Probability cannot be conserved over time, because there is no translation-invariant probability measure on the space of times.
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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.
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Replying to @TheMichaelBurge
No, I mean the probability of it currently being between times t and t+𝛿 cannot be independent of t.
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Replying to @ModelOfTheory
Probabilities depend on what is currently "known". With the null context where nothing is known, surely every time is equally as likely as every other time? Or in a cyclic universe that repeats the "big bang", observable facts are relative time while t is absolute.
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But each time being equally likely is impossible, for the reason I mentioned. Also, the Born rule suggests that there may be an ontologically significant probability distribution over states of the universe. We probably do not live in a cyclic universe, since entropy increases.
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