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

[Perpetual Student]

I don't understand---what about MM's story do you think is accurate, or what version of our story is inaccurate? That Einstein didn't know that the CC term gives acceleration? That the CC term does not give acceleration?

This was my original post:

MM does make a good point that 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."

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 all I'm saying. The range of possible values given to the CC may very well account for varying degrees of expansion and/or acceleration (positive or negative). I cannot imagine that Einstein did not know that.
The fact is that Einstein was seeking only stability and that was the point MM was making.

 

[Tubbythin]

The fact is that Einstein was seeking only stability and that was the point MM was making.

He was seeking staticity (which probably isn't a real word). His static Universe solution was unstable since any perturbation would cause it to collapse or expand.

 

[schrodingasdawg]

He was seeking staticity (which probably isn't a real word).

I'm going to start using that word...

 

[Michael Mozina]

Michael - do you agree that when the plates are closer, there is a lower energy density between them?

Yes.

 

[Michael Mozina]

This isn't what the Casimir force is.

The Casimir effect is due to the zero-point energy of the EM field. Every mode of the EM field has a lowest-energy state which is non-zero. The allowed modes are restricted by the fact that the field must be zero on the surface of the plates. When the plates are closer together, there are fewer allowed modes and a lower zero-point energy.

When you talk about "zero point energy", what you mean is that the universe contains kinetic energy, even if we could remove all the atoms from the chamber. We can select a 'low' energy state as the "relative zero" starting point, but we can never achieve an "absolute" zero energy state. Sometimes the energy state can be slightly lower than our "relative zero", sometimes higher, but it has nothing to do with negative pressure in a vacuum.

Nothing is being pushed.

*Everything* is being pushed, some sides more than others.

The vacuum on the outside exerts no force, and thus no pressure.

That's simply not so. The vacuum energy exerts kinetic energy on everything.

In spite of this, the plates attract. In order for the "relative pressure" to be negative, the pressure between the plates must be negative.

No. The pressure between the plates simply has to be "less than" the overall ambient "pressure" from the EM field in the chamber. Those blue arrows point into all sides of all plates. Likewise the QM "foam" is everywhere, exerting kinetic energy everywhere. That's because we can never achieve a zero energy state. We can't even remove every atom from a "vacuum", let alone every EM carrier particle and every neutrino, etc. There will always be positive kinetic energy everywhere inside that chamber, and it will effect all sides of all plates.

 

[ben m]

When you talk about "zero point energy", what you mean is that the universe contains kinetic energy

Not kinetic. Why do you insist on slapping the word "kinetic" in front of every energy you can find? You were doing this with plasma physics too---you always wanted the magnetic energy to be "kinetic". (ETA: Or, wait---if you actually believe this residual-gas picture, then it would be all kinetic energy.)

The pressure between the plates simply has to be "less than" the overall ambient "pressure" from the EM field in the chamber.

The overall ambient pressure from EM in the chamber? What IS that overall ambient pressure? Go ahead and calculate the blackbody photon pressure at room temperature, it's really easy. (The equation is on Wikipedia.) Compare it to the Casimir calculation and Casimir results. THEY'RE DIFFERENT THINGS.

We can't even remove every atom from a "vacuum", let alone every EM carrier particle and every neutrino, etc.

We don't need to. The residual atoms, residual blackbody photons, and neutrinos (!!!) do NOT cause the observed 1/a^4 force. What makes you guess that they do?

 

[edd]

Yes.

Great.

Consider a classical gas with positive pressure. It pushes out on the two plates. In doing so, it performs work - the pressure P, times the area A, is a force F, which pushes the plates apart a distance d. The work done is F.d.

The volume change is A.d. The gas loses energy to perform the work, and cools down. Its internal energy drops, the work goes into pushing the plates apart.

Now, in the case of the stuff between the plates in the Casimir effect, the volume change is the same, but the stuff in the middle gains energy (remember you just agreed that a volume drop causes a drop in the energy density, and the converse that a volume increase also causes an increase in its density also holds true). As the energy change in the middle is the opposite sign, the work done must be negative rather than positive, so the force F is negative.

The pressure, being just F/A is therefore also negative.

How can you maintain the two contradictory points of view you've just displayed?

 

[Tubbythin]

We can't even remove every atom from a "vacuum", let alone every EM carrier particle and every neutrino, etc.

Were you intending doing the experiment in the vicinity of a supernova?

 

[Michael Mozina]

Were you intending doing the experiment in the vicinity of a supernova?

 

[Perpetual Student]

Great.

Consider a classical gas with positive pressure. It pushes out on the two plates. In doing so, it performs work - the pressure P, times the area A, is a force F, which pushes the plates apart a distance d. The work done is F.d.

The volume change is A.d. The gas loses energy to perform the work, and cools down. Its internal energy drops, the work goes into pushing the plates apart.

Now, in the case of the stuff between the plates in the Casimir effect, the volume change is the same, but the stuff in the middle gains energy (remember you just agreed that a volume drop causes a drop in the energy density, and the converse that a volume increase also causes an increase in its density also holds true). As the energy change in the middle is the opposite sign, the work done must be negative rather than positive, so the force F is negative.

The pressure, being just F/A is therefore also negative.

How can you maintain the two contradictory points of view you've just displayed?

That's a great explanation, thanks.

 

[Tubbythin]

[qimg]http://www.internationalskeptics.com/forums/images/smilies/confused.gif[/qimg]

They're the only places in the Universe that I know of where the neutrino pressure is anything other than utterly irrelevant.

 

[schrodingasdawg]

When you talk about "zero point energy", what you mean is that the universe contains kinetic energy, even if we could remove all the atoms from the chamber.

