# Thread: Heisenberg's Uncertainty Principle as applied to Black Holes

1. This is just an interesting question that came up in another thread. Does Heisenberg's Uncertainty Principle have anything to say about matter inside a black hole?

How precisely can we define the location? I'm thinking in one sense, we can't define it precisely at all. But in another sense maybe the accuracy is too precise?

If we can locate the event horizon on more than one side of it, then we can determine the location of the center. We know all or at least most of the mass is confined to a tiny dot in that space.

However, I'm not overly confident that we can locate the event horizon to high accuracy. Even matter coming very near the horizon would have trouble leaving. If we use gravitational lensing then we're subject to the limitations of the "lens" in precisely directing the light.

If we can determine location to very high precision, then does the indeterminacy of the speed present a problem? Clearly no matter how fast the matter is moving, it is still stuck there. Would high enough indeterminacy allow the matter to exceed C? (Create a range of possibilities wider than 0 to C?)

If we can't determine the location to very much precision at all, does that place tighter constraints on the speed? Would it have to be moving at a specific, narrow, and/or predictable range of velocities?

2.

3. At the outset of this discussion (if it becomes one), I want to make a clear distinction between saying we *don't* know something and saying we *can't* know something.

Clearly the fact I *don't* know some object's velocity places no restrictions on how precisely defined its position can be. But if I *can't* know, that's probably a bit different.

4. One problem is that we don't have a successful way of combining quantum theory and general relativity. Black holes are described almost exclusively using GR (there are exceptions such as the derivation of Hawking Radiation, but these tend to be approximations). This means that as we approach the singularity, quantum mechanics breaks down or no longer applies. We don't know whether there is some, as yet unknown, mechanism that would prevent everything become infinitely dense (I assume there is but that is a baseless assumption). My interpretation of the singularity is that even GR (as we currently know it) no longer applies at that point - but there is no theoretical justification for that view, as far as I know. And there are valid arguments that I am wrong!

I assume there is some quantum uncertainty associated with the event horizon. And there is all sorts of research (theoretical and experimental) going into quantum fluctuations of space time, in general.

As for what we can't know. Currently, it is thought that we can never have any direct knowledge of what happens inside the event horizon. That means we would never be able to directly observe whether a new theory of quantum gravity is correct in what it says about the singularity. But we should be able to test such a theory under less extreme conditions. And there is still the theoretical possibility of "naked singularities" (without an even horizon).

5. Originally Posted by kojax
This is just an interesting question that came up in another thread. Does Heisenberg's Uncertainty Principle have anything to say about matter inside a black hole?

How precisely can we define the location? I'm thinking in one sense, we can't define it precisely at all. But in another sense maybe the accuracy is too precise?

If we can locate the event horizon on more than one side of it, then we can determine the location of the center. We know all or at least most of the mass is confined to a tiny dot in that space.

However, I'm not overly confident that we can locate the event horizon to high accuracy. Even matter coming very near the horizon would have trouble leaving. If we use gravitational lensing then we're subject to the limitations of the "lens" in precisely directing the light.
You are correct, it is not possible to localise the event horizon to any arbitrary degree of accuracy; the obvious lower limit would be the Planck length, beyond which quantum fluctuations of the space-time background become so large that any measurements of length, location, energy and momentum simply loose their meaning.
Why would you want to do this in the first place, if I may ask ? Or is it purely academic ?

6. One thing I have always wondered: doesn't infalling matter that has crossed the event horizon change the shape of the event horizon until it has merged with the centre of the black hole?

7. i would imagine if it did the effect would probably be dependant on the size of the black hole itself one would imagine some kind of a change though but pushing a wall i suppose

8. Originally Posted by KALSTER
One thing I have always wondered: doesn't infalling matter that has crossed the event horizon change the shape of the event horizon until it has merged with the centre of the black hole?
My understanding is that once beyond the event horizon, it is all just part of the mass of the black hole and increases the overall radius. If there was a huge mass flying around just below the event horizon (if such a thing were possible) there wouldn't be a "bump" on the surface. After all, that would allow information from the inside to get out and that is not allowed.

