Undergrad Is quantum collapse an interpretation?

[stevendaryl]

I think that's a difference without a difference. Photon B is vertically polarized in exactly the same sense as a photon that has passed through a vertical polarizing filter. All subsequent measurements performed on Photon B will be the same in both cases.

The point is that in a twin-pair experiment, we perform a measurement on twin A and we learn something about twin B. The question then is: Whatever we now know about twin B, was it true before the measurement, and our measurement is just updating our knowledge, or did it become true through the process of measurement?

It seems that it is inconsistent (given Bell's theorem, if we reject superdeterminism and many-worlds) to claim that we are just updating our knowledge about B.

 

[tom.stoer]

May be I misunderstand what your claim is. But to me it seems that you are claiming that such a theory cannot exists ...

I never said that!

I don't deny the possibility of different interpretations or theories. I am talking about (some aspects of) Everett's Interpretation. Your ideas are not forbidden, but they are not compatible with Everett's.

Given that there are attempts as GRW, your claim seems in the need of some justification.

There is no such claim.

And GRW try to solve the problem via a modification of the mathematical formalism of quantum mechanics, whereas Everett doesn't.

As to Everett, if Born's rule is not part of the postulates it doesn't (although it may) mean that it has to be derived from them. It could be logically independent. No one demands that Euclid's fifth postulate has to be derived from the rest. So couldn't that be the case with Born in Everett?

The whole starting point was that one is looking for a consistent set of axioms describing aspects of "reality out there". Logically contradicting axioms would mean that this reality is logically inconsistent. You may add - as the zeroth axiom - that reality is logically consistent.

As far as I can see Everett's Interpretation is the only interpretation which is both realistic with an "ontic interpretation" of the state vector and which is mathematically equivalent to the orthodox of "textbook" quantum mechanics - provided that the apparent collapse and Born's rule follow as theorems.

 

[stevendaryl]

The whole starting point was that one is looking for a consistent set of axioms describing aspects "reality out there". Logically contradicting axioms would mean that this reality is logically inconsistent.

I don't think that the Born rule contradicts smooth evolution. As I said in a reply to @atyy, you could have an ontology in which there are two different types of object:

1. Classical configurations
2. Wave function

The wave function determines the probability of various classical configurations via the Born rule, but the classical configuration has no effect on the wave function, which always evolves according to Schrödinger's equation.

 

[tom.stoer]

I don't think that the Born rule contradicts smooth evolution. As I said in a reply to @atyy, you could have an ontology in which there are two different types of object:

1. Classical configurations
2. Wave function

The wave function determines the probability of various classical configurations via the Born rule, but the classical configuration has no effect on the wave function, which always evolves according to Schrödinger's equation.

That goes into the direction of de Broglie–Bohm theory. I haven't seen any attempt to incorporate spin, isospin etc. and to introduce particle creation and annihilation which is really satisfactory. The ontology and the axioms are quite complicated compared to Everett.

 

[Mentz114]

The point is that in a twin-pair experiment, we perform a measurement on twin A and we learn something about twin B. The question then is: Whatever we now know about twin B, was it true before the measurement, and our measurement is just updating our knowledge, or did it become true through the process of measurement?

It seems that it is inconsistent (given Bell's theorem, if we reject superdeterminism and many-worlds) to claim that we are just updating our knowledge about B.

In a projective measurement work is done on the object and the state goes into an eigenstate of the projector. Before that we actually don't know (or care?) what the state was.
As I understand it updating information is what we do but projecting the state of the atom is a well understood physical process independent of 'the state of our knowledge'..

 

[stevendaryl]

That goes into the direction of de Broglie–Bohm theory. I haven't seen any attempt to incorporate spin, isospin etc. and to introduce particle creation and annihilation which is really satisfactory. The ontology and the axioms are quite complicated compared to Everett.

Well, I think that Bohmian mechanics is attempting something more ambitious, which is to make the classical configurations deterministic. What I'm suggesting is really nothing more than Copenhagen reinterpreted. It's nondeterministic. But the classical configurations are macroscopic, rather than microscopic. Spin, particles, etc., are not part of the classical configuration, but are part of the microscopic state, which evolves according to Schrödinger's equation, or quantum field theory.

