Lorentz violation and the physical vacuum....

[asimov42]

Posting as this was buried in another thread - If Lorentz invariance is broken in, e.g., whatever theory of quantum gravity turns out to be correct, what effect would this have (if one can speculate) on the physical vacuum? That is, for two observers, let's say, moving at different, constant velocities (so Unruh effect aside, for now) relative to the 'preferred' frame, would the vacuum 'appear differently'? My naive thought is that there would be some measurable effect on the field modes... does this have any influence on field excitations, or does the vacuum still look empty no matter which may you're going?

 

[PeterDonis]

what effect would this have (if one can speculate)

One can only speculate usefully if one has a particular model in mind. Do you?

 

[Haelfix]

Already in regular semiclassical gravity there are NO local gauge invariant observables, and if you read canonical texts like the ones from DeWitt, you can make the argument that quantum gravity in full generality cannot have such a thing. The only observables you can construct are ones that live at asymptotic infinity (like the Smatrix, or correlation functions in AdS)

But leaving aside General Relativity issues, if you break local Lorentz invariance, you already drastically change the properties of the vacuum. In particular this has observable consequences that are measurable in the lab. The famous text for simple standard model extensions is the following:
arXiv:hep-ph/9812418v3

 

[asimov42]

PeterDonis, very good point - I didn't have a specific model in mind (and you're right, I should have, in order to speculate) - I was wondering if perhaps there were some commonalities to all (existing proposed) theories of quantum gravity, i.e., constraints imposed by what we already know such a theory must contain, that would describe the structure of the physical vacuum.

In a posting from Prof. Neumaier in another thread, he noted that "local Lorentz invariance should not be broken in any consistent theory of quantum gravity." If one has local Lorentz invariance along the entire worldline for a particle (or observer), then isn't it the case that the physical vacuum must contain no physical particles (for that observer)? (otherwise Lorentz invariance would be broken...)

Haelfix may have just answered the above (and thanks for the link!). Also, for now, we do know that at all accessible energy levels probed to date, our data is consistent with the physical vacuum containing no physical particles - is that correct?

 

[PeterDonis]

our data is consistent with the physical vacuum containing no physical particles

The physical vacuum is by definition a state with no "physical particles"--more precisely, it is the ground state (state of lowest energy) of the field. The Unruh effect is a manifestation of the fact that "energy" is not the same for all observers: for observers with constant proper acceleration, "energy" has a different meaning than it does for inertial observers. (In more technical language, observers with constant proper acceleration follow orbits of a different timelike Killing vector field than inertial observers, and the meaning of "energy" is different for different timelike Killing vector fields.)

 

[asimov42]

Thanks PeterDonis - sorry, I should probably have used the term 'vacuum we observe' (although we don't really observe the vacuum since putting anything in it means it's no longer a vacuum of course).

But you've hit on one of the things I was wondering - does Lorentz violation have any effects on inertial observers, in terms of the contents on the vacuum two different inertial observers would 'see'.

 

[bhobba]

For inertial observers Lorentz invariance s NOT broken. For all such observers, via Normal ordering, the vacuum energy is zero. If the vacuum was different for different inertial observers Lorentz invariance would be broken and SR wrong - you would get an instant Nobel prize for proving SR wrong and physics in deep do do.

This is made clear when you see just how important symmetry is to physics:
https://www.amazon.com/dp/3319192000/?tag=pfamazon01-20

It must also be said the modern definition of energy is via Noethers theorem which relies on time translation invariance. This leads to the well known problem of even defining energy in GR and since via the principle of equivalence gravity is equivalent to acceleration (see note at end of post - there are subtleties involved here but it doesn't change the basic argument) defining energy in accelerating frames would seem equally problematical.

The caveat is the principle of equivalence has subtle aspects some textbooks do not discuss. An exception is the following:
https://www.amazon.com/dp/1107012945/?tag=pfamazon01-20

Thanks
Bill

 

[asimov42]

Thanks Bill. This is local Lorentz invariance, correct? But isn't there discussion now of Lorentz violation in, e.g., the Standard Model Extension (SME)? And some possible evidence from neutrino oscillations (although I realize the jury is still out on this)?

Or, is it the case that, even in the SME, Lorentz invariance holds for inertial observers?

 

[bhobba]

But isn't there discussion now of Lorentz violation in, e.g., the Standard Model Extension (SME)?

I don't know of any.

I will say if Lorentz invariance is violated in inertial frames we are in deep - no very deep do do. As the book I linked to on symmetry in physics explains it's one of the bedrocks on which all of physics is built.

To really understand it you need to read the book along with Landau's classic - Mechanics:
https://www.amazon.com/dp/0750628960/?tag=pfamazon01-20

Thanks
Bill

 

[Haelfix]

So I mean, you can trivially write down theories that violate local lorentz invariance. The paper I linked too, writes down 46 independent theories that have the standard model gauge structure, generations, that are CPT even and that are renormalizable. I'm sure more can be written down that relax some of those conditions.

You will find of course that the ensuing theories superficially make sense, but must include enormous finetuning. So for instance the following decay is forbidden in the standard model:
$$\nu _{\mu }\rightarrow \nu_{\mu } +e^{+}+e^{-}$$

You could write down the operators and attach a coupling coefficient to that process, and then ask, with what precision does experiment fix such terms, and what are the strongest constraints? Following their paper, you can find that in some cases they can bound the coefficients to smaller than 10^-23.

There are actually some pretty interesting effects that occur when Lorentz invariance is dropped (even ever so slightly), like vacuum Cerenkov radiation (photons will slow down in certain directions) and things of that nature. Anyway, I encourage people to read the famous paper, it is one of the more elegant papers that I know off in theoretical physics.

 

[asimov42]

Thanks Haelfix - in any of those 46 theories, is it ever the case that the vacuum energy depends on one's direction of motion or velocity relative to the preferred frame? (I'm not sure if this question even makes sense). Bhobba may also want to comment on the above?

 

[Haelfix]

So, that's a bit of a tricky question. In a world without gravity, vacuum energy is not a measurable quantity in standard lorentz invariant local QFT (only changes in energy is measurable).

However when you drop LI, things may change a bit. I *think* the answer to your question is no by assumption, at least in the case of the Coleman-Glashow construction. So for instance one might worry about the Higgs field and its vacuum expectation value, which is everywhere a nonzero positive constant. This of course trivially transforms as a Lorentz scalar and I don't believe they deform that structure in their paper.

Of course if you completely dropped Lorentz invariance and didn't care about following the standard model field content, you could imagine vector fields that carried vacuum expectation values, in which case you would definitely be able to measure that.

Now in general, if you couple things to gravity, everything becomes thornier, and I don't really have a good statement to make about that.

 

[asimov42]

Wow - thanks! I didn't realize that the question would delve so deeply into things! Very interesting - at least, given the constraints already in place on Lorentz invariance, the effects must be small, I would assume? (i.e., if vector fields carrying vacuum expectation values existed, those values must be very tiny, or we would have detected them already).