Reappearance of matter from a horizon

[ontodva]

Given enough time Boltzmann freak structures will appear, assembled from drifting matter, in the maximum-entropy universe if it is static, I.E. not expanding to eventually sweep all matter into the far horizon.

In a lecture http://www.cornell.edu/video/leonar...ervation-of-information-holographic-principle (about half way in) Leonard Susskind seems to say that given accelerated expansion of the universe (dark energy), after all matter has disappeared into the horizon Boltzmann freak structures will still appear, assembled from drifting matter, in the maximum-entropy, nearly always empty, universe.

This will happen because, from our viewpoint, nothing actually crosses a horizon - special relativity explains why things approach horizons asymptotically. Particles, frozen and piled up on the horizon, can get a spontaneous kick of kinetic energy which propels them back into the visible universe, where they will drift around until the expansion of space again displaces them to the horizon (and they will be back).

Is this possible, indeed inevitable? Can it be true that nothing ever leaves the visible universe, that everything - all particles, patterns, and structures - come back eternally, even though the expansion of space accelerates?

 

[Chalnoth]

The cosmological horizon, rather like the event horizon of a black hole, emits Hawking radiation. This gives the universe a finite, non-zero temperature at all times. When you have a finite, non-zero temperature, then discrete structures will (very rarely) form from the radiation that is bouncing around. Typical times for this to happen are vastly longer than the current age of our universe.

Edit: the cosmological horizon is a virtue of having a non-zero cosmological constant. If we don't actually have a non-zero cosmological constant, then there is no cosmological horizon, and the universe will tend to either recollapse or zero temperature in the far future.

 

[timmdeeg]

http://math.ucr.edu/home/baez/end.html

Perhaps this article is of interest.

 

[ontodva]

First, apologies for giving the wrong link in my original post. It's http://www.cornell.edu/video/leonard-susskind-1-boltzmann-and-the-arrow-of-time "Boltzmann and the Arrow of Time: A Recent Perspective", a talk by Leonard Susskind. Or - the same talk for Webkit browsers if the first link doesn't give video.

Susskind indeed explains clearly the argument I summarized in that post. His argument starts ~@ 38:30 minutes in. He explains why (he thinks) the visible universe is a finite system with only a certain number of states to cycle through, starting at 24:45. It is clear he does not have Hawking radiation in mind.

I think it is wrong. If the particle being carried to the horizon is Alice, and you and I are observers Bob and friends, it gives priority to Bob's coordinate system and neglects Alice's coordinate system or frame of reference.

From Alice's point of view, Bob is near the horizon, receding near light speed and accelerating. Soon, any random energy fluctuation that sends Alice back in Bob's direction will have to give it a velocity greater than the speed of light to transmit a photon from Alice to Bob. Before then, while Alice would only have to be kicked back at relativistic velocity, there is not much time available. The chances of Alice being returned to Bob's visible universe are very small indeed. So hardly any particles being carried near the horizon can be returned and, after some point, none at all.

Do we agree?

 

[ontodva]

Also, it's General Relativity that explains why things approach horizons asymptotically.

 

[ontodva]

@timmdeeg
Thanks for that very interesting link. The author mentions Susskind, contextualising: "... even if the universe consists of more or less empty space at a temperature of 10^-30 kelvin, random fluctuations will occaisionally [sic] create atoms, molecules... and even solar systems and galaxies! The bigger the fluctuation, the more rarely it happens - but eternity is a long time."

That author, John Baez, most likely meant vacuum fluctuations promoted at random into physical reality in empty space. Susskind, in his lecture, did not mean this unless he was talking at cross purposes with himself. BTW the existence of vacuum fluctuations qua virtual particles is not uncontroversial.

 

[Chalnoth]

Susskind indeed explains clearly the argument I summarized in that post. His argument starts ~@ 38:30 minutes in. He explains why (he thinks) the visible universe is a finite system with only a certain number of states to cycle through, starting at 24:45. It is clear he does not have Hawking radiation in mind.

Provided there is a positive cosmological constant, then the visible universe is a finite system. The horizon he's talking about definitely seems to be the horizon of a system with a positive cosmological constant.

I think it is wrong. If the particle being carried to the horizon is Alice, and you and I are observers Bob and friends, it gives priority to Bob's coordinate system and neglects Alice's coordinate system or frame of reference.

It's not too hard to translate to Alice's coordinate system. She'll interpret Bob's motion in the exact same way that Bob interprets Alice's.

