrong or a personal attack.

You took a comment in my post out of context and then said it should be qualified - by more or less precisely what I had qualified it with immediately before the part you quoted. That's irritating.

I admit I may be a little touchy, but on this forum I'd rather be correct than polite. Both is a luxury.

[martu]

How can something have mass and a volume of 0 and not be a Black Hole?

[sol invictus]

How can something have mass and a volume of 0 and not be a Black Hole?

Quantum mechanics.

A black hole with the mass of an electron would be incredibly small (in fact it would actually be a naked singularity because of the electric charge, but never mind). That would mean the electron would be squeezed down into an extremely small space. But because of quantum uncertainty, it's not possible to keep something confined to such a small space without a huge amount of energy... which you don't have (since the total energy is just the mass of the electron).

To put it another way, QM smears the electron's mass over a region much larger than a black hole of that same mass.

[martu]

I see.

The use of the word smears always puzzles me but then it's QM so I expect that.

[Perpetual Student]

Quantum mechanics.


To put it another way, QM smears the electron's mass over a region much larger than a black hole of that same mass.

So, if the electron is "smeared" over a region, why does that not imply that the electron has size?

[Perpetual Student]

If it had a finite size it would have additional degrees of freedom, like rotational angular momentum or vibrational modes.

I believe it is thought that quarks have no size. Do quarks have rotational angular momentum or vibrational modes? Why is it that size necessitates rotational angular momentum or vibrational modes?

[martu]

So, if the electron is "smeared" over a region, why does that not imply that the electron has size?

Good point that hinges on what 'smear' means. I have no idea how to picture it but I know the maths works. Hopefully one of the physicists will help.

[MRC_Hans]

So, if the electron is "smeared" over a region, why does that not imply that the electron has size?Because again it is a manner of speech. In reality, it means that the position of the electron is only knowable to a limited degree.

Hans

[Vorpal]

Let's be more clear as to what "size" means. Suppose that the electron is a little hard body, so that if we throw one of them at another, they'll bounce when they come into contact--or more precisely, that in addition to the standard long-range force, we'd see a short-range deviation. Thus, "size" in this sense involves the parts unexplained by modeling the electron as a point, which is different from the "smear" of positional uncertainty.

[Vorpal]

I believe it is thought that quarks have no size. Do quarks have rotational angular momentum or vibrational modes? Why is it that size necessitates rotational angular momentum or vibrational modes?
What do you mean? If your particle has parts, then obviously those parts can be rotating with respect to one another, or their center of mass. Or vibrate in place. It's a bit hard to see how that can happen with a lone point in a meaningfully detectable manner.

[martu]

Let's be more clear as to what "size" means. Suppose that the electron is a little hard body, so that if we throw one of them at another, they'll bounce when they come into contact--or more precisely, that in addition to the standard long-range force, we'd see a short-range deviation. Thus, "size" in this sense involves the parts unexplained by modeling the electron as a point, which is different from the "smear" of positional uncertainty.

If solid objects exist that are smaller than a Planck volume would we model these as point particles?

[MattusMaximus]

I see.

The use of the word smears always puzzles me but then it's QM so I expect that.

Read up on wave-particle duality (http://en.wikipedia.org/wiki/Wave_particle_duality) and it will start to make a bit more sense.

[Perpetual Student]

Doesn't the fact that an electron has spin imply it has size? How can a point spin?

[MattusMaximus]

Doesn't the fact that an electron has spin imply it has size? How can a point spin?

Again, this is another misnomer of a quantum-mechanical phenomenon. "Spin" in QM doesn't mean the same thing as in classical physics. Classically, when we talk about spin we talk about a rotating object (like a spinning top, for example). In QM, the particles (electrons) don't spin the the classical sense - there is no rotation involved, though we often look at it that way since our experience is so constrained. Try to think of "spin" in QM as just a term, nothing more. If you have a hard time don't worry; I've studied physics for over 20 years and I still get stuck on it all the time.

Incidentally, this is the reason why Murray Gell-Mann gave quarks (http://en.wikipedia.org/wiki/Quark) properties such as flavor (http://en.wikipedia.org/wiki/Flavour_(particle_physics)) - because he didn't want similar misconceptions to develop about quark theory.

