A mass of information II: Black Holes

[vincent]

“...we are entering an Era of physics based on information ...and meaning. For example, the surface area, or irreducible mass of a black hole—a quantity ostensibly as classical as anything...--is now known to measure the entropy of that black hole or, otherwise stated, the number of distinct ways in which such ...can be put together. -John A. Wheeler

 

I’m initiating this thread because I don’t think people appreciated that this was the key part of Wheeler’s remarks.

 

One of the main themes of the first thread was the obvious point that energy is needed to physically encode information. We don’t really need to examine the concepts of time or interpretive issues having to do with quantum mechanics to understand why this statement makes sense.

 

But the question of the relation between information and energy takes it’s sharpest form in the case of black hole physics. This is because of the famous black hole area-entropy relation which says that the entropy of the event horizon is completely determined by the mass of the black hole. There is no analogous statement relating the energy of a system and the information encoded in it anywhere else in physics. This statement doesn’t just say that the entropy of a black hole is encoded in it’s mass. It suggests that somehow black hole entropy and black hole mass are the same thing! The question than is what does this say about the nature of the fundamental degrees of freedom of black holes? Is it possible that in some sense black hole degrees of freedom don't gravitate in any ordinary way? Is it possible that (as I believe someone suggested in the other thread) information can in some sense gravitate?

 

Note that here we're discussing the entropy of a black hole and not the problem of how information encoded in matter that falls into a black hole is recovered. The problems associated with this latter subject are usually referred to as the black hole information problem.

[Martin]

I view this as a constructive refinement of Fred's earlier thread, and likely to help resolve the discussion.

 

Wheeler's statement has been edited so as to avoid suggesting that information has (in every case) mass. And it focuses on the fact that "energy is required to encode information".

 

Probably we can all agree on that, and also that in the case of a stationary black hole (since its mass and energy are equivalent and proportional to horizon area) we can more or less equate the information with the other quantities.

 

Personally I like this effort at resolution very much and expect eventually to combine this thread with Fred's earlier one, if that seems appropriate, after seeing how things go for a bit.

[vincent]

Wheeler's statement has been edited so as to avoid suggesting that information has (in every case) mass. And it focuses on the fact that "energy is required to encode information".

 

It appears that you have misjudged my intentions for intiating this thread. I'm not focussing on the idea that "energy is required to encode information".

 

What I'm focussing on is the possible implication of the black hole area-entropy relation that energy and information are somehow interconvertible in the context of black hole physics, sort of analogous to the way that the mass-energy equivalence says that energy and invariant-mass are interconvertible.

 

Personally I...expect eventually to combine this thread with Fred's earlier one, if that seems appropriate, after seeing how things go for a bit.

 

I'm sorry, but the idea of this thread was to refocuss the discussion on what in my opinion should have been the focus in the other thread. Merging the two threads not only makes no sense, but it would represent an abuse of authority on your part.

[YT2095]

Merging the two threads not only makes no sense, but it would represent an abuse of authority on your part.

 

Really? How so?

[vincent]

Really? How so?

 

I pm'd you.

[BenTheMan]

Personally I like this effort at resolution very much and expect eventually to combine this thread with Fred's earlier one, if that seems appropriate, after seeing how things go for a bit.

 

Why would you do this? Do you normally go around merging similar threads?

 

The discussion in that other thread has drifted pretty far affield from physics, and this is an attempt by vincent to actually start discussing physics again.

[fredrik]

It sure isn't easy to find answers, I think these are extremely interesting and relevant questions.

 

Some personal reflections.

 

I am one of those who strongly believe in looking for a deep unification of information frameworks with physical theories, and in particular associating generic learning frameworks with the scientific method itself since I consider these general scientific considerations to be a necessary foundation for any fundamental science, and physics in particular. I belive that any structures and reality itself, is in a sense emergent from the observers interactions with the environment, and even that the observers assembly is part of this dynamics. An observer is bound to develop successful relations with the environment in order to stay in business. This implies a sort of selection mechanism.

 

I ultimately think that one can understand the laws of physics by analysing the relational information in this picture. When this is done, there seems to arise natural concepts of intertia (as in resistance to change; not movement in space, but rather "change" in general, or alternatively reduction of uncertainty).

