Dark matter

[calcmandan]

I"m aware of the research being done to detect dark matter and such, with the silhouettes being photographed and such. I'm aware of the images made of dark matter maps based on its' gravitational influences of galaxies and clusters...

When I first read about dark matter in the early 90s, there were two hypothetical types, MACHO (MAssive Compact Halo Object) and WIMPs (Weakly Interacting Massive Particle). I always assumed MACHOs to be undetected matter like Oort clouds, ejected planets, brown dwarfs, diffuse nebulae... WIMPs being 'dark energy.'

Is it possible this dark energy is visible to the naked eye? When I look up in the sky, it's dark between stars and galaxies. Could this blackness be dark energy in its own right?

No, I don't smoke marijuana.

[arthwollipot]

Dark energy and dark matter are not the same thing. A WIMP would be something like a neutrino (but not really) that doesn't interact with other matter except through the weak nuclear force. Dark energy is the vacuum energy which counteracts gravity to accelerate the expansion of space. Different things entirely.

[Reality Check]

And a bit of clarification: MACHOs were thought to be brown dwarfs, red dwarfs, neutron stars, black holes or even rogue planets (fitting the Massive and Compact criteria). They have been excluded as a significant component of DM, e.g. there is an upper limit of 8% of the mass needed in stellar objects was detected.

Rogue ('ejected') planets are observed to be ~2 Jupiter sized planets per star (2500 such planets are needed for DM).

Oort clouds were never considered since they are an insignificant % of stellar masses. We need 5-10 times the total stellar mass in a galaxy in the halo to account for their rotation curves.

[Cuddles]

Originally Posted by calcmandan

When I first read about dark matter in the early 90s, there were two hypothetical types, MACHO (MAssive Compact Halo Object) and WIMPs (Weakly Interacting Massive Particle). I always assumed MACHOs to be undetected matter like Oort clouds, ejected planets, brown dwarfs, diffuse nebulae... WIMPs being 'dark energy.'

As arthwollipot says, dark matter and dark energy have nothing to do with each other. In fact, if you were reading about it in the early 90s, you won't even have heard of dark energy, since the term wasn't coined until 1998. WIMPs are exactly what the name suggests - particles with mass that only interact weakly with other matter (generally assumed to only interact via gravity and the weak force) and so are hard to detect. arthwollipot is actually wrong when he says "but not really" about neutrinos - neutrinos absolutely are WIMPs. Unfortunately, their mass is far too small to make up more than a small fraction of dark matter, and prevents them from behaving the way most dark matter seems to (they move too fast to orbit in the halos we infer are around galaxies, for example), so we think there must be other kinds of WIMPs around as well.

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Is it possible this dark energy is visible to the naked eye? When I look up in the sky, it's dark between stars and galaxies. Could this blackness be dark energy in its own right?

No. Darkness is the absence of light, nothing more.

In addition, one of the main points of WIMPs is that they can't interact with the electromagnetic force, since otherwise it would be easy to see them and there wouldn't be a problem in the first place.

[Ziggurat]

Originally Posted by calcmandan

Is it possible this dark energy is visible to the naked eye? When I look up in the sky, it's dark between stars and galaxies. Could this blackness be dark energy in its own right?

No, it could not be. I assume you're talking about dark matter, since dark energy is something different.

If you study thermodynamics, one of the major subjects you learn about is something called black body radiation. And a consequence of this theory is that if something absorbs light of a given frequency, it must also emit light at that same frequency based on its temperature. If something is perfectly absorbing, then it will also be a maximum emitter of thermal radiation. A perfect absorber is called a black body. The spectrum is referred to as a black body spectrum, which may confuse at first since the light coming from a black body can look white, but it's called a black body spectrum because it's the spectrum that a perfect absorber will have, even though a perfect absorber will also emit. And theory tells us exactly what the shape of that spectrum should be. It scales with temperature (the curve "expands" if you plot energy density vs. frequency), but it's always the same shape. Now, why do we have such confidence in the theory of black body radiation and the requirement that perfect absorbers must also be ideal thermal emitters? Well, aside from lots of experiments which show the equivalence of emission and absorption, the two MUST be the same or it would violate the 2nd law of thermodynamics. As in, you could make a perpetual motion, free energy machine if you had something that was a better emitter than absorber, or vice versa.

Now, that blackness you see between the stars? It's actually glowing. The temperature is just too cold to see with the naked eye. But it's not just glowing: it's the most perfect black body spectrum we have ever measured. The shape of the curve matches theory to within incredibly narrow experimental resolution. Every man-made black body is measurably imperfect: some remnant reflection always remains, and that shows up in an imperfect emission spectrum. But not the background radiation in the sky: we cannot detect any deviation from perfection. Although that's better than anything we can produce, we do actually know how one could obtain such a perfect blackbody spectrum: with very hot, very dense matter.

