Split Thread Michael Mozina's thread on Dark Matter, Inflation and Cosmology

[sol invictus]

Einstein introduced his CC to avoid instabilities in GR that would lead to a collapsing universe. After Hubble's discoveries he abandoned it and called it his "biggest blunder."

That's almost right. As others have noted, he introduced it to counterbalance the attractive gravitational force produced by ordinary matter. It doesn't avoid instabilities, and I'm not sure what Einstein thought about that at the time. Regardless, very shortly thereafter he knew the static solution was unstable. And of course Einstein's beliefs and motivations are utterly irrelevant to this discussion, which is (supposed to be) about facts.

As far as I know, the CC has since been a matter of debate related to questions about the ultimate fate of the universe (e.g.: continuing to expand eternally, ceasing to expand, ultimately collapsing) . So re-introducing it as a way to explain cosmological acceleration would be a new application. I believe this is a fairly accurate summary of the history of the CC. Can anyone demonstrate otherwise?

That's not quite accurate, no. Most physicists assumed the CC was zero after Hubble's discovery. Whether the universe expands forever or re-collapses does depend on the CC, but not only on it (it also depends on spatial curvature and the amount of matter and radiation). If the current acceleration is indeed due to a true positive CC, then we know that the universe will expand (and continue to accelerate) forever.

MM claims a positive CC doesn't cause acceleration, which is of course false. The fact that there exists a single unstable static solution has no impact on the truth of the statement that "a positive CC causes the expansion of the universe to accelerate". It's very similar (in fact nearly identical) to the statement that "if you stand an infinitely sharp pencil on its end, gravity makes it fall over". The fact that a well balanced pencil could remain upright for a long time (or even forever in some make-believe idealization where it's infinitely perfectly balanced) has no impact on the truth of that statement.

 

[Michael Mozina]

That's almost right. As others have noted, he introduced it to counterbalance the attractive gravitational force produced by ordinary matter. It doesn't avoid instabilities, and I'm not sure what Einstein thought about that at the time. Regardless, very shortly thereafter he knew the static solution was unstable. And of course Einstein's beliefs and motivations are utterly irrelevant to this discussion, which is (supposed to be) about facts.

His motivation is relevant to the discussion, as well as his motivation for setting it back to zero. Zero represents "nothing". If you want to put "something" back into GR where Einstein had a zero, you still have to explain what it is, and why you're putting it there. Einstein eventually realized he didn't need it, and "gravity" itself was perfectly "explained" without it. If you intend to do something new with his formulas, and where he had "nothing", you put "something", you should note the change don't you think?

 

[Michael Mozina]

MM claims a positive CC doesn't cause acceleration, which is of course false.

Actually my claim was Einstein's use of a constant didn't result in a universe that accelerates off into the sunset. It resulted, according to him at the time, in a static universe, one that didn't expand or contract, but stayed "static".

After reading my wording, your criticisms were both a little valid and a little misleading. Yes, you *COULD* use that term to create an accelerating universe, but no, Einstein didn't do any such thing with that term when he used it.

 

[Michael Mozina]

Again with the random use of kinetic. And ahem:

It wasn't random. It's kinetic energy from the carrier particles of the EM field that impart kinetic pressure to all sides of everything inside the chamber.

What can I say about the use of quote? I guess my old habits will take some time to break.