[Perpetual Student]

Again, this is another misnomer of a quantum-mechanical phenomenon. "Spin" in QM doesn't mean the same thing as in classical physics. Classically, when we talk about spin we talk about a rotating object (like a spinning top, for example). In QM, the particles (electrons) don't spin the the classical sense - there is no rotation involved, though we often look at it that way since our experience is so constrained. Try to think of "spin" in QM as just a term, nothing more. If you have a hard time don't worry; I've studied physics for over 20 years and I still get stuck on it all the time.

Incidentally, this is the reason why Murray Gell-Mann gave quarks (http://en.wikipedia.org/wiki/Quark) properties such as flavor (http://en.wikipedia.org/wiki/Flavour_(particle_physics)) - because he didn't want similar misconceptions to develop about quark theory.

Thanks for your response. I thought the "spin" of an electron was a real phenomenon which manifests itself in a magnetic field (i. e. the electron moves in a direction dictated by whether its spin is up or down. Is that not true? If it is, then its spin would appear to be real enough to be measured in a meaningful and real way. So why is the "spin" not real, but only a "term."

[MattusMaximus]

Thanks for your response. I thought the "spin" of an electron was a real phenomenon which manifests itself in a magnetic field (i. e. the electron moves in a direction dictated by whether its spin is up or down. Is that not true? If it is, then its spin would appear to be real enough to be measured in a meaningful and real way. So why is the "spin" not real, but only a "term."

No, you misunderstood me. I was saying that "spin" doesn't have to do with the rotation of a particle in the classical sense. "Spin" can be measured (for instance, read about the Stern-Gerlach experiment (http://en.wikipedia.org/wiki/Stern_gerlach)) and yes it has much to do with magnetic influences on particles, etc. But an electron with "spin" isn't acting like a toy top as if it's rotating away on a table-top. Electrons are many things, but toy tops they are not.

That was the point of my post. Sorry for any confusion.

[sol invictus]

So, if the electron is "smeared" over a region, why does that not imply that the electron has size?

It does, kind of - but see my post above. The size goes to zero at large momentum.

I believe it is thought that quarks have no size. Do quarks have rotational angular momentum or vibrational modes? Why is it that size necessitates rotational angular momentum or vibrational modes?

Extended objects have additional degrees of freedom beyond those of point particles, because they can rotate and vibrate. Point particles can carry a special kind of spin, and charge, mass, and momentum - but that's it.

Doesn't the fact that an electron has spin imply it has size? How can a point spin?

No. You'll need to study representations of the Lorentz group to understand that - it's not very intuitive.

[Solitaire]

Discover magazine had a wonderful picture of a single electron. It’s not clear from the photo if it’s the front of the electron or the back. Actually, it kind of hard to see any details. Source (http://discovermagazine.com/2009/jan/070)

[Perpetual Student]

"No. You'll need to study representations of the Lorentz group to understand that - it's not very intuitive."

I just looked at the Wikipedia article on the Lorentz group. Good Grief!

[martu]

Read up on wave-particle duality (http://en.wikipedia.org/wiki/Wave_particle_duality) and it will start to make a bit more sense.

I think I have a handle on that just about but I pictured smear to represent the probabilty distribution of all possible locations for a point particle. But this doesn't explain why that massive point isn't a black hole.

[martu]

Discover magazine had a wonderful picture of a single electron. It’s not clear from the photo if it’s the front of the electron or the back. Actually, it kind of hard to see any details. Source (http://discovermagazine.com/2009/jan/070)

That is fantastic thanks. I have no idea if this is even a sensible question but do electron shells have a size?

[Perpetual Student]

OK, is it true, then, that all fundamental particles have no "size" and only composite particles like mesons, protons, etc. have size? It would appear that the size of a particle is a function of the separation among and movement around fundamental dimensionless particles. Is that a reasonable description?

[Evilgiraffe]

That is fantastic thanks. I have no idea if this is even a sensible question but do electron shells have a size?

Yes and no. The size of orbitals in which electrons live is determined by the radial part of the wavefunction that describes the orbital. These usually decay exponentially from the nucleus and so fall away rapidly but never decay to zero.

Because of this it is possible for an electron to appear a very long way from the nucleus, it's just unlikely to do so. The pretty pictures of orbitals, such as these (http://images.google.co.uk/images?hl=en&q=atomic+orbitals&um=1&ie=UTF-8&sa=X&oi=image_result_group&resnum=4&ct=title), show the volume in which you are likely to find the electron most of the time, usually a 95% probability interval.