Sounds like a bit of a contradiction, doesn't it? We need a hot source to get a perfect black body line shape, but the peak of the curve tells us it's cold. What happened? Well, the universe expanded, and all that light emitted from the black body source cooled down as it expanded along with the universe. But it retained its line shape of a perfect black body.

Now, what does this have to do with dark matter? Well, dark matter is not black matter. Black means no reflection, which also means perfect thermal emission. You can see black things, as long as you can observe the right frequency range. The sun, for example, is fairly (but not perfectly) black. Hot black things you can see with the naked eye. Cold black things you can see with sensitive instruments. But dark means something different. It means that it doesn't give off light at all. Not emitted AND not absorbed. Basically, invisible. So the darkness between the stars can't be dark matter, because it's not actually dark, it's just cold.

[calcmandan]

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No, it could not be. I assume you're talking about dark [i]matter, since dark [i]energy is something different.

If you study thermodynamics, one of the major subjects you learn about is something called black body radiation. And a consequence of this theory is that if something [i]absorbs light of a given frequency, it must also emit light at that same frequency based on its temperature. If something is perfectly absorbing, then it will also be a maximum emitter of thermal radiation. A perfect absorber is called a black body. The spectrum is referred to as a black body spectrum, which may confuse at first since the light coming from a black body can look white, but it's called a black body spectrum because it's the spectrum that a perfect absorber will have, even though a perfect absorber will also [i]emit. And theory tells us exactly what the shape of that spectrum should be. It scales with temperature (the curve "expands" if you plot energy density vs. frequency), but it's always the same shape. Now, why do we have such confidence in the theory of black body radiation and the requirement that perfect absorbers must also be ideal thermal emitters? Well, aside from lots of experiments which show the equivalence of emission and absorption, the two MUST be the same or it would violate the 2nd law of thermodynamics. As in, you could make a perpetual motion, free energy machine if you had something that was a better emitter than absorber, or vice versa.

Now, that blackness you see between the stars? It's actually glowing. The temperature is just too cold to see with the naked eye. But it's not [i]just glowing: it's the most perfect black body spectrum we have [i]ever measured. The shape of the curve matches theory to within incredibly narrow experimental resolution. Every man-made black body is measurably imperfect: some remnant reflection always remains, and that shows up in an imperfect emission spectrum. But not the background radiation in the sky: we cannot detect [i]any deviation from perfection. Although that's better than anything we can produce, we do actually know [i]how one could obtain such a perfect blackbody spectrum: with very hot, very dense matter.

Sounds like a bit of a contradiction, doesn't it? We need a hot source to get a perfect black body line shape, but the peak of the curve tells us it's cold. What happened? Well, the universe expanded, and all that light emitted from the black body source cooled down as it expanded along with the universe. But it retained its line shape of a perfect black body.

Now, what does this have to do with dark matter? Well, dark matter is not black matter. Black means no [i]reflection, which also means perfect thermal emission. You can [i]see black things, as long as you can observe the right frequency range. The sun, for example, is fairly (but not perfectly) black. Hot black things you can see with the naked eye. Cold black things you can see with sensitive instruments. But [i]dark means something different. It means that it doesn't give off light at all. Not emitted AND not absorbed. Basically, invisible. So the darkness between the stars can't be dark matter, because it's not [i]actually dark, it's just cold.

Thank you for the clear and educational explaination. Now I need to find a good book on thermodynamics.

I've been following, as much as I can, scientific discoveries regarding the CMB, but all along I thought it was the super cool radiation from early epochs of the universe. I was not aware that the CMB encompassed all space too.

In the famous image of the CMB, is the entire map from the outer fringe of the observable universe? Or is some of it more local?


-- Sent from my Palm TouchPad using Communities

[Ziggurat]

Originally Posted by calcmandan

Thank you for the clear and educational explaination. Now I need to find a good book on thermodynamics.

I've been following, as much as I can, scientific discoveries regarding the CMB, but all along I thought it was the super cool radiation from early epochs of the universe. I was not aware that the CMB encompassed all space too.

In the famous image of the CMB, is the entire map from the outer fringe of the observable universe? Or is some of it more local?

What we see now is arriving to us from the outer fringes of the observable universe. In fact, it defines the edge of the visible universe.

Go back far enough and the universe was so dense that it was opaque. During this period, there was lots and lots of radiation, but like the interior of the sun, that radiation couldn't travel far before being re-absorbed. As the universe expanded and became less dense, it went through a transition where it became transparent. At that point, all that radiation was then free to start traveling. So we can see back to that transition, and that's what we see when we look at the CMB. We will never see farther back in time with light, because the universe was opaque before that.

