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ModelOfTheory's profile
Model Of Theory
Model Of Theory
Model Of Theory
@ModelOfTheory

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Model Of Theory

@ModelOfTheory

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Joined July 2016

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    Model Of Theory‏ @ModelOfTheory Jun 18

    Probability cannot be conserved over time, because there is no translation-invariant probability measure on the space of times.

    11:32 PM - 18 Jun 2018
    • 1 Retweet
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    • MYRALIS ⌬ ALZAPHARYX sina motamedi Bryce Weiner davidad  🎇 ejlflop Content of Media
    2 replies 1 retweet 7 likes
      1. Model Of Theory‏ @ModelOfTheory Jun 19

        Is this in conflict with the fact that time evolution is unitary?

        0 replies 0 retweets 0 likes
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      2. Michael Burge‏ @TheMichaelBurge Jun 18
        Replying to @ModelOfTheory

        This is because events become more certain as time passes? A coin flip with a 50% probability of heads becomes closer to 100% or 0% as time progresses.

        1 reply 0 retweets 1 like
      3. Model Of Theory‏ @ModelOfTheory Jun 18
        Replying to @TheMichaelBurge

        No, I mean the probability of it currently being between times t and t+𝛿 cannot be independent of t.

        2 replies 0 retweets 3 likes
      4. Shredder Rawflesh‏ @RadishHarmers Jun 19
        Replying to @ModelOfTheory @TheMichaelBurge

        Of course, what people really mean isn't that the total of P(X = x and Time = t) over all x is preserved/invariant over all times t, but rather, that the total of P(X = x | Time = t) over all x is invariant (indeed, invariantly 1) over all times t, no?

        1 reply 0 retweets 0 likes
      5. Model Of Theory‏ @ModelOfTheory Jun 19
        Replying to @RadishHarmers @TheMichaelBurge

        Sure, but if probability is squared norm in QM, and a time evolution operator changes total probability, wouldn't that be non-unitary? We could still scale the result back to norm 1, and the composition of the operator and the rescaling would be non-linear.

        1 reply 0 retweets 0 likes
      6. Shredder Rawflesh‏ @RadishHarmers Jun 19
        Replying to @ModelOfTheory @TheMichaelBurge

        The unitary time evolution operator is the one which evolves/yields information about P(X = x | T = t). You shouldn't think of it as giving you any information whatsoever about P(T = t); the information it encodes and acts upon is entirely separate from that.

        1 reply 0 retweets 0 likes
      7. Model Of Theory‏ @ModelOfTheory Jun 19
        Replying to @RadishHarmers @TheMichaelBurge

        Yes, but conditioning everything on what time it is strikes me as an odd thing to be happening in fundamental physics.

        1 reply 0 retweets 0 likes
      8. Shredder Rawflesh‏ @RadishHarmers Jun 19
        Replying to @ModelOfTheory @TheMichaelBurge

        It hardly seems like an odd thing for the "time evolution" operator to be doing, though...

        1 reply 0 retweets 0 likes
      9. Shredder Rawflesh‏ @RadishHarmers Jun 19
        Replying to @RadishHarmers @ModelOfTheory @TheMichaelBurge

        That is, it's precisely what it means to be the "time evolution" operator, to be the operator which evolves the probability distribution P_t into the probability distribution P_{t'}.

        1 reply 0 retweets 0 likes
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