On 3/20/2014 9:10 AM, John Clark wrote:
WHY?? How would it change anything about how we imagine the world works? Regardless of
what English word you call it if X is proportional to the logarithm of the number of
microstates something can be in and still have the same macrostate then X is also
proportional to the logarithm of the number of ways the thing could have been produced
and still have the same macrostate. AND if X is proportional to the logarithm of the
number of ways the thing could have been produced and still have the same macrostate
then X is also proportional to the logarithm of the number of microstates something can
be in and still have the same macrostate.
...
>> why in hell do you say Entropy is proportional to the logarithm of
the number
of microstates something can be in and still have the same macrostate,
but it
is not proportional to the logarithm of the number of ways the thing
could have
been produced?
> Because it's logically possible to have laws where, unlike in unitary QM,
it's NOT
true that two notions are equivalent--this would be true if information is
genuinely
lost when a black hole swallows up matter and later evaporates.
If Physics is not unitary then the old definition of Entropy becomes meaningless with
regard to Black Holes because it would contain no microstates you could take a logarithm
of, but it would still be true that the Entropy of a Black Hole is proportional to the
logarithm of the ways it could have been formed.
Among the ways a black hole could be formed are the different order in which things fall
in. As an object falls in it will in theory cause a temporary disturbance of the black
hole which is damped out by gravitational radiation (plus EM if it's charged) so the BH
returns to the macrostate defined by mass, charge, and angular momentum. But the BH
doesn't retain the information about when this happened. That information is in the
radiation. So although the overall physics is reversible it doesn't follow that the BH
contains all the information necessary for the reversal.
Brent
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