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As far as I know, the laws of physics are time-reversal invariant, which means there is no preferred direction of time. The arrow of time emerges with entropy which is a property of macrostates, not microstates. So, on a microscopic description of physical reality, why do we say the Big Bang happened first, or that it was the beginning of the Universe, if there is no preferred direction of time? Why can't we equally say the Big Bang happened last?

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    $\begingroup$ The Big Bang was a cosmological event, the largest spatial scale in physics. I don't think it is reasonable to think microscopically about it. $\endgroup$ Oct 6, 2023 at 9:13
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    $\begingroup$ It is not clear what microscopic description may be used for BB however questions seems to be quite good! I believe it is logical paradox described in your question, time is something fairly talled by today physics to thermodynamics, which is certainly not $\endgroup$
    – kakaz
    Oct 6, 2023 at 10:11
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    $\begingroup$ On cosmological scales isn't there a preferred direction of time? (The direction in which the universe is expanding) $\endgroup$
    – Allure
    Oct 6, 2023 at 10:11
  • $\begingroup$ If there is some macroscopic dynamics, then you are not at complete thermodynamic equilibrium. We observe that something is going on at the macro level. Therefore, there was an "initial condition" somewhere in the past. This initial condition was not at equilibrium, otherwise we wouldn't be here. We call this initial condition Big Bang, because (according to present cosmological observations) it seems that it was (from a macroscopic point of view) a sort of explosion/expansion. Related: physics.stackexchange.com/q/205358/226902 physics.stackexchange.com/q/220085/226902 $\endgroup$
    – Quillo
    Oct 6, 2023 at 10:22
  • $\begingroup$ As discussed in a paper ("Big Bounce or Double Bang?") that's freely visible online, the "Big Bounce" model formulated by Nikodem Poplawski implies a prevalent direction of motion (which would be inherited between each "parented" local universe and its "child"), and the astronomer Lior Shamir has found evidence for such a prevalence. However, Poplawski's model relies on Einstein-Cartan Theory (developed by Einstein, in collaboration with the mathematician Cartan, @1929), which (unlike GR) requires a tiny spatial extent (some orders of magnitude greater than the Planck length) for fermions. $\endgroup$
    – Edouard
    Oct 6, 2023 at 10:38

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In CPT-symmetric universe model, universe does not violate CPT symmetry. Instead, at the BigBang pair of universes are born. In one of them time goes forward, while in another - backwards. So, indeed for one of the universes BigBang would be a first event in time arrow, while for another - last event, because it rolls back in time. However, we can't tell these universes apart,- both of them see another counterpart as running backwards in time.

While currently there is no solid evidence of our "sister universe" running backwards in time, some interesting hints may exist. For example, in this Antarctic ANITA experiment, tau neutrinos were detected coming out from Earth. While there exists multiple explanations of this event, one of them (the exotic one) may be that $\nu_\tau$ travels back in time, so in effect we are capturing them from this alternate universe.

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