 

One of the things I'm currently trying to find out, is what the proper formalism must look like that realises this things. Once this is found, the formalism can be explored and then I expect to see probably several generations of structures as well as dynamics as the complexity increases. With complexity I imagine the information amount of the system. One would obviously expect that complex structures in general has more complex interaction properties that less complex structures.

 

I basically picture physical structures and their microstates as encoding the possible interactions, and that each concept and structure in the model has a more or less at least, one to one "representation" with supposed "physical reality". We humans represent with mathematics what nature represent in physical structures. But they supposedly are equivalent descriptions of the same "thing".

 

The observations I've done is that normal probability theory is inadequate to do this, because the probability spaces themselves as we normally think of it aren't observables. The frequentist interprations makes no sense. It's a very good approximation, but it does not hold water for a fundamental reconstruction. But still probability theory is crucial, and part of the game. So I think we need a dynamic probability theory where the probability themselves are dynamical, and can be given a indirectly observable status.

 

To embed the probability space in a larger (background) probability space of probability spaces does not solve the fundamental problem (IMO at least). It just iterates the flawed method! And it does help in the sense that it makes the flaw smaller, but it also has a disadvantage that it probably makes the background space unnecessarily large and there comes the next point - a low complexity observer can not (in my view) *relate* to arbitrarily complex structures (recall the ideal that there is a one-2-one relation between model and "relality").

 

I take the association of information and mass/energy very seriously and I think we so far don't understnad the full meaning yet.

 

I'm not sure I would personally be prepare to in detail discuss the black hole entropy before the fundamental conditional structure is discussed in detail in the appropriate formalism.

 

I guess this is what string theorists try to do in their formalism and LQG people in theirs, but for anyone that doesn't buy into the formalism in the first place the results is very uncertain.

 

To me, that the perception of reality may _possibly_ be constrained by the capacity of the observer to _relate_ to the environment is often overseen in the papers I've skimmed.

 

I think a measure of relational capacity is needed, and I tend to associate this to inertia.

 

I have not come very far myself with the formalism, but I suspect gravity and time can be understood as emergent in as intertial phenomena in a system of quasi-stochastic relations. I write quasi, just because of the problem to define the probability space properly (I think non-unitary features is required for consistency). I've started to elaborate this, and so far it's a basic combinatorical approach based on relations (where I consider the relations themselves to be subjective), where the basic task is to calculate transition probabilities to all possibilities allowed by current uncertainty, but also a mechanism that updates the calculational engine when unexpected information arrives. I figure thta in reality the fact that fundamentally unexpected thing cna happen can't be banned.

 

Another thing I've found is that the normal entropy definition is not very useful either. It basically suffers from the same flaws as does the foundations of probability theory. Instead I consider a recursive entropy, but there is no need to call it entropy, because IMO the mainly interesting use of the entropy anyway is the relation ot transition probabilites.

 

I have not come to that point yet but most probably ordinary QM will be something like a low order approximation where the approximation lies in the assumption that you can know your probability spaces (there will be many, that have relations with each other, so that prios are induced between them) with certainty.

 

So I have no formal answers yet but I think there is alot to happen in these areas in the future and if anyone else has ideas I'm interested. I think this is interesting and I'm interested to hear other peoples ideas. Since I suspect noone has the answer, I consider this to be all about exchanging ideas...

 

/Fredrik

[Fred56]

Comment: any and all discussion of "information", "quantum information", and "information energy" need more careful use. There is information in a single photon, which carries mass/energy, but there is also the "information" we have in our heads, which "doesn't"...

 

Maybe we should call them quantormation and logiformation, or quantumation and logication, ...

[fredrik]

Comment: any and all discussion of "information", "quantum information", and "information energy" need more careful use. There is information in a single photon, which carries mass/energy, but there is also the "information" we have in our heads, which "doesn't"...

 

...doesn't have energy?

 

Ours brain certainly have energy, right? Or do you suggest that your thoughts have an realisation independent of your physical brain?

 

/Fredrik

[Fred56]

How do we measure the mass/energy of this space -our "brain" -to determine this?

 

Are you saying the "superposition" of quantum states that we are so eager to exploit, exists other than in this space -actually contributes something (to the mass/energy of the universe) ?

