Ok.Well, you can quantify information in terms of the number of bits necessary to specify a situation, but I was just using it in the informal sense.
Suppose you don't perform the measurement. If you try to retrodict what the superposition was ten years ago, how do you know that the current superposition wasn't a result of some intervening measurements?But if an electron is initially in a superposition of two states, and then I perform a measurement, there is (as far as anybody knows) no way, even theoretically, to retrodict what the initial superposition was.
I'm not sure I understand the question. Are you saying that the information about the superposition might be encoded in the state of whatever device put the electron into a superposition in the first place? That might be a resolution to the information loss problem in quantum measurements, but it's not a part of standard quantum mechanics. A system can start in an arbitrary state, and after a measurement, the details of that initial state are (apparently) forever inaccessible.Suppose you don't perform the measurement. If you try to retrodict what the superposition was ten years ago, how do you know that the current superposition wasn't a result of some intervening measurements?
A good idea, but my thinking isn't that sophisticated. I'm only saying that the ability to retrodict doesn't seem to be a reliable indicator of whether information is conserved or lost - because you can't actually retrodict the history of a physical system without assuming there has been no "outside interference". (That's true even in classical deterministic physics.)I'm not sure I understand the question. Are you saying that the information about the superposition might be encoded in the state of whatever device put the electron into a superposition in the first place?
Huh? "Supporting MWI" does not mean believing that the black hole information paradox can only be formulated under the MWI. Indeed, the whole point of "supporting MWI" with regard to black holes and information is that there is no paradox at all under the MWI, since everything is always unitary. Only under a collapse interpretation is there a paradox at all.the reason is not that they support MWI. If that were correct, one would not be able to formulate the black hole information paradox in Copenhagen.
No, but it's an interpretation of standard QM.MWI is not standard QM.
This can't be right, since MWI is an interpretation of standard QM, and has entirely unitary time evolution with no collapse.Standard QM does contain a postulate of non-unitary time evolution, which can be called state reduction or collapse.
Even though collapse and apparent disappearance of information by black hole evaporation both violate unitarity, those two processes are not directly related. They violate unitarity in very different ways.Huh? "Supporting MWI" does not mean believing that the black hole information paradox can only be formulated under the MWI. Indeed, the whole point of "supporting MWI" with regard to black holes and information is that there is no paradox at all under the MWI, since everything is always unitary. Only under a collapse interpretation is there a paradox at all.
All of this is wrong.Huh? "Supporting MWI" does not mean believing that the black hole information paradox can only be formulated under the MWI. Indeed, the whole point of "supporting MWI" with regard to black holes and information is that there is no paradox at all under the MWI, since everything is always unitary. Only under a collapse interpretation is there a paradox at all.
No, but it's an interpretation of standard QM.
This can't be right, since MWI is an interpretation of standard QM, and has entirely unitary time evolution with no collapse.
Again, this can't be right, since MWI is an interpretation of standard QM and it doesn't have collapse.Standard QM has collapse
Do any of these texts claim that MWI is not a valid interpretation?see the texts by Dirac, Landau and Lifshitz, Cohen-Tannoudji et al, Weinberg, Sakurai, Griffiths.
"Everything is always unitary" is a solution, or at least a claimed solution; and that implies the MWI.MWI is not a solution to the black hole information paradox
Yes, but it does not imply MWI. The usual approach, eg, AdS/CFT to try to solve the paradox would also solve it for Copenhagen. The interpretations have nothing to do with the paradox. Introducing different degrees of freedom is the usual approach."Everything is always unitary" is a solution, or at least a claimed solution; and that implies the MWI.
I edited my reply above before seeing your reply. Carroll states that MWI has serious issues, as does David Deutsch. If even supporters of MWI still think there are major problems with MWI, then it cannot be considered textbook physics.Do any of these texts claim that MWI is not a valid interpretation?
But he also says, as you quote, that it is "way ahead of any proposed alternative".Carroll states that MWI has serious issues
By this reasoning, no interpretation of QM can be considered "textbook physics". Is that your position?If even supporters of MWI still think there are major problems with MWI, then it cannot be considered textbook physics.
Unless "everything is always unitary" is consistent with what you mean by "Copenhagen", I don't see how this could be true. And if "everything is always unitary" is consistent with what you mean by "Copenhagen", then I am very confused as to what you mean by "Copenhagen".The usual approach, eg, AdS/CFT to try to solve the paradox would also solve it for Copenhagen.
All interpretations have major issues - that's why we can spend so much time arguing about them, and also why pointing out the issues cannot settle these arguments.If even supporters of MWI still think there are major problems with MWI, then it cannot be considered textbook physics.
