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There is an extremely exciting footnote/remark from Prof. Frank Wilczek during the subsequent Question and Answer (Q&A) session (starting from 01 h 03 min 42 sec) of his recently held presentation:

Time Crystals: Past, Present, and Future | Prof. Frank Wilczek (08 March 2021)

Prof. Frank Wilczek (starting from 01 h 03 min 42 sec):

Another possibility that is more novel but more speculative is that there may have been in the early universe – all kind of things might have happened in the very early universe, we just don’t know – there might have been a period where you have not smooth evolution but a very rapidly oscillating behavior taking over for a while, so a time crystal in the more usual sense where you have many oscillations. But it is also interesting to speculate that under extreme conditions of a curvature so at the center of a black hole for instance as well as in the early universe you might have new phases of space-time that are crystalline in some sense. Because you are talking about space-time it would be very unnatural to just have crystals that are not also time crystals. So I think there is a small literature but it is an interesting possibility to consider time crystallization of space-time itself and possible application areas would be black holes and the early universe.

So the question here is: Are there any recent experimental results or literature from a reputable source to back up Prof. Frank Wilczek’s novel hypothesis of time crystallization of space-time itself in the very early universe or should it be treated at this time just as an interesting but speculative footnote?

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    $\begingroup$ Without a definition of "space-time crystal" there is not much we can say. $\endgroup$
    – Rexcirus
    Jul 31 at 20:13
  • $\begingroup$ Time crystals are classified as discrete or continuous depending on whether they spontaneously break discrete or continuous time translation symmetry. Researchers from the Institute of Laser Physics at the university of Hamburg have now succeeded for the first time in realizing a time crystal that spontaneously breaks continuous time translation symmetry as published online in Science on 9 June, 2022. The objective here is to learn more on the possible involvement of time crystals classified as continuous in the early universe. $\endgroup$
    – UN73
    Aug 2 at 15:39
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    $\begingroup$ That part is fine, but the speculation about "new phases of space-time that are crystalline" is poorly defined. Are crystal defined w.r.t a higher dimensional space? Otherwise how do we define periodicity in space or time for the space-time itself? $\endgroup$
    – Rexcirus
    Aug 3 at 12:24
  • $\begingroup$ Just to let you know that I have read your comment (Thanks!). I will think about it (maybe with some friends) and will come back to you... $\endgroup$
    – UN73
    Aug 3 at 16:32
  • $\begingroup$ Time crystals are not defined with respect to a higher dimensional space but defined according to the rules of quantum mechanics (and may potentially act as bridge between classical and quantum mechanics). $\endgroup$
    – UN73
    Aug 4 at 7:35

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