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Are there any physical systems that violate Lorentz invariance?

When I asked this question from an AI bot I got the following reply:

"Yes, there are physical systems in which Lorentz invariance is violated. These include condensed matter systems with background fields, such as those of superconductors and superfluids, and systems involving extra spatial dimensions."

But the Wikipedia article on Modern searches for Lorentz violation says

"No Lorentz violations have been measured thus far, and exceptions in which positive results were reported have been refuted or lack further confirmations."

It appears to me that the two statements disagree with each other. If so, which of them is correct? If they are both correct, how to understand this?

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    $\begingroup$ Both of them. The context is completely different in the two cases. $\endgroup$
    – Prahar
    Commented Jun 8, 2023 at 8:10
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    $\begingroup$ I do not think that PSE is the place for discussing the "goodness" of an AI bot. $\endgroup$
    – Farcher
    Commented Jun 8, 2023 at 8:14
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    $\begingroup$ The Wiki article is about whether Lorentz symmetry is violated at a fundamental level. This is different from the situation that the AI is referring to where the specific background breaks the Lorentz symmetry (akin to spontaneous symmetry breaking). The same comment is also made in Wikipedia. The difference is between whether the theory is Lorentz invariant vs whether the background is Lorentz invariant. Wiki is addressing the first, the AI is addressing the latter. $\endgroup$
    – Prahar
    Commented Jun 8, 2023 at 8:15
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    $\begingroup$ The background fields in those models are hypothetical. Doesn't mean that all background fields are hypothetical. A constant magnetic field breaks Lorentz invariance so any experiment performed in that very physical background will not preserve Lorentz symmetry. $\endgroup$
    – Prahar
    Commented Jun 8, 2023 at 8:44
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    $\begingroup$ If the question is simply "Are there any physical systems that violate Lorentz invariance?", it should be asked as such (and preferably in a more elaborated way). The way it is currently formulated (v1) looks like an inquiry about the validity of Wikipedia and chat bots, which is off-topic here AFAIK. $\endgroup$
    – Stéphane Rollandin
    Commented Jun 8, 2023 at 11:27

2 Answers 2

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Both. Simply put, condensed matter physics works in a non relativistic regime. It violates Lorentz invariance because it's not a relativistic theory. Like Newton's mechanics. Those are low energy limits of fully Lorentz invariant theories, they "break" Lorentz invariance because we humans neglect relativistic effects in our calculations, not because electrons in a crystal violate Lorentz invariance. We simply do not need it in those models and so we neglect the relativistic effects. For search of Lorentz violation it's intended a search for natural phenomena that violates Lorentz invariance at relativistic energies, not models intended to work in a non relativistic regime. Those obviously are not relativistic by definition.

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Don't trust the AI on scientific claims it makes. They are very good at sounding right, but being very wrong. At this point, they're really only useful as teaching tools since if you already know the truth, they can help you develop new ways of explaining it. You can't trust them to tell you the truth on their own though.

There is physics that we do outside of the relativistic picture simply because there wouldn't be any notable corrections made by relativity and it would complicate the math, but that doesn't mean that those systems being described actually violate relativity.

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