(alpha) Black Holes and Information Loss

This thread is for those who wish to discuss this topic from the perspective that there exist singular solutions to Einstein's theory which manifest themselves in this universe. If you do not agree with this statement, please start another thread somewhere else. If you do not understand the problem, then ask questions! I am by no means an expert, but can find the answers. My office mate is an expert in this area, and is infinitely patient.

http://motls.blogspot.com/2007/04/samir-mathur-comments-on-fuzzballs.html

This guest blog entry by one of the high energy faculty here at OSU is worth a read. It is a bit technical, but is very well written, from a man who is an excellent teacher.

Basically the problem is as follows: If you build a black hole from, say neutrons, Hawking has showed from completely general (classical) arguments, that the black hole decays. This process is called 'Hawking Radiation', and has a thermal profile. "Thermal" means it emits all of the states in your theory with equal probability. So, if we build the black hole out of neutrons, then it will emit all standard model particles---electrons, photons, protons, neutrinos, etc.

But this is a problem because it is a very easy result to show that a pure quatum mechanical state can never evolve to a mixed state. This is a feature of the unitarity of the theory, and unitarity ensures that we have a sensible interpretation of probability, among other things.

There are two stringy solutions to this problem---one by Samir, and one (of which I'm much less familiar with) due to Susskind (I think). Hawking recently (July 2004 I think) proposed a solution as well.

Anyway, I hope there is SOME interest in this thread. I will trust the moderators to ensure that the alpha rules are obeyed, and that no one hijacks the discussion.

 

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What is the difference between a pure quantum mechanical state and a mixed state?

 

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I tend to agree but mainly for the same reason I am troubled about where the magnetic monopoles are (or went). I.e. It is my belief, that if something is not forbidden (by physical laws we believe) then "mother nature" made some.

If you, or someone else better qualified than me, does not answer Pete's question, I will try.

BTW, did you ever explain my idea that small (stellar size) black holes were made "by the dozens" in three stages of a chain reaction, when the large first generation stars died? My idea is possible because the assumption of exactly spherical collapse to the mass canter, always assumed, is wrong because of the thermal instability in the fusion reaction rates exists. It is unlikely to be at the mass center. (Fusion rate is much stronger function of temperature, T, than the only square of reactant density, D. Thus any slightly hotter region near center has rapidly rising T and falling D to stay in hydrostatic equilibrium with the surrounding region (including the radiation pressure as the temperature rises in the hydrostatics balance, of course.). I.e. a "radiation bubble" briefly forms, slightly away from the mass center, while burns up all the reactants to iron and then collapse upon fuel exhaustion - sending shock waves into near by denser regions forming multiple black holes by compressing these regions above the black hole collapse density threshold. As these secondary black holes form more shocks are generated to produce (when to intersect) third generation of black holes even in plasma not yet near the critical density for black hole collapse.

Please no one discuss this here. Instead see old thread: "(alpha) Dark Matter - What is it?" especially posts:

http://www.sciforums.com/showpost.php?p=1302292&postcount=72

And for more detailed discussion of a star photo (now the “Eskimo nebulae”) that may have been captured in this three - stage, multiple small black-hole, formation process only a few thousand years ago. The photo fit’s the three stage model, with the one initial small black hole farthest away, etc. very well. (black holes can not be seen, of course. - but they appear in the photo as about 100 radially out bound, tail going first, "comets" for reasons explained in post 63. The first is the only one now "tailess" ("comet") for reasons also explained. I predict it will soon (few dozen years at most) be invisible.

http://www.sciforums.com/showpost.php?p=1301635&postcount=63


I only provide here a compressed account of my argument presented in that thread for Ben to print and show his office mate "expert." No one, Ben included, has given me strong reason to drop this idea. - I hope someone can. Perhaps the much greater number of small black holes can not account for "dark matter" - I mainly am interested to know if they may exist as assumed in Book Dark Visitor which you can read for free as web site under my name.