 

[Michael Mozina]

So the energy between the plates is dropping as you agreed to earlier,

Yes. We still seem to agree on that point. Let me ask you a question. What's happening to the energy density outside the plates in your opinion?

and on the outside of the plates whatever positive pressure material is in a growing volume

Hmmmm. I think I see where you're trying to go here, but QM pressure isn't quite that simple. The growing volume outside allows for more harmonic oscillations to occur outside the plates, effectively increasing the pressure on the outside of the plates. It's not diluted by the change in volume like an ordinary gas. We need to be careful about the limits of our analogy here. The geometry drives the process and determines if it's attractive or repulsive. That is due to the energy density on both sides of the plates. The larger region between the outside plate and the wall of the chamber simply allows for more harmonic oscillations to form outside than will form between the plates. It's still being pushed together by on overall higher pressure on the outside of the plates and a lower pressure from the dropping energy density between the plates. Even if the energy density outside the plates remains the same, the lower energy density between the plates will create a pressure difference on the outside of the plate and the inside. That difference results in what their/your? calling "negative pressure". It's not actually "negative", it's simply a "lower energy state". IMO you're still confusing the concept of "absolute pressure" with "relative pressure".

Give me a shout when you're ready to start conserving energy and we can pick this discussion up again.

It seems to me that all energy is conserved, there is just more of it on the outside, and less of it between the plates.

 

[Michael Mozina]

The modes outside the plate don't contribute to the attraction between the plates. They either have no effect at all, or actually inhibit the attraction.

Hmmm. Try this article and the paper it references:

http://focus.aps.org/story/v2/st28

The simplest explanation of the Casimir effect is that the two metal plates attract because their reflective surfaces exclude virtual photons of wavelengths longer than the separation distance. This reduces the energy density between the plates compared with that outside, and--like external air pressure tending to collapse a slightly evacuated vessel--the Casimir force pulls the plates toward one another.

That quote is pretty useful because it talks about both the decreasing energy density edd describes between the plates, but also the energy density on the outside. You can "visualize" the outside energy density having no effect and look only at the energy density between the plates in a "simplified" was of calculating the effect, but what's really occurring is a pressure drop between the plates to a "lower", not "negative' energy state. Once it drops to a lower energy state the outside energy acts to push things together. For calculations purposes the distance between the plates is more important than the rest of the chamber, so it's handy to think about it in terms of 'negative pressure' on the inside of the plate, but just like the diagram on Wiki shows, it's simply a "pressure difference" that these formulas seek to describe, not "negative pressure in a vacuum".

FYI, Guth needs "negative pressure" from his 'vacuum' because he intends to 'suck' the mass thingy apart it. Unfortunately he can't do that because all the pressure arrows will point into, not away from his mass object. The positive vacuum energy density will always push into his mass thingy. A zero energy density would create no "pressure" at all. There is no way to create a "negative energy density" in a vacuum, so his "negative pressure vacuum" is physically impossible. He chose the wrong limit for vacuum pressure. A "prefect" vacuum would have "zero" pressure, no EM pressures, no atomic pressures, no kinetic energy flow whatsoever. What would you even add or subtract from a "pure/perfect" vacuum to achieve "negative" pressure?

 

[Michael Mozina]

That is the problem with relying on pretty pictures for your understanding of physics. The oscillations do not physically exist!

They do exist which is what pushes your plates together.

The waves in the diagram are an (incorrect) representation of the QM mathematics.

Then the article I cited must also be wrong too?
http://focus.aps.org/story/v2/st28

The mathematics shows that the force on the outside of the plates is greater than the force on the inside.

Replace "force" with "pressure" and I agree with you.

This means that the plates move together.

The *NET* force is directional and geometrically driven. That's all your minus sign ultimately means.

Positive pressure would move the plates further apart.

Higher pressure between the plates would move them further apart. Likewise a lower pressure between the plates causes them to be pushed together.

Scientists call a pressure from a force that results in attraction rather than repulsion, negative pressure. It turns out if you do the math that the values of negative pressure are actually negative.

No. It just turns out you personally (and a few others) can't tell the difference between directional force of the EM field (what your minus sign ultimately relates to) and "negative pressure" in a "vacuum".

 

[edd]

Yes. We still seem to agree on that point. Let me ask you a question. What's happening to the energy density outside the plates in your opinion?

Well it depends very much on what is outside the plates. If you take the case of an infinite vacuum, then I guess nothing changes. In that situation the energy released by the Casimir effect goes into kinetic energy of the plates. That would be what happens in Casimir's original calculation.

