# Is information lost in wavefunction collapse?

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bhobba
Mentor
I don't know what it means for entanglement to be broken instantaneously or not instantaneously.
When you observe one part of an entangled pair at the end of the observation we know what we observed and the entanglement with what it is entangled with is broken. But what is going on during the observation to that entanglement - does it change instantaneously and discontinuously or is something else going on? We do not know.

Thanks
Bill

stevendaryl
Staff Emeritus
When you observe one part of an entangled pair at the end of the observation we know what we observed and the entanglement with what it is entangled with is broken. But what is going on during the observation to that entanglement - does it change instantaneously and discontinuously or is something else going on? We do not know.
I don't quite understand what it is that you're saying might be changing continuously. Let's make it concrete: We have a source of anti-correlated spin-1/2 pairs. We have two distant experimenters, Alice and Bob. Alice measures spin-up along the z-axis at time $t$. Then she knows instantly the following fact about Bob: "If Bob measures the spin of his particle along the z-axis, he will measure spin-down." I don't see how continuous versus noncontinuous evolution is relevant. There definitely isn't a time window in which Bob might get a different answer, so the breaking of the entanglement doesn't propagate slowly in that sense.

bhobba
Mentor
As if there were any ambiguity, p108 further shows that this is what he meant.
There is no ambiguity. He says the state changes unpredictably. Nobody disagrees with that. Its the other baggage associated with collapse that is the issue.

MW proves it does not have to happen using non-unitary changes and instantaneously, nor does the formalism require it to be. It may be like that or not - we do not know. It may be like GRW - again we do not know. The formalism is silent on it.

Thanks
Bill

bhobba
Mentor
I don't quite understand what it is that you're saying might be changing continuously. Let's make it concrete: We have a source of anti-correlated spin-1/2 pairs. We have two distant experimenters, Alice and Bob. Alice measures spin-up along the z-axis at time $t$. Then she knows instantly the following fact about Bob: "If Bob measures the spin of his particle along the z-axis, he will measure spin-down." I don't see how continuous versus noncontinuous evolution is relevant. There definitely isn't a time window in which Bob might get a different answer, so the breaking of the entanglement doesn't propagate slowly in that sense.
Does the measuring process of Alice happen instantaneously? Or is it like decoherence would suggest - continuous but in a very short time. During that time what happens to the entanglement with the other particle?

Thanks
Bill

stevendaryl
Staff Emeritus
Does the measuring process of Alice happen instantaneously? Or is it like decoherence would suggest - continuous but in a very short time. During that time what happens to the entanglement with the other particle?
Let's suppose that Alice's measurement starts at time $t_1$ and finishes at time $t_2$, and let's suppose that Bob's starts at $t_3$ and finishes at $t_4$. If Bob is far enough away from Alice so that there is no possibility of a light-speed or slower signal propagating from Alice at time $t_1$ to Bob at time $t_4$, then I don't see what difference it makes how long Alice's measurement took.

bhobba
Mentor
Let's suppose that Alice's measurement starts at time $t_1$ and finishes at time $t_2$, and let's suppose that Bob's starts at $t_3$ and finishes at $t_4$. If Bob is far enough away from Alice so that there is no possibility of a light-speed or slower signal propagating from Alice at time $t_1$ to Bob at time $t_4$, then I don't see what difference it makes how long Alice's measurement took.
Well let's be more precise. Suppose via slow transport Bob and Alice have syced clocks. And they both at exactly the same time observe the system (remember until entanglement is broken it is a single system). What happens then? That may be interesting to both analyse and do. I wonder if @DrChinese knows anything about that or has some papers to post.

My guess is its an entirely different setup - the observable will be a compound observable of observing both 'parts' of the entangled system which is different than what goes on in EPR.

Thanks
Bil

stevendaryl
Staff Emeritus
Well let's be more precise. Suppose via slow transport Bob and Alice have syced clocks. And they both at exactly the same time observe the system (remember until entanglement is broken it is a single system). What happens then? That may be interesting to both analyse and do. I wonder if @DrChinese knows anything about that or has some papers to post.
I don't know what tests have been done along those lines, but I'm willing to bet that it doesn't make any difference whether Bob's measurement is at the same time as Alice's, or slightly earlier, or slightly later.