But CMB light was emitted from everywhere within the universe, including where we are now. We just can't see the light which originated from where we are, because it's now billions of light years away. As the universe ages, we will see CMB light that originated from further and further away, but always from the same time in the universe's evolution.

[calcmandan]

Originally Posted by Ziggurat

What we see now is arriving to us from the outer fringes of the observable universe. In fact, it defines the edge of the visible universe.

Yes, this is what I always understood as the CMB

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Go back far enough and the universe was so dense that it was opaque. During this period, there was lots and lots of radiation, but like the interior of the sun, that radiation couldn't travel far before being re-absorbed. As the universe expanded and became less dense, it went through a transition where it became transparent. At that point, all that radiation was then free to start traveling. So we can see back to that transition, and that's what we see when we look at the CMB. We will never see farther back in time with light, because the universe was opaque before that.

Yes, I'm very clear on this too.

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But CMB light was emitted from everywhere within the universe, including where we are now. We just can't see the light which originated from where we are, because it's now billions of light years away. As the universe ages, we will see CMB light that originated from further and further away, but always from the same time in the universe's evolution.

What confused me was this:

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Now, that blackness you see between the stars? It's actually glowing.

In which you linked to the CMB. So I sat there confused because I always understood the CMB to be the outskirts of the observable universe, at a very low temperature (2K above absolute zero from what i recall).

Then the conversation branched off into an explanation of the CMB and what it represents.

Now I'm clear.

I'll do some reading on thermodynamics to better grasp black body radiation. And perhaps, in my pursuits, I'll see an image of this 'glowing' space between the stars if such images exist.

And now, I have more reading to do because of today's news about evidence for smooth space-time.

[Ziggurat]

Originally Posted by calcmandan

In which you linked to the CMB. So I sat there confused because I always understood the CMB to be the outskirts of the observable universe, at a very low temperature (2K above absolute zero from what i recall).

The edge of the visible universe is glowing. That CMB is the glow that was released when the universe went from opaque to transparent. And when that happened, the universe, and the CMB, were quite hot, and would have been VERY visible to the eye if someone had been around at the time. It would be like being surrounded by the sun from every angle.

Now, one of the things about this whole black body radiation theory is that not only do black objects glow with characteristic radiation, but you can actually assign a temperature to the radiation itself. At equilibrium, the radiation must obviously have the same temperature as the object. And that was the case at this point of transition from opaque to transparent.

But once the universe went transparent, it became decoupled from that radiation. The CMB radiation and the rest of the universe stopped interacting to any significant degree, and so they are no longer in thermal equilibrium. The CMB behaves in many ways like an ideal gas, so when it expanded it also cooled, and that's why it's now at 2.725 Kelvin. But again, the source for that radiation in the distant past was MUCH hotter. You shouldn't think of that 2.725 K as the temperature of the source, but as the current temperature of this "gas" of light that fills the universe. It will continue to get even colder as the universe continues to expand. Much of the matter in the universe has also cooled since then, but not uniformly, and not in equilibrium with the CMB.

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I'll do some reading on thermodynamics to better grasp black body radiation. And perhaps, in my pursuits, I'll see an image of this 'glowing' space between the stars if such images exist.

The problem with trying to make an image of it is two-fold. First off, the radiation involved is so cold that (per its name) it's far into the microwave region. So you obviously can't do a real-color image, because in the visible spectrum it's basically black. You have to do a false color image. The second problem, though, is that it's very uniform. If you make an image of something that's very uniform, well, that's a bloody boring image. But it's not completely uniform. So what people often do when making "pictures" of the CMB is to graph the difference in the CMB. And that's what you see in such images as this:



What's being plotted isn't the actual light from the CMB (which isn't visible anyways), but the variations in temperature. The average temperature is about 2.725 Kelvin, but the difference in temperature between red areas and blue areas is only about 0.0002 Kelvin. So very tiny differences, even though they're plotted in a high-contrast manner.

So the CMB is not only too cold to see in the visible spectrum, even if you scaled it to the visible spectrum it would look like a flat glow that you would still need equipment to see any variation in.

[Eggs Ackley]

Originally Posted by calcmandan

I"m aware of the research being done to detect dark matter and such, with the silhouettes being photographed and such. I'm aware of the images made of dark matter maps based on its' gravitational influences of galaxies and clusters...

When I first read about dark matter in the early 90s, there were two hypothetical types, MACHO (MAssive Compact Halo Object) and WIMPs (Weakly Interacting Massive Particle). I always assumed MACHOs to be undetected matter like Oort clouds, ejected planets, brown dwarfs, diffuse nebulae... WIMPs being 'dark energy.'

Is it possible this dark energy is visible to the naked eye? When I look up in the sky, it's dark between stars and galaxies. Could this blackness be dark energy in its own right?