In practice, there may be some other (much weaker) Casimir effect between the outside of the plates and whatever else is around - maybe this is all taking place in a metal box or something. In that case it may well be something like what you say here

The growing volume outside allows for more harmonic oscillations to occur outside the plates, effectively increasing the pressure on the outside of the plates.

with more energy allowed outside the plates and with the pressure not increasing in magnitude, but certainly becoming less negative.

In the case you have actual gases between and outside the plates, the plates don't hit and reach a point of equilibrium, with the energy transferred between the two gases.

Hmmmm. I think I see where you're trying to go here, but QM pressure isn't quite that simple.

Well that we agree on.


Well as I said above, that very much depends on what is outside the plates about how that happens. But I'm quite happy to concede there's a pressure difference here. It's just that it's a difference between two negative pressures.

It's not diluted by the change in volume like an ordinary gas.

Absolutely. That's pretty much entirely the point this is in a cosmological discussion. And that fact is down to the negative pressure.

The 'stuff' on side of the plate is applying a force. Each side's energy is going into doing work through that force. The energy change is a direct indicator of which direction that force is in, and the energy change is the opposite sign to that of a normal gas. Therefore the force is in the opposite direction, and the pressure is the opposite sign to that of a normal gas.

I'm really quite unconfused about the difference between absolute and relative pressure. You are labouring under the misconception that the negative relative pressure is down to a difference between two positive absolute pressures. It isn't. The negative relative pressure is a difference between two negative absolute pressures. The work that each side is doing demonstrates this.

 

[Tubbythin]

His motivation is relevant to the discussion, as well as his motivation for setting it back to zero. Zero represents "nothing". If you want to put "something" back into GR where Einstein had a zero, you still have to explain what it is, and why you're putting it there.

This is, of course, trivially false. As I mentioned we need no more justification than experimental or observational evidence. This is no different to any of the other fundamental constants in this respect. We do not know why the electron mass is (roughly) 511 keV/c² for example. But where we use equations that require the electron rest mass we don't use m_e = 0. Why? Because this would give us the wrong answer all the time.

Einstein eventually realized he didn't need it, and "gravity" itself was perfectly "explained" without it.

Nope. Gravity has never been and may possibly never be perfectly explained. Einstein merely realized based on the current set of observations of the Universe, that these observations could be explained with a CC value of 0. Observational cosmology has moved on in the years since Einstein died and have shown that this appears no longer to be the case.

If you intend to do something new with his formulas, and where he had "nothing", you put "something", you should note the change don't you think?

He didn't have nothing. He had a cosmological constant. At the time he was alive, observational data was consistent with the hypothesis that the constant was 0. This is no longer the case (at least not without introducing actual new physics).

 

[Michael Mozina]

It's getting late for me edd. Let me sleep on it and comment in the morning. I still think this comes back to a confusion between "absolute" energy density, vs relative energy density. Even if the outside outside energy density remains constant, the density gradient results in the movement. The minus sign in the math relates more to the direction of movement (due to pressure differences) than it relates to 'pressure in the chamber'. It's simply a directional component of movement related to the energy differences created by the plates/spheres.

I definitely need some sleep. Goodnight edd.

 

[Tubbythin]

Actually my claim was Einstein's use of a constant didn't result in a universe that accelerates off into the sunset. It resulted, according to him at the time, in a static universe, one that didn't expand or contract, but stayed "static".

After reading my wording, your criticisms were both a little valid and a little misleading. Yes, you *COULD* use that term to create an accelerating universe, but no, Einstein didn't do any such thing with that term when he used it.

Even this isn't really true. As be pointed to you by several of us, this is an unstable equilibrium. Any perturbation would have cause the Universe to collapse or expand at an accelerating rate. Einstein certainly new this at some point in his life.