 

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Hi Pete,

One way to make sense of the difference between a pure state and a mixed state is in terms of measurement outcomes. I would like to think about the very concrete example of a spin system like an electron where you have a vector called spin that you would like measure (you can do this with a magnetic field) The basic experimental fact is: If you measure spin along any axis you always get one of two values, call them 1 and -1, so that spin is quantized. Now imagine I have a big bucket of these particles and lots of machinery so that I can fiddle with them all I want.

Experiment 1: I prepare a bunch of particles in the vertical spin 1 state. I hand you these particles one by one and allow you to make measurements. If you measure in the vertical direction you always get 1 every time. If you measure in a horizontal direction you will find that you get 1 and -1 with no obvious pattern, and over many trials you get 1 and -1 each about half the time. This is quantum uncertainty. Precise knowledge of the spin along one direction precludes precise knowledge about spin along another perpendicular direction. This scenario is described by a pure state, or you could say I have prepared a pure state.

Experiment 2: Suppose now I give you particles from a batch I prepared with definite spin 1 in a certain horizontal direction. If you measure in the vertical direction you will now find that you get 1 and -1 each about the half the time. If you measure in the certain horizontal direction I chose you will find 1 every time. This scenario is also described by a pure state.

Experiment 3: Now I do something sneaky, I decide to give you particles randomly. I give you a particle from a batch with definite vertical spin 1 only half the time. The other half of the time I give you particle from a batch with vertical spin -1. The key point is that I don't tell you what I'm doing. What do you find now? If you measure vertical spin, you will get 1 and -1 each about half the time. If you measure horizontal spin, you will still get 1 and -1 about half the time. In fact, with a little effort you will discover that there is no spin direction you can measure which will give the same value each time. There is some extra uncertainty! This scenario is described by a mixed state.

In short, a pure state has the minimum allowed (quantum) uncertainty while a mixed state has some extra classical uncertainty.

This was a bit muddled, but does it help at all?

 

Thanks PhysicsMonkey.

So why can a pure state not evolve to a mixed state?

If you start with a batch of vertical spin 1 electrons, can't you pass them through a number of suitably aligned magnetic fields to get half spin 1, and half spin -1?


And Ben, I don't understand how this poses a problem for Hawking radiation?

 

Pete,

To answer your question, I must point out a distinction. The evolution of physical states can be either unitary or non-unitary. The physical distinction, stated very roughly, is that unitary evolution preserves information.

If we allow non-unitary evolution then it is quite true that pure states can evolve into mixed states. This kind of evolution tends to occur when you look at a system which is coupled to a big noisy environment. Information about your system tends to get lost.

On the other hand, if we only allow unitary evolution then pure states can't change into mixed states. Unitary evolution is typical of closed and isolated quantum systems.

For example, you're quite right that with a suitable combination of magnetic fields (unitary evolution) we could change our batch of spin up electrons into a batch of electrons which when measured give vertical spin 1 and -1 with equal probability. But this doesn't imply the state is mixed. As in experiment 2 above, there will be a new direction, some horizontal direction, in which you can measure the spin and always get the same answer. This is a general feature of pure states which is preserved under unitary evolution. In other words, there will always be a "certain direction" if your state is pure and the evolution is unitary. In contrast, the mixed state has no "certain direction", and it isn't too much of a mental stretch to imagine that the lack of such a "certain direction" corresponds to less information.

Another slightly more mathematical way to understand this notion of information preservation is in terms of entropy. The entropy of a pure state is always zero while the entropy of a mixed state is greater than zero. For the mixed state described above, the entropy is ln 2 in some units. Entropy, which is a measure of information, is preserved under unitary evolution, so unitary evolution can never connect a mixed state with a pure state.

 

Ben,

I wonder how N = 8 supergravity deals with such things. If N = 8 SUGRA really is UV finite, it would be interesting to know what happens with black holes in the theory (I assume the theory would have something like them).

 

It is considerable doubt and anxiety that I dare to question even slightly, what PM told Pete in post 4, but here goes:

Certainly from Pete's POV the "experiment 3" results are indistinguishable from a 50 / 50 mixed state, but not from PM’s POV. I.e. if Pete tells PM the angle he has it magnet analyzer set, then PM can predict which result will be dominate, on each trial, unless Pete has it set horizontal.