No, I don't smoke marijuana.

There is a possibilty that there is no dark matter in the sense expected here. The expectation of dark matter is based on the difference between the orbital velocity profiles of galactic matter compared to theoretical expectations. So, it's possible that the calculation of the velocity profile is simply being done incorrectly. Then, no dark matter would be needed to explain observations.

There is a fairly well-known modification of gravitation, I believe it is called MOND, that was described in a Scientific American article, that attempts to justify the observed orbital velocity profile without the need to invoke dark matter. It seems awfully ad hoc to me.

I find more interesting the suggestion by Ungar that "dark" matter is simply additional mass that's predicted by Einsteinian special relatively, but not generally recognized. Ungar argues that relativistically the total mass of a system of particles (in say the center of mass reference frame) is greater than simply the sum of the individual relativistic masses of the particles. Ungar's total, derived based on the reasonable assumption that the total relativistic four-momentum is additive, has additional terms, one for every possible pairing between particles with unequal velocities. See equation 16 in his paper here: http://www.ptep-online.com/index_fil...8/PP-14-05.PDF

Ungar's work is pretty recent. I don't know if anyone has yet tried to use it to predict (or retrodict, strictly speaking) what the galactic orbital velocity profile should be.


I have to mention that this http://en.wikipedia.org/wiki/Gyrovector_space article when I read it some time ago showed no evidence of understanding Ungar's equation for total mass. It is not simply the addition of the relativistic masses. Every physicist would naturally sum relativistic mass, not rest mass. Ungar's equation has additional, cross-correlation, terms that would provide an equivalent total mass equal to the expected total dark matter mass, that are not so obvious as simply summing relativistic mass. These guys also failed to understand Ungar's equation: http://cosmoquest.org/forum/archive/.../t-109162.html

What is really compelling about this, to me, is that if Ungar is right it is not just some possible ad hoc modification of relativity but rather a necessary consequence of the Minkowskian geometry of spacetime. (This geometry is not at all the same as that of Euclidian space. It is much richer. I think there are multiple important everyday observable aspects of it, that are not yet appreciated.) I think Ungar's hypothesis warrants more attention than it seems to be getting so far.

[Ziggurat]

Originally Posted by Eggs Ackley

I find more interesting the suggestion by Ungar that "dark" matter is simply additional mass that's predicted by Einsteinian special relatively, but not generally recognized. Ungar argues that relativistically the total mass of a system of particles (in say the center of mass reference frame) is greater than simply the sum of the individual relativistic masses of the particles.

That isn't simply something unrecognized in relativity, that is quite definitively something that is not in relativity. That alone doesn't mean it's wrong, but it does mean that you cannot actually derive it from relativity.

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Ungar's total, derived based on the reasonable assumption that the total relativistic four-momentum is additive, has additional terms, one for every possible pairing between particles with unequal velocities.

If it's got these additional terms, then it's not additive. Furthermore, it's bull ****. There's a glaring inconsistency staring him right in the face and he doesn't even notice it: his idea violated conservation of energy. He's got this extra mass which appears due to relative motion between multiple objects, but that extra mass will only equal the energy put into creating that relative motion if these extra terms of his don't exist. If they do exist, then you're creating more mass than the energy you put in. And that is, quite frankly, nonsense.

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Ungar's work is pretty recent. I don't know if anyone has yet tried to use it to predict (or retrodict, strictly speaking) what the galactic orbital velocity profile should be.

It's not worth the trouble. It's a nonsensical theory, and its primary justification (the Pioneer anomaly, which can't be explained by dark matter) has already been explained by conventional physics. It's no longer a mystery. It's simply thermal radiation pressure. For a complex object which generates heat (like an active space probe), that turns out to be non-trivial to calculate, but that's all it is.

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I think Ungar's hypothesis warrants more attention than it seems to be getting so far.

It doesn't deserve any attention.

[Eggs Ackley]

The four-momentum doesn't have additional terms, just the total mass.

How would we know at the galactic level whether the extra mass was breaking energy conservation? Do we have such a good accounting of what energy went in to creating the galaxy? That would surprise me.

Still, it seems to me to come down to either taking issue with his premise, that four-momentum is additive, or with his math deriving the total mass equation from it. Doesn't such conscientious hard work merit the effort, from at least one physicist, to find the point where he goes astray?

Also, I doubt he was motivated by the Pioneer anomaly, or the failure of dark matter to be detected so far. (Not that his motivation matters here anyhow.) He has clearly been working for a long time on the mathematical structure of spacetime, and I suppose the total mass equation came out of it naturally. As far as the anomaly being solved goes, what I read only claimed accounting for most of it. Since Ungar only makes a qualitative argument about it, I don't see it as damning.

