I meant for some while to write a post about the black hole information loss paradox, but despite my best intentions I haven't yet come around to doing so. As a warm up, for you and me, here is a poll:
Btw, here are the results of our last poll "Does the past and the future exist in the same way as the present?" From 153 votes, 41.2% decided for "Past, present and future exist in the same sense," 29.6% for "It is only the now that exists, but neither the past nor the future." And, surprising for me, only 15% voted for "The past exists as does the present moment, but the future doesn't.". The remainder chose "Other".
Friday, June 20, 2008
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At the very least with a toy model of classical gravitation, and a spice of special relativity, this is a no brainer.
ReplyDeleteConsider a particle in a stable orbit around a 1/r^2 field. For the particle to fall into the well it would have to radiate some amount of energy (light, matter, gravitation, really whatever your cup of tea is). This would be subtracted from the rest mass of the particle. Eventually there is an orbit where the particle no longer has rest mass...I wonder what happens then?
Perhaps, at that point the particle has radiated away all information except total charge, spin, and whatever other quantities a black hole is allowed to expose to the universe, within the restrictions of various no hair theorems.
Indeed. One can flesh this out a bit by considering multipole expansions and so on. I've played around with that for a while, but the quantum regime is significantly tougher.
ReplyDeleteI imagine the quantum formulation is significantly tougher.
ReplyDeleteBut using a bit of Linear Algebra you can readily show that GR constrains QM to having no more fundamental particles than the number dimensions describing the macro-state of a black hole (mass, spin, charge, ?colour?, etc...).
That is because all other information is radiated away, one must be able to compute from the macrostate of the black hole, what its micro-state configuration is.
Sorry, I fail to see what you mean with GR constrains the number of particles in QM. Besides this, the number of particles isn't the only relevant information. What you say doesn't even hold generally in classical GR. If you let collapse two perfectly spherically symmetric systems, they will form a black hole without any hair or multipole moments that need to be radiated off. There's no way to distinguish both since the asymptotic field is the same. Best,
ReplyDeleteB.
I hate long winded comments, and I have to get back to so I will be concise.
ReplyDeleteIf a thermodynamic system holds no information, that is it has minimum entropy, then the thermodynamic variables that describe the system must be an invertible function of the microstate variables.
In the case of the black hole, if for exampe it only exposes total charge, total mass, and total spin; then for those thermodynamic variables to be invertibly related to underlying microstates, there can only be three types of particles for which the macrostate is a sum over.
So either there are more thermodynamic variables a black hole can expose, or we have missed something big in the Standard Model. My bet is that black holes can expose more varialbes.
Did any of that make sense?
Hi Aaron,
ReplyDeleteThanks for the clarification. I think I know what you mean. People have played around with this possibility, it's called 'quantum hair' - in which case the black hole is not just described by the three parameters in the standard (no hair) case. I'm not entirely sure I recall correctly what the drawback is of that solution, but I think it's about what you say, it would mean we have missed quite a lot in the Standard Model (lots of charges that the black hole could carry), which doesn't seem to appealing. So, yes, it is an option, but as with all other offered explanations, the big question is the 'how so'. Thanks for mentioning this since I indeed forgot to add this option in the poll. Well, I guess it falls under 'other'. Best,
B.
btw, speaking of quantum hair, look at this :-)
ReplyDeleteQuantum Hair Styling
That's almost as good as the pi perfume!
ReplyDelete(As for the topic, I voted for the radiation option, but really only on the basis of "that's what smart people say (IIRC) and it kinda makes sense." I'm happy to defer to the experts in such an area...)
:-) And then there's the
ReplyDeletePi Supported Kneeling Kench
err, I meant 'bench'
ReplyDeleteLooks like the quantum shampoo also comes with quantum foam, Wheeler would approve.
ReplyDeleteHi Bee,
ReplyDeleteOf course the information loss paradox assumes black holes with event horizons actually exist. I'm not aware of any event horizon observations that have held up.
Einsten denied black holes ("Scwarzchild singularities") exist. I think John Wheeler held private doubts about them until the end. That's one reason he tasked his students in the 1960's to look for viable alternatives to general relativity. Also, he had nice things to say about a controversial gravity theory by Yilmaz, with an exponential metric, where black holes don't occur. (It also has the virtue of being renormalizable.) He called it "deputy general relativity."
A 1999 survey of black hole candidates in this galaxy, by Robertson, finds they bear a close resemblance to neutron stars. They give off the same types of x-ray flares seen when matter strikes the hard surfaces of the latter. (Robertson told me the referees noted a conflict between his observations and general relativity, and said he would have to develop an alternative theory before he could publish his observations. Eventually someone told him about the Yilmaz theory, and he was able to publish by citing that.)
At the location of the supermassive nucleus in this galaxy, Sgr A*, there seems to be a radio source. Many regard the dark nuclei of other galaxies as the best observational evidence of black holes. But they have other features in contradiction with the black hole model, discussed here.
Am I overlooking any good observational evidence? No black holes -- no paradox.
Best wishes,
Kris
Sorry about the Schwarzschild typo.
ReplyDeleteClicking on ArXiv version of Robertson's paper that I just linked to, I see it's been withdrawn. My apologies!
ReplyDeleteFor those new to this subject, John Baez's note here is excellent. It's also covered in Wikipedia here. Also H. Dieter Zeh considers it in Where has all the information gone?, basically coming to the conclusion that there is nothing special about black holes, there is no information loss - it's just everyday quantum decoherence.
ReplyDeletePersonally, I think it's all rather a fuss about nothing. I think the interesting point that arises from all this is why we think "information" is so important in physics, and why we consider it to be so fundamental.
... and a good answer to why we consider information to be so fundamental in physics is presented here.
ReplyDeleteI like the Horowitz-Maldacena solution.
ReplyDeletehttp://arxiv.org/abs/hep-th/0310281
It is a brilliant idea that puts the crazy stuff where it belongs ---near to the singularity.
Hi Andrew,
ReplyDelete“... and a good answer to why we consider information to be so fundamental in physics is presented here.”
Thank you again. Highly entertaining sabbatical reading. Last time I enjoyed at the same level was Hans Christian Andersen.
Two irrelevant side remarks:
1)The writer provides the infantile description of J. von Neumann “Theory of Measurements” based on bizarre abstract spectral decomposition theorem of D.Hilbert. It was formulated about 80 years ago. The writer treating of A.Zeilinger et al investigation and C.E. Shannon “Theory of communication” is truly original.
