mdjurfeldt
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Jan9-14, 09:26 AM
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In chapter 10 of Robert D. Klauber's excellent QFT book, there's a nice overview of different concepts occurring in the context of vacuum fluctuations. Inspired by that chapter I ask:

If one would state that there is no such thing as vacuum fluctuations, what counter arguments are there?

In particular, QFT doesn't seem to provide a mechanism for spontaneous pair production in the vacuum. The "vacuum bubble" term of the Dyson-Wick expansion in QED only describes virtual, not real, particles, does not have any measurable effects or interactions with the physical world, and is no reason to believe that anything physical is created in the vacuum. Also, the energy-time uncertainty relation *allows* for vacuum fluctuations but does not say that those occur.

Is there *any* reason to believe that particles are created and destroyed spontaneously in the vacuum other than that many physicists *believe* this is the case?
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ZapperZ
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Jan9-14, 09:28 AM
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How about pointing to the Casimir effect?

Zz.
mdjurfeldt
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Jan9-14, 09:54 AM
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Quote Quote by ZapperZ View Post
How about pointing to the Casimir effect?
Well, it seems like this effect can be explained by a relativistic, retarded van der Waals force between the plates (http://arxiv.org/abs/hep-th/0503158).

It's a bit unsatisfactory to have two explanations for this effect, so how do they compare?

First note that the zero point energy (ZPE) explanation you (implicitly) refer to is based on the ZPE half quanta which occur if you assume that Nature does not normal order its operators (something we can't measure, just as we can't measure the half quanta themselves---independently of the Casimir effect, i.e.). Second, Klauber argues that the ZPE Casimir effect explanation is just heuristic. It does not build on QFT but on standing waves between [and outside] the plates.

Besides, even if we do believe in the ZPE explanation, the net ZPE energy of the SM (if we do not assume normal ordering) would be negative and have the wrong magnitude. Also, even if we have some "solution" to that, the continuously existing standing waves in the ZPE explanation is no indication of spontaneous production and annihilation of pairs of particles, as Klauber points out.

All in all, my take is that the Casimir effect is due to van der Waals force. :)

ZapperZ
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Jan9-14, 10:14 AM
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Vacuum fluctuations do not exist


The Casimir effect isn't just "between plates", and also includes a repulsive Casimir force.

I do not see how van der Waals alone can account for the measure Casimir force, such as from Mohideen and Roy Phys. Rev. Lett. 81, 45494552 (1998). Have you tried a quantitative estimation to match that measurement?

Edit: For example, I don't see these measurements of the van de waals forces by Beguin et al Phys. Rev. Lett. 110, 263201 (2013) matching the above result at all.

Zz.
mdjurfeldt
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Jan9-14, 10:30 AM
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Quote Quote by ZapperZ View Post
The Casimir effect isn't just "between plates"
Sorry---this was an omission. I added "[and outside]" to my previous post.
mdjurfeldt
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Jan9-14, 12:33 PM
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Quote Quote by ZapperZ View Post
I do not see how van der Waals alone can account for the measure Casimir force, such as from Mohideen and Roy Phys. Rev. Lett. 81, 45494552 (1998). Have you tried a quantitative estimation to match that measurement?

Edit: For example, I don't see these measurements of the van de waals forces by Beguin et al Phys. Rev. Lett. 110, 263201 (2013) matching the above result at all.
I've looked at these papers now and don't understand your objections.

Mohideen and Roy show excellent quantitative agreement with the standard Casimir formula F = -(Pi^2 hbar c/240)(A/d^4) (given corrections due to their experimental setup such as spherical shape of one of the plates and roughness of the surface). Jaffe (2005) derives the Casimir result for the one-dimensional case without reference ZPE but arrives at the corresponding Casimir result. I guess it is just a matter of work to do the same for the 2D case and that this will result in the 2D formula above.