[Ziggurat]

Originally Posted by Eggs Ackley

The four-momentum doesn't have additional terms, just the total mass.

Not according to your source.

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How would we know at the galactic level whether the extra mass was breaking energy conservation? Do we have such a good accounting of what energy went in to creating the galaxy? That would surprise me.

You don't get it. I'm saying that if you take an object on earth, and accelerate it, this theory claims more energy is created than was used to accelerate it. You don't need the creation of the galaxy, it breaks under much more immediate conditions.

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Still, it seems to me to come down to either taking issue with his premise, that four-momentum is additive, or with his math deriving the total mass equation from it.

He's claiming that the four-momentum is NOT simply additive. That's the whole point. He's saying that each pairwise couple creates new mass. If you have N objects, then you have ~N² pairs, and hence a mass term that scales as N². That's not additive, that's multiplicative.

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Doesn't such conscientious hard work merit the effort, from at least one physicist, to find the point where he goes astray?

I already did. He broke energy conservation. That's the end of the story for me. I've got no reason to investigate further, given that he's got no actual evidence for his position.

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Also, I doubt he was motivated by the Pioneer anomaly

But it's the only thing he claims to explain that dark matter doesn't.

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or the failure of dark matter to be detected so far.

Dark matter has been detected. The only problem is that only a small fraction has been directly detected.

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He has clearly been working for a long time on the mathematical structure of spacetime, and I suppose the total mass equation came out of it naturally.

His equation doesn't come out of it naturally.

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As far as the anomaly being solved goes, what I read only claimed accounting for most of it. Since Ungar only makes a qualitative argument about it, I don't see it as damning.

That's even worse: if it's only qualitative, he's got no idea if the numbers from his theory are too small or even too big. Which means he didn't do the test of his own theory that he should have done. That's even more damning, because it's exactly the sort of thing that cranks all over the internet do with their pet theories: come up with qualitative explanations but never test them quantitatively. And it's the quantitative tests which separate the good theories from the bad ones.

[Eggs Ackley]

Here is a different Ungar paper, that I was remembering, where he states explicitly the assumption of additivity of four-momentum: http://www.phil-inst.hu/~szekely/pir...ngar_09_ft.pdf (at the bottom of page 27), and at the beginning of his derivation of the total mass equation.


Ungar is a mathematician. He apparently doesn't have much interest in quantitatively comparing his theory with oservation. Maybe he feels his time is better spent doing the pure math part and leaves it to others to do the empirical testing.

I expect the additional mass/energy added is undetectably small in ordinary circumstances. Seems to me it would be relevant in nuclear and sub-nuclear processes, though. There, we do have a total mass that's greater than the sum of the relativistic mass of the constituent matter particles, don't we? In nucleons, the extra mass is said to be in the gluons, I think. In nuclei, is it in the mesons? My working hypothesis is that Ungar's extra mass could be an alternative explanation for the mass currently thought to be in the force-bearing particles. The force particles seem potentially superfluous to me.

[Ziggurat]

Originally Posted by Eggs Ackley

Here is a different Ungar paper, that I was remembering, where he states explicitly the assumption of additivity of four-momentum: http://www.phil-inst.hu/~szekely/pir...ngar_09_ft.pdf (at the bottom of page 27), and at the beginning of his derivation of the total mass equation.

That's illegible. And regardless of what he claims, his equation IS NOT additive.

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Ungar is a mathematician. He apparently doesn't have much interest in quantitatively comparing his theory with oservation. Maybe he feels his time is better spent doing the pure math part and leaves it to others to do the empirical testing.

Well, it's not a better use of his time, because nobody else is going to checl it for him. He doesn't want to know the answer, because the answer might prove him wrong.

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I expect the additional mass/energy added is undetectably small in ordinary circumstances.

That doesn't matter. Either energy conservation is broken, or it isn't. A small break is still a break.

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Seems to me it would be relevant in nuclear and sub-nuclear processes, though. There, we do have a total mass that's greater than the sum of the relativistic mass of the constituent matter particles, don't we? In nucleons, the extra mass is said to be in the gluons, I think. In nuclei, is it in the mesons? My working hypothesis is that Ungar's extra mass could be an alternative explanation for the mass currently thought to be in the force-bearing particles. The force particles seem potentially superfluous to me.

Nuclear interactions don't break energy conservation. Ungar's theory does. So no, it's not a candidate to replace them. Especially since his theory involves zero distance dependence, which we know is not the case.

[sol invictus]

Originally Posted by Eggs Ackley

Here is a different Ungar paper, that I was remembering, where he states explicitly the assumption of additivity of four-momentum: http://www.phil-inst.hu/~szekely/pir...ngar_09_ft.pdf (at the bottom of page 27), and at the beginning of his derivation of the total mass equation.