[sol invictus]

OK, is it true, then, that all fundamental particles have no "size" and only composite particles like mesons, protons, etc. have size? It would appear that the size of a particle is a function of the separation among and movement around fundamental dimensionless particles. Is that a reasonlable description?

It's even weirder than that. For example, we usually say a proton is made of two up and one down quark. But when you actually look inside one, you'll find other particles as well - gluons, anti-quarks, even strange quarks and other flavors. How likely you are to see them, and how many of a given type come out of a given proton-proton collision, depends on how much energy goes into breaking them up (e.g. how hard you smash them together).

What's really going on is that QM is a theory of waves. "Particles" are really wavepackets - little lumps of wave that wiggle along. The "size of a particle" is the spread of that wavepacket, and that spread depends on the energy of the packet. Composite particles like the proton are bound states; you could try to think of them as wavepackets orbiting each other, but the space in between is not really empty - it's "waving" too, and the packets themselves overlap each other.

As you know if you understand Fourier transforms, any localized packet is composed of all frequencies. That means even very high energy states (energy is frequency in relativistic QM) are present in every packet, but with very small amplitude and very high frequency. To detect their presence requires taking a very fast snapshot in time, or equivalently a very high energy process, but if you can do it you will detect them some reasonable fraction of the time. That's why the particle content of bound states like the proton depends on the energy of the probe, and why concepts like "size" are a little slippery to apply.

[Perpetual Student]

Thanks. The flaw in my approach often appears to be attempting to gain an intuitive perspective of quantum stuff -- it just doesn't work.

[sol invictus]

Thanks. The flaw in my approach often appears to be attempting to gain an intuitive perspective of quantum stuff -- it just doesn't work.

Well, one needs to develop and apply the appropriate intuition. For example if you spent some time working with waves of any kind, you'd have a good intuition for phenomena like diffraction, interference, localized wavepackets, etc. That kind of intuition applies rather well to QM - but intuition about little hard balls flying around doesn't.

[Perpetual Student]

Well, one needs to develop and apply the appropriate intuition. For example if you spent some time working with waves of any kind, you'd have a good intuition for phenomena like diffraction, interference, localized wavepackets, etc. That kind of intuition applies rather well to QM - but intuition about little hard balls flying around doesn't.

I'm going to work on that. When considering the fundamental "particles" (6 leptons, 18 quarks, and 12 or 13 force carriers and all their anti-particles) all as "wave packets," my head spins (not like a top -- but like quantum spin:confused:). How could nature be so clunky? The motive behind the quest for unification and simplification becomes very obvious. I guess string theory currently holds the most promise. Any thoughts?

[sol invictus]

Thoughts?

Very often complexity arises from simplicity. Rarely, simplicity emerges from complexity.

String theory probably contains the standard model plus gravity - but the construction will be nearly as complex, if not even more so.

Maybe the world is an infinite onion, maybe it has a core. I doubt we'll ever know for sure.

[Perpetual Student]

Thoughts?

Very often complexity arises from simplicity. Rarely, simplicity emerges from complexity.

String theory probably contains the standard model plus gravity - but the construction will be nearly as complex, if not even more so.

Maybe the world is an infinite onion, maybe it has a core. I doubt we'll ever know for sure.

Simplicity can and does arise from complexity. Newton simplified diverse and seemingly complex phenomena like apples dropping, planets moving in ellipses, the existence of tides, etc. into a simple and elegant theory.

So, are you saying that it is not likely that the complexity and clumsiness of the current model will be improved or replaced by something more simple and elegant?

[MattusMaximus]

So, are you saying that it is not likely that the complexity and clumsiness of the current model will be improved or replaced by something more simple and elegant?

Perhaps, perhaps not. Right now string theory seems the most likely candidate, but if you ask anyone who actually works on string theory, they'll tell you it's really complicated. It's so complicated that we don't yet have the level of mathematics necessary to completely flesh it out.

I have a former student who is into this, and my conversations with him just make my head spin :faint:

[JoeTheJuggler]

To put it another way, QM smears the electron's mass over a region much larger than a black hole of that same mass.
I was sort of thinking that way. . . .I think. I think of an electron's "size" as the area of its orbital.

Really, what determines the "size" of a given atom?

[Perpetual Student]

Perhaps, perhaps not. Right now string theory seems the most likely candidate, but if you ask anyone who actually works on string theory, they'll tell you it's really complicated. It's so complicated that we don't yet have the level of mathematics necessary to completely flesh it out.

