On Sun, Jan 12, 2014 at 1:22 PM, Jesse Mazer <laserma...@gmail.com> wrote:
> We know better than to think classical physics represents an exact
> description of our universe, but it certainly describes a logically
> possible mathematical universe
Maybe but we don't know that with certainty, if we ever find a Theory of
Everything we might find that classical physics is logically self
>> 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?
> > It tells us that either we must use a nonlocal hidden variables
> interpretation like Bohmian mechanics
Yes, things might be nonlocal.
> or that hidden variables are wrong.
Yes, things might not be realistic. And things might not be local or
> Did you understand that in the sentence above that you quoted, I was
> saying that "there is nothing in principle preventing you from determining
> an exact quantum state for a system"
You can know the exact quantum state for a system, that is to say you can
know the exact wave function BUT that deals in nothing observable like
position or momentum; you must square that complex function for that and
even then it only gives you a probability not a exactitude. And it's even
worse than that because it is a complex function so two very different
functions ( F(x)=2 and F(x) = -2 for a trivial example) can produce the
same number when squared, and thus the same probability.
>> 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.
> > You are failing to specify whether you mean "state" to refer to
> microstate or macrostate and thus speaking ambiguously.
Oh for heaven's sake, one of the great beauties of the Game of Life is that
the meaning of "state" is simple and crystal clear; although in that game I
don't know the dividing line between microstates and macrostates so I just
call them states.
> even with reversible laws there is more than one way to get into a given
No. If there are 2 different states of the universe that could have
produced things as they are now then there is no way to decide between them
and history is unknowable (just as it is in the Game of Life) and the laws
of physics are not reversible.
> The entropy is defined not in terms of some vague notion of the "number
> of ways the system could have gotten into" its present microstate,
You mean its present macrostate. And I see nothing vague about it.
> > but rather as the number of possible microstates the system might be in
> at this moment given that we only know the macrostate
We don't even know for a fact that some macroscopic objects, like Black
Holes for example, even contain microstates; in fact the present thinking
(a minority disagrees) is that probably they don't and a Black Hole can be
completely described by just 3 numbers, its mass, spin, and electric
charge. A Black Hole contains enormous entropy because there are a
gargantuan number of ways it could have been formed, but if you know those
3 numbers then you know all there is to know about a particular Black Hole.
And in the real world only 2 numbers are important because the electric
charge is always zero.
> For example, suppose we consider a very small 2x2 board with only 4 cells
What are the laws of physics in this new game? A 2x2 board is MUCH too
small for the traditional rules of the Game of Life to be applicable.
> And if the macrostate is "0 black:4 white" there's only one possible
> microstate (same for "4 black:0 white"), so this is the lowest possible
I don't know about this new game of yours because I don't know what the
rules are but in the Game of Life a solid block of nothing but active cells
would be in the lowest possible entropy state because the fewest previous
states could have produced it. Actually I should have said the lowest
impossible entropy state because NO previous state could have produced it,
A solid block of nothing but dead cells would have the highest entropy
because more previous states than any other could have produced it, and
entropy is the logarithm of the number of those states.
> If it starts out in a macrostate of maximum entropy [...]
Then nothing the laws of physics do to it can increase it's entropy
regardless of what those laws of physics are.
> But there's another reason to be pretty confident that the Game of Life
> rules don't describe fundamental physics in our universe: they are local
> and realistic, so there'd be no way to construct a scenario in the Game of
> Life where Bell's inequality is consistently violated.
No, it could still work because although the Game of Life is local it is
NOT realistic, so it can produce a violation of Bell’s inequality just as
experimental results demand. You can not talk about definiteness of a
pattern within the Game of life universe before a measurement is made
observing it (which would take at least one clock cycle) because there is
more than one way the universe could have been and still have the laws of
physics to produce things as they are now. You can open a black box right
now (at this clock tick) and observe what’s in it, but you can’t speak
about what was in the box before you opened it. History is ambiguous in the
Game of Life universe. And although reversible computers are possible the
original Turing machine was logically irreversible, so the irreversible
laws in the Game of Life present no barrier in being able to emulate that
very important machine in the game.
> >>> No, they [ the rules of the Game of Life] apply to all squares in the
>>> ideal platonic infinite board whose behavior you want to deduce,
>> Then ratios become meaningless.
> Not if you are assuming an infinite universe that follows these rules
> everywhere, but are *not* trying to define the macrostate of the entire
> universe, but just of an isolated system
As I said you can draw any figure you like and decree that you should only
count cells within it, but I don't see how that arbitrary exercise can
bring us any closer to a universal truth about the entire infinite system
because if I draw a different figure than you I get a different ratio than
you. And my figure is just as good as yours.
John K Clark
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