On Fri, Jan 10, 2014 at 2:23 PM, Jesse Mazer <laserma...@gmail.com> wrot


> > In classical physics there is no limit in principle to your knowledge of
> the microstate.
>

Yes, 150 years ago every physicist alive thought that, today we know better.


> > And in quantum physics, there is nothing in principle preventing you
> from determining an exact quantum state for a system; only if you believe
> in some hidden-variables theory
>

And if you believe in some hidden-variable theory, ANY hidden-variable
theory, then you know that if things are realistic AND local then Bell's
inequality can NEVER be violated; and that would be true in every corner of
the multiverse provided that basic logic and arithmetic  is as true there
as here.  But experiment has shown unequivocally that Bell's inequality IS
violated. So you tell me, what conclusions can a logical person can draw
from that?


> > like a theory that says that particles have precise position and
> momentum at all times, even though you can't measure them both
> simultaneously
>

If things have properties, like position and momentum, even if they are not
observed and even if they can't be observed in principle, then that would
be a realistic theory. If such a theory was also local you would know it is
wrong, that is to say it would conflict with the observed facts.


> > Do you think my "Toroidal Game of Life" (a finite grid of cells with the
> edges identified, giving it the topology of a torus) is a mathematically
> well-defined possible universe?
>

 Yes.

 > Do you disagree that starting from a randomly-chosen initial state which
> is likely to have something close to a 50:50 ratio of black to white
> squares, the board is likely to evolve to a state dominated by white
> squares, which would have lower entropy if we define macrostates in terms
> of the black:white ratio?


 You said it yourself, the rules of the Game of Life are NOT reversible,
that means there is more than one way for something to get into a given
state. And the present entropy of a system is defined by Boltzman as the
logarithm of the number of ways the system could have gotten into the state
it's in now, therefore every application of one of the fundamental rules of
physics in the Game of Life universe can only increase entropy.

 > The 2nd law is not restricted to initial conditions of "very low
> entropy", it says that if the entropy is anything lower than the maximum it
> will statistically tend to increase, and if the entropy is at the maximum
> it is statistically more likely to stay at that value than to drop to any
> specific lower value.
>

If the universe started out in a state of maximum entropy then any change
in it, that is to say any application of one of the fundamental laws of
physics will with certainty DECREASE that entropy.  And If the universe
started out in a state of ALMOST maximum entropy then any application of
one of the fundamental laws of physics will PROBABLY decrease that entropy.

> > If the initial conditions deviated from maximum entropy even slightly,
> the second law says that an increase in entropy should be more likely than
> a decrease.
>
That would depend on initial conditions, just how slight the slight
deviation from maximum entropy was.


>  >> Well... you can make a Turing Machine from the Game of Life. And
>> according to the Bekenstein Bound
>>
>
>
 > The Bekenstein Bound is itself just a property of the particular laws of
> physics in our universe,
>

 This must be one of the few places where people talk about things that
"just" apply to our universe.


> > no one claims it would apply to all logically possible mathematical
> universes, so how is it relevant to this discussion about whether the 2nd
> law would apply to all such possible universes?
>

 That wasn't what I was responding to. You said:

"since even though it's possible our universe could be a cellular
automaton, I think we can be pretty confident it's not a 2-dimensional
cellular automaton like the Game of Life!"

 And I gave reasons why I am not "pretty confident"

>> So the rules of the Game of Life apply to some of the cells in the grid
>> but do not apply to others. What rules govern which cells must obey the
>> rules and which cells can ignore the rules, that is to say who is allowed
>> to ignore the laws of physics in that universe?
>>
>
> > No, they apply to all squares in the ideal platonic infinite board whose
> behavior you want to deduce,
>

Then ratios become meaningless.

> but there is no need to actually *simulate* any of the squares outside
> the region containing black squares, because you know by the rules
> governing the ideal platonic infinite board that those squares will stay
> all-white as long as long as they are not neighbors with any black square
>

I think you've got your colors backward because a solid block of active
cells does not stay a solid block. But never mind the point is that the
pattern of active cells is constantly expanding and shrinking in a
unpredictable way (that is to say the only way to know what it will do is
watch it and see). Many Game of Life patterns expand to infinity, so the
shape and size of any closed figure you draw and say you're only going to
count cells inside that figure to obtain a ratio would be entirely
arbitrary.

  John K Clark

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