I have a former student who is into this, and my conversations with him just make my head spin :faint:

That's disappointing. As a layman (with a mathematics background*) over the years I have read a number of articles about string theory from sources like Scientific American and ended up more bewildered than I started. (Stuff like 11 dimensions are hard to digest.)
In any case, even if the mathematics is more complex, a theory can be simplifying. One does not have to look beyond Newton again for an example. The calculus that Newton devised to explain motion, variables and solve mechanical problems added a significant mathematical complexity but was a unifying and simplifying tool in describing the universe. So, hopefully the mathematics of string theory adds complexity but simplifies in the same sense. Based on your own exposure to string theory, do you think otherwise?
BTW, I'm about to read Brian Greene's book The Elegant Universe, wherein he describes string theory for people like me. I hope it's worth the effort.


*Being familiar with mathematics is often of minimal help. Sometimes I'll look at a mathematical description of a complex physics question and find myself overwhelmed. Knowing what all the variables represent and having familiarity with the physical concepts involved is indispensable -- so that, often for me the mathematics looks like an "eye chart" using math symbols.

[sol invictus]

The calculus that Newton devised to explain motion, variables and solve mechanical problems added a significant mathematical complexity but was a unifying and simplifying tool in describing the universe. So, hopefully the mathematics of string theory adds complexity but simplifies in the same sense.

The theory underlying string theory is extremely simple. It is literally the quantum mechanics of a 1D string - an object characterized only by one single dimensionful parameter, the tension. But as I observed earlier, very simple rules often lead to extremely complex results.

An example, since you like math: group theory is just about the simplest set of rules one could devise for you a collection of objects could be combined. One can define a "prime" group as one with no factor groups other than itself and the identity group - very much like a prime number. But unlike prime numbers, there is a largest (finite) prime group, which turns out to have dimension 80801742479451287588645990496171075700575436800000 0000.

In string theory, the source of the complexity is the number of dimensions. Since there are 11 dimensions, at least 7 must be compactified. But there are an enormous number and variety of compact 7-manifolds, and each leads to different physics.

[Perpetual Student]

The theory underlying string theory is extremely simple. It is literally the quantum mechanics of a 1D string - an object characterized only by one single dimensionful parameter, the tension. But as I observed earlier, very simple rules often lead to extremely complex results.

An example, since you like math: group theory is just about the simplest set of rules one could devise for you a collection of objects could be combined. One can define a "prime" group as one with no factor groups other than itself and the identity group - very much like a prime number. But unlike prime numbers, there is a largest (finite) prime group, which turns out to have dimension 80801742479451287588645990496171075700575436800000 0000.

In string theory, the source of the complexity is the number of dimensions. Since there are 11 dimensions, at least 7 must be compactified. But there are an enormous number and variety of compact 7-manifolds, and each leads to different physics.

OK, thanks. I see the point. By the way, I'm not familiar with this largest "prime" group with dimension 80801742479451287588645990496171075700575436800000 0000. Can you define it?

[Vorpal]

Sol was being slightly imprecise, probably to avoid complications. If he's using "prime group" to mean a group with factor groups of only the identity and itself (i.e., simple groups), then is a countable infinity of finite prime groups--the cyclic groups Z/pZ for prime numbers p being a trivial example. What he likely meant is that the simple groups fall under a few algebraic patterns (and here at the complications), except for finitely many exceptions, of which that is the largest (cf. "sporadic groups").

[Perpetual Student]

Sol was being slightly imprecise, probably to avoid complications. If he's using "prime group" to mean a group with factor groups of only the identity and itself (i.e., simple groups), then is a countable infinity of finite prime groups--the cyclic groups Z/pZ for prime numbers p being a trivial example. What he likely meant is that the simple groups fall under a few algebraic patterns (and here at the complications), except for finitely many exceptions, of which that is the largest (cf. "sporadic groups").

Ahh -- got it. Thanks.

[martu]

Well, one needs to develop and apply the appropriate intuition. For example if you spent some time working with waves of any kind, you'd have a good intuition for phenomena like diffraction, interference, localized wavepackets, etc. That kind of intuition applies rather well to QM - but intuition about little hard balls flying around doesn't.

I think the problem I have is the more I read the more it seems that it is all about little hard balls hitting each other. It seems like one should be able to picture it if that is the case. Is this correct? Is there any force or property of the universe we can't model using particles?