2)It was pointed out by N.Bohr and explained by L.Rosenfeld why spin of the electron can’t be measured (also about 80 years ago).
Regards, Dany.
Hi Bee,
ReplyDelete“Information? Whose information? Information about what?”
-J.S. Bell
I said no for other reasons, that being I think that QM is foundationally incorrect, where information is not a fundamental quality in the normal sense considered. For instance in Bohmian Mechanics where there are both particles and waves, it is only the wave that has what is called information which is represented or displayed if you will by the particles. While the particles themselves may be removed (hidden) from the rest of the universe by gravity via the event horizon, there is no reason to believe the wave (its aspect of substance) is and therefore the information is retained. Of course I realize that they are still struggling to have BM consistent with SR, yet if it can be made so all this information thing may be simply much a do about nothing.
Of course this is just another crackpot theory and yet seeing as all of this is still up in the air I don’t feel inhibited enough to hold it back.
Best,
Phil
Hi Andrew,
ReplyDeleteThanks for the references, that will be useful!
-B.
Hi Kris,
ReplyDeleteI think most people believe that the singularity is overcome in some way by quantum gravitational effects. That however has nothing to do with the horizon, which is the feature I would say characterizes a black hole. Well, yes, it is pretty hard to obtain evidence for something that stands out by being a one-way membrane for information, but tell me, what would you consider convincing evidence? I find it very convincing that by now we have observations of regions in which there is a large amount of mass in a very small region of spacetime, such that GR lets us conclude it is a black hole. One can probably always cook up some very speculative alternative explanation for everything, but to me this is a case of If it quacks like a duck, I would call it a black hole. Best,
B.
Hi Phil,
ReplyDeleteWell, I too am 'No for other reasons' though for reasons other than yours. Should I find a job next year maybe I'd indeed follow up on it and write a paper, but so far it's only another believe ob mine. Anyway, your criticism is interesting, but I don't think the problem here is the concept of information in QM since you already have a problem classically, as I remarked in a comment to Aaron above. The black hole singularity is an attractor. It doesn't matter what initial state you had (classical or quantum), it all ends up in a singularity, but then everything is equally singular. This is basically the reason why I am convinced the problem is the singularity and not, as most people seem to argue, the horizon. The horizon is where information can be no longer recovered, but the singularity is where it gets lost. Anyway, as long as you are in the classical regime the black hole does not evaporate so you will never know it got lost. Best,
B.
My take on black holes is conditioned mostly by middle-brow treatments from the 70s. IAC, what I gathered was: to an outside observer, the flow of rate for the falling body is red-shifted/slowed down more and more, asymptotically as it approaches the horizon. Hence, it never really falls through and nothing about it is really totally lost (?) at any moment we can define.
ReplyDeleteBut, from the body's point of view, the fall is supposed to be finite. However, I have a problem with that. If throughout the entire infinite future of our universe the body is defined as ever slowing and approaching a limit of sequential time, how could it ever, even from its own perspective, proceed beyond that moment? It should just have to stop there because there is no world after eternity in effect for the rest of the progression to play out in.
Maybe I didn't frame that right, pun intended, but compare with ordinary time dilation. There, the rates still have to be consistent with all events actually being definable at some place and time for any observer, albeit not the same for every observer.
Hi Bee,
ReplyDelete“This is basically the reason why I am convinced the problem is the singularity and not, as most people seem to argue, the horizon. The horizon is where information can be no longer recovered, but the singularity is where it gets lost.”
Well to tell you the truth I also have struggled with this singularity concept for a long time along with the concept of an event horizon and of course Hawking and Bekenstein muddied the waters further by equating the area of the horizon with the entropy content and not just the mass contained. On the other hand the Bohmian perspective does cut between what one would call classical and typically quantum.
For instance, in the classical sense entropy is not something that is a consequence of a single particle yet only all when considered. In the straight forward quantum perspective it’s not a quality of the wave yet rather the density matrix which is a mixed state. However, in Bohmian mechanics it’s somewhat different with both particle and wave being considered as aspects of reality or beables they can be thought of separately.
Now let’s consider your minimum length idea and apply this only to the particles. In this case with a particle that has no wave component to manifest the forces between them, how close can they be? Perhaps you can’t say zero dimension, yet the density could be exponentially greater then that of a neutron star. Also, you might consider all particles to be in the same state and as such having no actual reality or meaning as being separate. Furthermore the entropy would now be considered reduced to a potential of what is below the horizon and above. So for me the horizon is where the wave aspect and the particle one get separated, which in truth may be how they were before the beginning.
I know more crackpot and yet fun to consider:-)
Best,
Phil
Hi Bee,
ReplyDeleteAs you point out, assuming a priori that general relativity is correct, a large enough mass in a small enough region implies a black hole. You could count the objects meeting that criterion, and take their existence as a confirmation of the theory, but of course that would be circular reasoning.
Only two very distinct classes of objects have been found which meet the criterion. Why?
Galactic nuclei, with masses on the order of millions of solar masses (these seem to be always about 0.2% the mass of the host galaxy), plus candidates observable in this galaxy, which only range up to roughly 20 solar masses. (You might expect the latter would sometimes accrete additional stars or black holes and become heavier. In comparison, the non-black-hole star Eta Carinae is over 100 solar masses.)
One type of black hole evidence people would like to see would be radiating matter which vanishes on passing through an event horizon.
There have been claimed observations of that kind, but none have held up.
The galactic candidates are in binary star systems, and accrete matter from their companions. As I mentioned, they emit x-ray flares closely resembling those from matter accreting to neutron stars. (If it looks like a neutron star, and it quacks like a neutron star...)
Since we "know" GR is correct, models have been constructed where the galactic black hole candidates are always surrounded by orbiting matter. Infalling matter collides with that to produce the flares. Wish I had the reference, but I've seen a proposal that we also need a new model of neutron stars, where those are always surrounded by orbiting matter -- to explain their close similarity to the black hole candidates. Martinus Veltman has complained that astrophysicists are tying themselves up in knots to make their results agree with general relativity.
Assuming GR is the only viable gravity theory, any alternative explanation of phenomena could be called "speculative." Some theories, like the Yilmaz exponential metric or my own, predict massive bodies ("red holes") without event horizons. There may be direct evidence of such things in Sgr A*, and in certain quasar observations.