Mentz114
Gold Member
I don't know what tests have been done along those lines, but I'm willing to bet that it doesn't make any difference whether Bob's measurement is at the same time as Alice's, or slightly earlier, or slightly later.
That is correct because the singlet state tells us nothing about times or time-ordering, so we can say nothing about those times.

The singlet state is also silent on states before the measurement, so nothing is ruled out. Even the pair having a fixed value. It is irrelevant because of the imminent re-projection.

atyy
There is no ambiguity. He says the state changes unpredictably. Nobody disagrees with that. Its the other baggage associated with collapse that is the issue.

MW proves it does not have to happen using non-unitary changes and instantaneously, nor does the formalism require it to be. It may be like that or not - we do not know. It may be like GRW - again we do not know. The formalism is silent on it.

Thanks
Bill
That is not correct. MWI and GRW are research directions on which consensus has not been reached in the community. Even supporters of MWI like Carroll and Wallace state that it has open problems. It is misleading false advertising to place them on the same level as textbook physics. This false advertising also does not benefit those research programmes, since if the issues are settled, we should now stop research into MWI and GRW.

atyy
Does the measuring process of Alice happen instantaneously? Or is it like decoherence would suggest - continuous but in a very short time. During that time what happens to the entanglement with the other particle?

Thanks
Bill
That is not correct. Decoherence does not solve the measurement problem. Within the standard formalism, if one includes decoherence, the appearance of the measurement result still needs an instantaneous "measurement" on the measurement apparatus. One has to go to something like MWI for decoherence to remove collapse, but MWI is not yet textbook physics.

That is not correct. Decoherence does not solve the measurement problem. Within the standard formalism, if one includes decoherence, the appearance of the measurement result still needs an instantaneous "measurement" on the measurement apparatus. One has to go to something like MWI for decoherence to remove collapse, but MWI is not yet textbook physics.
Is there not an observable of the composite system, system + apparatus + rest of the universe, that, if measured, would indicate whether system + apparatus + rest of universe is in a superposition or not?

atyy
Is there not an observable of the composite system, system + apparatus + rest of the universe, that, if measured, would indicate whether system + apparatus + rest of universe is in a superposition or not?
Basically, there is no rest of the universe, because the rest of the universe excludes the final measurement apparatus. So if we include a measuring apparatus in the quantum state, we need another measuring apparatus to measure the first apparatus, otherwise no measurement outcome is obtained.

This is, as you know, the measurement problem, which remains unsolved. I think it is an important problem, but approaches to the measurement problem should not be brought up (as Peter Donis and bhobba did) in a thread which only refers to and makes sense within standard QM.

PeterDonis
Mentor
a thread which only refers to and makes sense within standard QM.
I don't think we have agreement on this point. Your position appears to be that simply saying "wave function collapse isn't the same as black hole information loss" is enough to answer the OP's question. But the OP's question was whether information is lost in wave function collapse; the fact that the OP also brought in a mistaken analogy with black hole information loss does not mean his question was only about whether wave function collapse and black hole information loss are the same.

As I've already said, I don't think the question of whether information is lost in wave function collapse is answerable within standard QM. The question of whether wave function collapse is the same as BH information loss is answerable within standard QM (the answer is that the two are not the same), but, as above, that's not a complete answer to the OP's question.

atyy
I don't think we have agreement on this point. Your position appears to be that simply saying "wave function collapse isn't the same as black hole information loss" is enough to answer the OP's question. But the OP's question was whether information is lost in wave function collapse; the fact that the OP also brought in a mistaken analogy with black hole information loss does not mean his question was only about whether wave function collapse and black hole information loss are the same.

As I've already said, I don't think the question of whether information is lost in wave function collapse is answerable within standard QM. The question of whether wave function collapse is the same as BH information loss is answerable within standard QM (the answer is that the two are not the same), but, as above, that's not a complete answer to the OP's question.
If you read the OP and his clarifications in subsequent posts, you can see that he is asking for an answer within standard QM. He is aware of still speculative approaches beyond standard QM.

atyy
@PeterDonis, just to clarify - I am not objecting to the discussion of interpretations as one part of the answer to this thread. I am objecting in interpretations being brought up as a primary answer, and as if MWI is part of standard QM or that MWI has anything to do with the most common attempts (like AdS/CFT) to restore unitarity in the black hole information paradox.