From Alice's point of view, Bob is near the horizon, receding near light speed and accelerating. Soon, any random energy fluctuation that sends Alice back in Bob's direction will have to give it a velocity greater than the speed of light to transmit a photon from Alice to Bob.

No, this isn't how it works. First, the speed of far-away objects is ill-defined, and doesn't really have much of anything to do with the cosmological horizon (we can see many objects today that are now and always have been receding faster than light). I think Suskind was being rather misleading here.

Second, we never observe an object crossing any horizon (as Suskind describes). If we imagine that Alice is holding a clock, what we will observe is that that clock will tick more and more slowly as we see Alice get closer and closer to the horizon. But it will never stop: the image of the clock will get closer and closer to the time that Alice crossed the horizon, never quite reaching that point in time. This is sort of an after-image, as the photons that were released right at the cusp of the horizon take longer and longer to reach us.

 

[ontodva]

Provided there is a positive cosmological constant, then the visible universe is a finite system. The horizon he's talking about definitely seems to be the horizon of a system with a positive cosmological constant.

I certainly have trouble grasping that. It is quite counterintuitive to me, with no physics training. A positive cosmological constant means zero density everywhere eventually, no? Could you post a link or two that would explain why it's a finite system?

we can see many objects today that are now and always have been receding faster than light

'are now' - sure, granted; it would be your selection of a 'now', but it's orthodox as I understand it.
'always have been' - I think its the first time I have seen that claim. Would you post a link or two for my benefit and maybe for anyone else reading this who might be baffled by the statement, thanks.

the image of the clock will get closer and closer to the time that Alice crossed the horizon, never quite reaching that point in time. This is sort of an after-image, as the photons that were released right at the cusp of the horizon take longer and longer to reach us.

I shouldn't have used the image of a photon reaching Bob from Alice - it confuses the issue. It is the Alice particle itself that has to become able to collide with Bob to form part of a structure. When it has already crossed the horizon (according to Alice, or your words anyway) or is within a Planck length of it (according to Bob) or Bob is within a Planck length of Alice's horizon (according to Alice, second interpretation), how can Alice collide with Bob?
That is my original post in 6 words: how can Alice collide with Bob?

 

[ontodva]

This is ridiculous. I should have titled the original post 'All matter bounces off event horizons and returns'. And subtitled it 'There are no black holes, only white holes: official'

It's ridiculous. How can it stand? It's unphysical.

 

[Chalnoth]

I certainly have trouble grasping that. It is quite counterintuitive to me, with no physics training. A positive cosmological constant means zero density everywhere eventually, no? Could you post a link or two that would explain why it's a finite system?

It's finite in that it has a horizon. Yes, it keeps expanding, and it gets more and more empty as time passes. But the distance to the horizon remains finite. In the far future, this horizon sits at a constant distance from an observer.

'are now' - sure, granted; it would be your selection of a 'now', but it's orthodox as I understand it.
'always have been' - I think its the first time I have seen that claim. Would you post a link or two for my benefit and maybe for anyone else reading this who might be baffled by the statement, thanks.

This may help:
http://arxiv.org/pdf/astro-ph/0011070v2.pdf

Short version: the expansion early-on was much, much faster than it is today, and as it slowed down, some photons that were once being carried away from us due to the expansion eventually started to gain ground.

I shouldn't have used the image of a photon reaching Bob from Alice - it confuses the issue. It is the Alice particle itself that has to become able to collide with Bob to form part of a structure. When it has already crossed the horizon (according to Alice, or your words anyway) or is within a Planck length of it (according to Bob) or Bob is within a Planck length of Alice's horizon (according to Alice, second interpretation), how can Alice collide with Bob?
That is my original post in 6 words: how can Alice collide with Bob?

Alice can't. Ever. Once past the horizon, Alice and Bob can never communicate again, let alone meet.

 

[ontodva]

Alice can't. Ever. Once past the horizon, Alice and Bob can never communicate again, let alone meet.

So you are as sceptical as me about Susskind's claim for future Boltzmann structures in a universe with accelerated expansion?

 

[Chalnoth]

So you are as sceptical as me about Susskind's claim for future Boltzmann structures in a universe with accelerated expansion?

No. That claim is solid, but it's a completely different claim. It's not about Alice coming back, but about a random configuration of thermal fluctuations coming together for a moment in the same configuration as Alice. This kind of event takes an inconceivably long amount of time to occur even once, but the probability isn't zero.