Is information lost in wavefunction collapse?

[Stephen Tashi]

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.

Ok.

I don't understand whether the question in thread title can be formulated precisely - or whether any of the replies assume a particular formulation.

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.

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?

 

[stevendaryl]

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?

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.

On the other hand, if you have a mechanism that can reliably place an electron into a superposition of states, then many repeated measurements can reveal the coefficients (up to an undetectable phase). But for a one-off state, there is no way to know what the state was. Measurement seems to destroy that information.

 

[Stephen Tashi]

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?

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.)

To get a technical definition that relates information loss to retrodiction loss, we could pursue defining an "instaneous" retrodiction that retrodicts the prior state of the system to an "infinitely less different" previous time such that no outside interference could have intervened.

 

[PeterDonis]

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.

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.

MWI is not standard QM.

No, but it's an interpretation of standard QM.

Standard QM does contain a postulate of non-unitary time evolution, which can be called state reduction or collapse.

This can't be right, since MWI is an interpretation of standard QM, and has entirely unitary time evolution with no collapse.

 

[Demystifier]

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.

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.

To answer the initial question, I would say that in a collapse the information is not really lost, but replaced by new information. For an analogy, suppose that someone burns your old phone book and gives you the new updated edition. Would you say that you lost the information in this process? No, you just updated it.

 

[atyy]

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.

All of this is wrong.

MWI is not a solution to the black hole information paradox, in any sense that Copenhagen is not.

The Carroll post you put in support of MWI states "These are the serious issues for EQM ..." and "But even given the real challenges of the preferred-basis issue and the probability issue, I think EQM is way ahead of any proposed alternative."

Standard QM has collapse - see the texts by Dirac, Landau and Lifshitz, Cohen-Tannoudji et al, Weinberg, Sakurai, Griffiths.

 

[PeterDonis]

Standard QM has collapse

Again, this can't be right, since MWI is an interpretation of standard QM and it doesn't have collapse.

see the texts by Dirac, Landau and Lifshitz, Cohen-Tannoudji et al, Weinberg, Sakurai, Griffiths.

Do any of these texts claim that MWI is not a valid interpretation?

 

[PeterDonis]

MWI is not a solution to the black hole information paradox

"Everything is always unitary" is a solution, or at least a claimed solution; and that implies the MWI.

 

[atyy]

"Everything is always unitary" is a solution, or at least a claimed solution; and that implies the MWI.

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.

 

[atyy]

Do any of these texts claim that MWI is not a valid interpretation?

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.

 

[PeterDonis]

Carroll states that MWI has serious issues

But he also says, as you quote, that it is "way ahead of any proposed alternative".

If even supporters of MWI still think there are major problems with MWI, then it cannot be considered textbook physics.

By this reasoning, no interpretation of QM can be considered "textbook physics". Is that your position?

 

[PeterDonis]

The usual approach, eg, AdS/CFT to try to solve the paradox would also solve it for Copenhagen.

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".

 

[Nugatory]

If even supporters of MWI still think there are major problems with MWI, then it cannot be considered textbook physics.

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.

It would be a bad thing if this thread were to degenerate into another form of "your interpretation is uglier than mine".

 

[Stephen Tashi]

What is the technical definition for "information" in the context of this thread?

 

[romsofia]

I had a similar question months ago, (https://www.physicsforums.com/threads/where-does-the-energy-go.930637/)


Even though it wasn't mentioned in the thread, if you take the collapse interpretation to be true, I believe you are essentially saying that your information (states) are not coupled to the environment until a measurement is taken place. So no information is loss even in the Copenhagen interpretation because as far the environment knows, there was really only one option?

If your information is coupled to the environment, then in theory, you would be able to measure the energy output of each state via some gravitational wave (I think Davies worked out some hand-wavy calculations in the 60/70s, i'll send references for anyone interested).... but maybe that's not for this thread :).

There are so many ifs when dealing with which is why....

What is the technical definition for "information" in the context of this thread?

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?

Just to clarify, as far as I'm aware Launder's principle might not apply to quantum systems, but I'm not an expert in quantum computing nor computing in general!

 

[atyy]

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".

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.

 

[atyy]

By this reasoning, no interpretation of QM can be considered "textbook physics". Is that your position?

Yes, except for Copenhagen or whatever one wishes to call what is in the textbooks.

 

[atyy]

It would be a bad thing if this thread were to degenerate into another form of "your interpretation is uglier than mine".

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).

 

[atyy]

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.

 

[stevendaryl]

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'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:

1. 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.
2. 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.

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.

 

[PeterDonis]

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.

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.

 

[PeterDonis]

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

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.

 

[PeterDonis]

it depends on what one means by "everything"

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).

 

[Demystifier]

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:

1. 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.
2. 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.

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.

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.

 

[stevendaryl]

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.

Thanks. So that really is something new.

So the idea is that you create an EPR pair---an electron and positron with entangled anticorrelated spins. You throw the positron into a black hole, which then vanishes in a puff of Hawking radiation. Now, you still have the electron, but the electron by itself was not in a pure state, it was in an entangled state. So how do you describe it now that its entangled partner no longer exists? A mixed state.

Now that I say it out loud, it occurs to me that in the case of spin entanglement, you might still have the electron entangled, rather than in mixed state. When the positron falls into the black hole, it imparts a tiny bit of angular moment to the black hole. When the black hole evaporates, that angular momentum is distributed among the particles produced by the Hawking radiation. So in that particular case, it seems that the electron's spin would be entangled with the resulting Hawking radiation. So I think to really illustrate the information loss, you would need some property of a pair of particles that is nonconserved?