B Collapse and unitary evolution

[Fra]

Huh? So "we can't model a human being at the level of subatomic particles" means "human beings are not made of subatomic particles"? That's nonsense. But I can't see any other way of reading this claim.
...
Which in no way implies that human beings and other macroscopic objects are not made of the subatomic particles we know of.

Of course we are made of subatomic particles if your smash a human to parts. This is the mechanistic or ontologicsl reductionism. And we know how say any two subatomic paricles interact.

But this is not a viable strategy for one human interacting with other humans. Instead the complex systems develops behaviour that due to chaos can not be inferred from knowledge of interaction of parts. It is not even viable for a genious with the mosy powerful computer om earth.

I talk about methodological reductionsm.
https://en.m.wikipedia.org/wiki/Reductionism

This method of course works - but only up to the point where we hit chaos limit. Here, the viable organisms find NEW more significant interaction rules that fit to the "information processing" resources at hand. And thes resources are physical properties of the observing system. A human can afford to adopt more refleticive behavioural strategies than a cell.

/Fredrik

 

[martinbn]

The standard statistical interpretation of quantum mechanics that its predictions apply to statistical ensembles is given in many textbooks, eg. Messiah, Quantum Mechanics, Volume 1, Chapter IV, Section 2.

And many of those textbooks do not include collapse in the interpretation. So, can you write down what your view is (bhobba alluded to it but I haven't seen it) and explain why you insist on collapse being part of this type of interpretations? Can you also narrow down the reference to Messiah? I couldn't find anything about collapse in that section?

 

[PeterDonis]

Of course we are made of subatomic particles if your smash a human to parts.

So you're saying we're not made of subatomic particles if we're left intact?

this is not a viable strategy for one human interacting with other humans. Instead the complex systems develops behaviour that due to chaos can not be inferred from knowledge of interaction of parts.

Yes, but that just means we can't model intact humans directly as conglomerations of interacting subatomic particles. It does not mean that intact humans are not made of subatomic particles. The latter is the only claim that "reductionism" is making.

 

[Fra]

So you're saying we're not made of subatomic particles if we're left intact?

No, I'm just saying that what complex systems are "really made of" if we take it apart is not the only important thing. To take something apart required less information that putting it back together.

What I focus on is fitness of models/theories in a competitive survival perspective. Theories contritube to real predictability
and a good adaptive learning methodology are likely preseved by nature.

Yes, but that just means we can't model intact humans directly as conglomerations of interacting subatomic particles. It does not mean that intact humans are not made of subatomic particles. The latter is the only claim that "reductionism" is making.

Right. But what we are "made of" in the ontological sense means notthing to me. Its what reactions to perturbation this has, that gives this all meaning. And chaotic predictions have not predictive value.

The question is, which modelling strategy can a given observer(having given resources) adopt to make maximal progress and survive? This is the question i focus in. And here, reductionism seems sterile.

/Fredrik

 

[PeterDonis]

I'm just saying that what complex systems are "really made of" if we take it apart is not the only important thing. To take something apart required less information that putting it back together.

And I'm saying that "reductionism" is in no way incompatible with that. I'm a reductionist and I agree with this statement. So, I suspect, do most reductionists.

 

[bhobba]

Is that written somewhere so that the rest of us can see what that view is? Also why? I thought that one strict rule here was that only peer reviewed sources are acceptable. Then why a view expressed on a forum is taken as the rule on terminology when peer reviewed sources, including textbooks, say that at least some ensemble interpretations do not have collapse!

Atty has sent me a private message, but I would rather he explain than I repeat the message. There has been long threads where me and ATTY go to and fro about this issue. It''s really just semantics IMHO, and I shouldn't do it - we are here to help people rather than confuse them. So it was agreed to take whatever definition ATTY takes it to be. For the time being just take it as after an observation it is in an eigenstate of the observable.

Since that is part of the formalism it always true - when looking at it in the usual way eg some care is required in MW. In MW overall there is no state change, but in a specific world there is.

Thanks
Bill

 

[bhobba]

Yes, but it seems that there is an agreed upon view that whatever is meant by an ensemble interpretation it has collapse.

That one is easy. Its as detailed in Ballentine's text, and proposed by good old Einstein, although in light of later research (eg the Kochen-Specker theorem) it had to be modified a bit. My interpretation is not strictly the ensemble interpretation - I call it the ignorance ensemble because I only apply the ensemble interpretation after de-coherence - so its slightly different.

