Does the Bekenstein bound apply to gravitational waves as well?

[Dmitry67]

Here: http://en.wikipedia.org/wiki/Holographic_principle
I read: "Entropy, if considered as information (see information entropy), is measured in bits. The total quantity of bits is related to the total degrees of freedom of matter/energy"
Bold is mine.

Here is my question. I believe that gravitational waves propagating thru empty space also carry information (do you agree?). Is Bekenstein bound also applicable to that sort of matter-less "storage"?

 

[bcrowell]

I believe that gravitational waves propagating thru empty space also carry information (do you agree?). Is Bekenstein bound also applicable to that sort of matter-less "storage"?

My understanding of this sort of thing is limited to the level of Smolin's popularizations, but I think that's sufficient to say that the answer is yes. If you look at pp. 70-84 of Smolin's Three Roads to Quantum Gravity, he describes the subject, and it's pretty clear that you don't need matter, and in fact you don't even need gravitational waves. E.g., he applies it to the event horizon seen by an accelerated observer in Minkowski space.

 

[Dmitry67]

Yes, it makes sense - (I don't have the book) but if we pack so much information into little space in a form of gravitational waves, space will be very bumpy, probably having horizons and generating many particles via Hawking radiation...

But the idea that empty space can be in different states without any matter still fascinates me (even it seems to be very logical if matter and space are 2 manifestations of the same entity) ... Empty space must have temperature then.

I have an impression that most of gravitational radiation exists in a form of (relatively) long G-waves (seconds, minutes) hence very very cold. So space is very far from thermal equilibrium with matter... What's about far future and time very close to the Big Bang?

 

[bcrowell]

But the idea that empty space can be in different states without any matter still fascinates me (even it seems to be very logical if matter and space are 2 manifestations of the same entity) ... Empty space must have temperature then.

It's not really a property of the space, it's a property of the observer. An observer in Minkowski space who has proper acceleration a will observe a horizon with a temperature T that is proportional to a. Unaccelerated observers see no horizon, no radiation.

 

[Dmitry67]

Not an observer but a frame I guess, because Unruh effect exists even when there are no observers. But in any case accelerated and non-accelerated observer would agree somehow on ‘what had happened’, so in that case we have just different views of the same thing.

I was talking about space in different states with the same boundary conditions – an imaginary box in flat universe, where void inside the box encodes nothing, or G-waves flying inside encode 1000 digits of PI, or some poem encoded in ASCII. So space are really in different states.

I have another related question, is flat space really flat or is it filled with ‘null’ G-waves? (‘Null’ in the same sense as null electromagnetic waves which are responsible for Casimir effect). I am aware of spacetime foam on Planck scales, but these effects (like Casimir) exist even on almost macroscopic scales…

 

[haael]

I believe that gravitational waves propagating thru empty space also carry information (do you agree?). Is Bekenstein bound also applicable to that sort of matter-less "storage"?

Space with gravitational waves is not matter-less. The excitation of the spacetime is in fact a graviton. Waving spacetime may be as well described as particles traveling through it - it is the particle-wave duality.

The general relativity alone states that gravitational waves carry mass and pressure. The limit on the information density stored in gravitons is no different than in any other matter. In principle, you could focus so much gravitons in a single point so they collapse into a black hole.

I have another related question, is flat space really flat or is it filled with ‘null’ G-waves?

Space without any mass is not flat - it is in fact negatively curved and obeys the de-Sitter solution of the Einstein equation.

What the empty space lacks is gravitational waves. That means, the excitations of spacetime or equivalently cyclicaly changing Weyl curvature. It is also possible to be no gravitational waves in a space with some mass but without accelerating objects. Every acceleration of any particle produces gravitational waves, just as every acceleration of a charged particle produces electromagnetic waves.

The analogy with electromagnetic field goes further: a static charged object is surrounded by a static electromagnetic field (yet changing with position). An accelerating charged object produces electromagnetic waves (excitations or cycliclicaly changing electromagnetic field). The same goes for gravity: a static massive particle is surrounded with curved but static spacetime. An accelerating particle generates Weyl curvature vibrations, that means gravitational waves.

(‘Null’ in the same sense as null electromagnetic waves which are responsible for Casimir effect).

Cassimir effect is caused by virtual photons. We don't know if virtual gravitons exist, since we don't have any sound quantum gravity theory. But it is possible.

Even if they were virtual gravitons, they would not carry any information. Virtual particles do not carry information, you can even say that they represent the lack of information. Virtual particles do not give us any discrimination between physical states. If you have two systems that are almost identical and they only differ (mathematicaly) only in the virtual particles, then they are in fact physically identical. The virtual particles would not give you any bit of information to distinguish between them.

That said, the most cool thing about Bekenstein bond is that it predicts fractional information for very light systems. Fractional information means in fact corellations. Yes, the correlations we see in the quantum mechanic experiments and in Bell inequality. Maybe Bekenstein bond is the key to explain the quantum nature of microscopic world.

 

[bcrowell]

But in any case accelerated and non-accelerated observer would agree somehow on ‘what had happened’, so in that case we have just different views of the same thing.

