# Vacuum Fluctuations and a Preferred Frame

1. Oct 22, 2014

### MattRob

So, from what I understand, quantum uncertainty means these vacuum fluctuations occur, and out of them come virtual particle and antiparticle pairs.

How does this not create a preferred frame of reference? A particular particle pair must have a certain amount of energy, and in one frame where they're stationary, the energy will be much smaller than in another frame moving near c with respect to those particles. So how does the velocity of these virtual particles not create a preferred frame of reference?

*They couldn't be random, could they? Because in order for a random spread to be truly random over all frames of reference, it couldn't be randomized velocity, since 0.9c + 0.9c =/= 1.8c, so if it were a random spread of velocities from frame x, then frames near c with respect to x would observe fewer particles at low velocities and more at high velocities, thus selecting frame x as a preferred frame.

Using relativistic kinetic energy as the criteria for the random spread (random energies) could satisfy the requirement that vacuum fluctuations be the same in every frame, but since there's no limit to relativistic kinetic energy, this means the probability a random particle having kinetic energy within E would be something like $\frac{E}{\inf}$ since the range of possible energies is unlimited.

Last edited: Oct 22, 2014
2. Oct 22, 2014

### atyy

Observers moving at constant velocity in the vacuum don't see radiation. Only accelerated observers see radiation, via an effect called the Unruh effect. If there is an accelerated observer, an observer moving at constant velocity may see the accelerated observer to be radiating (not sure, apparently not settled according to http://www.scholarpedia.org/article/Unruh_effect). In any case, the accelerated observer breaks the isotropy of the vacuum, so it doesn't contradict the idea that if there are only observers moving at constant velocity, they will all see the same vacuum.

3. Oct 23, 2014

### bhobba

Actually the situation is a bit subtle.

Vacuum fluctuations, these days, are generally thought to be the result of the perturbation techniques used in Quantum Field Theory (QFT). Perturbation methods are approximation methods. They do not appear if such methods are not used such as lattice field theory.

That said, QFT is a relativistic theory so the vacuum looks the same in all inertial frames - you cant violate the assumptions its based on.

Thanks
Bill

4. Oct 23, 2014

Staff Emeritus
Right, the vacuum is frame invariant, so it looks the same independent of one's velocity.

Also, the question makes a bunch of assumptions about virtual particles that are not so: that they can be counted, that they have a definite energy, etc.

5. Oct 23, 2014

### Staff: Mentor

I think that is the important point. You cannot say "look! There was a virtual particle!" There is no observation you could compare between observers in different reference frames.

6. Oct 23, 2014

### bhobba

That's a VERY important point.

One can never directly observe virtual particles - simply their effects such as the Lamb shift or the screening of charge.

And again I must emphasise the perturbation methods used in QFT are approximation methods - when not done that way and using exact methods on a computer in Lattice Field Theory they never occur. It would seem simply an artefact of the formalism.

Thanks
Bill

Last edited: Oct 24, 2014
7. Oct 26, 2014

### MattRob

How would the Casimr effect not be a solid verification that vacuum fluctuations are a real, physical phenomenon, rather than a mere artifact of formalism? That is, even ignoring other effects such as Lamb shift.

I thought the uncertainty principle ensured that vacuum fluctuations do, in fact, occur. Or perhaps I'm calling it by the wrong name? I'm referring to how space is never truly "empty" because of the uncertainty principle...

Thanks for all the insight so far.

8. Oct 26, 2014

Staff Emeritus
Do you know that it is possible to derive the Casimir Effect without any reference to vacuum fluctuations at all? There is a paper by Jaffe doing exactly this.

9. Oct 26, 2014

### bhobba

There is no experiment ever that observes directly virtual particles - we only observe effects the formalism attributes to them.

When using methods like lattice theory they never even appear.

The quantum uncertainty principle doesn't imply virtual particles. Its simply a statement about the statistical relation of observations of non-commuting observables.

The Wikipedia article gets it right:
http://en.wikipedia.org/wiki/Virtual_particle
'In physics, a virtual particle is a conceptual entity that is found in mathematical calculations about quantum field theory. It refers to mathematical terms that have some appearance of representing particles inside a subatomic process such as a collision. Virtual particles, however, do not appear directly amongst the observable and detectable input and output quantities of those calculations, which refer only to actual, as distinct from virtual, particles.'