General relativity is said to be a strong, well-tested theory. But on that grounds, any observation needs to confirm it to be accepted. For example, in the case of the Pioneer anomaly, that must due to some unknown systematic effect...
All the best,
Kris
Hi Bee and Kris,
ReplyDeleteBee:” I think most people believe that the singularity is overcome in some way by quantum gravitational effects. That however has nothing to do with the horizon, which is the feature I would say characterizes a black hole. Well, yes, it is pretty hard to obtain evidence for something that stands out by being a one-way membrane for information, but tell me, what would you consider convincing evidence?”
You use notion of “membrane”. But it is valid in non-relativistic Newtonian mechanics only. Already at the relevant limit (v -> c) the notion of rigid body ceases to exist. In addition, ED, GR and QM are field theories. Let forget about QM for a moment (it is field theory with dispersions added). What do you mean “membrane” in the classical field theories?
Regards, Dany.
P.S. I have no problem with the definition of surface for the neutron star.
P.P.S. “but to me this is a case of If it quacks like a duck, I would call it a black hole.”:
http://www.youtube.com/watch?v=YsCR9Y4Ymvo
Hi Dany,
ReplyDeleteYeah, I know the Berlitz ad, it never fails to make me laugh. I didn't mean 'membrane' in the sense as that it is constituted of actual particles, but just as a surface that can only be passed one way. Best,
B.
Hi Bee,
ReplyDelete“Yeah, I know the Berlitz ad, it never fails to make me laugh.”
Great. Here we never disagree.
“I didn't mean 'membrane' in the sense as that it is constituted of actual particles.”
That is the meaning of “membrane” in classical physics, you have no choice.That is the meaning of r=rg (rigid spherical surface) and it is produced by the point mass. In math that is known as most powerful method to prove the statement:” Reductio ad absurdum”. The alternative conclusion compliant with QM may be: the point mass doesn’t exist in Nature.
Regards, Dany.
Dany,
ReplyDeleteI am not even remotely interested to argue about the use of words. The event horizon is a feature of a classical theory and it is not constituted of particles (unless you want to argue that space itself emerges in some way from particles possibly). I really don't know how I can possibly make that clearer. If you don't like the analogy to a one-way-membrane, well, I suggest you just ignore it. Best,
B.
Hi Bee,
ReplyDelete“unless you want to argue that space itself emerges in some way from particles possibly”
YES (wave packets). It is A.Einstein original statement, supported by H.Weyl, E. Cartan, E. Schrödinger, P.A.M. Dirac, E.P.Wigner, R.Utiyama and everybody else.
It is mainstream physics POV.
Regards, Dany.
Dany, I have no clue where you get your idea from what a 'mainstream' POV in physics is. I even doubt there is one. But if I had to guess I'd expect most people in the field to say that on a fundamental level, particles and spacetime are just the same 'stuff' (whether that is strings or braids or swhatever). That is conceptually very different from saying one is made of the other. But that's a quantum gravity expectation and you were talking about the classical theory. GR is a perfectly classical theory that describes something called space-time. In GR, space-time is fundamental, it isn't 'made' of anything. There were many ideas in the history of science that didn't work out. Best,
ReplyDeleteB.
http://www.youtube.com/watch?v=ONiWmzrmfuY&feature=related
ReplyDeleteRegards, Dany.
"Btw, here are the results of our last poll "Does the past and the future exist in the same way as the present?" From 153 votes, 41.2% decided for "Past, present and future exist in the same sense," 29.6% for "It is only the now that exists, but neither the past nor the future." And, surprising for me, only 15% voted for "The past exists as does the present moment, but the future doesn't.". The remainder chose "Other"."
ReplyDeleteI voted with the majority, however, that was with reluctance, since, to be most accurate semantically, I do not believe that NOW exists, so I only believe that past and future exist equally. But rather than vote the nebulous "other", I voted for the Past, Now and Future ... since that was roughly closest to my views.
All REAL physical processes destroy information, how could black holes be different?
ReplyDeleteFor information to be preserved whole you'll need all processes to be reversible and no reversible process is real.
Voted "No ... for other reasons'
ReplyDeleteA yes vote conflicts with determinism, so that can't be the case, in my belief system.
Ultimate guiding principles are unitaritiness of the universe (determinism) and maximum symmetry in the quantum and temporal realms.
How the information survives I have no idea, but I believe it must survive.
Although, like Kris, I also have some doubts about the existance of black holes. All in all, black holes are a lot to swallow, although the evidence for their existence seems to have grown to be quite massive.
btw: If black holes radiate, which makes sense to me, then they aren't "black" holes anyway ... they are gray ones?
Blackholes destoy certain information paramiters, and similtaineously creates other information paramiters?
ReplyDeleteIf a particle cannot be detected outside of a blackhole with absolute certainty, according to QM, then if one tags a particle with certain information at the horizon of a blackhole, then one cannot expect to have evidence of its actual "being"? an Hydrogen Atom may be absorbed by a BH, and a High Energy Proton may be emmitted, as one particle is theoretically destroyed, another is born!..but tracing one back to the other is really tricky!
The tracks left in a particle accelerator, are really not representitive of the track left in cosmological spactime?
William: Quantum mechanics alone is already non-deterministic. Best,
ReplyDeleteB.
Hi Bee,
ReplyDeleteDon't think that's been proven. For example, see this.
Happy vacation!
Kris
I wanted to say a bit on this subject to make it a bit clearer - as much for my own purposes as anything else. The following borrows quite heavily from Lee Smolin's book "Three Roads to Quantum Gravity":
ReplyDeleteEntropy is the amount of randomness in a system. The Second Law of Thermodynamics states that the entropy of an isolated system will show an irreversible increase. However, when matter falls into a black hole, its entropy has gone for good and the Second Law appears to have been broken. Black holes also behave in a way which is irreversible in time, because things fall into a black hole but nothing can come out. Stephen Hawking showed that the area of the horizon of a black hole can never decrease with time. This analogy with the tendency of entropy to increase irreversibly led Jacob Bekenstein to propose that a black hole has entropy which is proportional to the area of its horizon. When matter falls into a black hole, the increase in black hole entropy compensates for the "lost" entropy of the matter.