 

[Tubbythin]

It wasn't random. It's kinetic energy from the carrier particles of the EM field that impart kinetic pressure to all sides of everything inside the chamber.

What can I say about the use of quote? I guess my old habits will take some time to break.

So do you think the carrier particles in question are real or virtual? And what do you think the kinetic energy of said particles is?

 

[edd]

It's getting late for me edd. Let me sleep on it and comment in the morning. I still think this comes back to a confusion between "absolute" energy density, vs relative energy density. Even if the outside outside energy density remains constant, the density gradient results in the movement. The minus sign in the math relates more to the direction of movement (due to pressure differences) than it relates to 'pressure in the chamber'. It's simply a directional component of movement related to the energy differences created by the plates/spheres.

I definitely need some sleep. Goodnight edd.

Sure, I just got up though. What happens outside is something of a confusing factor - I'm quite happy to discuss a situation like this, where there aren't ambiguous or infinite spaces around:
Consider simply a metal box with a metal dividing wall between two compartments. Kind of like a big entirely metal piston. Then you have a Casimir effect on either side, and the movement of the plate in one direction is a decrease in distance between one pair of metal plates, and an increase between another. We keep the outside walls fixed by applying an external force to do so, so we don't have to worry about any pressure from outside. It's just the absolute pressures and the pressure differences on this internal central plate that we care about, and the 'stuff' on either side of this plate.

 

[schrodingasdawg]

Hmmm. Try this article and the paper it references:

http://focus.aps.org/story/v2/st28

Man, I don't have a phys rev subscription. (Well, presumably, I'm supposed to get some sort of access as an SPS member, but I haven't really looked into it. I'm just a student, and I've been getting by with just e-prints on arxiv... yeah.) But as for the page you linked to, I don't think the explanation on it is strictly accurate. It is "the simplest explanation", but in the act of simplifying, something is lost. As far as I know, virtual photons don't have anything to do with the effect.

 

[ben m]

After reading my wording, your criticisms were both a little valid and a little misleading. Yes, you *COULD* use that term to create an accelerating universe, but no, Einstein didn't do any such thing with that term when he used it.

Good! So now you can drop the "GR only ever attracts" and "you can't get acceleration from GR" and "CC doesn't actually predict acceleration" baloney.

Under the hypothesis that the Universe has a vacuum energy density of 10^-29 g*c^2/cm^3 and a mass-energy density of 10^-28, General Relativity does predict an outward acceleration.

 

[ben m]

It's getting late for me edd. Let me sleep on it and comment in the morning. I still think this comes back to a confusion between "absolute" energy density, vs relative energy density. Even if the outside outside energy density remains constant, the density gradient results in the movement. The minus sign in the math relates more to the direction of movement (due to pressure differences) than it relates to 'pressure in the chamber'. It's simply a directional component of movement related to the energy differences created by the plates/spheres.

I definitely need some sleep. Goodnight edd.

When I did the math on the exact same situation using a known-positive-pressure gas and the ("unknown") Casimir system, all but one of these signs were the same. Same direction of force, direction of displacement, same volume change, same external work. The only difference was the total energy change.

 

[Perpetual Student]

...

Einstein merely realized based on the current set of observations of the Universe, that these observations could be explained with a CC value of 0.

...


He didn't have nothing. He had a cosmological constant. At the time he was alive, observational data was consistent with the hypothesis that the constant was 0. This is no longer the case (at least not without introducing actual new physics).

It seems to me that setting the CC to zero and eliminating it are pretty much the same thing. Those two actions certainly have the same result.
Look, he called the CC his biggest blunder! I have no problem with using a value of the CC that is consistent with modern observations. But the claim that it is Einstein's GR that somehow requires the CC when he totally rejected seems to be a bit bogus.