However, I think the event horizon might warp out very slightly to meet an infalling mass. I suspect for any reasonable mass, this is insignificant. But if you look at simulations of black hole mergers, they do reach out to each other before forming a single black hole (and then there is a "ring down" phase while it settles back into a sphere again).

9. I also thought about the information issue, but if you say there is a ring down phase, doesn't that convey information about the masses that has just merged? Also, the radius being increased instantly after a mass had entered also violates transmission of information laws, as an observer at the other end of the event horizon would then be able to tell immediately when the mass had crossed the horizon?

10. Originally Posted by KALSTER
I also thought about the information issue, but if you say there is a ring down phase, doesn't that convey information about the masses that has just merged? Also, the radius being increased instantly after a mass had entered also violates transmission of information laws, as an observer at the other end of the event horizon would then be able to tell immediately when the mass had crossed the horizon?
No, because in both cases, all it is telling you about is the total mass (*) which you knew already. You are not forbidden from knowing when it crossed the event horizon, but no information (about the fate of the infalling object) is allowed out after that.

(*) The ring down after a merger probably also depends on the angular momentum of the two black holes, how and when they merged, etc. But, again, all this was known (or knowable) before hand. It doesn't tell you anything about the internal state.

I am reasonably confident about that because there was quite a heated discussion about this on another forum a while ago.

11. Originally Posted by KALSTER
I also thought about the information issue, but if you say there is a ring down phase, doesn't that convey information about the masses that has just merged? Also, the radius being increased instantly after a mass had entered also violates transmission of information laws, as an observer at the other end of the event horizon would then be able to tell immediately when the mass had crossed the horizon?
A black hole has three global degrees of freedom, which can always be determined from the "outside" - total mass, total electric charge, and total angular momentum. Notice the word "total" - you could not determine anything about how those are distributed below the event horizon, or how they originated or any other information for that matter.

12. the internal state of a black hole is fairly simple

13. Originally Posted by fiveworlds
the internal state of a black hole is fairly simple
Yes, since it is unknowable

14. not really i mean it should be obvious

15. Cool, so what happens to the event horizon at the other end of the black hole as, say, a planet crosses the event horizon? Does it instantly swell as the planet crosses?

16. Originally Posted by fiveworlds
not really i mean it should be obvious
I can't wait, please elucidate.

17. ill draw one later

18. Is grated cheese involved? Elephants?

19. Originally Posted by KALSTER
Cool, so what happens to the event horizon at the other end of the black hole as, say, a planet crosses the event horizon? Does it instantly swell as the planet crosses?
The planet takes a finite ( proper ) time to cross the event horizon, so the event horizon takes a finite ( proper ) time to expand. Basically, the radius of the event horizon is proportional to the amount of mass enclosed within it, so it will expand as more and more of the planet crosses the boundary.
Just a word of caution in this context - what we call "event horizon" is an abstract concept, not a physical, tangible boundary of some sort.

20. Originally Posted by fiveworlds
the internal state of a black hole is fairly simple
This also depends how you look at it. In GR, the inside of a black hole is indeed very simple. If you add quantum effects however, things more than likely become a lot more complicated. See the "Fuzzball" model.

21. Originally Posted by Markus Hanke
Originally Posted by KALSTER
Cool, so what happens to the event horizon at the other end of the black hole as, say, a planet crosses the event horizon? Does it instantly swell as the planet crosses?
The planet takes a finite ( proper ) time to cross the event horizon, so the event horizon takes a finite ( proper ) time to expand. Basically, the radius of the event horizon is proportional to the amount of mass enclosed within it, so it will expand as more and more of the planet crosses the boundary.
Just a word of caution in this context - what we call "event horizon" is an abstract concept, not a physical, tangible boundary of some sort.
The boundary where escape velocity equals C and where space is warped on to itself, loosely speaking of course (my only method of speaking).

The problem I have is making sense of the information of the mass crossing the event horizon making it to the other side of the black hole. What I mean is, lets say half of the planet has crossed at t= x from the frame of reference of an outside observer*. Does that mean that at t=x the event horizon at the opposite end would already have expanded by the appropriate amount for half of the planet's mass?

