Lorentz violation, multiple preferred frames, vacuum energy

[asimov42]

Hi all - hope I'm not beating a dead horse here, but I'm following up on at least two other threads (made sense to consolidate):

There are theories of quantum gravity (or the Standard Model Extension) that allow for local Lorentz violation. So, my first question: is there any reason why there has to be one preferred frame (across the whole universe). Could there not be multiple preferred frames, if, e.g., the values of fundamental 'constants' changed in both space and time?

My second question follows from another thread in which I asked whether, in a universe where Lorentz symmetry is broken, one would expect to see different vacuum energies when moving in different directions. The relevant thread is here:

https://www.physicsforums.com/threads/lorentz-violation-and-the-physical-vacuum.900243/

Now, if one did see different vacuum energies (non-zero vacuum expectation values), one would expect to see particles when moving in certain directions, while not in others, no? Haelfix kindly commented on this:

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.

I'm wondering if anyone has any input on this? Final question: given the constraints on Lorentz violation established so far, it must the be case that, were it true that differences in vacuum energy existed, these differences must be very small or they would have been detected in laboratory experiments (i.e., I should not expect that, by moving in a certain direction, I run into a bunch of electrons or protons, etc.).

Thanks all - sorry for the lengthy post. It seems the more you dig, the more interesting things become.

 

[asimov42]

Or perhaps just the first question, if there's no clear answer to the second?

 

[PeterDonis]

There are theories of quantum gravity (or the Standard Model Extension) that allow for local Lorentz violation.

Can you give some specific references? The answer to your question will depend on which specific theory you want to ask about.

I'm wondering if anyone has any input on this?

If they do, they can give it in the other thread.

given the constraints on Lorentz violation established so far, it must the be case that, were it true that differences in vacuum energy existed, these differences must be very small or they would have been detected in laboratory experiments (i.e., I should not expect that, by moving in a certain direction, I run into a bunch of electrons or protons, etc.).

Yes, this is correct.

 

[asimov42]

Thanks PeterDonis - let me find a couple of candidate theories to ask about.

Regarding the last response - from current constraints on Lorentz possible violation, if vacuum energy did have a directional component, would it be possible to place a bound on the magnitude of that component? In turn, based on the (directional) vacuum expectation value, could one then estimate the expected number of low energy photons, electrons, etc. encountered when moving in that direction (per unit time)? (which might inform how long a laboratory experiment would have to make observations in order to identify the directional component)

 

[PeterDonis]

from current constraints on Lorentz possible violation, if vacuum energy did have a directional component, would it be possible to place a bound on the magnitude of that component?

I'm not sure how one would do this; I haven't seen this question treated in any discussion of Lorentz violations.

 

[asimov42]

I wonder if Prof. Neumaier might have any thoughts? It seems like this would be one question to ask, so given that PeterDonis hasn't seen this in any discussion of Lorentz violation, perhaps there's a reason why the vacuum energy must be the same in all directions.

 

[asimov42]

Resurrecting this thread after a long time as another question came up that I was wondering about. I'm probably not going to pose it well, but here's a shot:

If Lorentz invariance is violated in some way in quantum gravity, giving a preferred frame, and I carry out the standard perturbative expansion of QFT, are there terms that don't cancel? I'm sure it depends on the exact model and maybe nothing can be said...

In another thread I gave the example of a single electron sitting alone in the vacuum, and @PeterDonis pointed out that QED gives an answer (the electron simply continues to be an electron with probability one), and that including 'virtual particles' in the analysis has no effect (the amplitudes for the virtual particles cancel). Is this still true if a preferred frame is introduced?

 

[PeterDonis]

I'm sure it depends on the exact model and maybe nothing can be said...

Yes.

Is this still true if a preferred frame is introduced?

I have no idea without some specific preferred frame theory to use to make predictions.

 

[asimov42]

Perhaps picking one from here: https://arxiv.org/abs/hep-ph/9812418

I don't have a good example in mind, except to ask if there is some theory in which the perturbative expansion changes... (or whether there's a reason why it cannot).

 

[PeterDonis]

I don't have a good example in mind, except to ask if there is some theory in which the perturbative expansion changes...

Mathematically, I expect you could always concoct some theory that has some particular property. Whether that theory would make sense or make reasonable predictions is another matter.

