Vacuum Fluctuations and a Preferred Frame

[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.

 

[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.

 

[bhobba]

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

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 can't violate the assumptions its based on.

Thanks
Bill

 

[Vanadium 50]

That said, QFT is a relativistic theory so the vacuum looks the same in all inertial frames - you can't violate the assumptions its based on.

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.

 

[mfb]

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.

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.

 

[bhobba]

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.

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

 

[MattRob]

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.

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

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.

 

[Vanadium 50]

How would the Casimr effect not be a solid verification that vacuum fluctuations are a real, physical phenomenon

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.

 

[bhobba]

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...

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

 

[MattRob]

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.

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

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)

 

[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

 

[MattRob]

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

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?

 

[bhobba]

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?

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

 

[MattRob]

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

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.

 

[bhobba]

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"?).

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:
https://www.physicsforums.com/threads/how-is-qed-solved-non-perturbatively-basic-outline.674904/

Thanks
Bill

 

[atyy]

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?

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.)

 

[bohm2]

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.

You might find this summary in the FAQ useful:

Just outside the event horizon there will be virtual pairs of particles, one with negative energy and one with positive energy. The negative particle is in a region which is classically forbidden but it can tunnel through the event horizon to the region inside the black hole where the Killing vector which represents time translations is spacelike. In this region the particle can exist as a real particle with a timelike momentum vector'' But he says at the bottom of the page: ''It should be emphasized that these pictures of the mechanism responsible for the thermal emission and area decrease are heuristic only and should not be taken too literally.'' What happens is that the high energy of the gravitational field of the black hole creates real particle-antiparticle pairs -- that before that event it could be viewed in terms of Feynman diagrams as virtual is completely irrelevant to his argument. One of these real particles is swallowed by the black hole, the other is radiated away. As a result, the black hole loses radiation, hence total energy, and its effective mass decreases because of mass-energy equivalence.

http://arnold-neumaier.at/physfaq/topics/hawking

 

[Jilang]

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

 

[bhobba]

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

I wouldn't say that.

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

Thanks
Bill

 

[Creator]

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.Bill

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

 

[bhobba]

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

No. I am saying the virtual particles that appear in the usual perturbation calculations do not appear in non-perturbation methods.

This leads people to believe they are simply an artefact of the approximation method used, perturbation theory being a method to get better and better approximations, but not giving an exact answer.

In QFT zero point energy is set to zero by what's known as normal ordering:
http://en.wikipedia.org/wiki/Normal_order
'This is particularly useful when defining a quantum mechanical Hamiltonian. If the Hamiltonian of a theory is in normal order then the ground state energy will be zero: ⟨0|H^|0⟩=0.'

Thanks
Bill

 

[anorlunda]

There used to be a highly readable and useful FAQ on virtual particles here on PF, but I can't find it now to provide the link.

 

[mfb]

This leads people to believe they are simply an artefact of the approximation method used, perturbation theory being a method to get better and better approximations, but not giving an exact answer.

To make things worse, it uses a divergent power series (as function of the coupling constant) as approximation. The first few terms are good approximations, but calculating more and more terms would at some point make the approximations worse.

 

[TrickyDicky]

But if vacuum fluctuations are just artifacts of the perturbative formalism, how come they are used to explain the origin of structure in cosmology as per the inflationary theory?
Can an approximation math method originate galaxies?

 

[atyy]

But if vacuum fluctuations are just artifacts of the perturbative formalism, how come they are used to explain the origin of structure in cosmology as per the inflationary theory?
Can an approximation math method originate galaxies?

Here is the celebrated paper by Mukhanov and Chibisov http://arxiv.org/abs/astro-ph/0303077v1 (the original paper starts on p4). Looking at Eq 6 and Eq 8 on p6, it looks like they calculate the average observed fluctuations, so it would not be "virtual particles" in the sense that bhobba or mfb are thinking about, since this is the expectation value of an observable.

Mukhanov and Chibisov do use the term "quantum fluctuations". But in the context of the path integral, "quantum fluctations" would refer to the "sum over all paths", while "virtual particles" would refer to individual terms in the perturbative expansion of the path integral. As a matter of fact, it looks like they canonically quantize, so even "quantum fluctuations" or the "sum over all paths" is a calculational tool. So terminology probably varies. But the upshot is that the final output of their calculation is the average observable fluctuation.