Not necessarily. This is what black hole complementarity is all about. It's not a trivial thing to resolve, and it's not at all obvious that different observers do agree on what happened. Concretely, accelerated and unaccelerated observers disagree on how many quanta there are, and this is different from anything that happens in QFT. Also, the difference between their observations violates the equivalence principle.

 

[Dmitry67]

That said, the most cool thing about Bekenstein bond is that it predicts fractional information for very light systems.

But very light systems have long wavelength, so they can't be located in a small region of space. As I understand, you can always take a bigger region, where information about light system will be complete?

 

[Dmitry67]

Not necessarily. This is what black hole complementarity is all about. It's not a trivial thing to resolve, and it's not at all obvious that different observers do agree on what happened. Concretely, accelerated and unaccelerated observers disagree on how many quanta there are, and this is different from anything that happens in QFT. Also, the difference between their observations violates the equivalence principle.

Lets talk about more limited statement. For clarity, let's look at it from the "shut up and calculate = macroscopic realism" point of view (even I don't share this vision, this interpretation is self-consistent and simple).

So we assume that only macroscopic events are real, and particles (both 'real' and 'virtual') are just math to calculate the correlations and probabilities between macroscopic events.

Do you agree that from that point of view, observers always agree on the events, and equivalence principle is valid? So, if I touch a ball heated by Unruh radiation and my hand got burnt, all observers agree on that?

 

[haael]

But very light systems have long wavelength, so they can't be located in a small region of space. As I understand, you can always take a bigger region, where information about light system will be complete?

It's not about the information. It's about the correlation.

The information of an isolated system is always complete. If you have a photon in a box, you know everything about that photon no matter how small is the box. You don't need to take any bigger box; it will not tell you anything more about the small box compared to looking at the small box alone.

However, if you have two small boxes and you suddenly want to join them into one bigger box, then the information capacity of the bigger box will be strictly smaller than the sum of information capacities of the smaller boxes. The small boxes exhibit correlations in their information content. If you query one box for some bits of information, then you automaticaly get some information about the second box. Experiments performed in the second box must be correlated with the first box.
This sounds very familiar, doesn't it? It's the same thing as the quantum entanglement. Bekenstein bond may be the reason behind the quantum nature of the Universe.

 

[Dmitry67]

However, if you have two small boxes and you suddenly want to join them into one bigger box, then the information capacity of the bigger box will be strictly smaller than the sum of information capacities of the smaller boxes.

Thank you, I understand it now.

So if we take bigger and bigger boxes, we get smaller and smaller max. information density. If our box is too big matter inside it will collapse into BH, but if we go beyond the isolated systems, we can take regions of our expanding Universe (as they won't collapse into BH because of the expansion).

As I understand, if we take it into extreme, when box grows infinitely large the density of information reaches 0. And it makes sense - if our Universe is infinite, it is filled with the repeating regions of matter, so no region of space contains anything really unique or new. Am I right?

 

[haael]

If our box is too big matter inside it will collapse into BH

The opposite - if it is too small, the content will collapse into BH, reaching maximum information density.

As I understand, if we take it into extreme, when box grows infinitely large the density of information reaches 0. And it makes sense - if our Universe is infinite, it is filled with the repeating regions of matter, so no region of space contains anything really unique or new. Am I right?

Wow, I never thought of it like that. But it makes sense.

 

[bcrowell]

Do you agree that from that point of view, observers always agree on the events, and equivalence principle is valid? So, if I touch a ball heated by Unruh radiation and my hand got burnt, all observers agree on that?

No. That's the whole point of black hole complementarity.

 

[Dmitry67]

No. That's the whole point of black hole complementarity.

That's crazy.
We don't know WHY different observers should came to the same macroscopic observations, but we know that they should somehow find an agreement.

It is a mere consequence of the Block Time - all events for all observers are consistent just because of the nature of the Block Time. Because the opposite claim, your claim, is that they don't find an agreement, hence the whole universe splits into version where I am alive and where I am dead, like in bad movies about time travel, where you can go into the past to change something there, affecting the future.

Wiki claims that:
Although Unruh's prediction that an accelerating detector would see a thermal bath is not controversial, the interpretation of the transitions in the detector in the non-accelerating frame are. It is widely, although not universally, believed that each transition in the detector is accompanied by the emission of a particle, and that this particle will propagate to infinity and be seen as Unruh radiation.

P.S.
It is not about the fatal destiny of the infalling observer, but about Hawking/Unruh radiation. It occurs outside of the 'fatal' horizons, so different observers have a chance to peacefully meet together after a trip.

 

[bcrowell]

That's crazy.

Yep, black hole complementarity is crazy. But try reading the WP article to understand what it's about.

 

[Dmitry67]

I had read it before posting the P.S. in my previous post.
Theory of mr. Susskind is not compatible with Block Time, and the idea of 'stretched horizon' looks artificial while the complementarity itself is beautifully crazy.
Let's wait for TOE to see if it is true...

 

[Dmitry67]

After thinking about it for a while, the idea of 'stretched horizon' is not compatible even with the standard GR.

"stretched horizon, which is a membrane hovering about a Planck length outside the event horizon" - what horizon?

It can't be neither apparent horizon nor an absolute horizon.
It can't be apparent horizon because different observers don't agree on it's position.
It can't be absolute horizon because the precise position of absolute horizon depends on the all objects which will fall in BH in the future.