My point is that with a cosmology we do not have the same sort of scientific observership role. We can observe a sample space of black holes, gravitational waves etc, but this is not quite the same with cosmologies. We observer only one, and it does not permit localization of mass-energy, and at best we may be able to infer a few things from the so-called multiverse by some fingerprints in the CMB. We are faced with a different limitation to what we can observe and know.
LC On Friday, July 15, 2022 at 12:51:45 PM UTC-5 [email protected] wrote: > 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 <[email protected]> > To: Everything List <[email protected]> > 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. > > LC > On Thursday, July 14, 2022 at 10:25:14 AM UTC-5 [email protected] 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 > <https://groups.google.com/g/extropolis> > tif > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To view this discussion on the web visit > > https://groups.google.com/d/msgid/everything-list/99e18b05-95d6-4934-8e68-ff3bc6d8835bn%40googlegroups.com > > <https://groups.google.com/d/msgid/everything-list/99e18b05-95d6-4934-8e68-ff3bc6d8835bn%40googlegroups.com?utm_medium=email&utm_source=footer> > > . > -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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