But there was a problem with this: if nothing can come out of a black hole then it has zero temperature, but ordinarily a system cannot have entropy without it being hot (random motion of particles). Stephen Hawking realised that if black holes were hot then there was no problem. So he proposed that an outside observer would see the black hole as having a temperature. He suggested that the black hole emitted thermal radiation (Hawking radiation). From the equivalence of mass and energy, this radiation also had to carry away mass. This implies that a black hole in empty space must lose mass, for there is no other source of energy to power the radiation it emits. So the black hole will slowly lose mass and evaporate.
Now, to move onto the question of "information". Entropy is closely related to the concept of information. If we have a gas at a certain temperature, a large amount of information is coded in the motion of the molecules. However, if we just consider the molecules to be in random (thermal) motion, and simply assign a numeric temperature to the gas, then we have thrown away (lost) a large amount of information. So entropy (randomness) could be considered to be the amount of information lost to random motion: entropy = lost information. In a black hole, the amount of trapped information is proportional to the area of the horizon.
Now lets consider two quantum-entangled particles, spontaneously produced from quantum fluctuations of the vacuum. The process Stephen Hawking suggested as creating his radiation was that one particle of the pair gets sucked into the black hole while the other is emitted as radiation. Because we have no way of obtaining information about the entangled pair particle which has disappeared into the black hole, we have to consider the emitted particle as having random properties (i.e., thermal radiation). So, in quantum terms, our particle which was in a superposition state (described by a wavefunction), is no longer in a superposition state: it has clearly defined (eigen)values (see this page on my site). In quantum parlance we say a "pure" state has become a "mixed" state - all those extra superposition components have vanished (see here).
So where has all that information vanished? Is it trapped in the black hole? Does it come out again when the black hole evaporates? This apparent paradox is the cause of all the arguments.
Now here's my take on it ...
There really isn't a problem if we imagine that quantum entanglement can survive the crossing of the event horizon of the black hole. After all, quantum entanglement can apparently cross the universe instantaneously, I don't see why a black hole event horizon should bother it. As the Wikipedia article suggests, "the predominant belief among physicists is that information is preserved and that Hawking radiation is not precisely thermal but receives quantum corrections" - see here. And as Zeh realised in his paper here, the transition from a quantum pure state to a mixed state happens around us all the time during quantum decoherence - that's not a big deal at all. If we just imagine that a black hole event horizon is not such a barrier where underlying quantum entanglement/decoherence is concerned, then the whole "information loss paradox" really becomes not so much of a big deal.
Every time I try to look at this stuff I get completely lost because I immediately find myself realizing I still don't have a good picture of what definition of the word "information" physicists are using here. I'm used to thinking of information in the information theory context, so I keep trying to map statements about physical information to one or the other of the definitions of "information" that get used in information theory... the mappings I'm using are clearly not correct. What *exactly* is the quantity we are measuring when we talk about "information" being lost in black hole evaporation? On what grounds is it a problem if this "information" is lost? (It seems like if you can't be specific about what it is that is being lost, maybe you never had it in the first place...)
ReplyDeleteI find Andrew Thomas' posts here interesting-- if I understand him correctly he seems to be describing that entropy is the process of losing information. This seems to give a sort of very vague definition of information-- information is the structure that entropy erases. This is a little surprising to me (since Shannon information is a measure *of* the entropy of a system, so we'd have two definitions of "information" out there that were basically opposites?) but seems like a fair starting point. Is this really correct though? And if it is correct, then why do we mind losing information, since by this definition we're "losing" information all the time as the universe's entropy increases?
Is the thing we're really complaining about with the "black hole information paradox" that somewhere in there information is getting erased "for free", without an appropriately proportional increase in entropy...?
Badly confused CS person here, please help. :)
Hi Colin, don't worry - you're not the only one confused. In fact, a big reason I posted my previous comment was because I was not clear on some points in my own head and I wanted to get things clear and written down somewhere.
ReplyDeleteFirst, the good news: you are absolutely right in thinking of information in the information theory context - Shannon information. Again from Lee Smolin's book: "The information carried by a signal is defined to be equal to the number of yes/no questions whose answers could be coded in that signal. The information content of a signal is thus equal to the number of bits".
However, it's not correct to say "entropy" = "information". This guy suffered the same confusion as you by equating the two - see here. In my previous comment I was very careful not to equate information with entropy. I stated "Entropy could be considered to be the amount of information lost to random motion".
Are you aware of the concept of information entropy? This term is the cause of the confusion with physical entropy. Apparently John von Neumann persuaded Shannon to call it "information entropy", thus consigning generations of phyicisists to confusion! The "information entropy" of a signal is the part of the signal which is not determined, not known in advance. So it's basically the part of the signal which can be used to send useful data. The concept is useful because often not all of, say, a binary data string is available to transmit useful data - there is often redundancy. From that Wikipedia link: "Shannon's entropy measures the information contained in a message as opposed to the portion of the message that is determined (or predictable). Examples of the latter include redundancy in language structure or statistical properties relating to the occurrence frequencies of letter or word pairs, triplets etc."
Now, there is a connection with information entropy and physical entropy. For example, if we have random thermal radiation from a black hole, none of that radiation is known in advance, so it has a high information entropy (as well as a high physical entropy, obviously). However, it doesn't have much information because we can encode the thermal radiation by giving it a single temperature value. So we have lost a lot of information when matter is converted to thermal radiation in a black hole. Information has been lost to random motion (physical entropy).
(However, if the quantum entanglement correlations are, in fact, not lost when particles enter a black hole then no information is lost because the radiation we observe only appears random - it is in fact correlated with particles within the black hole so no information is lost)
I hope that makes sense!
Hi Kris,
ReplyDeleteThanks, I think I actually read this paper. It is of course true that it is not experimentally proven quantum mechanics is fundamentally non-deterministic, but to be honest, if it was, I don't think one could ever prove that. So the necessity for proof seems to be one the other side: if you claim it is not, show it is deterministic. Anyway, what I was referring to above is the standard interpretation of QM in which the collapse is fundamentally non-deterministic. Best,
B.
Hi Andrew,
ReplyDeleteThanks for your comment. You know, the actual reason why I meant to write the post about the black hole information loss paradox, was our exchange in an earlier post (forgot which), and unfortunately it seems you still didn't understand what I wrote there as a reply. You are completely correct in saying that it isn't a problem that part of the state is behind the horizon, but that is just not the information loss problem. Best,
B.