Interesting thing about Ballentine - he believes de-coherence has nothing to do with interpretation issues - he says its a real and interesting phenomena of course - but of no interpretive value. Interesting isn't it.

Thanks
Bill

 

[bhobba]

Yes, but it seems that there is an agreed upon view that whatever is meant by an ensemble interpretation it has collapse.

Well for our purposes we will say it has - but the Wikipedia article on various interpretations says otherwise:
https://en.wikipedia.org/wiki/Interpretations_of_quantum_mechanics

That of course is not a peer reviewed source.

Thanks
Bill

 

[Fra]

And I'm saying that "reductionism" is in no way incompatible with that. I'm a reductionist and I agree with this statement. So, I suspect, do most reductionists.

Ok, i guess the subtle point i wanted to convey got lost.

I thought it related the information loss paradox issue, because in what i suggest, information is unavoidably observer dependent. And to compare the information possessed by any two observers in some way, you need a third observer etc. There is no "master observer". Its completely democratic. The only difference is, that some observers are bigger and more dominant.

When you wrote this:

...you don't need any new laws of physics or any new fundamental constituents of matter to make, say, US citizens, as opposed to, say, rocks. You just need to put together the same fundamental constituents, using the same laws of physics, in different ways.

In a way i actually to disgree on this. But the reason is subtle but important. It has todo with how you understand the origin and evolving nature of physical law in the first place. If you think that the laws are just eternal truths about nature, then there is not way to make sense of what i suggest indeed.

If you consider instead effective laws, which are physically inferred by a physical observer by means of an actual interaction history, then, for any given observer, the inferred distinguishable laws, from studying particle physics in colliders, will come from a different windows in theory space, and one that will not contain the same information as if you inferred optimal laws from the hole human, if the same observer did social interaction experiments. And if you take this few, these inferreed effective laws are epistemological more "real" and fundamental, than are the idea of eternal timeless laws. The only painful insight is that laws are actually evolving along with development of the universe and its "spieces" (wether biological organisms, or particles during cooling from big bang).

This all gives us a drastically different perspective to things. In particular one, where the premises in the semiclassical information paradox don't quite hold.

Any my impression is that many reductionists will strongly adhere to the idea of timeless eternal laws? Instead they may say that there is a different between the real eternal laws, and our incomplete knowledge of them. And this is exactly what makes one look for a bigger and bigger supertheory, instead of focusing on the abductive mechanism on how nature implements the rules of what corresponds to laws.

How does an electron "know" what laws to obey? Of course it does not "know" in the human conscious senset, but still, HOW is the physically implemented, that it response as per apparently strict laws? In some way, it seems the electron must have be physical encoded structure that implies this. And during unification, how is this structured challenged. Is there a "DNA of physical law"?

I might recommend https://www.amazon.com/dp/0544245598/?tag=pfamazon01-20 as a background to why one would bother with these crazy ideas. The implied question of smolins argument is, HOW can we get predictability from evolution of law, without secretly adding some hidden metalaw - the metalaw dilemma. This is an open question and smolins sniffs some answers only, but to understand why one would bother create such a new hard question, the argument looking at crisis in physics is in smolins book.

/Fredrik

 

[bhobba]

Is that written somewhere so that the rest of us can see what that view is? Also why? I thought that one strict rule here was that only peer reviewed sources are acceptable. Then why a view expressed on a forum is taken as the rule on terminology when peer reviewed sources, including textbooks, say that at least some ensemble interpretations do not have collapse!

The rule is peer reviewed sources, respected textbooks, course material from respected universities like MIT, and exceptions for things the mentors agree are OK - we occasionally get those.

The issue here is some textbooks make mistakes eg the famous one in Ballentine about Copenhagen. And most definitely we have had a number of peer reviewed papers discussed here with errors - it seems rife in the area of weak measurements and what it means. Also use of virtual particles is another such as in the peer reviewed derivation of the Casmir force by Milonni. That was considered OK at the time - but things do move on.