 

[stevendaryl]

In a projective measurement work is done on the object and the state goes into an eigenstate of the projector. Before that we actually don't know (or care?) what the state was.

As I said, it's fine if you are just claiming to be able to predict the probabilities for measurement outcomes, and are silent about ontology. That's a perfectly respectable approach (the "shut up and calculate" interpretation). But if you claim that a measurement is a matter of updating our knowledge, that goes beyond "shut up and calculate", and I don't think it's consistent. If a measurement is only a matter of updating of knowledge, then the polarization of photon B cannot be changed by measurement of photon A, and if you find out that B is vertically polarized, then it must have been vertically polarized immediately before the measurement. So saying it is a matter of updating of knowledge is not consistent with saying "we don't know and don't care what the state was before the measurement". It implies something definite about the state before the measurement.

 

[Mentz114]

As I said, it's fine if you are just claiming to be able to predict the probabilities for measurement outcomes, and are silent about ontology. That's a perfectly respectable approach (the "shut up and calculate" interpretation). But if you claim that a measurement is a matter of updating our knowledge, that goes beyond "shut up and calculate", and I don't think it's consistent. If a measurement is only a matter of updating of knowledge, then the polarization of photon B cannot be changed by measurement of photon A, and if you find out that B is vertically polarized, then it must have been vertically polarized immediately before the measurement. So saying it is a matter of updating of knowledge is not consistent with saying "we don't know and don't care what the state was before the measurement". It implies something definite about the state before the measurement.

I don't follow. You just repeated your original argument in a more convoluted way. Anyway - the only thing I believe is the actual physics of the spin and the field. So your arguments are irrelevant to me seeing as they don't even mention the physics of the experiment.

 

[stevendaryl]

I don't follow.

I think that's a choice on your part.

What does it MEAN to say that a measurement is "simply a matter of updating our knowledge"? It seems that people don't intend for that statement to have any implications. So why say it?

 

[Mentz114]

Well, what does it MEAN to say that a measurement is "simply a matter of updating our knowledge"? It seems that people don't intend for that statement to have any implications. So why say it?

I think they mean that
1) the WF does not exist in the way a field exists but is a calculational aid.
2) therefore it cannot collapse, and all that happens to it is that we change it.

The problem is the association of 'collapse' with measurement. Projective measurements don't necessarily 'collapse' anything so in the sense you take for measurement they are not measurements.

In fact, far from collapsing the state, the result is a coherent superposition which can be recombined to the original state ! So nothing changed except the basis.

[I was wrong about the work, I think]

 

[vanhees71]

With all due respect, all this says at the end nothing about what “quantum theory” tries to tell us. To use some mathematics doesn't mean to "understand" the semantics. As long as you are “bogged down” in Einstein’s world view, there is no way out.

There is no other way to talk about quantum physics than quantum theory and the only adequate language for it is mathematics, as for all of physics.

 

[stevendaryl]

What does it MEAN to say that a measurement is "simply a matter of updating our knowledge"? It seems that people don't intend for that statement to have any implications. So why say it?

What happens in discussions about QM is that there is a core that everyone agrees with. The core is the rules for calculating the answers to questions of the form:

• If I set up a system in such-and-such a way, and later perform such-and-such a measurement, then what is the probability that I get such-and-such a result?

That's what I consider to be the true minimal interpretation, but it's actually the "shut up and calculate" interpretation. It leaves completely unanswered such questions as:

1. Is there something special about measurements, compared with other types of interactions?
2. Does a measurement of one particle of a twin pair affect its twin?
3. Is measurement revealing a pre-existing property, or does the property come into existence in the process of measurement?
4. Do parts of an entangled system affect each other nonlocally?
5. Do particles have properties even when they aren't being measured?
6. Etc.

Those questions aren't answered by the shut up and calculate interpretation. Maybe some people think that they don't need to be answered, which is a perfectly respectable attitude to take. But if you claim to have an answer to one of the questions I have listed, then you are going beyond the shut up and calculate interpretation.