I think to make any movement in a thread like this, this is the right way to go. Otherwise we will all just talk around each other using ambiguous words. Math triumphs. As far as I'm aware, information in QM is referred to as states! But what states are we considering? An energy operator is different than a position operator, and then some other people started talking about bits! If we start talking about bits, then there is already a reason how THAT information loss is handled! If we start to think as information as bits, then why not just invoke Launder's principle and call it a day?What is the technical definition for "information" in the context of this thread?
Well it depends on what one means by "everything". For the information paradox, there is a reasonable definition of everything. In Copenhagen, everything is unitary between measurements.Unless "everything is always unitary" is consistent with what you mean by "Copenhagen", I don't see how this could be true. And if "everything is always unitary" is consistent with what you mean by "Copenhagen", then I am very confused as to what you mean by "Copenhagen".
Yes, except for Copenhagen or whatever one wishes to call what is in the textbooks.By this reasoning, no interpretation of QM can be considered "textbook physics". Is that your position?
It has nothing to do with ugliness, but correctness. It is not correct, in a thread which mentions standard QM, and makes sense within standard QM, to tell the OP that his question doesn't make sense, by bringing in speculative approaches to the measurement problem as if it is settled physics - here I use speculative in the sense that string theory is speculative and not settled physics (although I do think it is the leading approach to quantum gravity).It would be a bad thing if this thread were to degenerate into another form of "your interpretation is uglier than mine".
To add to my comment above, the OP is not a question about interpretations. Bringing in interpretations as Peter Donis did is irrelevant to the OP. The point is that the non-unitary evolution of collapse, and that of the information paradox are not related as I tried to say in post #20, and as Demystifier says clearly in post #30.It would be a bad thing if this thread were to degenerate into another form of "your interpretation is uglier than mine".
I'm not sure I understand the distinction you are making. The way I understand "mixed state" in quantum mechanics, there are two different sources of mixed states:Even though collapse and apparent disappearance of information by black hole evaporation both violate unitarity, those two processes are not directly related. They violate unitarity in very different ways.
In a collapse, a pure state evolves (jumps) into another pure state.
By black hole evaporation, a pure state evolves into a mixed state.
I agree with the point you and @Demystifier make that these two things (collapse vs. BH information paradox) are different. Are you saying that that, in itself, is a sufficient answer to the question in the OP? If so, I would like the OP to say whether he agrees with that.To add to my comment above, the OP is not a question about interpretations. Bringing in interpretations as Peter Donis did is irrelevant to the OP. The point is that the non-unitary evolution of collapse, and that of the information paradox are not related as I tried to say in post #20, and as Demystifier says clearly in post #30.
But in "standard QM", the OP's question can't be answered, because standard QM allows both kinds of interpretations: interpretations in which information is not lost in "wave function collapse" (because "collapse" is not a real process but just a calculational rule, no real non-unitary processes ever happen--for example, the MWI), and interpretations in which information is lost in collapse, because collapse is a real, non-unitary process.It is not correct, in a thread which mentions standard QM, and makes sense within standard QM, to tell the OP that his question doesn't make sense, by bringing in speculative approaches to the measurement problem as if it is settled physics
Yes, which is exactly why the answer to the OP's question must be interpretation dependent: some interpretations, like the MWI, mean by "everything" literally everything--nothing non-unitary ever happens, anywhere in the universe. Whereas other interpretations only interpret "everything" to mean "everything between measurements" (and some go on to claim that during a measurement, an actual non-unitary process, wave function collapse, happens, while others are agnostic about this).it depends on what one means by "everything"
It is neither #1 nor #2. It isI'm not sure I understand the distinction you are making. The way I understand "mixed state" in quantum mechanics, there are two different sources of mixed states:
When people say that a black hole turns a pure state into a mixed state, I'm not exactly sure what notion of "mixed state" is meant. But if it is #1, then it seems to me equivalent to a measurement collapsing the wave function, but you don't know what the measurement result was.
- If you don't know what the state of a system is, then you can represent it as a mixed state, where the probabilities reflect your subjective uncertainty about what the pure state is.
- A pure state involving two subsystems (the system of interest and the environment, say) can be treated as a mixed state of just one of the subsystems, by a kind of averaging over the system that you're not interested in.
Thanks. So that really is something new.It is neither #1 nor #2. It is
3. Initially you have a pure state involving two entangled subsystems, one inside the black hole and the other outside of the black hole. So initially it corresponds to your 2. But then the inside subsystem gets destroyed in the black hole singularity, so what remains is only the outside subsystem, which is in a mixed state but no longer entangled with anything.