As far as collapse goes take The Emergent Multiverse by Wallace - he states categorically - page -22 - collapse is not part of the formalism of QM - same with Schlosshauer who has his own defintion that he thinks not all interpretations obey. But a course on OCW at MIT disagrees - they say it's part of the axioms of QM so all interpretations have it - see axiom 3b:
https://ocw.mit.edu/courses/nuclear...s-fall-2012/lecture-notes/MIT22_51F12_Ch3.pdf

We do not want to confuse people here so we will just stick with collapse being axiom 3b, which I think Atty agrees with..

Thanks
Bill

 

[Demystifier]

I have always wondered why the absorption of matter by a black hole could not be considered a type of measurement, which would then take care of the loss o information. I am sure this is stupid for some reason but I have never seen a clear explanation why so.

The problem is not associated with absorption of matter but with Hawking radiation.

 

[PaleMoon]

hi demystifier
you told me that there is a loss of unitarity when there is a measurement on a black hole.
how can one say that there is no loss of information during the life or a black hole (including evaporation) if once a measurement was done?

 

[stevendaryl]

The problem is not associated with absorption of matter but with Hawking radiation.

Is that right? It seems to me that it's the combination that causes a problem. If you have a source of correlated particle pairs, and one drops into a black hole, and later the black hole evaporates, then you're left with the remaining particle from the pair. It can't be in a pure state, because it was entangled with the particle that disappeared into the black hole. But it's not an "improper" mixed state, either, because it's no longer part of a composite pure state.

So it's the combination of particle absorption and black hole evaporation that has the effect of turning pure states into mixed states.

 

[Demystifier]

Is that right? It seems to me that it's the combination that causes a problem. If you have a source of correlated particle pairs, and one drops into a black hole, and later the black hole evaporates, then you're left with the remaining particle from the pair. It can't be in a pure state, because it was entangled with the particle that disappeared into the black hole. But it's not an "improper" mixed state, either, because it's no longer part of a composite pure state.

So it's the combination of particle absorption and black hole evaporation that has the effect of turning pure states into mixed states.

This is an information paradox, not the information paradox. I mean yes, that's a version of the information paradox too, but dropped matter is not essential because in the standard version the dropped matter is in a pure state and the problem arises from Hawking radiation only.

By the way, I have proposed a version in which Hawking radiation is completely irrelevant.
https://arxiv.org/abs/1802.10436

 

[Demystifier]

hi demystifier
you told me that there is a loss of unitarity when there is a measurement on a black hole.
how can one say that there is no loss of information during the life or a black hole (including evaporation) if once a measurement was done?

Loss of unitarity by measurement and loss of information by evaporation are different things.

 

[PeterDonis]

If you consider instead effective laws

Reductionism has no problem with effective laws. Sure, you can formulate effective laws for, say, human social interactions. And such effective laws will not be timeless, because humans and human social interactions evolve. None of that poses any problem for reductionism.

All reductionism is saying is that, for example, the electrons inside human brains work the same as the electrons inside rocks. The difference between a human brain and a rock--or, for that matter, between a human brain now and a human brain 100,000 years ago, given the evolutionary and social changes that took place over that time span--is not that the electrons, quarks, etc. work differently; it is that there are different highly complex arrangements of the electrons, quarks, etc. All the differences that you talk about when you talk about effective laws and how they might evolve are in the arrangements, not in the electrons, quarks, etc. That's all reductionism is saying.

This all gives us a drastically different perspective to things. In particular one, where the premises in the semiclassical information paradox don't quite hold.

I don't see how anything you've said has anything to do with the information paradox. Can you clarify what you mean here?

 

[PaleMoon]

Loss of unitarity by measurement and loss of information by evaporation are different things.

i wondered how information could NOT be lost if there is measurement and you tell me that there are several ways to lose information. it seems that you read my question too fast

 

[stevendaryl]

This is an information paradox, not the information paradox. I mean yes, that's a version of the information paradox too, but dropped matter is not essential because in the standard version the dropped matter is in a pure state and the problem arises from Hawking radiation only.

By the way, I have proposed a version in which Hawking radiation is completely irrelevant.
https://arxiv.org/abs/1802.10436

Hmm. It seems to me that maybe there is something that I don't understand about black hole entropy. I believe it's supposed to be true that the entropy is purely a function of the black hole mass (it's something like the area of the event horizon). But if you consider an entangled electron to have a different amount of entropy than an electron in a pure state, then the entropy increase due to dropping in an electron is not just a function of the mass increase.