[fredrik]

It's true that information needs a formal definition, and a measure. Shannons or the nuemann entropy has limitations IMO. This is part of the problem IMO. The problem I see seems to be how to find an observable measure of what informtion that is missing.

 

My starting point is the observers set of relations, and try to consider the transition probability for the set of relations - this should be induced from the current state of relations, which is my the information capacity of the observer itself limits it's predictive power. A given configuration can be given a measure of its uncertainty (how likely it is to be seen), this is related to the normal shannon and cross entropies of this state.

 

One can define another measure say P(f|p), which is basically the probability to observer a given relative frequency, given a prior distribution. Take the logarithm of this and one will find an interesting relation between what can be interpreted as a transition probability and the information divergence. But the problem is that the prior is also nothing but estimated, which yields an expansion. But then the one-2-one principle suggest that the expansion itself also takes up some memory. If one does the combinatorics on this one will find that the expansion is driven by the dataflow, but constrained by the observers relational capacity. I am trying to elaborate this very simple idea to allow dynamic probability spaces. The spaces themselves are selected as the observer communicates with the environment. The selection mechanis is based on the fitness of the "selected" view/theory/structure.

 

I am not posting any math yet because I have no formalism yet that reflects my thinking. Once the formalism is done, the rest of it is pure maths of exploring the formalism and training it against real data.

 

Once i have done more I intend to provide the math, but this first part is I think harder, also to communicate to others as we are elaborating the common formalism that is normally a prerequsitie for communication.

 

In this way, the concept of entropy can not be entirely separated from the dynamics in any fundamental way except as an approximation.

 

/Fredrik

 

Are you saying the "superposition" of quantum states that we are so eager to exploit, exists other than in this space -actually contributes something (to the mass/energy of the universe) ?

 

Good quesiton. If I have to answer quick, I'd say yes.

 

I'm on my way to a b-day parth so I'll get bakc more later!

 

/Fredrik

[Fred56]

OK, two things to deal with here for me:

1. post something about black hole research

2. continue discussion of entanglement and information and the (non)determinism of reality...

 

... after turning down (or maybe it was up) the tv, thinking a bit, looking through the several browser pages open, drawing on my trusty pipe a bit, redolent with Longbottom's finest, I have the following for your perusal:

 

Bugger, this all ended up elsewhere, looks like I got hit by a random cosmic event, folks. You'll have to look here:

 

http://www.scienceforums.net/forum/showpost.php?p=366628&postcount=56

[ydoaPs]

...doesn't have energy?

 

Ours brain certainly have energy, right? Or do you suggest that your thoughts have an realisation independent of your physical brain?

 

/Fredrik

I think he's trying to say there's a difference between what is coded and the code itself, but I could be wrong.

[Fred56]

Hmm. We sure know that the process of thinking uses energy. Anyone who's gone to any school or studied for an exam knows how tiring it can be. I'm not sure but I think the brain can use up to about a third of the body's energy...

But how much does thought weigh?

 

The thing is, entangled states are "unknown" to us until we "select" a state (measure it). It isn't real until we project "ourselves" onto it... weird.

[fredrik]

The thing is, entangled states are "unknown" to us until we "select" a state (measure it). It isn't real until we project "ourselves" onto it... weird.

 

This is why I think that until then the superposition is the as close to real we get, and I imagine this superposition as a representation in the observers internal state - in this sense, the superposition is "real". But the reality is not the unknown that's "out there", the reality is the projection of that, which lives in the observer. Which ultimately means that reality is subjective - which btw, does not bother me one bit, on the contrary does it make perfect sense.

 

This may seem strange if you are coming from the deterministic philosophy of classical mechanics, but once you get over that, this is IMO very naturaly, intuitive and it does make sense.

 

But current standard models is not designed along these principles. But my hope is that the next generation of models will.

 

The picking I'm doing is not picking on QM in favour of determinism, it's rather the opposite direction, that I pick on the determinism of "probability mechanics" and the idea that has be be an objective reality. If we really take the concepts of QM to heart, the consistency of reasoning is stabbed if we stop at a the second quantization, or any any fixed level.

 

First quantisation has issues to handle many indistinguishable particles, so it leads us to second quantization. There are still problems... so some people come up with strings, but what about a third quantization?

 

I always had the feeling the string theory is a special case, or alternative route to a generic third quantization. But the problems persists... at what level of quantization does things stop - maybe there is principle that that answers this that prevents the degrees of freedom to get uncontrollable?