Hi Bee, I do remember something of our exchange! I think it went on for a while - something about the singularity? I've done my bit - you'll have to write your post sometime and make your views clear. Go for it!
ReplyDeleteWill do :-) When I'm done with preparing my seminar for tomorrow.
ReplyDeleteHi Bee,
ReplyDelete“It is of course true that it is not experimentally proven quantum mechanics is fundamentally non-deterministic, but to be honest, if it was, I don't think one could ever prove that. So the necessity for proof seems to be one the other side: if you claim it is not, show it is deterministic.”
Hint: H^2=I.
Best regards, Dany.
Hi Dany,
ReplyDeleteIt would really help if you could be somewhat more specific. I am not in the mood to guess what you mean just to find out we are talking about something different anyway. Best,
B.
Hi Bee,
ReplyDelete“Will do :-) When I'm done with preparing my seminar for tomorrow.”
Take your time. I guess it may wait at least two-three months. I mean indeed Hadamard operator (matrix). And I am talking about digital signal and image processing. Working practical (engineering) knowledge of digital communication, pattern recognition and statistical target detection may be useful. If you like, you may call it CI which is “the standard interpretation of QM in which the collapse is fundamentally non-deterministic.”
Regards, Dany.
Hi Dany,
ReplyDeleteThanks for the clarification, but I don't see what this has to do with what I said above. Are you claiming something of what you said proves QM is fundamentally non-deterministic? Best,
B.
Dany likes to have his bit of fun.
ReplyDeleteWe seem to have a very different sense of humor. I find it merely an annoying waste of time.
ReplyDeleteThinking out loud...
ReplyDeleteSo is a black hole a perfect fermi gas inside of the event horizon? (With exactly the number of levels as there are particles).
One could make a heurestic estimate of the energy of the ground state of a particle inside of the event horizon from the Lagrangian of the metric. And then estimate the highest available level based on the radius of the event horizon.
The toy model is that a new particle entering the event horizon modifies the metric just enough that exactly one more level is allowed inside the event horizon.
There is probably a really good reason why this is a bad idea.
Hi Bee,
ReplyDeleteIt is of course true that it is not experimentally proven quantum mechanics is fundamentally non-deterministic, but to be honest, if it was, I don't think one could ever prove that. So the necessity for proof seems to be one the other side: if you claim it is not, show it is deterministic. Anyway, what I was referring to above is the standard interpretation of QM in which the collapse is fundamentally non-deterministic.
Suppose a man is convicted of murder, sent to prison for life. The conviction was based one informant's testimony, but it comes to light twenty years later that was wrong. Still, the man has no alibi to prove his innocence. Should we leave him in prison?
de Broglie had a deterministic theory of quantum mechanics, but von Neumann published a proof that any such theory was impossible. The proof was widely cited for over twenty years. (The philosopher Grete Hermann had pointed out a fatal flaw, but she was ignored.) Then David Bohm made von Neumann's mistake clear, by resurrecting de Broglie's approach and showing it works.
The position of the mainstream physics community then became (at least until recently) that none of this matters; Bohm's deterministic approach to QM can't be proven correct because it only makes the usual predictions. Is this your position also?
Cheers,
Kris
P.S.: The discussion of the black hole information paradox in the Nikolic paper I cited seems relevant to me.
Hi Kris,
ReplyDeleteI think you are talking about two different things. The one is the question of determinism (if I prepare a system carefully, can I predict the outcome of the measurement?), the other one is a question of realism: is that non-determinism stochastic or fundamental. What I was referring to with non-determinism is not one in the formulation, but one in the actual measurement, and what I was saying is, if somebody claims one can predict the measurement it's up him to show that, and not up to those who don't to show that it's not.
Besides, you can never prove any theory correct. As far as that is concerned, if two theories produce the same results in all cases it's a matter of taste which you like. I have no particular problem with the general spirit of Bohm's approach, just that the attempts to come up with a relativistic version don't quite convince me. I know there's collapse models that actually make predictions, so maybe there will be some progress there.
Best,
B.
Hi Kris,
ReplyDeleteIn as I would consider myself a Bohmian in respect to Quantum Theory, I would be interested to learn if you’re a first order one as Bell, Goldstein and Durr or a second order one as Bohm and Hiley? In reading your papers along with Ben Kristoffen’s that you have on your home page I’m not all that certain. I myself am a second order Bohmian and therefore take the quantum potential seriously. I realize the so called modern Bohmians find this to be more of a embarrassing contrivance and yet I find their approach leads their thinking closer and closer to becoming simply standard QM with its ontology becoming singular only with the wave becoming real and the particle more the ignored component. I find your approach similar and thus my question.
Best,
Phil
Hi Bee,
ReplyDelete“Are you claiming something of what you said proves QM is fundamentally non-deterministic?... We seem to have a very different sense of humor. I find it merely an annoying waste of time.”
Empirically Berlitz ad demonstrated the opposite. However, I admit that I never understood women and women’s logic:
CI claim that the measurement apparatus (detector) must be macroscopic, that is, obey the laws of classical physics and statistical mechanics intrinsically. Therefore the collapse of wave packet has nothing to do whatsoever with QM. Consider now the UUT which consist the single electron/photon or two electrons/photons. It is not a statistical system. The statistical behavior of the physical system emerges starting N>4; “you don’t NEED something more in order to get something more. That what the emergence means”.
A few words about Hadamard transformation. I guess that the story started from 1980 V.Degiorgio discussion of Michelson interferometer (yet another example of relearning and the “illusion of knowledge”). A.Zeilinger reduced it to the math description of the general lossless beam splitter. The beam splitter (or equivalently our old friend Lloyd’s mirror) is real life realization of the double slit. It is macroscopic device which is not a detector, it doesn’t perform any measurement. Further analysis leaded A.Zeilinger and D.Bouwmeester to the Hadamard transformation (“The Physics of Quantum Information”,2000,p.3;definition of qubit). Then “a Mach-Zehnder interferometer is a sequence of two Hadamard transformations”. Notice that the laws of statistical mechanics prevent the possibility to combine back the original single particle wave packet from the intermediate statistical ensemble. Now, look at A.Tonomura et al, “Double –biprism electron interferometry”, Applied Physics Letters, 84(17), 3229 (2004); Fig. 3(b),(c),(d) and (a). What my eyes see is the detailed picture (image) of the single E. Schrödinger coherent wave packet, originally ejected from the electron gun (H^2=I). The detailed discussions of that and related material you may find in Bible of modern ED (M&W,“Optical coherence and quantum optics”).