The "feel" of gravity at constant motion is instant (earth orbits the sun where it is now, not where it was 8 minutes ago), but once you jiggle it, the information of that happening travels at C, as you know.

*Let's say he views the black hole edge on with the planet crossing at the left edge.

22. Originally Posted by KALSTER
Does that mean that at t=x the event horizon at the opposite end would already have expanded by the appropriate amount for half of the planet's mass?
Ok, I understand what you mean now. This is an interesting point, particularly for very large black holes on the order a few dozen or even hundred AUs, where such a delay would be on the order of some minutes or even hours.
My understanding here would be that this is indeed the case, i.e. that the information must travel at finite speed across the volume enclosed by the event horizon; what that means is that the BH would show a "bulge" where the planet enters it, and then returns to perfect spherical symmetry ( with larger radius then before ) within a finite time. This appears to tally with what Strange said in post 7 about the merger of two BHs.

23. Originally Posted by Markus Hanke
Originally Posted by KALSTER
Does that mean that at t=x the event horizon at the opposite end would already have expanded by the appropriate amount for half of the planet's mass?
Ok, I understand what you mean now.
It probably took a while, because I am not that good at getting my thoughts across. Hate it when that happens.

Love it when that happens.

So the next question is how would that information propagate? A ripple along the border in 3D all the way to the antipode?

Then also, this would mean that there would be an infinitesimal ripple going round for every particle that crosses the event horizon?

24. Originally Posted by KALSTER
So the next question is how would that information propagate? A ripple along the border in 3D all the way to the antipode?
From what I remember when I read about this before, the ripples propagate in spacetime (both through the black hole, and outwards, creating gravity waves). There is no easy way of calculating this; it was all done as numerical simulations. (Maybe I should try and find some of the papers I saw when this came up before.)

Then also, this would mean that there would be an infinitesimal ripple going round for every particle that crosses the event horizon?
I assume so....

25. So the next question is how would that information propagate?
In order to answer this we would first have to have a precise model of what exactly goes on behind the event horizon, i.e. a model of quantum gravity. I think we are not quite there yet. The best that can be done with current models would be an approximation, like assuming the mass of the BH is uniformly distributed throughout its volume, and then calculating how gravitational waves would propagate through that mass distribution; even that would be pretty darn difficult.

Which is interesting once again, because I have never seen a mathematical treatment of the behaviour of gravitational waves in the interior of masses, only in vacuum. You have a way of bringing up interesting stuff, Kalster

26. just add speed

2013-01-27 21.47.15.jpg

27. Er "add speed"?
How does that "diagram" explain what the "internal state of a black hole is"?

28. a lot of speed magnetic field spins really fast magnetic field gets so strong it can rip a nucleus apart eletrons are dragged closer to the nucleus as spin increases etc

29. To take a rather extreme case, here are some animations of black holes colliding: black-holes.org&mdash;Movies of Extreme Spacetimes

30. it would do all of that and more but basically really really large fast moving atoms. of course one would imagine they are only stable because they are moving so fast which makes it possible to have an unstable black hole

31. What?

32. Originally Posted by fiveworlds
a lot of speed magnetic field spins really fast magnetic field gets so strong it can rip a nucleus apart eletrons are dragged closer to the nucleus as spin increases etc
Originally Posted by fiveworlds
it would do all of that and more but basically really really large fast moving atoms
Stop this nonsense. The thread is about black holes not atoms.

33. are black holes not composed of atoms? particles etc the normal rules we apply should apply and if the nucleus moved really fast this would occur. and those spin diagrams follow expected paths

34. Originally Posted by fiveworlds
are black holes not composed of atoms?
We don't know.
That's already been stated.

35. yeah which is what makes it fun. like if its made of particles what particles are they how would they possibly interact would there be many new exciting particles we have never seen

36. So you're basically ignoring what's said and just trolling?

37. not really i read everything just making guesses am i allowed to?? I am assuming that most of what goes here is pretty theoretical anyways and black holes are open to discussion because we dont know everything about them. i think they are really large atoms. what do you think?

