## The "Vacuum Energy" is fictitious.

I have bad news for the nice folks who thought that by clapping our hands together we could have free energy from the vacuum. The vacuum energy is an artifact of the way the Casimir Effect is described.

Here are three websites that have good descriptions of the effect.

http://physicsweb.org/article/world/15/9/6

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

They describe an attractive force between two perfectly reflective plates that goes as:

F=pi2h-bar*CA/240r4

where A is the area and r is the separation between the plates.

The problem with assuming that the energy involved is "in the vacuum" is that it completely omits the question of the energy used to make the surfaces of the plates. Note that while the force varies as the inverse fourth power, the energy varies as the inverse third power. So we should think of the energy as asociated with a field of virtual photons emanating from the surface of the plates, and the Casimir Effect as being due to a kind of distance dependent surface tension, whereas ordinary surface tension, whch has the dimensions of energy divided by area, is independent of distance.
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 Originally posted by Tyger The vacuum energy is an artifact of the way the Casimir Effect is described.
Just to be sure, it's your understanding that vacuum energy doesn't exist. Correct? If so, where'd you get this from?

 Originally posted by jeff Just to be sure, it's your understanding that vacuum energy doesn't exist. Correct? If so, where'd you get this from?
From the realization that the people who described the experiment had failed to take into account the possibility that the putative "vacuum energy" may actually have been expended in making the surface of the plates. When you consider that the force and energy go as r&minus;4 and r&minus;3 respectively, that pretty much clinches the notion that the energy belongs to the plates and not the vacuum.

Alas, the fuzzy thinking of the people describing the experiment has fed the fuzzy thinking of the people who want to get free energy out of the vacuum!

## The "Vacuum Energy" is fictitious.

The Casimir Effect is indeed a result of vacuum energy. It is, to put it more correctly, a result of virtual particles/waves. By the laws of quantum mechanics, waves must be quantisized, and between two plates (non-conducting I note), only certain wavelenghts are allowed between them. Outside the plates, there are infinitely more virtual ones allowed. Hence you get a virtual energy density difference. Result: The plates are pushed (or pulled) together. Nothing coming from the plates themselves.

As for the powers of the various items in the equation, the dimensions still come out correct, and it would make sense considering a normal inverse square drop off of force combined with the fact it is a force related purely to surface area.

Side: Yes, it is a symmetric force, hence you can't get energy from it to power things.

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 When you consider that the force and energy go as r?4 and r?3 respectively, that pretty much clinches the notion that the energy belongs to the plates and not the vacuum.
I'm sorry, I don't see why that would follow.
 or otherwise demonstrate that there is such a thing as vacuum energy you will need something besides the Casimir Effect to do it. The concept isn't neccessary to describe the CE. All that is neccessary is that we introduce the idea that it takes a certain amount of energy per unit area to form the surface, over and above the normal surface tension, and this energy is associated with a field which is distance dependent. There's a pretty simple test which can be applied to anything electromagnetic, and that is scale invariance. Which interpretation (and that is what we're talking about here) is scale invariant.

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 Originally posted by Tyger From the realization that the people who described the experiment had failed to take into account the possibility that the putative "vacuum energy" may actually have been expended in making the surface of the plates....
So this is your invention. Correct?
 if it's correct that The "Vacuum Energy" is fictitious than there should be modification to theories such as string theory loop quantum gravity wont it?

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 Originally posted by Tyger or otherwise demonstrate that there is such a thing as vacuum energy you will need something besides the Casimir Effect to do it. The concept isn't neccessary to describe the CE.
True, vacuum energy is not the only possible explanation for the Effect. However, the CE was predicted as a result of vacuum energy. The agreement between prediction and observation is a very strong argument for the correctness of a theory. It is, in fact, the only test of correctness or incorrectness the scientific comunity can accept.

 Originally posted by jeff So this is your invention. Correct?
You got it. Be back in a while with more on the subject.
 on a web search a few minutes ago. http://www.sciam.com/askexpert_quest...88F2D7&catID=3 http://alsystems.algroup.co.uk/casimir/VED2.html http://www.xs4all.nl/~mke/vacuum.htm On the SciAm page I especially liked the comments of John Baez which are pretty much the way I see it, that at least for the CE they are an artifact of our bookkeeping. The second page is an interesting but not very convincing derivation of the idea that the VE doesn't really belong to the vacuum at all. I'm afraid he really lost me on the "space curvature" part. The third page is one of the kookier pages on the subject I ran across. Consideraring that cosmic rays millions of times more energetic than anything the particle accelerators put out srike the Earth every day I think we're safe. So the basic idea I have is that the putative VE is really just energy associated with a kind of surface tension, perhaps the ordinary surface tension, or the material work function, and is not associated with any ambient vacuum energy. If anyone knows of any convincing paper on the subject I would appreciate knowing about it.

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 Originally posted by Tyger on a web search a few minutes ago. http://www.sciam.com/askexpert_quest...88F2D7&catID=3 .... On the SciAm page I especially liked the comments of John Baez which are pretty much the way I see it, that at least for the CE they are an artifact of our bookkeeping. ....
BTW Rutwig posted this in another thread discussing Casimir Effect. It is the 1996 experimental report of measuring the effect:

 Originally posted by rutwig You can find the announcement of the first measure in here: http://www.aip.org/enews/physnews/19...t/pnu300-3.htm

Since your view is close to those expressed by Baez, as a convenience, here are Baez comments on the SciAm board:

<<John Baez is a member of the mathematics faculty at the University of California at Riverside and one of the moderators of the on-line sci.physics.research newsgroup. He adds some context:

"The concept of vacuum energy shows up in certain computations in quantum field theory, which is the tool we use to conduct modern particle physics. In reality, particles interact with one another through a variety of forces. This is a complicated business, so in quantum-field theory we start by studying an idealized model in which particles do not interact at all. This is called a 'free-field theory.' Then we use this free-field theory as the basis for studying the 'interacting-field theory' we are really interested in.