If after those points have been discussed in standard QM, I do think it is perfectly fine to mention that more generally there is the measurement problem etc. Personally, I would not bring it up, since I prefer to have fewer discussion on interpretations in QM forum, and I don't like that every time collapse is brought up in the colloquial, innocuous sense of the word referring to standard QM, that interpretations are brought into the discussion. However, if no physics errors are made, I usually try (I confess, not always successfully ) to shut up. Here I entered the discussion to clarify that MWI is not part of standard QM and that MWI has nothing to do with the most common attempts (like AdS/CFT) to restore unitarity in the black hole information paradox.

[I think you agree, but bhobba entered the discussion on a post in which I was replying to you, and reintroduced the erroneous idea that MWI is part of standard QM].

PeterDonis
Mentor
If you read the OP and his clarifications in subsequent posts, you can see that he is asking for an answer within standard QM.
An answer to what question? I am saying the question he wants an answer to is the title question of this thread. And that question cannot be answered within standard QM, for reasons I've already explained. So if you're right that the OP is only interested in an answer within standard QM, then all we can tell him is that there isn't one.

I am not objecting to the discussion of interpretations as one part of the answer to this thread. I am objecting in interpretations being brought up as a primary answer
I am fine with that. I agree that the MWI is an interpretation, not standard QM, and can't be an answer to any question that asks what standard QM says.

Apparently disagreeing with others (perhaps more knowledgeable); I think information is gained after a measurement. We are going from uncertainty to certainty. I don't know how others define "information" but I would take that as an increase in information. I think any form of Shannon's formula would agree, but I will write it out if requested. I view "measurement" as a "filter" that selects some particular future effects; i.e. determines the future.

Stephen Tashi
I think any form of Shannon's formula would agree, but I will write it out if requested.
Within the thread, no one has yet offered a technical definition of information. What I get from the focus on unitary evolution (or a violation of it) is that a physical law specifying how the "state" of system changes from time t to time t+dt is considered to lose information if that law is a many-to-one-mapping. That definition defines "looses information" without specifying a quantitative measure of information. There's nothing wrong with such a definition from a logical point of view, but it would help to know explicitly if that's the definition that most participants have in mind.

The Shannon definition of information applies to a probability distribution, so it raises the question of what random variable you wish to look at. Various properties of a physical system can be measured. Measuring one property may increase the dispersion in a subsequent measurement of a different property. Applying the Shannon definition of information to a physical system is not straightforward.

The Shannon definition is related to the entropy of a probability distribution. Just stringing words together, there is such a thing as the "von Neumann entropy" in quantum statistical mechanics. There are also controversies about whether it is the best way to define entropy. Perhaps someone can comment on a relation between "information" as discussed in this thread and the various definitions of "entropy".

.Scott
Homework Helper
I'm curious why knowing more about something would be called a "loss" of information.

If a experiment is performed involving a probabilistic phenomena and the experimenter learns the outcome, why isn't this a gain in information?
I totally agree.

Let me state the other (ie, wrong) logic explicitly and as I understand it:
They are saying that before the measurement or collapse, there are many possible outcomes. But once the measurement is made, there is only one. They believe this could indicate a loss of information.

Before I attack that logic, let me say that I do not believe there is a change in the amount of information.

That said: Going from many possibilities to one is an increase in information. If I tell you that the killer has 012 as the first 3 digits of his social security number, that is some information - but there are still hundreds of thousands of possibilities. If I then said the first 5 digits are 012-34, then I have given you more information and thus left you with fewer possibilities.

I suspect that MWI is not an "interpretation" since, in its simplest form, it requires a continuous increase in the amount of information in the universe. Without it, an event can be identified by initial conditions (for example, Big Bang), three spacial coordinates and a time coordinate. With it, the event also requires a "which world" parameter.

The way to avoid this increase in information is to presume that, although it was theoretically impossible to know what the outcome would be, that it was never-the-less predestined - and that it was entirely determined from information that existed before the measurement was made.

The only alternative I see is to allow the amount of information to increase steadily. Then, to avoid "coin flipping", we would need to invoke either an "external" information source or MWI.

Within the thread, no one has yet offered a technical definition of information. What I get from the focus on unitary evolution (or a violation of it) is that a physical law specifying how the "state" of system changes from time t to time t+dt is considered to lose information if that law is a many-to-one-mapping. That definition defines "loses information" without specifying a quantitative measure of information. There's nothing wrong with such a definition from a logical point of view, but it would help to know explicitly if that's the definition that most participants have in mind.