Regards, Dany.
Sorry Bee,
ReplyDeleteI assumed you were referring to "causal determinism." Wikipedia defines that this way:
...causal determinism has a direct relationship with predictability. (Perfect) predictability implies strict determinism, but lack of predictability does not necessarily imply lack of determinism. Limitations on predictability could alternatively be caused by factors such as a lack of information or excessive complexity.
In that sense, de Brogie/Bohm quantum mechanics is fully deterministic -- one just doesn't have access to all the information needed to make definite predictions.
My personal contention is that pursuing this version of QM in the area of gravity leads to measurable effects at large scales. (I have a cute new result for the flyby anomaly which agrees precisely with observations. Will post it to ArXiv in a month or so.)
All the best,
Kris
Hi Phil,
ReplyDeleteLike you, I take the quantum potential seriously. But I think the modern work fills in some missing details. If you have any questions on the "Ben Kristoffen" paper, or whatever, feel free to contact me at the email address on my papers!
Best,
Kris
Kris,
ReplyDeleteSo with this solenoid concept we have wave within wave instead of wave and particle. This does have an enfolded aspect as Bohm recognized and was searching for and yet is somewhat hard to get my head around. I will indeed look more closely at Kristoffen’s paper and your own and perhaps in time may understand enough to ask a relevant question and thanks for being open to one if the time arises.
Best,
Phil
P.S. Bee, I apologize for the brief temporary drift off topic.
Hi Dany,
ReplyDeleteMy comment about the sense of humor was directed at Andrew. Thanks for the clarification, that is interesting, but I still don't see what has this to do with what I said. Do you want to say this shows that quantum mechanics is fully deterministic? Or that it isn't? I have no idea how what you describes should either prove or disprove that. Best,
B.
Hi Kris,
ReplyDeleteBut the point is we can to our best present knowledge not predict quantum measurements so how are we to tell whether the theory is fundamentally deterministic or not? What I was saying is in the standard interpretation it isn't, in the Bohm interpretation it is, but it results in all cases in the same outcome so for me it's a matter of taste. What would be convincing for me is a theory that allows to predict measurement outcomes (at least better than in QM). Sorry for the confusion with the terminology. Best,
B.
Hi Bee,
ReplyDelete“My comment about the sense of humor was directed at Andrew.”
I apologize for misidentification.
“I still don't see what has this to do with what I said. Do you want to say this shows that quantum mechanics is fully deterministic? Or that it isn't?”
I will answer your question after clarification of your terminology. I don’t know what it means “fully deterministic”. I may compare QM with the classical field theories (ED, GR). I say that standard Hilbert space math formalism of QM is the description of the field theory of the same type (the only difference that it is field theory of extended objects, like clouds). The statistical ensemble of that objects behave similarly to the classical counterpart, however one should take into account FD/BE symmetrization.
“What would be convincing for me is a theory that allows to predict measurement outcomes”
There is no such theory in physics and never was. The measurement must be presented by the statistical sample of outcomes, in classical physics also (repeatability). In classical field theories the obtained images are points, in QM they are 3-D holograms.
Regards, Dany.
Hi Dany,
ReplyDeleteAs I already said to Kris above with apologies for the sloppy use of words, what I meant with fully deterministic is that the outcome of the measurement can be computed from the specification of the initial state 'in principle'. If you don't exactly know the initial state (hidden variables) that might not be possible though, same goes if you induce randomness through the detector or environment and so on - all these are deterministic 'in principle'. If you trace back where this discussion comes from I said to William QM is already non-deterministic and clarified later I was referring to the standard interpretation. My discussion with Kris was about the question whether or not one can decide how it is (fundamentally) deterministic or not.
I was trying to express the opinion that one can indeed show a theory is deterministic, by predicting measurement outcomes or making predictions other then in standard QM that favor a different underlying theory. I know there is no such theory that allows us to predict measurement outcomes in QG and there has never been, but that would be an example of theory that I'd like to see (as I said, it would already be sufficient if in possibly specific circumstances the predictions where better than in QM). Either way, if one has a theory that is fundamentally deterministic as QM isn't then I'd want to see some evidence for that theory to be true, may that be through some measurable modification in the collapse or whatever.
I hope that clarifies it? Now are you trying to say that whatever you are talking about can be used to decide this question?
Best,
B.
Hi Bee,
ReplyDelete“I hope that clarifies it?”
No. Sorry, I am not able to follow your arguments. Please, give me concrete existing example of “fully deterministic” and/or “fundamentally deterministic” theory for illustration. Is the classical ED the “fully deterministic” and/or “fundamentally deterministic”? Please specify the concrete physical system under consideration and illustrate your statements on that concrete example. Now, please take double slit A.Tonomura et al experiments (1989, 2004) and explain the difference.
“Now are you trying to say that whatever you are talking about can be used to decide this question?”
I need to understand the question in order to try answering it or deciding whether what I said is related to that question. Please use J.v Neumann terminology: U- and R- processes only and not yours individual and undefined for me metaphysical notions. Please consider the closed physical systems only. Please consider the canonically conjugated variables only (I have no idea what “hidden variables” are and why we NEED them). Please use standard specification parameters to describe the wave packet (longitudinal/transversal coherence length, etc; M&W). Please use PDE (hypergeometric eqs.) with standard and concrete initial and boundary conditions described in any standard textbook on QM. Then our information base will be matched and we will be able to establish communication.
Then you will understand that for thus defined description of the physical system we always know exactly everything what we NEED to know (indeed the question what is the exact position of classically modeled electron (ball) at the ground state of the hydrogen atom is idiotic question as was explained by W.Heisenberg: imagine the experimentalist running with rod inside the hydrogen atom with the velocity ~c/4 in order to catch the electron; even the attempt to catch the pigeon would look much more reasonable).
Regards, Dany.
P.S. For those who didn’t follow the previous discussions, I refer again to:
http://www.youtube.com/watch?v=ONiWmzrmfuY&feature=related
Listen carefully what THE father of elementary particle physics say.