38. But your "guesses" have already been shown to be wrong.

39. really wow perhaps you could direct me to it so i might know disproved by whom? how, when etc

40. Er, didn't you say that you'd read it?
Post #12 specifically.

41. its unknowable?? that doesnt prove im wrong. it just says we have no idea that my guess isnt valid

42. Originally Posted by fiveworlds
its unknowable?? that doesnt prove im wrong. it just says we have no idea not that my guess isnt valid
Er, if it's unknowable then it means exactly that your "guess" that it's "atoms" is invalid.
We know what it isn't, and "atoms" is one of those things.

43. so what else are they not + reasons?

44.

45. Originally Posted by fiveworlds
are black holes not composed of atoms?
Almost certainly not. The force of gravity is even higher than a neutron star; neutron stars do not consist of atoms so it is impossible for black holes to consist of atoms. The best theory we have says that everything is crushed to zero size. We don't know if that is realistic or not. But your random guesses are not.

46. i didnt say they consisted of atoms i meant an atom. ps i read that very interesting stuff why always angular momentum?

47. You mean a large clump of protons and neutrons surrounded by a fuzzy cloud of electrons? That is preposterous. Like already said, atomic structure is lost even before a star collapses into a black hole. How could it then suddenly become a giant atom again?

48. Originally Posted by fiveworlds
i didnt say they consisted of atoms i meant an atom.
Oh right. All of the atoms in the matter that collapses into a black hole gets squished into a single atom.
How does that work?

49. a lots of energy and speed would be my guess. What about those ring singularities? supposedly they are hypothetical wormholes to traverse the universe how does that work is it because of the change in spin of the particles?Why is the chandrasekhar limit the maximum mass of a stable white star is another stable isotope of a white dewarf absolutely impossible?

50. Originally Posted by fiveworlds
a lots of energy and speed would be my guess. What about those ring singularities? supposedly they are hypothetical wormholes to traverse the universe how does that work is it because of the change in spin of the particles?
Fiveworlds, it is obvious that you have been reading quite a lot about this stuff, but have understood very little and now your mind is going all over the place thinking about it all and it is spitting out gibberish. All I can suggest is that we take it step by step. We'll explain one thing and once you have demonstrated that you have a basic understanding, then we can move on. This means you have to stop your mind racing through all this information you don't understand and start from the beginning. Can you do that?

51. yeah sure

52. Originally Posted by fiveworlds
a lots of energy and speed would be my guess.
Energy and speed turn lots of atoms into one?

What about those ring singularities?
Kerr black hole?

supposedly they are hypothetical wormholes to traverse the universe how does that work is it because of the change in spin of the particles?
I think you mean "hypothetically" rather than "supposedly".
Uh, what's spin got to do with it?

53. yes kerr black hole and it goes on about it being a hypothetical 'wormhole' Ring singularity - Wikipedia, the free encyclopedia i was asking how this would hypothetically work.

54. Originally Posted by fiveworlds
yeah sure
Great! First off, I want to commend you for showing interest and an enthusiasm for this stuff at all. Then, you have to recognise that you are largely ignorant about most of it, but ignorance is nothing to be ashamed of. Indeed, ignorance plus enthusiasm plus the right teacher/s equals knowledge! And the more you learn, the more fascinating it will become and you'll have that satisfaction of knowing that you know something real.

First off, what level of education do you have? Did/do you have physics in high school?

55. You haven't bothered to look at the relevant Wiki page?

56. physics yeah and biology and chemistry

57. Originally Posted by fiveworlds
i didnt say they consisted of atoms i meant an atom.
Well, that is even more ridiculous then. And the same argument applies. A neutron star doesn't consist of "an atom".

58. Originally Posted by Dywyddyr
Uh, what's spin got to do with it?

59. i would imagine still reading here that a neutron star is composed of neutrons. is overall neutral and very large but it would not be true to say it is neutral really. Is a neutron not composed of charged subatomic particles? and if those subatomic particles were moving fast one charge outlies the other it would appear to have charge at that particular point?

60. Originally Posted by fiveworlds
i would imagine still reading here that a neutron star is composed of neutrons. is overall neutral and very large but it would not be true to say it is neutral really.
It depends on what you mean by "very large". And, by definition, neutrons are neutral.

