On 8/22/2014 7:17 AM, John Clark wrote:
On Thu, Aug 21, 2014 at 7:19 PM, LizR <lizj...@gmail.com
<mailto:lizj...@gmail.com>> wrote:
>> Yes but it's not always obvious what is physically possible and what
is not.
Is it physically possible that Germany could have won the second world
war? Yes.
Is it physically possible that 2+2=5 ? No. Is it physically possible
that the
second law of thermodynamics is wrong? No. Is it physically possible
that the
first law of thermodynamics is wrong? I don't know.
> So it isn't obvious. (The second law can be wrong for arbitrary amounts
of time,
actually.)
The second law is not wrong about that because the second law says nothing about what
entropy might do over arbitrarily short amounts of time, it only speaks about what
entropy is certain to do as time approaches infinity.
The second law is only approximately true for finite systems (in either time or space).
Globally it's a tautology: the arrow-of-physical-time points in the direction of
increasing entropy, whichever way you chose coordinate time.
The second law is wrong in the same universe that 2 +2 =5, that is to say the same
universe where logic does not hold. I do not think such a universe exists.
Perhaps the first law is just as fundamental as the second, perhaps not. Right now we
believe in the first law not because it would be illogical to believe otherwise but just
because so far we've never seen mass-energy created or destroyed. I doubt it but it's
not inconceivable that tomorrow we will, but it is inconceivable that tomorrow 2+2 will
be 5 or that the second law is wrong.
In a general relativistic universe that's expanding there's no time-like Killing field and
so there's no canonical way to define total energy. GR conserves stress-energy locally
but in general the total is undefined. John Baez has a nice discussion of the problem.
Brent
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