 

[PeterDonis]

I have proposed a version in which Hawking radiation is completely irrelevant.
https://arxiv.org/abs/1802.10436

I have a question about this argument. Basically you seem to be saying that an extremely low energy photon can "fit" inside the black hole because, as it falls in, its wavelength gets strongly blueshifted. But you are also saying that the mass added to the hole in this process is negligible, which implies that the photon's energy is not strongly blueshifted, even though its wavelength is. I don't see how you can have it both ways. If the photon's energy is not blueshifted (which I don't think it should be, since the general rule for objects falling into black holes is that the object's energy at infinity is what gets added to the hole's mass), then its wavelength should not get blueshifted either.

Also, when we talk about an ingoing photon being blueshifted, this is observer-dependent; the blueshift is relative to an observer hovering close to the horizon. But such an observer has a large outward proper acceleration. I don't think the blueshift relative to this observer can just be assumed to be relevant to the photon's interaction with the black hole itself.

 

[PeroK]

This is not correct.

Consider the parallel argument: we can't "read off" from a particular configuration of chemical elements, that some particular piece of matter is a US citizen. Therefore, US citizens are not made of chemical elements.

The first question is whether a person is a quantum object in the sense that everything about them can be explained by the QM of their constituent particles.

I believe it is not possible, for example, to resolve legal issues about someone solely from the particles that make them up. Or, issues relating to their background and history, for example.

This history inasmuch as it exists physically at all, is now encoded in particles belonging to other quantum objects.

A person is, at any point in time, a set of particles, but this doesn't imply that that is all they are.

The second question is whether QM could, indeed, be used theoretically to explain everything - about a human being, human society etc. I wouldn't say this is necessarily wrong but I'd say there is a shortage of evidence. There must be reasonable doubt about this.

Then, I suggest, it's a moot point whether the "reductionist" position is accepted as there is no evidence to the contrary; or, not accepted because it involves largely untestable proposition.

Personally, I would say I'm agnostic on the reductionist position.

 

[PeterDonis]

The first question is whether a person is a quantum object in the sense that everything about them can be explained by the QM of their constituent particles.

Obviously we don't have the ability to do this. But that does not show that people are not made of those constituent particles.

This history inasmuch as it exists physically at all, is now encoded in particles belonging to other quantum objects.

Yes, that's true; you can't "read off" the history of a system just by looking at the system, since at least a portion of that history is encoded in the states of other systems. But once again, that does not show that the system is not made of its constituent particles.

The second question is whether QM could, indeed, be used theoretically to explain everything - about a human being, human society etc. I wouldn't say this is necessarily wrong but I'd say there is a shortage of evidence.

The point @Fra makes about chaos is relevant here. If the dynamics at some level are chaotic, then it might be impossible to explain phenomena above that level in terms of fundamental constituents below that level--at least if "explain" means "model quantitatively in detail". Since it is extremely likely that there is at least one such chaotic level between humans and fundamental particles, that means it might be impossible to explain humans in terms of fundamental particles. But, once more, that does not mean humans are not made of fundamental particles.

 

[PeroK]

Obviously we don't have the ability to do this. But that does not show that people are not made of those constituent particles.
Yes, that's true; you can't "read off" the history of a system just by looking at the system, since at least a portion of that history is encoded in the states of other systems. But once again, that does not show that the system is not made of its constituent particles.
The point @Fra makes about chaos is relevant here. If the dynamics at some level are chaotic, then it might be impossible to explain phenomena above that level in terms of fundamental constituents below that level--at least if "explain" means "model quantitatively in detail". Since it is extremely likely that there is at least one such chaotic level between humans and fundamental particles, that means it might be impossible to explain humans in terms of fundamental particles. But, once more, that does not mean humans are not made of fundamental particles.

I'm not sure who said people weren't made of particles. Being a quantum object suggests to me more than that. E.g. being in a superposition of states. Dead or alive; rich or poor; physicist or lawyer; US Citizen or not. The question is whether all those "real world" observables can indeed be defined in terms of quantum mechanically defined observables.

 

[PeterDonis]

I'm not sure who said people weren't made of particles.

I have been saying that "reductionism" is simply the claim that all macroscopic objects, including people, are made of particles. Reductionism doesn't say we have to be able to quantitatively model people or other macroscopic objects using the equations we use to model particles. I have been making this point because it seemed like @Fra was interpreting "reductionism" to mean the latter claim, not just the former.