"In quantum-field theory, the vacuum state is defined to be the state having the least energy density. Something funny happens when we use a free-field theory to study an interacting-field theory: the vacuum state of the free-field theory is different from vacuum state of the interacting-field theory. The vacuum state of the interacting-field theory may have more or less energy than that of the free-field theory; the difference is called the vacuum energy.

"One should not take this vacuum energy too literally, however, because the free-field theory is just a mathematical tool to help us understand what we are really interested in: the interacting theory. Only the interacting theory is supposed to correspond directly to reality. Because the vacuum state of the interacting theory is the state of least energy in reality, there is no way to extract the vacuum energy and use it for anything.

"It is a bit like this: say a bank found it more convenient (for some strange reason) to start counting at 1,000, so that even when you had no money in the bank, your account read $1,000. You might get excited and try to spend this$1,000, but the bank would say, 'Sorry, that \$1,000 is just an artifact of how we do our bookkeeping: you're actually flat broke.'

"Similarly, one should not get one's hope up when people talk about vacuum energy. It is just how we do our bookkeeping in quantum field theory. There is much more to say about why we do our bookkeeping this funny way, but I will stop here." >>

Tyger, I noticed at the beginning of the thread that you have a link to
the Usenet FAQ explanation of the Casimir Effect----your first link is to a Physics FAQ mirror site in IIRC Australia.
The same explanation of the CE is at the John Baez site.

this explanation does not depend on the actual position of the zero (energy zeros are often just a bookkeeping point of reference and what matters are the differenences, as you know well)

the explanatation, which you posted at the start, does not depend on saying there is some amount of energy density in the vacuum. it depends on saying that this VARIES depending on how far the conducting plates are apart.
(i.e. with whatever zero in whatever theoretical framework in whatever units, the energy density varies as IIRC the inverse fouth power of separation)

this IIRC is what an experimental test should show is true or not true

in principle, I think, this fourthpower variation can be proven true or false experimentally even if the energy scale is adjusted so that the energy in the generic vacuum is zero (the position of the
zero does not seem to matter). My guess is that this is obvious to you and that I am just making it explicit.

I take no position on this. Rutwig posted a link to the 1996 experiment by someone at Los Alamos. It dont know how solid this experiment was or to what extent it verified the fourth power
dependence on the distance. I thought it was an odd detail
that in the actual experiment he used a gold sphere---it was
not two parallel plates after all.
 Recognitions: Science Advisor Writing the ground or vacuum state of a quantum system as |0>, we can calculate the VEV (vacuum expectation value) <0|H|0> of the hamiltonian. This is just the ground state energy of the system. However, although the vacuum is a writhing ocean of quantum fluctuations, because we are generally interested only in energies relative to the vacuum, we conventionally perform a "subtraction" in the hamiltonian by setting <0|H|0> = 0. However, we can detect the vacuum by inducing a shift Δε in it's energy through the introduction of a source and sink where particles would be created and annihilated with the interceding propagation of particles between source and sink creating a force between them. Although the VEV of the energy is not observable, the force resulting from it's shift created by disturbing the vacuum in this way is. In the Casimir effect the source and sink are thin parallel conducting plates with the Casimir force between them given roughly by Δε/d where d is the separation between the plates.
 Recognitions: Gold Member Science Advisor Tyger, do you happen to know if Lamoureux or whoever measured the force in 1996 actually found a recipr. fourthpower dependence on the separation? that would be evidence of the same recipr. fourthpower dependence of the energy density----wouldnt clinch it but would fit the common picture people have if he just found some attractive force at some distance and then did not vary the distance it wouldnt seem to be very meaningful also, any idea why he used a gold sphere and a plate, instead of the two plates that people frequently think of as schematic for the Casimir effect?
 that the real cognizenti already realize that vacuum energy is fictitious, that it's a sort of "urban myth" in physics. I'm going to make some general comments, mostly relating to Marcus's and Jeff's posts. I really liked Baez' description, something meaningful to a physicist and the man in the street. Now energy is both conserved and localizable (conservation at all vertexes, etc.), so this phony bookkeeping will eventually catch up with you. In this case there really is energy in the vacuum, but it is associated with virtual photons from the plates, not ambient vacuum energy. What's more, to stretch the plates out, increase their area, you would have to do work, so indeed it does represent a surface tension. Whether it repressents all the plates surface tension is a very good question. After all, if you let the plates come together, all that energy will disappear and their area will be halved. You may remember that I used the surface tension of the electron gas to explain why metals were strong in the physics puzzle. Everything fits together in one way or another. The fellow used a sphere because a thin plate tends to warp and throw off the measurements. And yes, the fourth power law held. This is something Jeff should be interested in, which is the best way to look at electromagnetism/electrodynamics. People often say that the photon has rest mass zero but this is somewhat misleading. In reality the photon can have any rest mass squared from minus to plus a very large value. Till the point where it merges with the weak interaction, to be precise. This leads to a very simple but important fact, the electromagnetic interaction is scale invariant, par excellence. You can deduce many things from this scale invariance, from the law of black body radiation to atomic radiation moments. You can use it to check your equations, in much the same way people use dimensional analysis, before you begin to make you calculations. If scale invariance applys in a situation, you know it is electromagnetic, if it doesn't apply, then something is involved too, or else. None of the other interaction are fully scale invariant.

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