Ungar is a mathematician. He apparently doesn't have much interest in quantitatively comparing his theory with oservation. Maybe he feels his time is better spent doing the pure math part and leaves it to others to do the empirical testing.

I expect the additional mass/energy added is undetectably small in ordinary circumstances. Seems to me it would be relevant in nuclear and sub-nuclear processes, though. There, we do have a total mass that's greater than the sum of the relativistic mass of the constituent matter particles, don't we? In nucleons, the extra mass is said to be in the gluons, I think. In nuclei, is it in the mesons? My working hypothesis is that Ungar's extra mass could be an alternative explanation for the mass currently thought to be in the force-bearing particles. The force particles seem potentially superfluous to me.

You can derive the velocity addition formula and everything else in special relativity from Lorentz invariance, the symmetry of Minkowski space (the correct version of Ungar's equation (82), for example, follows trivially and immediately from standard 4-vector addition). Therefore you cannot possibly derive anything inconsistent with Lorentz invariance from the velocity addition formula. Therefore, Ungar is wrong.

Furthermore, relativistic corrections are unimportant for dark matter in most cases, because the speed of stars around the galactic center is a very small fraction of c.

[sol invictus]

Originally Posted by Ziggurat

There's a glaring inconsistency staring him right in the face and he doesn't even notice it: his idea violated conservation of energy. He's got this extra mass which appears due to relative motion between multiple objects, but that extra mass will only equal the energy put into creating that relative motion if these extra terms of his don't exist. If they do exist, then you're creating more mass than the energy you put in. And that is, quite frankly, nonsense.

I don't think it's nonsense, at least not the math - it's simply a triviality obscured by silly notation ("gyrovectors") and surrounded by wrong English statements.

His equation (82) for example is correct, at least assuming his notation means what I think it means (it's just the norm of the energy-momentum 4-vector for a collection of particles). There are cross terms in that since you sum and square, physically that's because relative velocity between particles means there's kinetic energy in the system in any frame, and therefore the total invariant mass is larger than the sum of the rest masses.

But of course this has nothing whatsoever to do with dark matter, and it's completely standard special relativity.

[Eggs Ackley]

Originally Posted by sol invictus

I don't think it's nonsense, at least not the math - it's simply a triviality obscured by silly notation ("gyrovectors") and surrounded by wrong English statements.

His equation (82) for example is correct, at least assuming his notation means what I think it means (it's just the norm of the energy-momentum 4-vector for a collection of particles). There are cross terms in that since you sum and square, physically that's because relative velocity between particles means there's kinetic energy in the system in any frame, and therefore the total invariant mass is larger than the sum of the rest masses.

But of course this has nothing whatsoever to do with dark matter, and it's completely standard special relativity.

I took a few minutes to try to evaluate Ungar's eq. 82 for a simple galaxy model consisting of N equal-mass stars and assuming their relative velocities were all the same. I was expecting that I could make up for the small relative velocities with having a lot of stars, since we are going to sum all possible pairs. But, since both of the sum terms end up contributing an N^2, this ends up factoring out and I get left with simply (roughly) a (average) relative gamma factor on the total relativistic mass, which is very close to unity and not the factor of something like 10 needed.

So, I can't see how to make Ungar's equation explain dark matter, after all, at least at the moment.

I still think it could be important in nuclei, however.

[Ziggurat]

Nevermind, not worth it.

[Eggs Ackley]

Originally Posted by Ziggurat

According to his model, you need to consider every pair of masses. Properly, this should not be every pair of stars, but every pair of particles.

I was thinking that since we can assume that the measurable mass of a star would consist of both its bright and dark components that I could just consider the stars, but on further thought I think I agree this is not right. So then that will recover a not insignificant relative gamma factor for many many particles, seems to me. I makes it a lot more difficult to do a simple notional calculation, though.

[Eggs Ackley]

Originally Posted by Ziggurat

Nevermind, not worth it.

Ha ha, you edited too late.

[sol invictus]

Originally Posted by Eggs Ackley

I took a few minutes to try to evaluate Ungar's eq. 82 for a simple galaxy model consisting of N equal-mass stars and assuming their relative velocities were all the same. I was expecting that I could make up for the small relative velocities with having a lot of stars, since we are going to sum all possible pairs. But, since both of the sum terms end up contributing an N^2, this ends up factoring out and I get left with simply (roughly) a (average) relative gamma factor on the total relativistic mass, which is very close to unity and not the factor of something like 10 needed.

So, I can't see how to make Ungar's equation explain dark matter, after all, at least at the moment.

I still think it could be important in nuclei, however.