[sol invictus]

Sol was being slightly imprecise, probably to avoid complications.

Yes, thanks - what I said isn't true (I guess I should have qualified it with "sporadic"). But the point remains: that extremely simple rules often lead to surprising and very complex structures.

I think the problem I have is the more I read the more it seems that it is all about little hard balls hitting each other. It seems like one should be able to picture it if that is the case. Is this correct? Is there any force or property of the universe we can't model using particles?

Yes - nearly all of them. The most direct is simply particle scattering. If particles were little balls, they'd scatter like billiard balls (only in 3D) - so not at all unless they come very close, and then a lot. But they don't behave that way at all. There is no hard core, there are all sorts of long and short-range interactions, and it's easy to observe interference patterns which can only arise from waves. You can even interfere a particle with itself - in fact you can interfere a molecule with itself.

The theory of these things is well understood (at least in some things, like predicting the results of electron-electron scattering) and mind-bogglingly well tested. There are no little balls.

[Perpetual Student]

....If particles were little balls, they'd scatter like billiard balls (only in 3D) - so not at all unless they come very close, and then a lot. But they don't behave that way at all. There is no hard core, there are all sorts of long and short-range interactions, and it's easy to observe interference patterns which can only arise from waves. You can even interfere a particle with itself - in fact you can interfere a molecule with itself.

The theory of these things is well understood (at least in some things, like predicting the results of electron-electron scattering) and mind-bogglingly well tested. There are no little balls.

That description would seem to eliminate the concept of a fundamental particle existing at a point, which is the usual description when considering a fundamental entity as a particle. "Interference patterns, long and short range interactions" would not seem possible to come from a point. I know I'm probably making the mistake again of trying to "see" the particle intuitively. But it would appear the only reality of a particle is its wave characteristics, even though I know they have a dual nature and at times behave as particles. :confused:

[sol invictus]

That description would seem to eliminate the concept of a fundamental particle existing at a point, which is the usual description when considering a fundamental entity as a particle.

The particle behavior arises because the wave mode occupation numbers are quantized. That means the amplitude of each mode is an integer in some units.

So for example, monochromatic light consists of an integer number of photons, each with almost exactly the same energy (recall that the energy depends on the frequency). Hence the photoelectric effect.

[Perpetual Student]

The particle behavior arises because the wave mode occupation numbers are quantized. That means the amplitude of each mode is an integer in some units.

So for example, monochromatic light consists of an integer number of photons, each with almost exactly the same energy (recall that the energy depends on the frequency). Hence the photoelectric effect.

So, are you saying that the wave/particle duality of fundamental particles is really a fiction? Instead they are all really waves that, at times, have the characteristics of particles -- like the photoelectric effect?

[sol invictus]

So, are you saying that the wave/particle duality of fundamental particles is really a fiction? Instead they are all really waves that, at times, have the characteristics of particles -- like the photoelectric effect?

I'm not very comfortable saying something is "really" this or "really" that. We have a theory which describes particles as localized wiggling lumps in a continuous field which fills all spacetime. That field classically and quantumly satisfies a wave equation (plus interactions and various other corrections). The Lagrangian describing this whole mess is local, in the sense that it contains only products and powers of local fields and finitely many derivatives acting on them. The higher the energy, the smaller the spread of the wavepacket describing a particle and the more particle-like it becomes..

In contrast, something like string theory really doesn't describe particles. If you give more energy to a string past a certain point it gets bigger, not smaller, and it has lots of modes of rotation and vibration. So it means something very important to say a theory is a theory of point particles - but it doesn't mean the theory consists of little balls flying around.

[Perpetual Student]

s. i.:
In my view, this is the single most inaccessible area of science for a layman. The insights you have provided have been helpful. Thank you.

[ingoa]

Take for example a space probe like Voyager. In terms of planetary trajectories you can treat it as a point-like mass travelling between the planets. But it is NOT a point like mass. It is just a description that fits in this case. If you enter the atmosphere of a planet the model breaks immediately down (air friction and so forth).

In a similar fashion under certain conditions quanta can be described in a fashion that looks like everyday particles. Under other conditions they look like waves. But strictly speaking they are neither.
We simply lack a concise description for quanta that is applicable under all circumstances that can be mapped to traditional things like waves or particles. Of course these concise descriptions exist but are highly counter-intuitive (welcome to the Standard Model).

