Do the laws of physics allow an infinite number of calculations?

[John Clark]

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

tif

[Brent Meeker]

At some point the amount of localized energy will form a black hole.

Brent

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[Jason Resch]

Interesting ideas. You might also be interested in this, which uses the expanding and cooling universe to perform infinite computations with finite energy:

https://en.m.wikipedia.org/wiki/Dyson%27s_eternal_intelligence

Also, reversible computers can compute without energy expenditure.

Jason

[spudb...@aol.com]

In the real world does energy need to be described by information? Is there a behavior of physics that indicates this? 

[spudb...@aol.com]

I started consider if Tipler's Omega Point was instead, his Tipler Cylinder? 
Tipler-cylinder Definitions | What does tipler-cylinder mean? | Best 1 Definitions of Tipler-cylinder (yourdictionary.com)

It could hypothetically recover all information within the Hubble Volume.

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[John Clark]

On Thu, Jul 14, 2022 at 3:49 PM Brent Meeker <meeke...@gmail.com> wrote:

> At some point the amount of localized energy will form a black hole.

Maybe, probably, but I can't help but think that the formula we use today to determine the point where a black hole forms from too much information might only be an approximation because if the acceleration of the universe is itself accelerating because Dark Energy is getting stronger and we're heading toward the Big Rip then in the deep future it's gonna be harder to make a black hole than it is now. That's just my intuitive hunch, I could be dead wrong.

  John K Clark    See what's on my new list at  Extropolis

ydd

 

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[Lawrence Crowell]

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

[Lawrence Crowell]

On Thursday, July 14, 2022 at 4:28:48 PM UTC-5 johnk...@gmail.com wrote:

On Thu, Jul 14, 2022 at 3:49 PM Brent Meeker <meeke...@gmail.com> wrote:

> At some point the amount of localized energy will form a black hole.

Maybe, probably, but I can't help but think that the formula we use today to determine the point where a black hole forms from too much information might only be an approximation because if the acceleration of the universe is itself accelerating because Dark Energy is getting stronger and we're heading toward the Big Rip then in the deep future it's gonna be harder to make a black hole than it is now. That's just my intuitive hunch, I could be dead wrong.

  John K Clark    See what's on my new list at  Extropolis

ydd

The extraction of energy from dark energy is possible. Given two galaxies a tether between them could serve as a way of generating energy. However, once the two galaxies separate so they have a mutual z > 1 there is no tether that can hold. It is for the same reason one could not lower a camera on a tether into a black hole and then pull it out. As the number of galaxies in the cosmic O-region bounded by the horizon is finite it is then not possible to extract an infinite amount of energy.

LC

[John Clark]

On Thu, Jul 14, 2022 at 7:07 PM Lawrence Crowell <goldenfield...@gmail.com> wrote:

> The extraction of energy from dark energy is possible. Given two galaxies a tether between them could serve as a way of generating energy. However, once the two galaxies separate so they have a mutual z > 1 there is no tether that can hold. It is for the same reason one could not lower a camera on a tether into a black hole and then pull it out. As the number of galaxies in the cosmic O-region bounded by the horizon is finite it is then not possible to extract an infinite amount of energy.

Thanks Lawrence.

John K Clark    See what's on my new list at  Extropolis

ydd

ebx

[spudb...@aol.com]

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. ;-)

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From: Lawrence Crowell <goldenfield...@gmail.com>
To: Everything List <everyth...@googlegroups.com>
Sent: Thu, Jul 14, 2022 7:02 pm
Subject: Re: Do the laws of physics allow an infinite number of calculations?

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[Lawrence Crowell]

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

[Brent Meeker]

As I understand Phillip Gibbs papers (see attached) we can define a localized conserved quantity, which is the mass-energy, or at least equates to the mass-energy where that is defined.

Brent

[Lawrence Crowell]

I guess I am not quite sure what you are alluding to here. With type D, II, III and N solutions there are Killing vectors (Killing is the name of a mathematician) which give an isometry and thus conservation laws. The conservation of qubits should then be demonstrable. This though remains an open question, but people are closing in. I just published a paper on this with black holes, but just as with the Page curve calculation approach mine has a certain loophole or gap. I think there is a subtle issue of topology and that we need to generalize the concept of unitary evolution. 

With cosmologies there are no Killing vectors in these spacetimes. This does not mean mass-energy or qubits etc are not conserved, but there is no fundamental principle that enforces their conservation. Also, cosmologies are not something we observe multiple copies of. At best, if we are fortunate, we may detect signatures of other cosmogonies that left an early signature on the CMB. We can never causally interact with them, and science fiction scenarios aside we cannot observe into them or travel into them. So there is a very different meaning to statistics here. We do not have a statistical sample space in the sense of orthodox statistics, nor do we have the ability to perform Bayesian prior updates in the Bayes statistical system. If you want to detect physics in other cosmogonies directly, though you could still not go into them, you could go into a black hole.It would need to be a huge black hole that you could exist in for enough time to make measurement before being absorbed into the singularity.

LC

[spudb...@aol.com]

Ok, one observer, no free tickets, no cutting in in line, Got it! 

Much thanks, LC.

Or as Bill Clinton once intoned, "We play the hand we're dealt." 

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