Hi Dany,
ReplyDeleteIt is not an argument, I was merely expressing my opinion. Yes, classical ED would be fully/fundamentally deterministic. There is no 'concrete physical system' I could use as example because we know ED has to be quantized. In the classical theory you fully specify the initial state and make a measurement. You repeat that and you will get the same measurement. In the quantized theory you generally won't. In the standard interpretation the reason for this is that the collapse is non-deterministic. I didn't say anything about the precision that is possible for any measurment. I never said one needs hidden variables. Best,
B.
Hi Bee,
ReplyDeleteListen carefully what THE father of elementary particle physics say.
Your only problem is that you apparently don’t want to listen (nevertheless continue discussion: that what I call women’s logic). You reject everything done by those who did physics. But then you remain with Hollywood movies and without physics.
“Yes, classical ED would be fully/fundamentally deterministic. There is no 'concrete physical system' I could use as example because we know ED has to be quantized.”
Every statement is completely wrong:” They follow from more fundamental things plus accidents. That is GENERAL rule”. Notice, that you still didn’t explain how you define “fully/fundamentally deterministic”.
“In the classical theory you fully specify the initial state and make a measurement. You repeat that and you will get the same measurement.”
Never. Go to the lab and check your statements apparently first time in your life.
Physics is the empirical science.
Bee, it seems to me that we already completely understand each other and it is tasteless to continue. The other question emerges from our discussion: what happen with the present generation of high energy theoretical physicists and it is entirely different topic - the quality of education (who are/were the teachers).
Regards, Dany.
Hi Dany,
ReplyDeleteListen carefully what THE father of elementary particle physics say.
Your only problem is that you apparently don’t want to listen (nevertheless continue discussion: that what I call women’s logic).
? I have no idea what this has to do with me being a women, but I don't check links that people produce if they don't say what it is and that I should have a look. If anything, they should be glad if I don't delete them.
But so now I watched that video. Nice. I was talking to Stefan only yesterday about Gell-Mann's book, unfortunately neither of us read it but anyway, I have no idea what the topic of emergence has to do with what we apparently don't manage to talk about.
Go to the lab and check your statements apparently first time in your life.
Physics is the empirical science.
Indeed. I thought it would have been clear that I was talking about the theory, not the practice. In case that's what you meant to say, why didn't you just say in practice there are always uncertainties and nothing can ever be predicted with absolte certainty. I surely agree on that.
Notice, that you still didn’t explain how you define “fully/fundamentally deterministic”.
Well, I can copy once again what I wrote earlier: what I meant with fully deterministic is that the outcome of the measurement can be computed from the specification of the initial state 'in principle'.
It is a statement about the theory and 'in principle' can be read as 'theoretically'. This, as I already said before, is not the case in standard QM.
Bee, it seems to me that we already completely understand each other and it is tasteless to continue.
Dany, I honestly have not the slightest idea what you are talking about or what you are trying to communictate. I am genuinely sorry about it because I apparently fail to extract any information from what you say, but it seems we are completely talking past each other. To repeat what I said above, all I wanted to say is if you have a theory that yields the same outcome as QM in the standard interpretation in all cases, I don't care how you call it, to me its standard QM and you can interpret it as you like.
I am not sure why you bring up this Gell-Mann movie maybe you want to say something emerges from something, yet I don't know what from what or why this is relevant, and I neither have the time not the patience to guess. You either tell me what you are talking about and stop making stupid 'hints' and insults about my women's logic and bad education, or I will conclude you have nothing to say except producing confused irrelevant comments and just ignore anything further. Best,
B.
Hi Bee,
ReplyDelete“I have no idea what this has to do with me being a women, but I don't check links that people produce if they don't say what it is and that I should have a look. If anything, they should be glad if I don't delete them.”
This has nothing to do with you being a woman. This is connected with another woman. My parents wanted to raise me an educated individual. It took at my mother the level of the Greek tragedy:” The child does not read books!!!” She was former master student of É. Claparède and his PhD student J.Piaje and I was the lab practical implementation of the theory. My mother had access to the “deleted” literature at USSR and she was glad to do things which were strictly forbidden. Among others she considered that I should read O.Weininger “Sex and Character”. The writer developed the standard (today) two level model similar to our qubit. Indeed I didn’t understand what was so dangerous if the average citizen will read that book also. According to him, the standard collapse may leads to the particular outcome woman to be up to 100% man and vise versa. Then the measurement sample present adequate picture of humans.
BTW mother didn’t succeed her goal to raise the intelligent species. As a demonstration I will remind you that doing simulations (computer measurements) are similar to masturbations: more you are busy with it, more you think that it is real.
Regards, Dany.
P.S. We usually use an inaccurate wording as a memory for initial state of confusion. Heisenberg dispersion relations have nothing to do with the statistical uncertainties. Heisenberg desperately tried to explain that to everybody but it was too late.
Hi Bee,
ReplyDeleteJust wanted to mention another consideration for choosing a theory of quantum mechanics, besides its predictions. As to whether or not it is causal and deterministic (as in de Broglie/ Bohm) or not, there is also the issue of retrodiction. Yakir Aharonov has pursued that over the years.
This paper by Albert, Aharonov and D'Amato describes a classic example of retrodiction using particles with spin 1/2. They note it's possible in principle to measure, say, the x component of a particle's spin and leave it in that state indefinitely. (Any future measurement of the x spin that would give the same result.) At a later time, one may measure the y component. Although the uncertainty relation prevents us from measuring x and y simultaneously, this suggests the particle existed in some specific state during the time between the two measurements. They conclude:
Bell has pointed out that in spite of the argument of Gleason and of Kochen and Specker, and without violating the statistical predictions of quantum mechanics, it can be consistently supposed (within certain hidden-variables theories) that noncommuting observables can be simultaneously well defined. The present considerations suggest something stronger: In spite of that argument, and given those statistical predictions [given, particularly, Eq. (1)], it is inconsistent to suppose anything else.
Best wishes,
Kris
Hi Kris,
ReplyDelete“Bell has pointed out that in spite of the argument of Gleason and of Kochen and Specker, and without violating the statistical predictions of quantum mechanics, it can be consistently supposed (within certain hidden-variables theories) that noncommuting observables can be simultaneously well defined. The present considerations suggest something stronger: In spite of that argument, and given those statistical predictions [given, particularly, Eq. (1)], it is inconsistent to suppose anything else.”