 

[mfb]

But if vacuum fluctuations are just artifacts of the perturbative formalism, how come they are used to explain the origin of structure in cosmology as per the inflationary theory?
Can an approximation math method originate galaxies?

I can use calculus to predict a trajectory of a moving object. That does not mean the symbols I use in the calculation (like "dx") are real physical objects.

 

[bhobba]

But if vacuum fluctuations are just artifacts of the perturbative formalism, how come they are used to explain the origin of structure in cosmology as per the inflationary theory? Can an approximation math method originate galaxies?

Just take a step back for a minute.

We do not observe virtual particles - simply their effects in the standard formalism.

What non pertubative methods suggest, and from what I can gather is generally thought to be true, is they don't actually exist - every observation can be calculated without them.

But as pointed out in a link I gave QED in the usual formalism is not even thought to be mathematically valid - QCD yes - QED is much more problematical:
http://arnold-neumaier.at/physfaq/topics/consistentQED.html

But then again long before it mathematical issues such as the Landau pole rear its ugly head its replaced by the electroweak theory.

Thanks
Bill

 

[TrickyDicky]

I can use calculus to predict a trajectory of a moving object. That does not mean the symbols I use in the calculation (like "dx") are real physical objects.

This is a really strange answer.
Are you saying that an artifact of the perturbation formalism is what forms, say static EM fields according to QED or not?
I never even hinted at trading math symbols for physical objects. I don't even consider quantum fluctuations as objects, I thought you seem to be defending the view that math artifacts are behind physical phenomena like the Lamb shift or beta decay and not merely its calculation which is a purely mathematical process for calculating anything in physics as your calculus trajectory example shows, not only when vacuum fluctuations are involved, and nobody says trajectories are just an artifact of calculus. (Well, except for Zeno in his paradox:p)

 

[mfb]

Are you saying that an artifact of the perturbation formalism is what forms, say static EM fields according to QED or not?

No. Static fields are not particles, neither virtual nor real.

I thought you seem to be defending the view that math artifacts are behind physical phenomena like the Lamb shift or beta decay

The lamb shift is a shift relative to an unphysical value - a value you would get in a universe that is not ours. Our physical theories give "shifts" relative to things that would require different physical laws or constants. That should not be surprising.

 

[TrickyDicky]

No. Static fields are not particles, neither virtual nor real.

I didn't ask if static fields were particles, virtual or not so I take it you mean by this that static fields according to QED are indeed an artifact of perturbation theory when dealing with the empty space between charges.

The lamb shift is a shift relative to an unphysical value - a value you would get in a universe that is not ours. Our physical theories give "shifts" relative to things that would require different physical laws or constants. That should not be surprising.

This remark about the Lamb shift seems really deep but I have not yet been able to settle it. I'll ponder over it some more.

 

[mfb]

I didn't ask if static fields were particles, virtual or not so I take it you mean by this that static fields according to QED are indeed an artifact of perturbation theory when dealing with the empty space between charges.

QED is a field theory. It tells you how fields (including the electromagnetic field) behave. There is nothing wrong with the application of field equations to fields.

 

[TrickyDicky]

Quoting a physics Nobel: we may ask, is there a fatal fault in the structure of field theory? Could it not be that the divergences – apparent symptoms of malignancy – are only spurious byproducts of an invalid expansion in powers of the coupling constant, and that renormalization, which can change no physical implication of the theory, simply rectifies this mathematical error?
This hope disappears on recognizing that the observational basis of quantum electrodynamics is self-contradictory . . . virtual quanta – the dynamical variables in the theory – are treated as free particles, uninfluenced by their coupling to the electromagnetic field, but there is no way to attribute this status to these particles as they can never be observed as such, exactly because their localization with arbitrary precision requires for its realization a coupling with the electromagnetic field, which can attain an arbitrary large magnitude. The divergences, thus, are not a mathematical artifact at all; instead, they deny the very observational basis of the theory!
A convergent theory cannot be formulated consistently within the framework of present spacetime concepts. To limit the magnitude of interactions while retaining the customary coordinate description is contradictory, since no mechanism is provided for precisely localized measurements.​