I wonder if we had Master Schrodinger's Meow-Meow, in a box, where we also have
a follower observer (The observer who opens the box) an that Observer is
Wigner's Friend. Now conceive this phenomena as something that is
exponentiating, ceaselessly, asymptotically? No halting state here. just one
big Divide Overflow Function!
"This limitation means there is not possible way to account for all quantum
information in the universe. The conservation of qubits may hold for type D,
II, III, and N Petrov solution types, here black holes, Robinson-Trautman
solution and finally gravitational waves, because they have asymptotic
conditions that allow for localization of mass-energy, momentum and angular
momentum."
Thus, LC, discovers the function of the multiverse, as buffering for continuous
propagation of qubits. For this one, I'm going straight to the airport and
start handing out flowers and pamphlets. I'll split the donations. ;-)
-----Original Message-----
From: Lawrence Crowell <goldenfieldquaterni...@gmail.com>
To: Everything List <everything-list@googlegroups.com>
Sent: Thu, Jul 14, 2022 7:02 pm
Subject: Re: Do the laws of physics allow an infinite number of calculations?
An infinite number of calculations is not possible. There are three instances I
can think of. Actually to be honest these are I think a part of a single
system. The universe I think obeys the Church-Turing thesis, which means all
that is dynamical or computable can be demonstrated on a Turing machine.
Symmetries that swap QCD color charge or the flavor charge, the strong and weak
nuclear forces respectively, are at least locally algorithmic in nature. I will
wrap this up at the end.
On the largest scale there is inflation, which stretched out space enormously
to 60-efolds or about 10^{26}, which means early data is difficult to measure.
A graviton in the extremely early universe, say around 10^{-30} seconds to
10^{-35}seconds into the big bang has a wavelength of around 10^{-30}cm. By
expansion and inflation a coherent state of such gravitons could be stretched
into a classical scale gravitational wave of millions of kilometers to billions
of light years. An eLISA type gravitational interferometer would imply a change
in wavelength by a z factor of z ≈ 10^{42}. For even longer say billions of
light years these could be detected as polarizations on the CMB and this is a z
≈ 10^{55}. This z factor has an exponential dependence on the distance out, and
so this is around 50 times the CMB distance or 20 trillion light years out. In
other words, the sources of these observed gravitational waves are now on the
Hubble frame, a frame more or less simultaneous everywhere in time, are now
around 2 trillion light years out. This has a further multiplier effect of
around 1,250,000. So how about up to 7.5 billion-trillion galaxies. That would
mean around a billion moles of stars, if you remember Avagadro’s number of
atoms in a gram molecular weight or 6.02×10^{23} atoms. If a water molecule
represented a galaxy this would be as much water as in a million tons of water
--- about a lake’s worth of water.
This is large, but it is the ultimate boundary. Anything beyond this is lost.
The e-LISA and increasingly it is thought fluctuations in pulsar timing will
detect early coherent gravitons as long wavelength gravitational waves. These
may have fingerprints on the CMB. Anything further out than this is
unobservable. Their fingerprints in the early universe are longer than the
cosmological horizon scale. Inflation enforces a rule that the observer cannot
witness an infinite universe --- even if it is infinite.
Quantum mechanics enforces a form of this. Local hidden variables would
indicate that as the action S → 0 there is a UV divergence of degree of freedom
for hidden variables. In fact it would be infinite. Quantum mechanics further
eliminates infinite observable content.
Then there are black holes. The event horizon prevents observers from
witnessing a divergence. With the Kerr black holes and that the inner horizon
is Cauchy, which has been suggested as a way hypercomputation can be
accomplished. This would be a work around the Church-Turing thesis. However,
black holes are quantum mechanical, and the decay of a black hole prevents the
infinite condition necessary for an observer to perform a hypercomputation from
data piling up on the inner horizon. This actually has the effect of enforcing
a quantum form of the Bekenstein bound.
In effect the theorems of Turing and Gödel raise their heads and prevent any
observer from witnessing or performing an infinite computation. Any attempt to
perform hypercomputation, an infinite computation without problems with Gödel,
is prevented by what I call a general horizon condition. This means it is not
physically possible to acquire data about observables in such as way as to
loophole around axiomatic incompleteness. This applies to any physical system,
that by virtue of its interacting is a sort of “observer.”
This means the universe is a fundamentally open system. This limitation means
there is not possible way to account for all quantum information in the
universe. The conservation of qubits may hold for type D, II, III, and N Petrov
solution types, here black holes, Robinson-Trautman solution and finally
gravitational waves, because they have asymptotic conditions that allow for
localization of mass-energy, momentum and angular momentum. These solutions
have Killing vectors that as isometries establish Noetherian conservation
rules. However, this does not apply for cosmologies.
LCOn Thursday, July 14, 2022 at 10:25:14 AM UTC-5 johnk...@gmail.com wrote:
The Bekenstein bound says if a volume of space has access to a finite amount of
energy then the amount of information necessary to describe it is also finite,
and that implies Bremermann's limit which says there is a maximum rate of
information that can be processed in that volume, and it works out to be
c^2/h= 1.4*10^50 bits per second per kilogram of mass/energy. However I think
it should be possible, at least in theory, to extract work out of the expanding
universe (see next paragraph), and if the expansion of the universe is
accelerating then it seems to me the amount of energy you could have access to
in that volume of space could potentially be infinite, not finite.
Suppose you had 2 spools of string coiled in opposite directions connected by
an axle and you extended the 2 strings to cosmological distances 180 degrees
apart from each other. As long as the Dark Energy force between the atoms in
the string that were trying to force them apart was not stronger than the
attractive electromagnetic force holding the atoms of the string together the
string would not expand as the universe expanded, so there would be a tension
on the strings, so there would be torque on the spool, so the axle would
rotate. The axle could be connected to an electric generator and you'd get
useful work out of it. Of course you'd have to constantly add more mass-energy
in the form of more string to keep it operating, but the amount of mass per
unit length of string would remain constant, however because the universe is
accelerating the amount of energy per unit length of string you'd get out of it
would not remain constant but would increase asymptotically to infinity. If the
theories about the Big Rip turn out to be true and the acceleration of the
universe is itself accelerating then it should be even easier to extract
infinite energy out of the universe, provided we take care to continually
shorten the string to keep it from breaking. So it would all just be a simple
case of cosmological engineering. What could go wrong?
And If you have infinite energy then you can perform an infinite number of
calculations, so you could have an infinite number of thoughts, so you would
have no last thought (the definition of death), so subjectively you would live
forever. Of course the objective universe might have a different opinion on the
matter and insist that everything including you had come to an end, but that
hardly matters because subjectivity is far more important than objectivity; or
at least it is in my opinion. John K Clark See what's on my new list at
Extropolis
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