[martu]

Yes - nearly all of them. The most direct is simply particle scattering. If particles were little balls, they'd scatter like billiard balls (only in 3D) - so not at all unless they come very close, and then a lot. But they don't behave that way at all. There is no hard core, there are all sorts of long and short-range interactions, and it's easy to observe interference patterns which can only arise from waves. You can even interfere a particle with itself - in fact you can interfere a molecule with itself.

The theory of these things is well understood (at least in some things, like predicting the results of electron-electron scattering) and mind-bogglingly well tested. There are no little balls.

I don't want to derail further but can you give me links to the following so I can look up exactly what you're talking about please:

1) long and short-range interactions
2) interfere a molecule with itself

thank you, appreciate your posts as ever.

[martu]

Take for example a space probe like Voyager. In terms of planetary trajectories you can treat it as a point-like mass travelling between the planets. But it is NOT a point like mass. It is just a description that fits in this case. If you enter the atmosphere of a planet the model breaks immediately down (air friction and so forth).

In a similar fashion under certain conditions quanta can be described in a fashion that looks like everyday particles. Under other conditions they look like waves. But strictly speaking they are neither.
We simply lack a concise description for quanta that is applicable under all circumstances that can be mapped to traditional things like waves or particles. Of course these concise descriptions exist but are highly counter-intuitive (welcome to the Standard Model).

Surely there is a chance that they are just particles (or indeed just waves) and the fact is we lack a piece of knowledge? A hidden variable perhaps?

[Dancing David]

Surely there is a chance that they are just particles (or indeed just waves) and the fact is we lack a piece of knowledge? A hidden variable perhaps?
[/lurk]
Yes could be, but is? We may never know. looks like waves.
[lurk]

Great thread BTW!

[sol invictus]

I don't want to derail further but can you give me links to the following so I can look up exactly what you're talking about please:

1) long and short-range interactions

http://www.geocities.com/angolano/Astronomy/FundamentalForces.html

2) interfere a molecule with itself

http://www.nature.com/nature/journal/v401/n6754/abs/401680a0.html

[martu]

http://www.geocities.com/angolano/Astronomy/FundamentalForces.html

Which force in particular are you refrerring to? All those forces have a corresponding boson that implies a particle is carrying the force. I think.

*digs out Ken Ford's book on QM*

[martu]

[/lurk]
Yes could be, but is? We may never know. looks like waves.
[lurk]

Great thread BTW!

Also looks like particles. Arrggghhhh.

A deterministic theory of QM would settle the matter wouldn't it?

[Perpetual Student]

Surely there is a chance that they are just particles (or indeed just waves) and the fact is we lack a piece of knowledge? A hidden variable perhaps?

The question of hidden variables has been thoroughly explored. Consider Bell's theorem and the EPR paradox. See the following link: http://en.wikipedia.org/wiki/Hidden_variable_theory

[sol invictus]

Which force in particular are you refrerring to? All those forces have a corresponding boson that implies a particle is carrying the force. I think.

That's correct. But bear in mind that the so-called "virtual particles" which are exchanged to carry the force are even less particle-like than standard ones. For example, they can have any mass - they don't have to satisfy E2=p2c2+m2c4.

Also looks like particles. Arrggghhhh.

A deterministic theory of QM would settle the matter wouldn't it?

No, probably not. We know experimentally that electrons can interfere with themselves like waves, but that they also behave like particles in many ways. Any theory that didn't incorporate that would be wrong.

[martu]

The question of hidden variables has been thoroughly explored. Consider Bell's theorem and the EPR paradox. See the following link: http://en.wikipedia.org/wiki/Hidden_variable_theory

Not a problem for Bohmian Mechanics (http://plato.stanford.edu/entries/qm-bohm/) and Bell agrees.

[martu]

That's correct. But bear in mind that the so-called "virtual particles" which are exchanged to carry the force are even less particle-like than standard ones. For example, they can have any mass - they don't have to satisfy E2=p2c2+m2c4.

But these virtual particles are successfully modelled as small 'balls' hitting other 'balls'. No action at a distance I guess is my point.

No, probably not. We know experimentally that electrons can interfere with themselves like waves, but that they also behave like particles in many ways. Any theory that didn't incorporate that would be wrong.

Yes obviously but I do not see a logical reason why a deterministic theory could not be found that did incorporate that do you?

[sol invictus]

But these virtual particles are successfully modelled as small 'balls' hitting other 'balls'.