So this was joint authored by David Z. Albert who wrote the book “Quantum Mechanics and Experience”. Well I certainly spent many hours with this book and still consider it my primer on the subject. Strangely this book in my opinion should be something read more often by the pros not only the novices like me. The paper interests me and yet it is another $25.00 hit. When I have more time I probably will cough up and download it since as Albert is involved I can’t resist.
Best,
Phil
Hi Dany,
ReplyDelete“ You don’t need something more to get something more”.
Well Dany I hope that you don’t credit this idea of emergence being original as to be attributed to Murray Gell-Mann since it was in truth first stated by Rene DesCartes in 1637 within his great treaties [Discourse on The Method: of Rightly Conducting The Reason, and Seeking Truth in the Sciences] when he said:
“But this is certain, and an opinion commonly received among theologians, that the action by which he now sustains it is the same with that by which he originally created it; so that even although he had from the beginning given it no other form than that of chaos, provided only he had established certain laws of nature, and had lent it his concurrence to enable it to act as it is wont to do, it may be believed, without discredit to the miracle of creation, that, in this way alone, things purely material might, in course of time, have become such as we observe them at present; and their nature is much more easily conceived when they are beheld coming in this manner gradually into existence, than when they are only considered as produced at once in a finished and perfect state.”
So then I’m sorry to report this emergence is not a new concept or solely related to QM. I wouldn't even give Gell-Mann sole rights to Quarks outside of the name. That is also in 1964 George Zweig wrote a paper where he called them “Aces”. He was however better at PR and marketing for he got the Nobel Prize and not Zweig.
Best,
Phil
Hi Bee,
ReplyDelete“Nice. I was talking to Stefan only yesterday about Gell-Mann's book, unfortunately neither of us read it but anyway, I have no idea what the topic of emergence has to do with what we apparently don't manage to talk about.”
As for “The Quark and the Jaguar” if you are interested in reading 375 pages of Gell-Mann self promotion which in part is aided and abated by what I would call trash talk in relation to physicists who are no longer around to defend themselves, then it could be deemed as a good read.
Best,
Phil
Hi Kris,
ReplyDelete“it can be consistently supposed (within certain hidden-variables theories) that noncommuting observables can be simultaneously well defined.”
They missed a point. The EPR set up must include EM field (signal) to communicate the information to the same ref frame. But in the presence of EM field the momentum is not gauge invariant quantity and therefore can’t be measured (paradoxically it is the content of AB phenomenon). EPR are obviously right, P.A.M. Dirac definition of observable was not precise (complete).
Regards, Dany.
Hi Phil,
ReplyDelete“I hope that you don’t credit this idea of emergence being original as to be attributed to Murray Gell-Mann”.
No. It is much more ancient idea, much earlier than Rene DesCartes, it is guides line all of the physics: the idea of Elementary Particles Physics.
We discuss here the theory of measurements. I spent last years working on that. I briefly mentioned above what one should know to attack the problem. Eventually I addressed to my natural environment at this territory: Y. Aharonov, S.L. Adler, L.P. Horwitz, A.Zeilinger and others. I used Bee blog to describe the motivation which I can’t include in my forthcoming paper entitled “On the problem of Eigenchaften in the quantum and classical mechanics”. It will be dry, emotionless math paper with the minimum words decoration. We don’t formulate the theories for undefined purpose. In the paper it will be presented how to read the output of quantum computer. As I mentioned above I need about two-three months to check and recheck it.
Regards, Dany.
P.S. “I wouldn't even give Gell-Mann sole rights to Quarks outside of the name.”
To the best of my knowledge the existence of additional fundamental fermions first time was predicted by Y.Neeman (NP,1962). I have no ref handy but there is CERN report written by G. Zweig which describes the history of that discovery. D.Gross in his Nobel lecture added some interesting details.
Hi Kris,
ReplyDeleteThanks. Well, I have a certain interest in the foundations of quantum mechanics, so I don't mind all these investigations, it's just that in many cases I don't quite see what it's good for. But I could say the same about completely other fields. If I had to guess where progress will come from, I'd but my bets on foundations of QM, so it's an area that I certainly regard worth support despite my puzzlement about some of the discussions (To express my ignorance and impatience: if something isn't releativistically invariant and second quantized why are we discussing it at all?). Best,
B.
Hi Bee,
ReplyDeleteThanks for letting me toss in the retrodiction reference.
...if something isn't relativistically invariant and second quantized why are we discussing it at all?
Nikolic noted some myths that those limitations of Bohmian mechanics can't be overcome. I think work like this from Duerr et al. suggests they can.
The world gets more complicated if you have to invent completely new rules for each situation -- causality for the macroscopic world, acausality for the quantum world.
On the role of relativity in their work, Duerr et al. say:
...we will not attempt to achieve full Lorentz invariance; that would lead to quite a different set of questions, orthogonal to those with which we shall be concerned here. But we note that though the theories we present here require a preferred reference frame, there can be no experiment that would allow an observer to determine which frame is the preferred one, provided the corresponding QFTs are such that their empirical predictions are Lorentz invariant.
My own work involves a similar preferred-frame representation of relativity, extended to gravity. However, for nonuniform gravitational potentials, the empirical predictions are not Lorentz invariant. If someone wants to be dogmatic, they could say this approach is wrong automatically. But of course the real question is, does it agree with experiments?
A few months ago, Anderson et al. published a very concise empirical description of the flyby anomaly. In a month or so, after it's written up, I'll post a result from this non-covariant theory, which shows exact agreement. (Not obtained from general relativity.)
Best wishes,
Kris
Hi everybody,
ReplyDeleteI would like to mention a possible solution of the black-hole information paradox that has not been mentioned so far on this blog. The idea is to allow information destruction without violating unitarity of quantum mechanics. This means that not all information is present at times after the complete evaporation, but the state of the universe is still described by a pure state. This can be achieved by treating time in quantum mechanics on an equal footing with space. In particular, it means that the notion of "time evolution" of the wave function does not have any fundamental meaning, just as the notion of "space evolution" of the wave function does not have any fundamental meaning. In simple terms, the information is not destroyed because it is present in the past. For more details see an old paper of James Hartle
http://xxx.lanl.gov/abs/gr-qc/9705022
and a recent paper of myself
http://lanl.arxiv.org/abs/0905.0538
published as Phys. Lett. B 678 (2009) 218