Is a neutron not composed of charged subatomic particles?
Except that a neutron is composed of 1 up quark (charge 2/3) and two downs (each -1/3 charge) = zero net charge.

and if those subatomic particles were moving fast one charge outlies the other it would appear to have charge at that particular point?
Huh? Why do you think "speed" has anything to do with charge?

61. well it has a net charge of neutral an up and two downs or anti up and two anti downs right? But they dont get destroyed do they surely they co-exsist together as a system of interlinked subatomic particles each of individual charge like atomic bonds

62. I don't get your point.

63.

64. Yes. An illustration of what I've already said.
A neutron is neutral.

65. look at it take a protractor and draw three circles and lines from each one. it is net neutral but it is not composite neutral

66. Originally Posted by fiveworlds
look at it take a protractor and draw three circles and lines from each one. it is net neutral but it is not composite neutral
Uh that's a diagrammatic representation.
Quarks do not actually "sit inside" a neutron in a neat little triangle like that.

67. do they move??

68. Originally Posted by fiveworlds
it is net neutral but it is not composite neutral
It is neutral. What does "not composite neutral" mean?

69. i mean that in order for a neutron to be neutral it needs a spin greater than a specific number to neutralise itself what is the spin speed?

70. Not sure, but I'd say not in the way most people think of "moving".
Maybe as a probability wave, like an electron.

71. Originally Posted by fiveworlds
do they move??
Yes.

Originally Posted by fiveworlds
i mean that in order for a neutron to be neutral it needs a spin greater than a specific number to neutralise itself
Why? Neutral is neutral. Why would speed change that? The quarks orbit around each other pretty much at random, as far as I know.

72. Originally Posted by fiveworlds
i mean that in order for a neutron to be neutral it needs a spin greater than a specific number to neutralise itself what is the spin speed?
"Spin" in physics doesn't actually mean that anything is spinning.
Ergo there isn't a "spin speed".

73. no in order to be neutral its not random and even then im not sure if itd really be neutral but as close to a possible
http://en.wikipedia.org/wiki/Electric_dipole_moment

74. Originally Posted by fiveworlds
no in order to be neutral its not random and even then im not sure if itd really be neutral but as close to a possible
I don't think the charges of the quarks can be detected outside the neutron. Although that is an interesting point. Hang on ... <google google> ...

An article published in 2007 featuring a model-independent analysis concluded that the neutron has a negatively charged exterior, a positively charged middle, and a negative core
Neutron - Wikipedia, the free encyclopedia

So, fiveworlds, I have learnt something from your random musings. Thank you.

75. one would also imagine that an electron itself must be influenced by the nucleus therefore a change in nucleus spin equals a change in the energy level of its electrons which accounts for planks constant as the change in energy level would equal a change in the spin of the particles in a nucleus which must follow a symmetrical pattern

76. Here's a different diagram of a neutron.
Wiki again: Structure and geometry of charge distribution within the neutron[/h] An article published in 2007 featuring a model-independent analysis concluded that the neutron has a negatively charged exterior, a positively charged middle, and a negative core.[27] In a simplified classical view, the negative "skin" of the neutron assists it to be attracted to the protons with which it interacts in the nucleus. However, the main attraction between neutrons and protons is via the nuclear force, which does not involve charge.

And again: The neutron electric dipole moment (nEDM) is a measure for the distribution of positive and negative charge inside the neutron. A finite electric dipole moment can only exist if the centers of the negative and positive charge distribution inside the particle do not coincide. So far, no neutron EDM has been found. The current best upper limit amounts to |dn| < 2.9×10−26e·cm.[

77. How does somebody create An AC magnetic field pulse as in CryoEDM - Wikipedia, the free encyclopedia

78. Fiveworlds, you are still all over the place. Your mind is spewing out one random idea after the other and we are getting nowhere. Rather pick ONE subject to talk about and then once you have a good idea of what is going on, choose another and furthermore, please do so in your own threads. Agreed?

79. okay. i didnt think it was off topic though to know the exact point a planet or particle enters an event horizon one must know a little bit about the event horizon. but maybe it isnt on topic

80. But you've been all the way from black holes to neutrons to electrons to magnetism, to particle spin, etc. in about as many posts. The fact that black holes are not huge atoms should have been the end of it. Rather choose something and start a thread about it. Thanks

81. Originally Posted by kojax
This is just an interesting question that came up in another thread. Does Heisenberg's Uncertainty Principle have anything to say about matter inside a black hole?

