But if you throw out causality along with time, it is hard to see how a low-entropy terminal condition and high-entropy initial condition could produce the same pattern of similar and dissimilar regions.
Aren’t you assuming an expanding universe here? Some physicists speculate that if the universe were to contract in a Big Crunch, quantum decoherence would reverse and macroscopic entropy would decrease as highly correlated quantum fluctuations would be erased by destructive interference. The end effect is that the thermodynamic arrow of time is reversed and such a situation becomes indistinguishable from an expanding universe with increasing entropy. I’m not sure if this is a widely accepted view.
But if you throw out causality along with time, it is hard to see how a low-entropy terminal condition and high-entropy initial condition could produce the same pattern of similar and dissimilar regions.
Aren’t you assuming an expanding universe here? Some physicists speculate that if the universe were to contract in a Big Crunch, quantum decoherence would reverse and macroscopic entropy would decrease as highly correlated quantum fluctuations would be erased by destructive interference. The end effect is that the thermodynamic arrow of time is reversed and such a situation becomes indistinguishable from an expanding universe with increasing entropy. I’m not sure if this is a widely accepted view.