Beguin et al measure van der Waals force between two atoms. In what way does their result apply here?
ZapperZ
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Jan9-14, 01:15 PM
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Quote Quote by mdjurfeldt View Post
I've looked at these papers now and don't understand your objections.

Mohideen and Roy show excellent quantitative agreement with the standard Casimir formula F = -(Pi^2 hbar c/240)(A/d^4) (given corrections due to their experimental setup such as spherical shape of one of the plates and roughness of the surface). Jaffe (2005) derives the Casimir result for the one-dimensional case without reference ZPE but arrives at the corresponding Casimir result. I guess it is just a matter of work to do the same for the 2D case and that this will result in the 2D formula above.

Beguin et al measure van der Waals force between two atoms. In what way does their result apply here?
It boils down to the fact the Beguin at all never claim that these are equivalent to Casimir force, that we do know when we have van der Waals forces and when we don't. See, for example, Palasantzas et al. Ap. Phys. Lett., 93, 121912 (2008) in which they determined the transition between van der Walls to Casimir. It clearly shows that these two are not the same beast.

But really, if you think that these really are nothing more than van der Waals forces, how come you are not writing a rebuttal to correct many of these papers that are claiming that these are due to vacuum fluctuations?

Zz.
mdjurfeldt
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Jan9-14, 01:24 PM
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Quote Quote by ZapperZ View Post
But really, if you think that these really are nothing more than van der Waals forces, how come you are not writing a rebuttal to correct many of these papers that are claiming that these are due to vacuum fluctuations?
Ah... I'm a novice and not in a position to do that---just learnt a bit of QFT during Christmas. I was so amazed when I saw that QFT does *not* predict vacuum fluctuations. Yet everybody are talking about them. I hope this thread can give a good reason for that.
ZapperZ
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Jan9-14, 01:39 PM
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Quote Quote by mdjurfeldt View Post
Ah... I'm a novice and not in a position to do that---just learnt a bit of QFT during Christmas. I was so amazed when I saw that QFT does *not* predict vacuum fluctuations. Yet everybody are talking about them. I hope this thread can give a good reason for that.
But this is just an aspect of a more general concept of quantum fluctuation! If you are claiming that this doesn't really exist, then you are also striking out whole subject area on quantum criticality and quantum phase transition. When you do that, you need to answer the numerous formalism and evidence we already have from condensed matter physics. See:

http://arxiv.org/pdf/cond-mat/0503002v1.pdf

...for example. And a more comprehensive overview of quantum criticality can be found here:

http://arxiv.org/abs/1102.4628

In case you haven't realized it, the fermionic ground state that condensed matter physicists often deal with is analogous to the vacuum ground state. Guess what the equivalent "vacuum fluctuation" in such a system represents?

Zz.
mdjurfeldt
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Jan9-14, 03:02 PM
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Quote Quote by ZapperZ View Post
But this is just an aspect of a more general concept of quantum fluctuation! If you are claiming that this doesn't really exist, then you are also striking out whole subject area on quantum criticality and quantum phase transition. When you do that, you need to answer the numerous formalism and evidence we already have from condensed matter physics. See:

http://arxiv.org/pdf/cond-mat/0503002v1.pdf

...for example. And a more comprehensive overview of quantum criticality can be found here:

http://arxiv.org/abs/1102.4628

In case you haven't realized it, the fermionic ground state that condensed matter physicists often deal with is analogous to the vacuum ground state. Guess what the equivalent "vacuum fluctuation" in such a system represents?
I hope I do not misrepresent Klauber when he argues that the situation in standard QFT, with free fields, isn't really analogous to bound state systems. In the former case, the ground state can have zero energy. The half quanta are suspect and do not contribute to energy which can drive pair production. I can claim that there are *no* particles in the vacuum such that the uncertainty relation between position and momentum which drives the fluctuations you refer to does not have anything to apply to.

In bound state systems, the ground state has non-zero energy and we do have particles to apply the uncertainty relation to.


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