It's not "Ungar's equation" - it's bog-standard special relativity. If stars moved with relativistic velocities, relativistic effects would be important... and would have been taken into account years ago when the data first became available. Since they don't move with relativistic velocities, people usually don't bother and do Newtonian analyses instead - but it's certainly possible to do a fully (general) relativistic calculation that shows, once again, that dark matter is needed.

As for nuclei, relativity is extremely important for many processes - and of course, it's fully taken into account by physics as it's been understood for the last 107 years or so.

[theprestige]

Originally Posted by Eggs Ackley

I was thinking that since we can assume that the measurable mass of a star would consist of both its bright and dark components...

Why would you assume that?

Why would you assume that stars even have dark components?

How would your assumption account for repeated observations that the bright components of a star already account for all its measurable mass?

How would your assumption account for the fact that the star's measurable mass matches what is predicted by a theory that assumes it has no dark components, only bright ones?

[Eggs Ackley]

Originally Posted by sol invictus

It's not "Ungar's equation" - it's bog-standard special relativity.

I just wanted to refer to that particular equation in Ungar's paper, foremost, but I was under the impression it isn't widely appreciated or found elsewhere. Is it in textbooks? I don't recall seeing it explicitly in any of mine (Rindler, French and others). Or, are you simply saying it's completely obvious and would become naturally involved in the analysis. It might be too obscure for a textbook.

Originally Posted by sol invictus

If stars moved with relativistic velocities, relativistic effects would be important... and would have been taken into account years ago when the data first became available. Since they don't move with relativistic velocities, people usually don't bother and do Newtonian analyses instead - but it's certainly possible to do a fully (general) relativistic calculation that shows, once again, that dark matter is needed.

I was thinking that the impulse of most people would be to simply add the relativistic masses of the objects, without the cross terms. Ziggurat apparently thought this. This is what someone might do who didn't derive the necessary form from the assumption that four-momentum is additive.

As I said above, I was expecting that the cross-terms could add an unexpectedly large contribution even for the slowly moving stars based on there being many stars in the galaxy. I thought this was Ungar's expectation or else why claim the equation is an explanation for dark matter. It simply wasn't borne out when I finally took a few minutes to try it out. Now I wish I'd done it sooner.

Originally Posted by sol invictus

As for nuclei, relativity is extremely important for many processes - and of course, it's fully taken into account by physics as it's been understood for the last 107 years or so.

Can you give an example from the literature or a textbook where these cross-terms (that Ungar refers to as "dark") are acknowleged in nuclear physics? I was thinking that they could be possibly accounted for in other ways, such as in the mass of force-carrying particles. I would be nice to know if they are separately accounted for.

I recently got a nice old nuclear physics book for reference (by Bethe) I will look through to see how it covers nuclear masses, and the mass "anomaly".

[Eggs Ackley]

Originally Posted by theprestige

Why would you assume that?

If the mass of a star is estimated from measurements of the motion of panets or other stars nearby, then the mass estimate would include dark components, if present. If the mass is estimated from a star's brightness (or color), I would guess the brightness-to-mass table or function was originally developed with some reference to nearby stars with mass estimates developed this way. For example, we can estimate the mass of Sol (the star, not the poster) from the orbital velocities of its planets. If Sol has a dark mass component, it will naturally be included in the estimate.

Originally Posted by theprestige

Why would you assume that stars even have dark components?

If Ungar's contention is true, then they certainly do. Also, one doesn't particularly need much motivation to make such an assumption, as it's simply an enabler for carrying out a calculation in service of testing a hypothesis. I was only attempting to evaluate Ungar's suggestion, and wanted to make it simple enough to be able to do in a few lines, and with the information I had available.

Originally Posted by theprestige

How would your assumption account for repeated observations that the bright components of a star already account for all its measurable mass?

I'm sure that no matter how well stellar models predict star brightness from purely-theoretical calculations based on composition and total mass, there is some margin of uncertainty in the mass. Anyhow, it's entirely beside the point. I was only making an assumption to facilitate a calculation. The assumption was not meant to imply such a sweeping claim.

Originally Posted by theprestige

How would your assumption account for the fact that the star's measurable mass matches what is predicted by a theory that assumes it has no dark components, only bright ones?

My assumption doesn't need to account for this at all, and is fully consistent with it. If the theory is perfect and predicts bright mass perfectly, and this mass is consistent with the observed orbital velocities of the planets (how else do you know it's perfect?) then there must be no dark mass stellar component, which is consistent with my assumption.

[sol invictus]

Originally Posted by Eggs Ackley

I just wanted to refer to that particular equation in Ungar's paper, foremost, but I was under the impression it isn't widely appreciated or found elsewhere. Is it in textbooks? I don't recall seeing it explicitly in any of mine (Rindler, French and others). Or, are you simply saying it's completely obvious and would become naturally involved in the analysis. It might be too obscure for a textbook.