 

[PeterDonis]

Perhaps picking one from here

None of those appear to involve electrons decaying into other particles spontaneously, so no, they would not change what I said about an electron sitting alone in vacuum.

 

[asimov42]

Mathematically, I expect you could always concoct some theory that has some particular property. Whether that theory would make sense or make reasonable predictions is another matter.

Right - I'm actually wondering specifically about a preferred frame in the vacuum, and whether there's a situation where including the virtual particle contributions from the vacuum leads a different result in, e.g., a scattering experiment or similar.

 

[asimov42]

Right - I'm actually wondering specifically about a preferred frame in the vacuum, and whether there's a situation where including the virtual particle contributions from the vacuum leads a different result in, e.g., a scattering experiment or similar.

Where perhaps I should have referred to "content" of the vacuum rather than virtual particle contributions of the vacuum state.

 

[PeterDonis]

perhaps I should have referred to "content" of the vacuum rather than virtual particle contributions of the vacuum state.

The vacuum has no "content"; that's why it's called the vacuum.

 

[asimov42]

The vacuum has no "content"; that's why it's called the vacuum.

Thanks @PeterDonis - understood that we have an isotropic and 'empty' vacuum. Now if I introduce a preferred frame, braking Lorentz invariance, don't I necessarily change the vacuum such that this preferred frame can be identified? (i.e., something has to change w.r.t. particle interaction(s) - I think @vanhees71 had previously said that a physical electron cannot interact with the physical vacuum... doesn't this change in a non-isotropic or anisotropic vacuum?)

 

[PeterDonis]

if I introduce a preferred frame, braking Lorentz invariance, don't I necessarily change the vacuum such that this preferred frame can be identified?

Again, this is going to depend on the specific theory being proposed. As far as evidence goes, we have no evidence whatever that there is any preferred frame.

a physical electron cannot interact with the physical vacuum

Nothing can "interact" with the physical vacuum since there is nothing to interact with.

doesn't this change in a non-isotropic or anisotropic vacuum?

Once more, this is going to depend on the specific theory being proposed. As far as evidence goes, we have no evidence whatever for any non-isotropy to the vacuum.

Also consider that, if we were to discover some kind of non-isotropic property in what looked like vacuum, our first hypothesis to consider would probably not be "there must be some kind of non-isotropy to the vacuum, possibly due to a preferred frame", but rather "there must be something here that makes this region that looks like vacuum, not actually vacuum". In other words, we'd start looking for some new kind of field in that region that was not in its vacuum state.

 

[Elias1960]

If one wants to quantize gravity and, given the situation with quantum nonlocality, wants to use a preferred frame, the first question is, of course, how to incorporate the preferred frame into GR. I would think there are two possibilities, either the preferred frame is local, or it is global.

An example of a local preferred frame is Jacobson's Einstein Aether.

Jacobson, T., Mattingly, D. (2001). Gravity with a dynamical preferred frame, Phys.Rev.D 64:024028, arxiv:gr-qc_0007031

Eling, C., Jacobson, T., Mattingly, D. (2004). Einstein-Aether Theory, arXiv:gr-qc:0410001

An example of a global preferred frame is Schmelzer's General Lorentz Ether.

Schmelzer, I. (2012). A Generalization of the Lorentz Ether to Gravity with General-Relativistic Limit, Advances in Applied Clifford Algebras 22, 1, 203-242

The problem would be how to continue with quantization. Once we have a Newtonian background of absolute space and time filled with some condensed matter named "ether", as in Schmelzer's approach, one could follow standard quantization of condensed matter theory. The result would be something similar to the quantization of GR in the field-theoretic version, which has also a common background of spacetime, as an effective field theory:

Donoghue, J.F. (1994). General relativity as an effective field theory: The leading quantum corrections. Phys Rev D 50(6), 3874-3888
Anber, M.M., Donoghue, J.F. (2012). Running of the gravitational constant. Phys Rev D 85, 104016

Instead, in Jacobson's local variant, you have a covariant theory, with all the conceptual problems of quantization of such a theory. Think about superpositions of two such fields. Without a rigid background, the preferred frames of both would be locally different. What would be, then, the preferred frame of the superposition?