In a true 50/50 mixed state, no one can predict. As I understand it, a mixed state is not a statistical mix of pure state events repeated many times, but EACH event is mix of both states.

Let me switch to photons and one or no polarizer analyzer with a hot filament photon source and a very rapid brief shutter (Perhaps a combination of reflections off spinning mirrors etc.) so I only get two photons at the detector every second on the long-term average.

The last mirror of the set is very light weight and as the photon leaves it to the distant detector there is a slight down frequency shift to provide the mirror recoil energy and I know the time of travel to the detector and when each photon left the last mirror, but not its polarization. I.e. I can tell when detections may occur, and when none will from the ToF and the shutter open time (or mirror recoils).

Now a perfect polarizer is inserted in front of the detector and only one every second, on the long-term average, is detected, for all orientations of the polarizer. No one can give any information about which will pass and which will not on each event. - these photon are AND MUST BE described as in a mixed state of polarization.

In PM's spin experiment 3 case PM could give some information if Pete told PM how the analyzer was set. Thus, only from Pete's POV were they indistinguishable from a mixed state. PM knew for each electron sent if it was in the pure spin up or spin down state (As he selected which to send, but randomly - used perfect coin to set filter to "up or down" pass).

A true mixed state exist on each event (photon or electron) ONLY if, in principle, no one can predict anything about the out come of each event (assuming that the two out comes are equally probably in the long-term average to keep it simple. I.e. the "mixed state" is a 50 / 50 mix of only two possible orthogonal "pure states" in each and every event.)

Hope my point is both correct and clear.

 

hello all. Sorry for starting this thread and then abandoning it!

PhysicsMonkey---your question about N=8 SUGRA is a good one. It was one of the first thoughts I had when I read the abstract of the paper that came out a few months ago by Michael Green and Bern and others. Green, Schwarz, and Oooguri(?) just came out with another paper, placing N=8 SUGRA in the "swampland". As far as I know, the "swampland" is inhabited by theories that are uninteresting in the sense that they have absolutely nothing to do with our universe. For example, one could build a perfectly consistent string theory with the space-time symmetry U(1)^248, but it is never studied for obvious reasons. That being said, I don't know the answer to your question. I will think about it and ask some people who are more familiar with the subject that me.

Billy---

The monopoles, if there were any, were inflated away. This is one of the great things to come out of Linde's work... Before the early eighties, everyone was really worried that we should have many monopoles. Linde showed everybody that if there were monopoles. they were formed before inflation, and thus it is highly unlikely that there would be many in our hubble volume. One at the most.

I'll try to contribute more to the discussion, if there is any. Have a good day.

 

Thanks. I accordingly cancel my claims about small black holes being a component of the Dark Matter; however, I still think dozens of small, essentailly undetectable, black holes are formed during the final hour of the large star's dying process, but that is off thread here and no one seems interested in discussing it in the miss-named, but appropriate thread. If interested in doing so, see post:
http://www.sciforums.com/showpost.php?p=1302292&postcount=72

PS - I am definitely a "before the eighties" physicist. 20 or more years ago most of my interest switched to economics and how the mind works. (Especially vision and if free will is possible belief for a physicist. It was not for Einstein.)

 

Billy---this may be. I am far from an expert in the subject of stellar collapse. Your idea that density fluctuations in the star right before collapse seems reasonable, but I am probably the wrong person to be taking advice from in this respect. Assymetrical collapse is probably a very difficult problem to study, and the spherical symmetry of a dying star is probably the only thing that makes the problem solvable.

 

In first paragraph of post 1 you said:

"My office mate is an expert in this area, and is infinitely patient."

So in post 3 I made very condensed summary of why I think the standard results must be wrong. Please print and show to him. If he is at all interested, help him to read the two links I also gave in post 3. Would very much like to know what an "expert" thinks of my idea.

Agreed. -It probably is well beyound man's current ability to analytically model, but certainly idea could be simulated realistically (if you had the money to do so.)