It's obvious, at least when written in standard notation and not wrapped in absurd and confused statements.

Quote:

I was thinking that the impulse of most people would be to simply add the relativistic masses of the objects, without the cross terms. Ziggurat apparently thought this. This is what someone might do who didn't derive the necessary form from the assumption that four-momentum is additive.

You do simply add the relativistic masses, if what you're interested in is the first component of its energy-momentum 4-vector (i.e., its energy). That's "Ungar's" eq. (83). But if you're interested in the invariant mass of the collection, you have to take the momentum into account when you square the 4-vector, and that gives you cross terms when written in terms of the momenta of the constituent particles.

Quote:

Can you give an example from the literature or a textbook where these cross-terms (that Ungar refers to as "dark") are acknowleged in nuclear physics? I was thinking that they could be possibly accounted for in other ways, such as in the mass of force-carrying particles. I would be nice to know if they are separately accounted for.

I recently got a nice old nuclear physics book for reference (by Bethe) I will look through to see how it covers nuclear masses, and the mass "anomaly".

http://en.wikipedia.org/wiki/Invariant_mass:

Originally Posted by wikipedia

If objects within a system are in relative motion, then the invariant mass of the whole system will differ from the sum of the objects' rest masses....Because the invariant mass includes the mass of any kinetic and potential energies which remain in the center of momentum frame, the invariant mass of a system is usually greater than sum of rest masses of its separate constituents. For example, rest mass and invariant mass are zero for individual photons even though they may add mass to the invariant mass of systems. For this reason, invariant mass is in general not an additive quantity (although there are a few rare situations where it may be, as is the case when massive particles in a system without potential or kinetic energy can be added to a total mass)....In particle collider experiments...

[theprestige]

Originally Posted by Eggs Ackley

If the mass of a star is estimated from measurements of the motion of panets or other stars nearby, then the mass estimate would include dark components, if present. If the mass is estimated from a star's brightness (or color), I would guess the brightness-to-mass table or function was originally developed with some reference to nearby stars with mass estimates developed this way. For example, we can estimate the mass of Sol (the star, not the poster) from the orbital velocities of its planets. If Sol has a dark mass component, it will naturally be included in the estimate.




If Ungar's contention is true, then they certainly do. Also, one doesn't particularly need much motivation to make such an assumption, as it's simply an enabler for carrying out a calculation in service of testing a hypothesis. I was only attempting to evaluate Ungar's suggestion, and wanted to make it simple enough to be able to do in a few lines, and with the information I had available.



I'm sure that no matter how well stellar models predict star brightness from purely-theoretical calculations based on composition and total mass, there is some margin of uncertainty in the mass. Anyhow, it's entirely beside the point. I was only making an assumption to facilitate a calculation. The assumption was not meant to imply such a sweeping claim.




My assumption doesn't need to account for this at all, and is fully consistent with it. If the theory is perfect and predicts bright mass perfectly, and this mass is consistent with the observed orbital velocities of the planets (how else do you know it's perfect?) then there must be no dark mass stellar component, which is consistent with my assumption.

Thanks I think I get what you're trying to say.

It seems to me that there's a big problem with looking for dark matter within stellar masses: The more accurate the bright matter mass prediction, and the closer the observation matches the prediction, the smaller the proportion of dark matter necessary to make up the overall mass.

That is, if your observation matches the bright mass prediction to 99% accuracy, that leaves only enough room for dark mass to make up 1% of the total stellar mass.

If you then observe that the rotation curves of a galaxy imply that 99% of its mass is dark, that suggests that the dark mass is not located within that galaxy's stars, and thus there is no reason to assume that it's there.

[edd]

http://www.ox.ac.uk/media/science_blog/100712.html
You might do better to look for other effects if you want to narrow down how much dark matter a star has picked up.

[deaman]

I wonder if any "Dark Matter" has been detected around, Uranus?

[Dancing David]

Originally Posted by deaman

I wonder if any "Dark Matter" has been detected around, Uranus?

It was wiped out with the Klingons!

[Croydon Bob]

When I visited the UK dark matter detector (http://hepwww.rl.ac.uk/ukdmc/ukdmc.html), which is at the bottom of a potash mine, I asked them how they were going to get the dark matter out of the mine once they had found it.

Wooshh! Total failure to realise I was joking. . .

[Cuddles]

Sol and Ziggurat have answered the scientific parts, but I thought this was worth a comment as well:

Originally Posted by Eggs Ackley

Doesn't such conscientious hard work merit the effort

No. No it doesn't. Making an effort might be important for your school report, but out in the real world all that matters is results. Anyone can make claims, if you want them to be taken seriously you have to show that they're worth it. Merely spending a lot of time coming up with them isn't close to good enough.