Thanks
Bill

10. Oct 27, 2014

### MattRob

But what about the Unruh effect and curved spacetime, where the virtuality of these particles is relative (ie, particles are only virtual in some frames, but are actual particles in others)? If vacuum fluctuations like this don't actually, physically exist, then wouldn't that mean that Hawking Radiation wouldn't happen?

(Important, related discussion here)

11. Oct 27, 2014

### vanhees71

To stress it again: The Casimir effect is about interactions between charges not about vacuum fluctuations. There is no Casimir effect to observe without charges present.

What is done in the most simple derivation, using two metallic plates (a huge number of charged particles!) and considering the problem effectively by treating the plates via boundary conditions for the em. field. Have a look at

R. L. Jaffe, The Casimir Effect and the Quantum Vacuum, Phys.Rev. D 72 (2005) 021301
http://arxiv.org/abs/hep-th/0503158

12. Oct 27, 2014

### MattRob

Very insightful! Not to derail the topic from Hawking Radiation, but does this have implications on the negative energy density in the vacuum in-between the plates, or is that still the same as when derived with the vacuum fluctuation method?

13. Oct 27, 2014

### bhobba

Again none of those things observes virtual particles. Why you think they do has me beat.

When charged particles accelerate photons appear - but again that is not observing virtual particles. And acceleration is not relative - as the reaction force you feel in your car when you do it readily attests to. The Wikipedia article had it right - don't know why you seem to have trouble with it.

Thanks
Bill

Last edited: Oct 27, 2014
14. Oct 27, 2014

### MattRob

Oh no, it's not about frames of reference and attempting to observe virtual particles anymore - at this point I'm just replying to the assertion that virtual particles are non-physical (synonymous to "an artifact of formalism"?). In curved spacetime particles that are virtual in a non-accelerated frame are actual, measurable particles in an accelerated frame. And as I understand it, Hawking Radiation depends on virtual particles being actual physical phenomenon rather than artifacts of formalism, otherwise it wouldn't occur.

15. Oct 27, 2014

### bhobba

Again what don't you get that when non-perturbative methods are used they do not appear, yet the calculations give the same result - well if the limit is taken correctly anyway - sometimes its different. The issue however is difficult and soon gets out of my depth.

At present non perturbative theory does not have the precision of perturbative methods - but that's simply they are computationally more intensive.

If you do a search on this issue there is a bit of stuff about eg:

Thanks
Bill

Last edited: Oct 27, 2014
16. Oct 27, 2014

### atyy

The issue is one of terminology - Unruh radiation and Hawking radiation are predictions of real phenomena (they are predicted to be real, but not confirmed by experiments so far) - but although some people use the term "virtual particles", others find it confusing because "virtual particles" also refers to terms in intermediate steps of a calculation which do not correspond "directly" to what is observed. It is a little bit like saying I have an apple, and virtually I also have 2 half apples - people may object that you don't have two half apples until you cut the apple.

Observers moving at constant speed in the quantum vacuum in flat spacetime will not see any radiation. One has to deviate from "constant speed" or "flat spacetime" or cause some sort of disturbance to see radiation.

In Hawking radiation, spacetime is curved in such a way as to "cut the apple", and produce radiation that you measure.

In Unruh radiation, the acceleration of the observer disturbs the vacuum.

In the Casimir effect, you also disturb the vacuum by putting in the plates.

As for the idea that the uncertainty principle requires virtual particles, this is actually shorthand for saying that in the path integral picture, we must sum over all paths, and not just the classical path. Usually the sum over all paths is hard to calculate, and we develop a perturbation series around the classical path, and the terms in this approximation correspond to virtual particles. But the idea is not so much these calculational difficulties, but the sum over all paths. (I should also mention that the Feynman path integral is also a trick, a very powerful trick, but it cannot stand alone to construct a quantum theory, and we still need the traditional Hilbert space definition.)

Last edited: Oct 27, 2014
17. Oct 27, 2014

### bohm2

You might find this summary in the FAQ useful:
http://www.mat.univie.ac.at/~neum/physfaq/topics/hawking

18. Oct 30, 2014

### Jilang

Are virtual particles a sort of book-keeping device, somewhat like i ?

19. Oct 30, 2014

### bhobba

I wouldn't say that.

I would say they are simply a by-product of the perturbation formalism.

Thanks
Bill

20. Nov 1, 2014

### Creator

So you are saying that zero point energy doesn't exist?