 

Complex models may have the potential to be more accurate, but they require a higher representational capacity in the observer, and they will "possibly" be slower in their adaptive responses unless they evolve a more clever selection mechanism. So there is probably a balance between potential and response times. This may suggest and answer why "100th quantization" is not realized.

 

/Fredrik

[Farsight]

Anybody see the Black Holes article in the October 6th edition of New Scientist?

 

It rather reminds everybody just how much talk surrounding black holes is conjectural. And it vindicates what I said in Black Holes Explained.

[Martin]

Anybody see the Black Holes article in the October 6th edition of New Scientist?

Would you like to provide a link to it, just to save folks time if they want to look it up?

 

(Personally I don't remember seeing it.)

[BenTheMan]

Anybody see the Black Holes article in the October 6th edition of New Scientist?

 

It rather reminds everybody just how much talk surrounding black holes is conjectural. And it vindicates what I said in Black Holes Explained.

 

Like it or not, the physics involved in calculating the Hawking radiation is not very hard---it is a semi-classical calculation, which any graduate student could do, if given enough time. One just has to understand how a scalar field behaves on a changing gravitational background. We understand quantum field theory very well, and we understand how to make QFT consistent with general relativity (there is a book on it by Paul Davies and Birrell, if I've spelled his name correctly). If you want to do a google search, the actual method is called the Bogolubyov transformation (which I have probably hopelessley misspelled).

 

The point of all of this rambling is that the loss of information in a black hole is very easy to show (I don't remember very many calculations in Hawkings 1972 paper). IF this calculation is wrong (i.e. if you think informaiton is not lost), then you should be prepared to explain why you think it is wrong, and how to fix the derivation from the point of view of quantum field theory on a curved space-time.

[fredrik]

I take it that regardless of any final resolution we can agree that this is an interesting topic.

 

If I read Vincent properly, it seems you are attracted by the concept of an "Era of physics based on information".

 

I am a little curious to hear what your view as a string thinker is on the unification of that with the string framework?

 

Do you consider information as something encoded in the state of the microstructure suggested by the string framework? Do you also ask what the support for that particular microstructure in terms of information supporting it?

 

/Fredrik

[Farsight]

Would you like to provide a link to it, just to save folks time if they want to look it up? (Personally I don't remember seeing it.)

 

It was this one: http://space.newscientist.com/article.ns?id=mg19626241.300&feedId=space_rss20

 

Sorry that link is just a stub, you need a subscription to see it all. It was the main feature, and included Lawrence Krauss and others.

 

 

Like it or not' date=' the physics involved in calculating the Hawking radiation is not very hard---it is a semi-classical calculation, which any graduate student could do, if given enough time. One just has to understand how a scalar field behaves on a changing gravitational background. We understand quantum field theory very well, and we understand how to make QFT consistent with general relativity (there is a book on it by Paul Davies and Birrell, if I've spelled his name correctly). If you want to do a google search, the actual method is called the Bogolubyov transformation (which I have probably hopelessley misspelled).

 

The point of all of this rambling is that the loss of information in a black hole is very easy to show (I don't remember very many calculations in Hawkings 1972 paper). If this calculation is wrong (i.e. if you think information is not lost), then you should be prepared to explain why you think it is wrong, and how to fix the derivation from the point of view of quantum field theory on a curved space-time.[/quote'] Perhaps there's some confusion here. I've said previously that I and many others do not consider Hawking Radiation to be proven in actuality, and that we should make a distinction between this and a mathematical proof. On the other hand I've also referred to Neil Cornish saying "the fluctuations we see in the CMB are thought to be generated by a process that is closely analogous to Hawking radiation from black holes." So whilst I have doubts, I wouldn't say I've claimed that Hawking Radiation can not exist. I've also said I think information is irrevocably lost when an object falls into a black hole. Perhaps you're thinking of somebody else, or I'm misreading something.

[BenTheMan]

I've also said I think information is irrevocably lost when an object falls into a black hole.

 

This represents a breakdown of unitarity, then, because no unitary operator could ever ``lose' information. But you don't seem to have a problem tossing unitarity in WW scattering (i.e. killing the higgs), so I shouldn't be surprised.