No, they're not - not in any theory known to physics, at least. They're wave-packets.

No action at a distance I guess is my point.

That's another matter. The interactions of standard field theories are local in the sense I described above, as well as according to some other more technical definitions.

Yes obviously but I do not see a logical reason why a deterministic theory could not be found that did incorporate that do you?

I don't understand the point of the question. Determinism is an entirely separate issue from that of the size of particles.

[martu]

No, they're not - not in any theory known to physics, at least. They're wave-packets.

And when wave-packets interact with other pieces of matter they are considered point particles am I right?

That's another matter. The interactions of standard field theories are local in the sense I described above, as well as according to some other more technical definitions.

In layman’s terms this means that we can model everything as something hitting something else? Obviously the rules governing this are very complicated.


As to your other point I’ll create the conversation here:

I said this:

A deterministic theory of QM would settle the matter wouldn't it?

You replied with this:

No, probably not. We know experimentally that electrons can interfere with themselves like waves, but that they also behave like particles in many ways. Any theory that didn't incorporate that would be wrong.

To which I replied:

Yes obviously but I do not see a logical reason why a deterministic theory could not be found that did incorporate that do you?

Then you:

I don't understand the point of the question. Determinism is an entirely separate issue from that of the size of particles.

I thought we were talking about determinism and you had implied in post #59 that a deterministic theory could not account for wave-particle duality of electrons. Am I wrong?

[sol invictus]

And when wave-packets interact with other pieces of matter they are considered point particles am I right?

No.

In layman’s terms this means that we can model everything as something hitting something else? Obviously the rules governing this are very complicated.

I suppose in some vague sense of "hitting", yes.


I thought we were talking about determinism and you had implied in post #59 that a deterministic theory could not account for wave-particle duality of electrons. Am I wrong?

A theory which modeled particles as little deterministic balls would be wrong, since there would be no interference. A theory which behaved exactly or almost exactly like QM, but deterministically (as Bohmian QM does in the non-relativistic case) would not alter any of what I've been saying. So it's really not very relevant.

[martu]

A theory which modeled particles as little deterministic balls would be wrong, since there would be no interference.

Now this is the bit I don't understand. Let us consider water - water is made up of water molecules which, for the purpose of modelling waves, we can consider as particles. Agreed? If so the behavior of water waves, interference, diffraction and so on, is an emergent property of water molecule (the particle) behavior.

For the record I am not saying this is how electrons behave merely disagreeing that a particle system could not result in interference.

[martu]

And when wave-packets interact with other pieces of matter they are considered point particles am I right?

No.

Can you elaborate please?

Let us consider two wave packets of light hitting each other. When I read Feynman's QED he says that I can consider this to be two photons hitting each other, two point particles in other words. What subtlety have I obviously missed? Again.....

[sol invictus]

Now this is the bit I don't understand. Let us consider water - water is made up of water molecules which, for the purpose of modelling waves, we can consider as particles. Agreed? If so the behavior of water waves, interference, diffraction and so on, is an emergent property of water molecule (the particle) behavior.


Water waves result from the collective behavior of 10^26 molecules or so. In QM, a single particle can interfere with itself.


Let us consider two wave packets of light hitting each other. When I read Feynman's QED he says that I can consider this to be two photons hitting each other, two point particles in other words. What subtlety have I obviously missed? Again.....

If the photons have sufficiently high energy (relative to the inverse size of the experimental apparatus, for example), they behave much like conventional particles. And as a matter of semantics, the word "photon" means a quantum wavepacket of the electromagnetic field.

Look - what it really boils down to is the mathematics. Words are inherently imprecise, and they mean different things to different people. The equations that do such an incredibly good job describing particle physics are quantized wave equations. That can be described in many ways, but it is not a theory of little balls.

[martu]

Look - what it really boils down to is the mathematics. Words are inherently imprecise, and they mean different things to different people. The equations that do such an incredibly good job describing particle physics are quantized wave equations. That can be described in many ways, but it is not a theory of little balls.

Ok thanks for the responses.

[Perpetual Student]

Not a problem for Bohmian Mechanics (http://plato.stanford.edu/entries/qm-bohm/) and Bell agrees.

Bohmian mechanics has its own problems. Rather than rehash it all here, take a look at an old thread (which I started some months ago) on this subject:

http://forums.randi.org/showthread.php?t=119364