No, what I mean is

Every mode of the EM field has a lowest-energy state which is non-zero.

Every mode of the electromagnetic field is a quantum harmonic oscillator. Read the wiki article for more details,
http://en.wikipedia.org/wiki/Quantum_field_theory#Second_quantization_of_bosons
In particular,

These are precisely the relations obeyed by the ladder operators for an infinite set of independent quantum harmonic oscillators, one for each single-particle state.

Here is another Wiki article on the quantum harmonic oscillator,
http://en.wikipedia.org/wiki/Quantum_harmonic_oscillator
In particular

Secondly, the lowest achievable energy is not zero, but \hbar\omega/2, which is called the "ground state energy" or zero-point energy.

Does this clarify things any?

 

[Michael Mozina]

Great.

Consider a classical gas with positive pressure. It pushes out on the two plates. In doing so, it performs work - the pressure P, times the area A, is a force F, which pushes the plates apart a distance d. The work done is F.d.

The volume change is A.d. The gas loses energy to perform the work, and cools down. Its internal energy drops, the work goes into pushing the plates apart.

Now, in the case of the stuff between the plates in the Casimir effect, the volume change is the same, but the stuff in the middle gains energy (remember you just agreed that a volume drop causes a drop in the energy density, and the converse that a volume increase also causes an increase in its density also holds true).

I'm with you to this point.

As the energy change in the middle is the opposite sign, the work done must be negative rather than positive, so the force F is negative.

The energy density and force from that energy density is simply 'greater' on the outside of the plates, and 'less' between them. There is still some small force pushing into the insides of the plates. That force is simply "less than" the energy density that is pushing the plates together.

The pressure, being just F/A is therefore also negative.

If all we did is look at "pressure" from a single surface (like my wing analogy), you might be "tricked" into believing that the pressure on the top of the wing is "negative". It's not. The pressure under the wing is "greater" that the pressure on top of the wing, and the "pressure difference" causes upward lift. The same analogy is true here. The *whole* chamber has an energy density, not just the region between the plates. The "ambient energy density" is simply greater than the energy density between the plates and the plates are 'pushed together' from the outside force of that ambient energy density.

 

[Tubbythin]

If all we did is look at "pressure" from a single surface (like my wing analogy), you might be "tricked" into believing that the pressure on the top of the wing is "negative".

Analogies are worse than utterly useless if the analogy isn't analogous to the thing being described.

 

[temporalillusion]

[qimg]http://www.internationalskeptics.com/forums/images/smilies/confused.gif[/qimg]

I'd guess because you'd probably have to be right beside a supernova in order to get enough neutrinos to have them have any impact on a Casimir experiment.

You remember when someone calculated for you that in normal circumstances you'd have to run your experiment for a year before you'd get a single interaction with a neutrino?

 

[Michael Mozina]

Analogies are worse than utterly useless if the analogy isn't analogous to the thing being described.

The analogy is entirely valid and demonstrates the flaw in your argument. The energy density outside the plates is simply "greater than" the energy density between them. There's no form of 'negative pressure' in a vacuum. Those blue arrows and those blue quantum foam bubbles push into all sides of everything in the chamber. The ambient energy density outside the plates is simply greater than the energy density between them.

 

[Michael Mozina]

I'd guess because you'd probably have to be right beside a supernova in order to get enough neutrinos to have them have any impact on a Casimir experiment.

You remember when someone calculated for you that in normal circumstances you'd have to run your experiment for a year before you'd get a single interaction with a neutrino?

I'm not claiming that the neutrino has anything to do with the casimir effect. I think we all agree the energy density in question is related to the EM field. I was simply pointing out that the term "zero point energy" relates to the kinetic energy of everything we can't remove from our experiments.

 

[ben m]

The energy density and force from that energy density is simply 'greater' on the outside of the plates

You are mixing up force, pressure, and energy density. The "force from an energy density" is nonsense. Forces arise only because of changes in energy. Anywhere you look and find a force---springs, newtonian gravity, gases, E&M, etc.---you will find some form of potential energy. Keep track of that potential energy and how it changes, and that's where you find a force showing up; the force arises only because displacing something does work and dW = F dx. You do NOT just look at the "energy density" and say "if the energy density is higher the force is higher." It's simply wrong.

This is called Hamiltonian mechanics and it is more basic than either quantum mechanics or relativity. At my university we teach it to juniors (and the faster sophomores) in full detail. The first-quarter freshmen, even the engineers and premeds, even get a simplified special-case version, F = -dU/dx, which edd just tried to explain to you and whose core ideas you just completely ignored in favor of the same math-free mental image. How many times do we have to do this?

At least, next time, you could begin the thread with "I understand that mainstream physicists explain the Casimir effect using some sort of dU/dx term that I reject. However, I think the Casimir effect arises from (a) real photon pressure (b) imperfect vacuum chambers, and (c) an "energy density = force" effect that I think must be true no matter what dU/dx says." That would be honest and would waste less of everyone's time.

 

[Tubbythin]

The analogy is entirely valid

No, it isn't.

and demonstrates the flaw in your argument.

No it doesn't.

The energy density outside the plates is simply "greater than" the energy density between them. There's no form of 'negative pressure' in a vacuum.

Yes there is.

Those blue arrows and those blue quantum foam bubbles push into all sides of everything in the chamber.

. You think the Casimir setup actually has blue arrows in it?

The ambient energy density outside the plates is simply greater than the energy density between them.

So if you push the plates together what happens?

 

[Michael Mozina]

Every mode of the electromagnetic field is a quantum harmonic oscillator.

Does this clarify things any?

Not really because these oscillations occur both outside and between the plates. There are simply more of these oscillations going on outside the plates than between them.