On 3/18/2014 8:14 AM, John Clark wrote:
Jesse, somehow our conversation has bifurcated into 2 quite different topics,
environmental concerns and fundamental physics, today I'll just talk about the physics.
On Sun, Mar 16, 2014 at 8:05 PM, Jesse Mazer <[email protected]
<mailto:[email protected]>> wrote:
> I already addressed your confusion about the implications of black hole
entropy
in detail in my post at
https://groups.google.com/d/msg/everything-list/hJ9bNWqoAzI/QTrL0CopHJ8J
which you
never replied to.
And I never responded to it because it was incoherent, I give the following exchange as
a example:
John: "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.
Jesse: "You think in classical statistical mechanics there can't be 2 different ways to
get to a given *macrostate*??? If so you are badly confused."
And I'm the one who is supposed to be confused??? There is not one drop of Quantum
Mechanics or probability in the Game of Life, it is 100% classical mechanics, and yet
there CAN be 2 or more ways to get to a given macrostate. It's 100% deterministic so if
I show you a Game of Life pattern you can calculate what it's future evolution will be
(there doesn't seem to be anything analogous to chaos in the Game) but you can't figure
out it's history was, or at least not a unique history.
>> Today the deepest understanding of entropy comes from the study of
Black
Holes. From:
http://www.phy.olemiss.edu/~luca/Topics/bh/entropy_origin.html
<http://www.phy.olemiss.edu/%7Eluca/Topics/bh/entropy_origin.html>
"S [entropy ] is the log of the number of quantum mechanically distinct
ways
that the black hole could have been made, or information lost in the
creation of
the black hole"
> Are you suggesting that this new "deep" understanding invalidates the
older
understanding of entropy as the number of microstates for a given
macrostate, the
one you yourself quoted in your last post?
I am saying that Kip Thorn, one of the world's best physicists, wrote on page 446 of his
book "A Black Hole's entropy is the logarithm of the number of ways that the hole could
have been made". And I'm saying that in classical physics a state can produce only one
future state, but any given state can have been produced in more than one way, therefore
the number of microstates in a Black Hole must equal to k times the number of states
that made it where k is some constant integer. Therefore if Entropy is proportional to
the logarithm of the number of microstates in a system then according to the laws of
logarithms Entropy MUST also be proportional to the logarithm of the number of ways the
system could have been produced.
But Kip is speaking loosely. If you look at the original paper with Zurek
http://journals.aps.org.proxy.library.ucsb.edu:2048/prl/pdf/10.1103/PhysRevLett.54.2171
you see that they are counting up the number of states by imagining adding quanta of
energy as small as possible at each step to building up a black hole. But this is just a
way to aid the counting, the result has no dependence on the imagined order. It's just a
way to calculate the number of internal states consistent with the macro-states of the
no-hair theorem.
> Assuming the unitary nature of quantum mechanics is preserved so that
information
is not "lost" when things fall in [into a Black Hole]
That is quite a assumption, today it's one of the greatest controversies in physics and
nobody knows if that assumption is valid; see Leonard Susskind's book "The Black Hole
Wars".
> the number of quantum microstates that any macrostate can have NOW must
be the
same as the number of initial quantum microstates in the PAST which would
have led
to the current macrostate, so the number of "distinct ways it [the current
macrostate] could have been made" would be exactly the same as the number of
"distinct quantum microstates it could be in now"
So 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?
> in practice, I think almost any real-world experiment you could do in an
elevator
in free fall in deep space wouldn't show any divergence from the
predictions of
special relativity that would be measurable by modern equipment.
Not true. As far back as 1963 it was noticed that clocks tick slower on the first floor
of the physics building at MIT than they do on the second floor, Special Relativity had
no explanation for this but General Relativity did, clocks on the first floor were
closer to the center of the Earth than those on the second floor and thus were in a
stronger gravitational field and thus ticked slower. And today the standard GPS
receiver in your car must synchronize it's internal clock with the clocks in 3 or more
navigation satellites, to do this it must take into account some pretty exotic things;
for example, the satellite is moving very fast so due to Special Relativity the
satellite's clock will LOSE 7210 nanoseconds a day, but the satellite's clock is in a
weaker gravitational field than the clock in your car because it is further from the
Earth's center, so due to GENERAL RELATIVITY the clock will GAIN 45850 nanoseconds a
day. Taking these 2 factors into account the satellite's clocks gains 45850 -7210 =
38,640 nanoseconds a day relative to the clock in your car. If your car GPS receiver did
not take this correction into account your indicated position would drift by 6 miles
each and every day, but it knows about General Relativity so it doesn't drift at all and
can find its position to within a few inches.
>> And by the way, according to General Relativity in addition to mass
and
energy pressure and tension can curve spacetime too.
> That's true, although I would think ultimately the pressure and tension
at each
point could be derived from knowledge of the mass and energy at every point,
I once thought that too but it turns out not to be the case. Yes something under
pressure (or tension) does contain more energy than something not being compressed and
that does bend spacetime, but in addition to that there is a additional contribution
made by pressure itself.
> I'm not saying you're wrong that curvature does not depend on the
observer, of
course I agree with that. I'm saying you're wrong that in the SR case where
curvature due to mass/ene/pressure/tension is negligible, spacetime would
still be
curved by acceleration.
Special Relativity says nothing about gravity curving something and Einstein never even
mentioned spacetime. It was a year after Einstein's 1905 Special Relativity papers came
out that Hermann Minkowski introduced the idea of Spacetime, and at first Einstein
didn't like Minkowski's paper at all and said it clarified nothing and was needlessly
mathematical, although he soon changed his mind and embraced spacetime with a vengeance,
and after working so hard it nearly killed him ten years later he discovered General
Relativity.
> the angle formed by 3 lasers is NOT a valid way of measuring spacetime
curvature.
Bullshit. From http://en.wikibooks.org/wiki/General_Relativity/Curvature
Einstein's brilliance was to suggest that although gravity manifests itself as a force,
it is in fact a result of the geometry of spacetime itself. He suggested that matter
causes spacetime to curve positively. The sun, for instance warps spacetime, and it is
this warping of geometry to which the planets react and not directly to the sun itself.
/*This is a central tenet of the General theory of Relativity*/. This local curvature
can be described in mathematical terms using tensor calculus, an incredibly elegant tool
which provides consistent results, regardless of the chosen frame of reference."
"This predicts that if a giant triangle was to be constructed around the sun, the angles
at its vertices would in fact add up to more than 180^o . This is easy to imagine if one
thinks of the sun as warping geometry, causing the triangle to have "wonky" sides.
However it is /incredibly/ important to note that these lines are in fact the
/*straightest lines possible*/ (/geodesics/) in this warped geometry. These predictions
can be tested, and have been to a very high degree of accuracy."
But that doesn't show that you can't get a triangle in flat spacetime whose included
angles exceed 180deg. A good example is in the frame of a rotating disk. You can infer,
for that frame, that *space* is not flat, but *spacetime* is still flat. The same applies
to the accelerating elevator.
> Do you understand the difference between the coordinate-invariant
curvature of 4D
SPACETIME,
Yes. Do you understand it takes TIME for a Laser beam to travel from one point
to another?
> In physics straight lines are defined as the path that light takes
> In general "straight lines" in spacetime are defined as geodesics,
And light always takes a geodesic path in spacetime. So if spacetime is curved then
triangles formed by light beams don't have 180 degrees.
No. You can't measure the curvature of *spaceTIME* with three points. See Synge pp 408
where he describes the five-point curvature detector.
Brent
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