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If we believe the spacetime structure(including the limit of speed) could emerge from some vacuum structure(such as string-net condensation),then, is it possible that the speed of mode of excitation in some strange quantum material could be faster than the speed of light in vacuum? Notice, is the speed of light in vacuum not in material. From the view point above, if there is no such material, the fact would look strange. After all, the amount of quantum material is far more than the vacuum that could be seen as a special material if it has some structure.

yalei lu
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  • In what way would the properties of this "strange quantum material" address the usual causality paradoxes? – WillO Jul 02 '19 at 18:18
  • Yeah, the causality paradox should been fixed in some mechanic. However, if we focus on the view point above, it looks strange if no such material. Why is the vacuum so special？ – yalei lu Jul 02 '19 at 18:33
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    "the causality paradox should been fixed in some mechanic" what do you mean? Which mechanic? Most mechanics I know would not have a clue about a causality paradox, the only paradox they deal with is which beer... –  Jul 02 '19 at 19:04
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    Have a look at this paper: Causality and the speed of sound. – A.V.S. Jul 02 '19 at 19:35
  • See https://en.wikipedia.org/wiki/Energy_condition and "Twilight for the energy conditions?," Barcelo and Visser, http://arxiv.org/abs/gr-qc/0205066 –  Jul 03 '19 at 01:31
  • Thanks for your recommended papers – yalei lu Jul 03 '19 at 06:18

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The most common reaction you will find is that the speed of sound has to be below the causality speed-limit $c$ (which is also the speed of light in vacuum). However, in the case of wave motion there are two (or more) different speeds that may be of interest. The two main ones are the phase velocity $\omega/k$ and the group velocity $d\omega/dk$. There is no speed limit on the phase velocity.

I haven't looked into this, but I think it is possible to construct media where the phase velocity of sound would be high, by combining two or more ordinary media. I don't know about group velocity, but in ordinary circumstances a sound wave has a causal influence at the group velocity so this suffices to say it could not exceed $c$.

Andrew Steane
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  • Thanks for your answer. Yeah, i know the difference between phase velocity and group velocity. So i mean the group velocity. In fact, i want to ask why the higher speed-limit can't emerge from the some solid or liquid if the speed-limit can emerge from vacuum. Of course, if always using the Lorentz transformation, then we can't break through the speed of light. However if we start from Galilei symmetry(condensed system)，why the emerging mode should abide by Lorentz symmetry? By the way, is there causality in Galilei symmetry system in which no limit of speed ? – yalei lu Jul 03 '19 at 05:57
  • To be more clear, why the emerging mode should abide by Lorentz symmetry even if the original components should abide by Lorentz symmetry in principle? is there a transmissible constraint from original component to emerging mode? – yalei lu Jul 03 '19 at 06:13
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    I don't know about field theory in general but I have followed the way causality works in QED and I guess it works similarly in other field theories that respect Lorentz covariance. I'm not sure what you mean by starting with Galilei symmetry, since I think all parts of the Standard Model respect Lorentz covariance and indeed this is one of the items we generally impose early on in putting forward ideas for consideration, if a theory is intended to be accurate at all velocities. – Andrew Steane Jul 03 '19 at 07:30
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No. It is not possible.

In the name of the physical constant called the "speed of light in a vacuum", the "in a vacuum" part adds nothing to the conversation and is basically anachronistic (it was named before the photon understanding of light and special relativity were invented).

In the sense used in regard to the speed of light, you statement that:

the amount of quantum material is far more than the vacuum that could be seen as a special material if it has some structure.

suggests a misunderstanding. A "vacuum" in this sense is defined to mean nothing. It isn't a material and it doesn't have structure.

The lack of any linkage between the speed of light and any medium is perhaps best illustrated mathematically by the Lorentz transformation in which the physical constant "c" is used whether the Lorentz transform involves a massless particle or a massive one, and which does not have a factor incorporating any particular medium.

Photons always travel at the speed of light at the fundamental particle scale (as do all fundamental particles with zero "rest mass", i.e. photons, gluons and hypothetically, gravitons).

Light only appears to travel more slowly through a non-vacuum medium because it is getting bounced around on different indirect routes between fundamental particles that make up the medium, and because it is being absorbed and re-emitted (usually) multiple times. What is called the speed of light in a non-vacuum medium is just a phenomenological estimation of the average impact of these factors in a simplified system with so many sub-particles that the law of averages makes the actual result very close to the average result for a system of that type.

When light passes through glass or water, the photon that comes out of the medium at the far end will generally not be the original photon that went in (although this is not really a meaningful distinction, because all photons of the same wave length, helicity, and polarization are identical).

If you are a picture person, the same thing is explained with diagrams, to which I don't have copyright privileges, here. Previous answers at Physics.SE to very similar questions are here.

The tags for this question suggest that you are wondering if quantum entanglement could play a part in a medium that would allow light to traverse it faster than the speed of light, and the answer to that is also no. The process of light passing through a medium is not one in which quantum entanglement is established.

ohwilleke
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  • I think you may have underestimated the level at which the question is being asked. – Andrew Steane Jul 02 '19 at 21:21
  • @AndrewSteane I think that there is a lot of confusion and confused understandings rooted in the question as illustrated by non-standard use of terminology and what looks like some conceptual issues. You covered phase velocity well, but didn't hit the basics and it isn't clear that the basics are understood in statements like "why is the vacuum so special?" Also complicating the matter is that it appears that there may be an ESL issue. – ohwilleke Jul 02 '19 at 22:53
  • I know special relativity and the spacetime language of SR. i also know the definition of vacuum in quantum field theory. That means nothing in there as you say. So i stress the pre-condition is that vacuum has structure(QFT can't answer) before the discussion starts – yalei lu Jul 03 '19 at 06:26