How precisely can we define the location? ...
If we can't determine the location to very much precision at all, does that place tighter constraints on the speed? Would it have to be moving at a specific, narrow, and/or predictable range of velocities?
Well, a simple and probably unsatisfying answer is: It doesn't matter. In quantum theory we can only make useful predictions about observables. Now Observables are operators, and all operators have some sort of uncertainty relation with another non commuting operator.

The thing is, inside a black hole, we cannot observe. So by construction, there are also no observables. Hence there is not observable uncertainty relation. It would be speculation, about as much as speculating about anything else which either doesn't exist, or cannot intrinsically be confirmed. Hence, from the Copenhagen interpretation of quantum theory: Inside the black hole there are no uncertainty relations.

82. Originally Posted by Kerling
The thing is, inside a black hole, we cannot observe.
Even though an observer can cross the event horizon into a well defined piece of spacetime in finite proper time?

83. An observer can't cross the event horizon. That is the whole idea.
The definition:
In general relativity, an event horizon is a boundary in spacetime beyond which events cannot affect an outside observer.

84. Originally Posted by Kerling
An observer can't cross the event horizon. That is the whole idea.
The definition:
In general relativity, an event horizon is a boundary in spacetime beyond which events cannot affect an outside observer.
An observer can fall in through the event horizon. But no information can come out again.

85. Originally Posted by Strange
An observer can fall in through the event horizon. But no information can come out again.
I see you are taking Thornes side in the Hawking-Preskill bet?

86. Originally Posted by river_rat
I see you are taking Thornes side in the Hawking-Preskill bet?
That is a slightly different issue (and one I don't have anywhere near enough understanding to comment on).

87. Originally Posted by Strange
Originally Posted by river_rat
I see you are taking Thornes side in the Hawking-Preskill bet?
That is a slightly different issue (and one I don't have anywhere near enough understanding to comment on).
Sure, but what would the use be?
If the observer falls in (and might I remind you that in quantum physics the observer, must also be an observable). That the moment he crosses the horizon, we have the same initial question over again? I don't see how your argument makes things different?

88. Just a quick question. Hypothetically, if we had an insanely long piece of wire that was attached to a camera (or any other type of measuring equipment), "lowered" that into the BH and connected the otherside of the wire to a computer. Wouldn't we able to get some information? However small amount it might be. I don't understand to much about black holes to say for sure.

89. Originally Posted by WaterWalker
Just a quick question. Hypothetically, if we had an insanely long piece of wire that was attached to a camera (or any other type of measuring equipment), "lowered" that into the BH and connected the otherside of the wire to a computer. Wouldn't we able to get some information? However small amount it might be. I don't understand to much about black holes to say for sure.
No, because no signals would be able to travel along the wire from inside the event horizon.

90. Originally Posted by Markus Hanke
No, because no signals would be able to travel along the wire from inside the event horizon.
And, unless the wire were infinitely strong it would be torn apart. It would be, anyway, because the electromagnetic force holding the atoms inside the event horizon couldn't propagate to the atoms outside.

91. And the camera would be somewhat flat...

92. ...And it would need light...

93. How they apply this rules in this tough terrain.

94. Originally Posted by Strange
After all, that would allow information from the inside to get out and that is not allowed.
That isn't a fundamental rule, though, is it? Isn't that what Hawking was busy trying to resolve for so long? How a black hole can exist without violating the conservation of information?

Certainly information goes in. I'd like to share Mr. Hawking's hope that maybe some of it can get back out. Certainly GR makes that difficult for this to happen. I hope not impossible, but maybe it is utterly impossible?

Originally Posted by fiveworlds
i didnt say they consisted of atoms i meant an atom. ps i read that very interesting stuff why always angular momentum?
Fiveworlds, I think other posters have already pointed this out, but I'll repeat it:

A neutron star is a huge atomic nucleus. That is..... if it were to contain even one proton, it would be an atomic nucleus. By very definition , that's exactly what an atomic nucleus is. They're just small clumps of protons and neutrons.

