On 12 Jan 2014, at 16:53, John Clark wrote:
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.
You keep saying this, but that is incorrect. The experiments have just
shown that the Bell's inequality are violated in our universe,
assuming that the outcomes of our experiments are definite, which they
are not in the multiverse. Those experiments show nothing about our
multiverse. The experiment are supposed to give definite outcomes, not
the never collapsing superposed entanglement described in the big
picture of the multiverse.
Read Deutsch and Hayden's paper, or Tipler's one, of just try to
conceive an experimental set up showing a quantum violation of Bell's
inequality in the many-world picture (if that can mean anything).
Others gave links and papers.
MW is realist on all outcomes. The wave never collapse, which already
suggest no action at a distance, but when you do the math, like
Tipler, or Deustch and Hayden, (using the FPI, though, but restricted
to the quantum computations, like Everett), you can see that nothing
non local ever occurs.
Bell uses "realism" in some of his context, to say that there is only
one (real) outcome, which is basically the contrary of the MW theory.
Bruno
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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