 

[QUTOE]"My office mate is an expert in this area, and is infinitely patient."[/QUOTE]

Black holes is a big field. He is working on a specific type of stringy black hole, not the types of black holes one might expect to find in the universe. I will ask him, but I doubt he knows much more than I do about these things.

 

Billy T, your point is very relevant because it illustrates an important property of mixed states. The notion of a mixed state can depend on the observer because the mixed state encodes information about the observer's knowledge of the system.

For example, if in experiment 3 I keep the up batch and the down batch separate, then it is quite true that I have additional knowledge. From my point of view I have not one ensemble but two, and each is described by a pure state. Because the density matrix represents my description of the ensemble its not hard to imagine that my density matrix will be different from Pete's since I have additional information. On the other hand, if I scramble my up batch and my down batch together in a box, then I have lost information and my density matrix will be the same as Pete's.

Thus a mixed state encodes information about two (apparently) distinct kinds of uncertainty. One kind of uncertainty is quantum, and so far as we know nothing can be done about this sort of uncertainty. The other kind of uncertainty is classical, like in thermodynamics, and one can think of it in terms of sloppy preparation. In other words, a pure state represents finest preparation with the minimal possible uncertainty.

 

I probably still suffer from the idea that things have definite properties, independent of our knowledge about them. (Not to be miss-understood as a "hidden variables" position.) Thus, I tend to consider that a system is in a "mixed state" only when it “truly” is, not when my (lack of) knowledge only forces me to model it that way. Although a classical system can not be in a "mixed state" (by definition), I will take a classical example to be clear:

Suppose I bought a new deck of playing cards, made with automatic production equipment and none of the "Jacks" were in it because of some brief technical problem during manufacture. I must describe* the state of a single card just taken, face down at random from the central region of the well shuffled deck, as a "mixed state" until I turn it over and look. On this we agree I think (Using cards, as I did not want to be cruel to a cat.

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)

In fact I can predict the probably of it being a "Jack" as 1/13 and continue to predict this for very many repetitions (perhaps a 100) of selecting one card at a time, if selected cards are replaced and deck re-shuffled. Eventually, as the repetitions increase, I will conclude the mixed state is not the mixed state I originally thought it was.

I reject calling this deck of cards or the single card, still face down just selected, an "evolving mixed state." It is my knowledge that is evolving - the state of the deck has never changed.
-----------------------------
*Reality may differ from my forced / necessary description.

 

ModNote: moved off-topic post by Lord Sithis and reply by BenTheMan to [thread=62837]Alpha rules and violations[/thread]

 

Why I think mixed states is "on topic":

Imagine a black hole swallowing one of two not yet observed entangled particles, but only one. I do not know much about this topic (entropy of black holes, information lost with things thrown in, like a dictionary or computer memory etc.) but think there is a lot of "food for thought" in the case I imagined to start this paragraph.

 

Hi BillyT...
It is to my understanding that inflation has diluted the magnetic monopole count; probably the reason we haven't seen one.

 

To Reiku: Glad you dug this 6 month dead thread back up. I had forgotten about it, but still think my post 17 of it is very interesting, I.e.:

Imagine a black hole swallowing one of two not yet observed entangled particles, but only one.

For example, what if some unfortunate physicist, whose space ship lab has just fallen inside the black hole's EH does "observe" the one entangled particle that is falling in with him along side his space ship. Does, or does not, that measurement also force the other mixed state particle (still out side the EH) to go into a pure eigen state? If it does, how does the information get out?

If so, when. (The hapless physicist is experiencing great time dialation. He made his measurement only 10 seconds, his time, after falling thru the EH but that is 10,000 years later for us out side the EH.) Will the external particle wait for 10,000 years before collapsing into the anternative eigen state? What happen if I make and observaiton it only 10 years after the physist and his space ship disappear inside the EH? Dose it some how clairvoiently "know" what state will be the anternative state when 9,990 years later (my time) the physicsit will make his?

I was hoping some one could say someting informative about this - and still am 6 months later.

 

This is a thought isn't it... can i just ponder it for a while, then post a reply?