Could the Lorentz symmetry be theoretically broken in vacuum?

[Suekdccia]

TL;DR Summary

Could the Lorentz symmetry be theoretically broken in vacuum?

In this paper [1] which considers the possibility that the Lorentz symmetry could be broken, at page 4-5 the author says:

"We now introduce a Higgs sector into the Lagrangian density such that the gravitational vacuum symmetry, which we set equal to the Lagrangian symmetry at low temperatures, will break to a smaller symmetry at high temperature. The pattern of vacuum phase transition that emerges contains a symmetry anti-restoration5. This vacuum symmetry breaking leads to the interesting possibility that exact zero temperature conservation laws e.g. electric charge and baryon number are broken in the early Universe. In our case, we shall find that the spontaneous breaking of the Lorentz symmetry of the vacuum leads to a spontaneous violation of the exact, zero temperature conservation of energy."

I have three questions:

1. Does this mean that there could be certain vacua where the Lorentz symmetry (and other symmetries) would be broken?
2. Does this mean that there could be a vacuum phase transition (a vacuum decay process) where the new vacuum would violate Lorentz symmetry (and other symmetries like time translational symmetry, leading to the violation of the conservation of energy as the author says)? Could there be a vacuum phase transition to another vacuum that would not have any symmetries at all?
3. If there could be such vacua, are they mentioned or used in any theory? Would the reference #5 in the article be examples of models/theories that would allow such vacua?

[1]: https://arxiv.org/pdf/gr-qc/9312017.pdf

 

[Fractal matter]

I hope, i can be of some help.
As far as i am aware, condensate, posessing Lorentz invariance in the ground state, can be thought of as a pseudovacuum. In that case the anwers would be :
1) Yes.
2) Yes. I don't know if the violation of the energy conservation can take place.
3) "It is proposed that the event horizon of a black hole is a quantum phase transition of the vacuum of space-time analogous to the liquid-vapor critical point of a bose fluid." "Quantum Phase Transitions and the Breakdown of Classical General Relativity" arXiv:gr-qc/0012094

I believe, all of the above is applicable to the quantum vacuum.

 

[Suekdccia]

I hope, i can be of some help.
As far as i am aware, condensate, posessing Lorentz invariance in the ground state, can be thought of as a pseudovacuum. In that case the anwers would be :
1) Yes.
2) Yes. I don't know if the violation of the energy conservation can take place.
3) "It is proposed that the event horizon of a black hole is a quantum phase transition of the vacuum of space-time analogous to the liquid-vapor critical point of a bose fluid." "Quantum Phase Transitions and the Breakdown of Classical General Relativity" arXiv:gr-qc/0012094

I believe, all of the above is applicable to the quantum vacuum.

What do you mean with "I don't know if the violation of the energy conservation can take place"? I mean, in the article I cited, the author proposes a violation of energy conservation

 

[ohwilleke]

Summary: Could the Lorentz symmetry be theoretically broken in vacuum?

In this paper [1] which considers the possibility that the Lorentz symmetry could be broken, at page 4-5 the author says:

"We now introduce a Higgs sector into the Lagrangian density such that the gravitational vacuum symmetry, which we set equal to the Lagrangian symmetry at low temperatures, will break to a smaller symmetry at high temperature. The pattern of vacuum phase transition that emerges contains a symmetry anti-restoration5. This vacuum symmetry breaking leads to the interesting possibility that exact zero temperature conservation laws e.g. electric charge and baryon number are broken in the early Universe. In our case, we shall find that the spontaneous breaking of the Lorentz symmetry of the vacuum leads to a spontaneous violation of the exact, zero temperature conservation of energy."

I have three questions:

1. Does this mean that there could be certain vacua where the Lorentz symmetry (and other symmetries) would be broken?
2. Does this mean that there could be a vacuum phase transition (a vacuum decay process) where the new vacuum would violate Lorentz symmetry (and other symmetries like time translational symmetry, leading to the violation of the conservation of energy as the author says)? Could there be a vacuum phase transition to another vacuum that would not have any symmetries at all?
3. If there could be such vacua, are they mentioned or used in any theory? Would the reference #5 in the article be examples of models/theories that would allow such vacua?

[1]: https://arxiv.org/pdf/gr-qc/9312017.pdf

The full abstract states:

A possible resolution of the information loss paradox for black holes is proposed in which a phase transition occurs when the temperature of an evaporating black hole equals a critical value, Tc, and Lorentz invariance and diffeomorphism invariance are spontaneously broken. This allows a generalization of Schr¨odinger’s equation for the quantum mechanical density matrix, such that a pure state can evolve into a mixed state, because in the symmetry broken phase the conservation of energy-momentum is spontaneously violated. TCP invariance is also spontaneously broken together with time reversal invariance, allowing the existence of white holes, which are black holes moving backwards in time. Domain walls would form which separate the black holes and white holes (anti-black holes) in the broken symmetry regime, and the system could evolve into equilibrium producing a balance of information loss and gain.

A violation of Lorentz symmetry is another way of saying that classical special relativity fails to apply to a system.

This paper assumes not the core theory of general relativity, special relativity and the Standard Model, but a particular version of a quantum gravity theory that is different from GR and special relativity with a BSM Higgs sector.

Of course, if you are modifying the laws of physics at all, one of the laws you can modify is the Lorentz symmetry, and indeed, you can violate any or all of them if you want to, even though this will leave you with a theory that is definitely inconsistent with our Universe and which is "not even wrong" with respect to unobservable hypothetical other Universes that might exist.

Determining the a quantum gravity theory could violate Lorentz symmetry is a bit of a double edge sword.

On one hand, the observational constraints on Lorentz symmetry violation a very strict, so if you assume that a Lorentz symmetry violation is possible in your quantum gravity theory, you will simultaneously rule out the correctness of your theory in our Universe unless you also have a mechanism in your theory to make those violations very slight in the kind of circumstances in which Lorentz symmetry violations have been tested (which are quite extreme in certain parts of the parameter space, because Lorentz symmetry comes into play in every particle accelerator interaction).

This goes double for a theory that also proposes violations of baryon number conservation, electric charge conservation, mass-energy conservation, and CPT invariance, each of which imposes additional extremely strict experimental and observational bounds on violations that still hold in the very highest energy environments we have been able to observe.

Proposing a violation of all of these bedrock well established laws of physics is a pretty big ask for the purpose of simply solving the "information paradox" in black holes, which have multiple, far less ambitious proposed resolutions, particularly because, unlike all of the conservation laws and symmetries this solution proposes to break to solve the paradox, the conservative of information hypothesis that gives rise to the information paradox is itself only a conjecture.

A potential to violate Lorentz symmetry is one of the things that has disfavored many variations on the loop quantum gravity approach to quantum gravity, suggesting that a simple naive discrete distance scale is problematic.

On the other hand, it isn't outrageous to imagine that a quantum gravity theory could violate Lorentz symmetry in some way that cancels out statistically very rapidly because in any quantum mechanical propagator function you need to consider paths in a path integral for massless particles like photons which are both faster and slower than the speed of light in a vacuum "c", to correctly calculate the probability that a particular photon ends up in a particular place, even though the probability of this actually happening is either zero or vanishingly small such that it would never be observed in real life.