# I Calculation of negative energy density in a Casimir cavity

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1. Feb 6, 2017

### OrigamiNinja

Hello,

I would like to know how to calculate the negative energy density in the region between two Casimir plates, given a distance between two parallel plates.

Thanks, much appreciated!

2. Feb 7, 2017

### Mentz114

It is far from certain that such a thing exists.

This is a recent paper on the subject

Proof that Casimir force does not originate from vacuum energy
Hrvoje Nikolic

https://arxiv.org/abs/1605.04143v3

3. Feb 7, 2017

### OrigamiNinja

That paper is definitely a minority opinion. Also, I believe that it is disproven due to the fact that the casimir effect can be reversed:

http://www.nature.com/nature/journal/v457/n7226/full/nature07610.html

If the Casimir force was caused by van der walls forces, I do not believe it would be reversible experimentally in this way; this method of reversing the Casimir force using a medium of permittivity constants between that of the two plates. I'm pretty sure that would not work if the Casimir force was due to van der wall forces.

Last edited by a moderator: May 8, 2017
4. Feb 7, 2017

5. Feb 7, 2017

### OrigamiNinja

You can ask him ask him if you wish. I'm not really interested for now; I'm mostly just here for the calculation.

6. Feb 7, 2017

### Mentz114

I'm sure there many learned papers on the subject. Did you know about the paper in your second post before your first post ?

7. Feb 7, 2017

### OrigamiNinja

I was aware of the paper that I referred you to before the conversation, but I was not aware of the paper you referred me to. But as far as I know, it's been pretty well established that the Casimir force is due to vacuum fluctuations. I'm not sure how the Croatian physicist came to his conclusions, but if they were right, I don't think you could reverse the Casimir force experimentally the way they have.

well I'll amend that; I was aware of the research where the Casimir force was reversed and that it was done by physicists from a group at Harvard, not the specific paper itself per se. Knowing that this had been done is how I found the paper.

Last edited: Feb 7, 2017
8. Feb 7, 2017

### Mentz114

As far as I can discern the idea of vacuum fluctuations is either completely wrong or a misnomer for field fluctuations. You will find articles and posts in this forum on these subjects.

Here's another reference

The Casimir Effect and the Quantum Vacuum
R. L. Jaffe
(Submitted on 21 Mar 2005)

https://arxiv.org/abs/hep-th/0503158v1

Last edited: Feb 7, 2017
9. Feb 7, 2017

### OrigamiNinja

Look, there are other effects of vacuum fluctuations, not just the Casimir Effect. Hawking radiation for example. It isn't a very contentious issue in the field. It's basically accepted. I'm not really interested in arguing. If you don't want to believe in vacuum fluctuations, fine. I'm just here for the calculations I mentioned in the first post. Thanks.

one edit, here is an article (the paper link is at the bottom of the article) about an experiment where a virtual photon was successfully extracted from the vacuum:

https://phys.org/news/2011-11-scientists-vacuum.html

10. Feb 7, 2017

### Mentz114

The Wiki article shows some calculations which could be what you're looking for. Treat with caution.

https://en.wikipedia.org/wiki/Casimir_effect

I had a quick read of the 'virtual photon' paper and as usual there is no vacuum in the experiment. The whole experimental volume is flooded with fields and the matter of the equipment. If they have detected something, they cannot claim it came from nothing.

Last edited: Feb 7, 2017
11. Feb 7, 2017

### OrigamiNinja

ok, thanks

12. Feb 8, 2017

### Demystifier

I am just writing a paper where I will explain in detail all these conceptual subtleties on Casimir effect. In short, to claim that Casimir effect is or is not a consequence of vacuum energy, one first needs to explain what one means by the word "vacuum". In particular, Casimir vacuum is not a state with a zero number of photons. It is a state with a zero number of certain quasiparticles which are mixtures of photons and polarization quanta.

Last edited: Feb 8, 2017
13. Feb 8, 2017

Staff Emeritus
This was pointed out to the OP six years ago. While it's true that he has a misunderstanding, it's also apparent that he's not about to give it up.

14. Feb 8, 2017

### OrigamiNinja

The wikipedia page had a formula for finding the force between two plates as a function of distance, but not one for energy density. Rather than trying to derive it myself I was hoping someone more experienced with it could provide a correct formula for this. Demystifier, this sounds like it could be your territory?

I'm hoping for a formula for energy density, as a function of plate distance, which should be normalized relative to empty space. So the resulting energy density, if I understand, should be negative.

15. Feb 8, 2017

### Mentz114

See Itzykson and Zuber, Quantun Field Theory (1986) McGraw-Hill, pages 138 ff. Enjoy.

16. Feb 8, 2017

### Jilang

17. Feb 8, 2017

### OrigamiNinja

Ok, there is ambiguity in this area.

A wikipedia article on Van der Walls suggests that each originate from vacuum energy:

"It can be shown that van der Waals forces are of the same origin as the Casimir effect, arising from quantum interactions with the zero-point field.[2]"

From:
https://en.wikipedia.org/wiki/Van_der_Waals_force

I've found this paper, which may help shed some light on it. I can't read all of it now I have something else to do, but I'm going to post it anyway, because it looks promising.

https://arxiv.org/pdf/quant-ph/0302072.pdf

My current interpretation is the Van Der Walls force is actually two things; 1) particle interaction via intermolecular forces such as London forces, and 2) effects from virtual modes (aka virtual particles, aka zero-point energy, aka vacuum energy, etc.) which some people appear to be very skeptical about, however, none the less these appear to be accepted in the literature at a high level, and also appear to explain various physical phenomena.

So despite the fact that all of these interactions occur on the scale of microns or less, the distance between surfaces, as well as the chemical composition of the surfaces appears to play a role in anticipating which of these forces dominates. What I am currently calling the 'Casimir force' essentially exclusively is due to actions of virtual modes; the van der walls force, I think, involves this also, but also can include other things, and is more dominant at very small distances, like nanometers.

Last edited: Feb 8, 2017
18. Feb 9, 2017

### Demystifier

Wait a couple of days to finish my paper, after which, I hope, no conceptual questions should remain.

19. Feb 9, 2017

### Demystifier

If you know the force $F(y)$, the you also know the energy $E=-\int dy\, F(y)$. The energy density is then just the energy divided by volume (between the plates).

Last edited: Feb 9, 2017
20. Feb 9, 2017

### Demystifier

There is only one effect, which can be described mathematically in two different ways. The vacuum-energy description is technically simpler, but lacks a full microscopic description. In vacuum-energy description for perfect conductors, one assumes that electric field vanishes at the plates, which sets up the boundary conditions. But why does electric field vanish in a perfect conductor? That's because the movable charges in the conductor rearrange themselves, to cancel any external electric field. But rearrangement means that charges are polarized, and polarization of charges gives rise to van der Waals forces. So it is really the van der Waals force that causes boundary conditions. Since boundary conditions cause the Casimir force (for otherwise the vacuum energy is a constant which does not depend on the distance between the plates, in which case it does not give rise to a force), it follows that that van der Walls force causes the Casimir force. Or more schematically,

charge-field interactions -> van der Waals force -> boundary conditions -> Casimir force