 

[Fra]

I don't see how anything you've said has anything to do with the information paradox. Can you clarify what you mean here?

I will try to explain in shortly with some summing hints.

QM predicts quantum states (the connection to individual measurements is only probabilisitic). Premises are initial conditions and timeless laws. From this it follows that - set aside the COMPUTATIONAL TASK to actually execut the deduction, the future is equivalent to the past. So its a "dead" system, information is of course preserved. All we have are equivalence classes of histories. And the laws governing the quantum state flow is assumed timeless. (this is like in classical mechanics)

I am suggesting that the computational procesess and chaos here are a key players. With this i don't mean human made computers, it mean natural processing. You can consider the evolution of a physical system as a computation, or decoding laws of nature from experiemntal data as computation, or scrambling data in a black hole. After all, a REAL human made computer is also a physical process, so this is just a generalisation of the computation concept. Information can be lost and then reconstructed given enough data and computational resources, you need to account for TIME, to talk about information (decoding speed etc).

So my point is that randomness, chaos, and informtion contents, must be dependent on the observer, and the observers information processing capacity and learning speed. And these parts are idealized away in QM. In fact the "equivalence of future and past"
in QM is worth nothing unless the computation is actually performed. Also except in mathemtics maybe, i see no physical rational
behind concepts like "real randomness" etc. If an observer can not distinguish a signal from noise, it will be classified as noice, and in particular TREATED as noise. Ie. you will not "save noise data", it will be discarded. So there are possible behavioural predictions from this. It also seems quite resonable that the radiation from a LARGE black hole is far more hard to decode than from a microscopic black hole.

The root cause of things here is the idea that the classical obsever in quantum mechanics, serves as a FIRM ground, to FORMULATE the quantum theory. This was also the point of the founders such as bohr etc. MY point here, is that it is TOO firm, and thus blurs of discintionc between the relative of randomness. "True randomness" requires an hypothetical infinite information processing machiney to actualy infer. This we can easily "imagine" an classical observer to have, and dismiss as practical matters. But i strongly dislike this, and it think its a deep mistake

Of course these are no formal arguments but then soley serve to briefly convey (human-to-human) the connection i see to the information paradox. Ie. i THINK (can not prove it) that it makes no sense to talk about "no-hair" or perfect infromation preservation, we need to revise the theory to account for the actual computational limits. How this relates to physical parameters is a harder question, but there are already lots of papers on where one considers black holes to be "optimal scrambler" objects etc. So without having answers, it seems the MASS for sure must constrain the computational power. An massive observer at least should ahve the physical possibility to "resolve" strucuture where a lighter observer responds with treating it like noise (and this can be OBSERVER, and VERFIED by a third observer, so there is predictive potential here)

So to sum up, it seems radiation from BH might well be random relatie to small orbiting observers, as they arent meant to be able to decode. But a large observer that can consume the black hole as it radiates away, might possible decode it. All idealisation in calculations that ignores removes my confidence in them.

Anothing think relating to this is the note that the interesting various dualities betweeen theories that many poeple research, like AdS/CFT, typically has traits that relate to computational issues. That two dual theories have different computational complexity, so that in a sense they are equivalent, from the point of view of information processing one may be preferred. This is why they are also useful as mathematical tools. Another theory "corresponds" to a different way to calculate the same thing that is easier. One might thing that, this is just a mathematical curiousoty, but i do not think so. The computational requirements has everythign to do with physical processes in nature.

/Fredrik

 

[DarMM]

Is it really true considering quantum field theory that things are "made" of particles?

Many states don't admit a well defined particle number, in fact one cannot even define a particle number operator on the interacting Hilbert space in some cases.

Also in the full interacting Hilbert space of QED for example, hydrogen states cannot be broken cleanly into electron and proton states. Many complex states like this in QFTs have to be added to the scattering asymptotic Hilbert space, as if independent of the simpler particle states.

This also ignores that electrons, due to infrared renormalisation aren't truly particle states, but infraparticles.

Quarks aren't even elements of the physical Hilbert space, due to colour, so I would wonder to what extent one could halfway state protons are made of them.