 

[Perpetual Student]

That's almost right. As others have noted, he introduced it to counterbalance the attractive gravitational force produced by ordinary matter. It doesn't avoid instabilities, and I'm not sure what Einstein thought about that at the time. Regardless, very shortly thereafter he knew the static solution was unstable. And of course Einstein's beliefs and motivations are utterly irrelevant to this discussion, which is (supposed to be) about facts.



That's not quite accurate, no. Most physicists assumed the CC was zero after Hubble's discovery. Whether the universe expands forever or re-collapses does depend on the CC, but not only on it (it also depends on spatial curvature and the amount of matter and radiation). If the current acceleration is indeed due to a true positive CC, then we know that the universe will expand (and continue to accelerate) forever.

MM claims a positive CC doesn't cause acceleration, which is of course false. The fact that there exists a single unstable static solution has no impact on the truth of the statement that "a positive CC causes the expansion of the universe to accelerate". It's very similar (in fact nearly identical) to the statement that "if you stand an infinitely sharp pencil on its end, gravity makes it fall over". The fact that a well balanced pencil could remain upright for a long time (or even forever in some make-believe idealization where it's infinitely perfectly balanced) has no impact on the truth of that statement.

I'm not sure what part of what I said is "not quite accurate." The fact that the geometry of space-time and other factors were relevant to speculations about the future of the universe, does not negate the fact that the CC had been abandoned and was only discussed in that context.
I was only agreeing with MM that using a positive CC to explain the acceleration of the expansion of the universe is a new application of the CC. That was not Einstein's original purpose and it was no longer part of cosmology until the discovery of cosmic acceleration.
Thanks for that "pencil" analogy. It provides a marvelous way to visualize "unstable" in the context a static universe.

 

[ben m]

But the claim that it is Einstein's GR that somehow requires the CC when he totally rejected seems to be a bit bogus.

We've been through this a few times: GR is a theory of gravity. Given GR, you have to tell it what the "sources" (energy densities & masses) are, solve the equation, and GR will tell you the equations of motion.

GR is perfectly happy to be told "there is an energy density in the vacuum". No GR problem at all. Einstein knew this, Eddington knew this, everyone knows it. Everyone also knows what the effect of this would be.

To find the equations of motion of the Universe you have to tell GR what you think the energy densities of the Universe are; you do this using the data, and people doing it in a different Universe could (using the same GR laws) do it differently and get the same answer.

The thing we want to emphasize: Einstein did not make a mistake in formulating GR, nor in predicting the CC's effect using GR. He didn't even make a mistake in deriving the GR equations-of-motion that matched the contemporary data. The mistake was that the data was wrong, and he ought to have been able to tell the astronomers to look twice at it.

 

[Perpetual Student]

We've been through this a few times: GR is a theory of gravity. Given GR, you have to tell it what the "sources" (energy densities & masses) are, solve the equation, and GR will tell you the equations of motion.

GR is perfectly happy to be told "there is an energy density in the vacuum". No GR problem at all. Einstein knew this, Eddington knew this, everyone knows it. Everyone also knows what the effect of this would be.

To find the equations of motion of the Universe you have to tell GR what you think the energy densities of the Universe are; you do this using the data, and people doing it in a different Universe could (using the same GR laws) do it differently and get the same answer.

The thing we want to emphasize: Einstein did not make a mistake in formulating GR, nor in predicting the CC's effect using GR. He didn't even make a mistake in deriving the GR equations-of-motion that matched the contemporary data. The mistake was that the data was wrong, and he ought to have been able to tell the astronomers to look twice at it.

I did not say that Einstein made a mistake in formulation GR. All the descriptions of the CC that I had seen until the discovery of the acceleration of cosmic expansion was that it was an add-on by Einstein to account for a static universe, which he abandoned after Hubble's discovery.

Was not the following:

[latex] R_\mu_\nu - \dfrac{1}{2}g_\mu_\nu R = \dfrac{8\pi G}{c^4}T_\mu_\nu [/latex]

the equation Einstein settled on after Hubble's discovery?