Thus spake Dirk Bruere at Neopax <dirk.bruere@gmail.com>
>Charles Francis wrote:
>
>> The singularity at the big bang is indeed a very special state. So
>>too,
>> if there is one, is a big crunch. Indeed it is the state which would
>> dominate the behaviour of everything during the latter part of the
>> universe, creating a law of decreasing, instead of increasing entropy,
>> thereby reversing the arrow of time. Creatures living there would
>> probably have to live their lives backwards (by our measure).
>
>Isn't that rather assuming that entropy is more fundamental than the
>arrow of time? Or that indeed the one *causes* the other? What reasons
>exist for believing this to be the case?
>
Yes. Entropy is the underlying reason for the arrow of time. The
fundamental laws of physics are time symmetrical  more strictly they
are PCT symmetrical. But I don't see the weak interactions coming into
play and directing the arrow of time. We derive the second law using
only statistical mechanics. It states that, given no outside
interference, a special state evolves into a general one whichever
direction you take for positive time. The corollary is that the only way
a special state can arise is through outside interference. This applies
as much to a memory, held as a pattern in the neurons.
Then we can trace entropy decreasing in the negative time direction.
Each time we get back to a special state of minumum entropy we have to
consider outside interference to see how it arose, and go to a larger
system. Ultimately this means we trace things back to the initial
singularity when entropy was minimum. In this case there is no outside
interference required to set up the initial state, but we see the
singularity arises from gravity, the large scale geometry of the
universe.
Regards

Charles Francis
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