Finally you can show a sort of "nuclear democracy" for many fields. Where for fields A, B, C the field algebra can have any two as its basis.

The reductionist program remains unclear to me in QFT.

 

[Fra]

Is it really true considering quantum field theory that things are "made" of particles?
...
The reductionist program remains unclear to me in QFT.

I get your point and i agree.

The discussion as well as subdiscussions here are very broad and deep, and with brief comments and we all have our own special fields we´re not always on the same page in discussions and sometimes that's main soure of disagreement.

/Fredrik

 

[PeterDonis]

Is it really true considering quantum field theory that things are "made" of particles?

You could say "made of quantum fields" if you want to be more precise. It doesn't change the substance of anything I said. The complications you mention are there, yes, but they are well beyond the scope of a "B" level thread.

 

[DarMM]

You could say "made of quantum fields" if you want to be more precise. It doesn't change the substance of anything I said. The complications you mention are there, yes, but they are well beyond the scope of a "B" level thread.

I'll start a new thread soon, as I think it does change something of substance and I'm not sure of the degree to which "made of quantum fields" is true either.

 

[PeterDonis]

I'll start a new thread soon

It probably needs to be "A" level if you really want to get into the complications you refer to.

 

[PaleMoon]

Please give a specific reference. We can't comment on out of context quotes.The models you are talking about do not contain any measurements, so the question of whether collapse takes place or not is irrelevant. These models are just the same as, for example, the "internals" of a double slit experiment, where even collapse interpretations agree that the evolution of the wave function is unitary; the only "collapse" is at the end of the experiment when the pattern is observed on the detector screen. The equivalent of that in the models you refer to is the universe in the infinite future, when all of the black holes have evaporated and all that is left is an infinite expanse of radiation at extremely low temperature. What "unitary evolution" means in this context is that, for a hypothetical observer in that infinite future universe, they can't tell from any of their measurements whether the infinite expanse of radiation came from the evaporation of black holes or from some other process (like matter-antimatter annihilation leaving only radiation behind) that didn't involve black holes at all.

this is perhaps the only answer i received to my opening question and i can accept it as correct but...
what you say is so obvious that i wonder why there was a "war" between Hawking and Susskind.
you are talking about two slits without hits on a screen. is it so simple?

 

[PeterDonis]

what you say is so obvious that i wonder why there was a "war" between Hawking and Susskind.

Because the issue they were having the "war" over had nothing to do with the question you are asking about collapse. (@Demystifier already pointed this out earlier in this thread.) It had to do with whether unitary evolution is truly universal in scenarios where there is no collapse, regardless of QM interpretation, because there is no measurement. The issue was that Hawking's original model of a black hole that evaporates away made it impossible for unitary evolution to apply even if no collapse or measurement ever occurred anywhere--any quantum state or portion of one that hit the singularity would be destroyed, which is a non-unitary process.

 

[Demystifier]

I believe it's supposed to be true that the entropy is purely a function of the black hole mass (it's something like the area of the event horizon).

Yes, many believe that it is so.

But if you consider an entangled electron to have a different amount of entropy than an electron in a pure state, then the entropy increase due to dropping in an electron is not just a function of the mass increase.

Exactly! In other words, I put arguments that the wide belief above might be wrong.

 

[Demystifier]

I have a question about this argument. Basically you seem to be saying that an extremely low energy photon can "fit" inside the black hole because, as it falls in, its wavelength gets strongly blueshifted. But you are also saying that the mass added to the hole in this process is negligible, which implies that the photon's energy is not strongly blueshifted, even though its wavelength is. I don't see how you can have it both ways. If the photon's energy is not blueshifted (which I don't think it should be, since the general rule for objects falling into black holes is that the object's energy at infinity is what gets added to the hole's mass), then its wavelength should not get blueshifted either.

Also, when we talk about an ingoing photon being blueshifted, this is observer-dependent; the blueshift is relative to an observer hovering close to the horizon. But such an observer has a large outward proper acceleration. I don't think the blueshift relative to this observer can just be assumed to be relevant to the photon's interaction with the black hole itself.

The energy, or more precisely the contribution of photon to the black hole mass, is not blueshifted from the point of observer staying at a fixed position far from the black hole.

 

[PeterDonis]

The energy, or more precisely the contribution of photon to the black hole mass, is not blueshifted from the point of observer staying at a fixed position far from the black hole.