The Shannon definition of information applies to a probability distribution, so it raises the question of what random variable you wish to look at. Various properties of a physical system can be measured. Measuring one property may increase the dispersion in a subsequent measurement of a different property. Applying the Shannon definition of information to a physical system is not straightforward.

The Shannon definition is related to the entropy of a probability distribution. Just stringing words together, there is such a thing as the "von Neumann entropy" in quantum statistical mechanics. There are also controversies about whether it is the best way to define entropy. Perhaps someone can comment on a relation between "information" as discussed in this thread and the various definitions of "entropy".
Well, my model is simple, if I use a fluorescent screen and see an electron light up a spot I can then determine where the electron was at that moment and with careful measurement probably the energy. So I have gained information that affects all my future calculations; i.e. I have filtered my future. There may be other "universes" but they don't affect my future. Of course I might not look for a while and the delayed choice experiments come into play. But for my future, I have greater certainty (and probably increased my entropy some way) thus more information. A sort of Bayesian attitude if you will.

PeterDonis
Mentor
I have gained information that affects all my future calculations; i.e. I have filtered my future.
But you have lost information about your past; that is, if there are many possible past states that all could have led to your current state, the one you are using for your future calculations, then you have lost information. When physicists talk about non-unitary transformations (such as an actual physical wave function collapse) leading to loss of information in quantum mechanics, that is what they are talking about.

But you have lost information about your past; that is, if there are many possible past states that all could have led to your current state, the one you are using for your future calculations, then you have lost information. When physicists talk about non-unitary transformations (such as an actual physical wave function collapse) leading to loss of information in quantum mechanics, that is what they are talking about.
Yes, I have always said the past is as uncertain as the future in QM; a radical oversimplification. But taking a Bayesian attitude, information allows future certainty. Otherwise, when we take measurements we are destroying knowledge of the past; sort of a squishy conserved thing that disturbs me. But let's think about this; you/that implies that my ignorance in the past has more "information" than after I take the measurement. I suppose that's possible but it seems that "information" now has two different meanings/measures. Which is reasonable if it's given two names with a conservation law linking them. Like "Potential Energy" and "Kinetic Energy" I guess?

An interesting thread. I have no math skills and am an avid fan. In my opinion many of the posts describing information were wide of the OP. The information the OP asks about exists only in the system to be measured. It has nothing to do with knowledge that an experimenter will gain, or probable outcomes, or what state the particle is in. There is an assumption that the system being measured contains information. Although this is reasonable, it is still only an assumption.

PeterDonis
Mentor
information allows future certainty
Not in general in QM, since QM only makes probabilistic predictions about the results of measurements. But if you know the result of a measurement you just made, using the state corresponding to that measurement result will give you better predictions about future measurements you can make than using the state before you made the measurement.

that implies that my ignorance in the past has more "information" than after I take the measurement

Within the thread, no one has yet offered a technical definition of information. What I get from the focus on unitary evolution (or a violation of it) is that a physical law specifying how the "state" of system changes from time t to time t+dt is considered to lose information if that law is a many-to-one-mapping. That definition defines "looses information" without specifying a quantitative measure of information. There's nothing wrong with such a definition from a logical point of view, but it would help to know explicitly if that's the definition that most participants have in mind.

The Shannon definition of information applies to a probability distribution, so it raises the question of what random variable you wish to look at. Various properties of a physical system can be measured. Measuring one property may increase the dispersion in a subsequent measurement of a different property. Applying the Shannon definition of information to a physical system is not straightforward.
Thanks!

I've been reading this thread, wishing people would take your question on. What I would say, having played with quantum computer simulators, is that the information relayed to an *observer* in bits is something like the base 2 logarithm of the reciprocal of the probability of *observing* the event.

So a qubit "in" some prepared state doesn't actually carry the information needed to specify the prepared state, because that can't be observed from the qubit alone. So no information is lost on measurement.

But where does the probability space come from in physical systems? If I give you a full gigabit removable drive, it's a gigabit of information *to the drive* in that it treats all 2 to the billion possible states as equally likely, allocates equal resources to each one. But if you already knew the info on the drive, I've given you personally zero bits of information with the same drive, in that your internal model, unlike the drive, remains unchanged. How can this be mapped to physical systems I wonder? I feel it has something to do with changes.