A black hole comes after the neutron star, and so it's reasonably safe to say that black holes are different from atomic nucleus's. Not entirely safe to say that.... but reasonably safe.

95. That isn't a fundamental rule, though, is it? Isn't that what Hawking was busy trying to resolve for so long? How a black hole can exist without violating the conservation of information?
Yes, and the answer is simply that BHs have entropy, the amount of which is proportional to the area of its event horizon. Thus information entering the BH is not lost, but simply "garbled", and reappears as entropy.

96. Originally Posted by Markus Hanke
Yes, and the answer is simply that BHs have entropy, the amount of which is proportional to the area of its event horizon. Thus information entering the BH is not lost, but simply "garbled", and reappears as entropy.
Hi Markus

I must disagree with you here, quantum information can't be re-encoded as entropy, radiated away and still be conserved. The transformation you are proposing is not unitary.

97. Originally Posted by river_rat
I must disagree with you here, quantum information can't be re-encoded as entropy, radiated away and still be conserved. The transformation you are proposing is not unitary.
It would appear you are correct, river_rat. I did some searches on the Internet, and my understanding of the matter is gravely faulty. In fact, the entire issue still seems to be in a state of active research, and the final word hasn't really been spoken :

AdS/CFT correspondence - Wikipedia, the free encyclopedia

I will have to have a closer look at this before commenting further. Thanks for pointing this out, river_rat.

98. You have got me thinking here, river_rat.

The event horizon of a black hole has a finite surface area, i.e. it is a more or less well defined area of space-time. Black hole thermodynamics now tell us that we can associate entropy with that surface area, and by definition entropy is in turn related to the number of micro-states of a system. So, the event horizon is not a material object but rather a region of space-time, and we can associate a well-defined entropy with such a region, which, in turn, allows us to compute a number associated to micro-states, and that number will be finite. Would this not automatically imply that the space-time region of the event horizon must be fundamentally discreet since it has a finite number of micro-states ? In the absence of anything but space-time ( the event horizon is not a tangible surface as such ) the entropy cannot be associated with anything but micro-states of space-time itself, so it ought to be impossible for such a space-time to be a continuum because the entropy would then be infinite.

Furthermore, since the entropy depends only on the area of the horizon and not on any other property of the black hole, we should in principle be able to choose any closed surface / connected region of space-time, regardless of whether that is an event horizon or not, and associate entropy to it, and that entropy should correspond to a finite number of micro-states. That would mean that space-time in general ought to be discreet on a microscopic level, and not a continuum.

What do you think ?

99. So the black hole has how many possible micro states? Like what's a good ball park figure for this? It must be more than just spin, charge, and mass if the particles it emits are to have a great deal of entropy to them. Or are they sufficient? (Perhaps the entropy comes from the vacuum fluctuations which gave rise to the particles that become hawking radiation - and therefore don't carry very much real information about the black hole anyway?)

Does this then imply that these internal states are detectable (perhaps indirectly?) If so, then how does us detecting them not violate Special Relativity's notion of causality? (Or perhaps I mean relativity of simultaneity?)

100. Originally Posted by kojax
So the black hole has how many possible micro states? Like what's a good ball park figure for this? It must be more than just spin, charge, and mass if the particles it emits are to have a great deal of entropy to them. Or are they sufficient? (Perhaps the entropy comes from the vacuum fluctuations which gave rise to the particles that become hawking radiation - and therefore don't carry very much real information about the black hole anyway?)

Does this then imply that these internal states are detectable (perhaps indirectly?) If so, then how does us detecting them not violate Special Relativity's notion of causality? (Or perhaps I mean relativity of simultaneity?)
These are all very good questions, to which I have no answers to offer at this point in time. I initially thought I had made a very simple point, but the more I think and read about it, the more complicated all of this becomes. This is a highly involved topic, and there is no consensus yet about what exactly goes on here.

101. Bohm postulates a zero state energy continuum for the universe. A continuum of wave frequencies so tiny that they overlap and become a straight sine wave.
I wonder if a black hole might not be a zero state matter singularity, where quantum actually stops from lack of space within the compressed singularity..

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