Yes, I agree; the energy the photon adds to the hole is its energy at infinity.

What I'm questioning is whether, in the light of that, treating the photon's wavelength as blueshifted near the horizon makes sense.

 

[Demystifier]

Yes, I agree; the energy the photon adds to the hole is its energy at infinity.

What I'm questioning is whether, in the light of that, treating the photon's wavelength as blueshifted near the horizon makes sense.

It makes sense because this blueshift concerns the size of the wave packet. The size must be smaller than the black hole in order for the black hole to absorb it.

 

[stevendaryl]

It makes sense because this blueshift concerns the size of the wave packet. The size must be smaller than the black hole in order for the black hole to absorb it.

It seems to me that worrying about photon wavelength is sort of a red herring if the same point can be made with entangled electron/positron pairs.

 

[Demystifier]

It seems to me that worrying about photon wavelength is sort of a red herring if the same point can be made with entangled electron/positron pairs.

It can't, because the energy of the electron cannot be made arbitrarily small.

 

[stevendaryl]

It can't, because the energy of the electron cannot be made arbitrarily small.

Okay. So you can't drop an unlimited amount of entropy into a black hole using electrons without increasing the size of the black hole.

 

[Demystifier]

Okay. So you can't drop an unlimited amount of entropy into a black hole using electrons without increasing the size of the black hole.

Yes, that's why I use photons.

 

[PeterDonis]

It makes sense because this blueshift concerns the size of the wave packet. The size must be smaller than the black hole in order for the black hole to absorb it.

I understand why the wavelength is relevant. I don't understand how you can consider the photon's wavelength to be blueshifted but not its energy.

 

[Demystifier]

I understand why the wavelength is relevant. I don't understand how you can consider the photon's wavelength to be blueshifted but not its energy.

Unlike wavelength, the energy is conserved. So when the photon energy is blushifted, one can say that what is increased is the kinetic energy of the photon, while its potential energy in the gravitational field is decreased (by becoming negative), so that the total energy does not change.

 

[PeterDonis]

when the photon energy is blushifted, one can say that what is increased is the kinetic energy of the photon, while its potential energy in the gravitational field is decreased (by becoming negative), so that the total energy does not change.

This is just another way of saying that the energy the photon adds to the hole is its energy at infinity, which I already agree with.

If I understand you correctly, you are basically saying that there is no "wavelength at infinity" corresponding to energy at infinity. But that still doesn't explain why it's justified to use the blueshifted wavelength as the criterion for whether the photon will "fit inside the black hole". The blueshifted wavelength is the wavelength that would be measured by observers hovering close to, but outside, the horizon--but those observers will also measure the photon's energy to be blueshifted (they will measure what you are calling the kinetic energy of the photon above). I'm not aware of any observer who will measure the photon's wavelength to be blueshifted but still measure its energy to be the same as its energy at infinity. So what justifies using the blueshifted wavelength while still using the energy at infinity?

 

[Demystifier]

This is just another way of saying that the energy the photon adds to the hole is its energy at infinity, which I already agree with.

If I understand you correctly, you are basically saying that there is no "wavelength at infinity" corresponding to energy at infinity. But that still doesn't explain why it's justified to use the blueshifted wavelength as the criterion for whether the photon will "fit inside the black hole". The blueshifted wavelength is the wavelength that would be measured by observers hovering close to, but outside, the horizon--but those observers will also measure the photon's energy to be blueshifted (they will measure what you are calling the kinetic energy of the photon above). I'm not aware of any observer who will measure the photon's wavelength to be blueshifted but still measure its energy to be the same as its energy at infinity. So what justifies using the blueshifted wavelength while still using the energy at infinity?

The observer far from the black hole (Alice) cannot measure the wavelength of the photon near the horizon. All what she can is to determine whether the photon was absorbed by the black hole or merely scattered. The blueshift of the wavelength makes sense only from the point of view of the observer near the horizon (Bob). So Bob will see a blueshift in both wavelength and energy. And due to the blueshift in wavelength, he will conclude that near the horizon the wavelength is sufficiently small so that the wave can enter the black hole. And so the photon will be absorbed from the point of view ob Bob. But Alice cannot disagree on the fact that the photon has been absorbed, so she will observe absorption (or more precisely the lack of scattering) too. How will Alice interpret this? She cannot see the shrinking of the wave (because she cannot see the wave at all because she is far from the wave when it gets shrinked), but she will say that the wave shrinked objectively, without her observation.

 

[PaleMoon]

You write that the photon is absorbed from the point of view of Bob.
Do you think that events are observer dependent?

 

[Demystifier]

You write that the photon is absorbed from the point of view of Bob.
Do you think that events are observer dependent?

No.

 

[PeterDonis]

Bob will see a blueshift in both wavelength and energy.

Yes, agreed.

due to the blueshift in wavelength, he will conclude that near the horizon the wavelength is sufficiently small so that the wave can enter the black hole

But if he concludes this, doesn't he also have to conclude that the absorption process adds the photon's blueshifted energy to the hole's mass?

Alice cannot disagree on the fact that the photon has been absorbed

Agreed, whether or not the photon is absorbed must be an invariant. But so must the increase in mass of the black hole as a result, correct? And yet it seems like Bob will see a different mass increase than Alice.

 

[Demystifier]

But if he concludes this, doesn't he also have to conclude that the absorption process adds the photon's blueshifted energy to the hole's mass?

No, because mass, unlike energy, is defined as an invariant, observer independent quantity. See e.g. https://en.wikipedia.org/wiki/Mass_...ndi_masses_in_asymptotically_flat_space-times

 

[PeterDonis]

mass, unlike energy, is defined as an invariant, observer independent quantity

This is quibbling. The mass of a black hole is its energy in the asymptotically flat frame normally used to describe it. And the photon's energy at infinity, which is the energy it adds to the hole, is also an invariant.

If your argument is that we should focus on invariants, then what invariant corresponds to the photon's blueshifted wavelength? Wavelength is no more invariant than the photon's blueshifted energy is, by the argument you are making.

 

[Demystifier]

The mass of a black hole is its energy in the asymptotically flat frame normally used to describe it. And the photon's energy at infinity, which is the energy it adds to the hole, is also an invariant.

If your argument is that we should focus on invariants, then what invariant corresponds to the photon's blueshifted wavelength? Wavelength is no more invariant than the photon's blueshifted energy is, by the argument you are making.

Ah, I think I understand now what bothers you, so now I think I finally have the answer that will satisfy you. One can introduce the observer-dependent black-hole mass $\tilde{M}(r)$, which depends on the observer's position $r$ according to the Tolman's law
$$\tilde{M}(r)=\frac{M}{\sqrt{g_{00}(r)}}$$
where
$$g_{00}(r)=1-\frac{2M}{r}$$
In particular,
$$\tilde{M}(\infty)=M$$
is the usual ADM mass seen by the observer at infinity. So now you can say that the observer at position $r$ sees a blueshifted mass given by the first equation above.

However, the Bekenstein-Hawking entropy is given by the equation
$$S_{BH}=\frac{A}{4}=4\pi M^2$$
and entropy does not depend on the observer. In my paper the mass is only needed to determine the Bekenstein-Hawking entropy, so for this purpose I need $M$, not $\tilde{M}(r)$. Of course, you can argue that the physical mass observed by observer at $r$ is $\tilde{M}(r)$, but then I can say - fine, the entropy can be written in terms of $\tilde{M}(r)$ as
$$S_{BH}=4\pi g_{00}(r) \tilde{M}^2(r)$$
which in fact does not depend on $r$. So you are right that there is a blueshift of mass, but it is not relevant in the context of my paper which is really about entropy. That's why I am allowed to talk only about the invariant mass $M$, and not about the blueshifted mass $\tilde{M}(r)$. On the other hand I keep talking about the blueshifted wavelength because it is relevant for the question whether the wave can fit into the black hole. I could rephrase the arguments in my paper in terms of the blueshifted mass $\tilde{M}(r)$, but that would sound somewhat unusual and would not influence the results.

 

[PeterDonis]

One can introduce the observer-dependent black-hole mass $\tilde{M}(r)$, which depends on the observer's position rrr

Do you have a reference for this? I've never seen it in any GR texts or papers I have read.

Also, what physical measurement does $\tilde{M}(r)$ correspond to? Measuring the mass of the hole by the usual methods--Keplerian orbit parameters--gives what you are calling $\tilde{M}(\infty)$, not $\tilde{M}(r)$.