 

[vanhees71]

Yes, the mathematics is simple enough, but it is not consistent with the words you use in describing the minimal interpretation. You have on the one hand, the mathematical description of what's going on, and on the other hand, you have your description of measurements as "selection". The words contradict the mathematics.

This I don't understand. If I use an idealized polarizer, it's a paradigmatic example for a von Neumann filter measurement. What should here contradict the mathematics?

Again: If a system is prepared in a pure state, described by the Statistical Operator $\hat{\rho}=|\psi \rangle \langle \psi|$, then any observable, which is described by a self-adjoint operator has a determined value if and only if $|\psi \rangle$ is an eigenvector of this self-adjoint operator. If it is not an eigenstate of the operator, the corresponding observable has not a determined value, and the probabilities for measuring a possible value of this observable is given by Born's rule.

This means, if $|a,\beta \rangle$ is a complete orthonormal set of eigenvectors of the self-adjoint operator with eigenvalue $a$, then the probability to find this possible value $a$ when measuring the corresponding observable, given the system is prepared in the above pure state $\hat{\rho}$ is
$$P(a|\hat{\rho})=\sum_{\beta} \langle a,\beta|\hat{\rho}|a,\beta \rangle=\sum_{\beta} |\langle a,\beta|\psi \rangle|^2.$$
This is the standard formulation. Where is, in your opinion, a contradiction?

 

[stevendaryl]

I think they mean that
1) the WF does not exist in the way a field exists but is a calculational aid.

That's going beyond the minimal interpretation. The minimal interpretation doesn't actually say what the nature of the wave function is. To state that it's not real is to make an ontological claim, and I think that it's difficult to make sense of that claim. You can ignore the question about the nature of the wave function, and just say "I don't have a clue". But if you're going to venture into making ontological claims, it seems that you need to more precise about what you're claiming.

 

[vanhees71]

The wave function is a representation of a vector in Hilbert space. The corresponding ray (or projector) represents a pure state. It's a mathematical description of a preparation procedure. In the lab, I don't find Hilbert-space vectors but, e.g., an accelerator (to prepare particles I want to collide) and a bunch of detectors to measure the outcome of collisions between particles, which are other particles, which I sort with respect to species ("particle ID"), energy and momentum and, sometimes, polarization/spin.

 

[stevendaryl]

This I don't understand. If I use an idealized polarizer, it's a paradigmatic example for a von Neumann filter measurement. What should here contradict the mathematics?

To describe it as updating information contradicts the mathematics. To say that measurement is only updating your knowledge about the photon to me implies that whatever is true of the photon after the measurement was true before the measurement, but you just didn't know it. That claim is contradicted by the mathematics.

You can say that that's not what you mean by the phrase "updating of information", but then that phrase is meaningless to me.

 

[Mentz114]

That's going beyond the minimal interpretation. The minimal interpretation doesn't actually say what the nature of the wave function is. To state that it's not real is to make an ontological claim, and I think that it's difficult to make sense of that claim. You can ignore the question about the nature of the wave function, and just say "I don't have a clue". But if you're going to venture into making ontological claims, it seems that you need to more precise about what you're claiming.

I don't know what' minimal interpretation' means and I don't care. This is just a waste of time because it has nothing to do with physics.
But I have enjoyed the discussion up to now. Thank you.

 

[vanhees71]

To describe it as updating information contradicts the mathematics. To say that measurement is only updating your knowledge about the photon to me implies that whatever is true of the photon after the measurement was true before the measurement, but you just didn't know it. That claim is contradicted by the mathematics.

You can say that that's not what you mean by the phrase "updating of information", but then that phrase is meaningless to me.

I think there is some misunderstanding here. Let me try again: The maximal possible knowledge about a quantum system is given, if I have prepared it in a pure state. This implies, which observables take determined values and which don't (see #103). QT tells you exactly that not whatever is true about the photon that is true after a preparation procedure (measurement doesn't imply that I still have a photon; you must have a preparation of one for that) was already true before this preparation procedure. I did NOT claim anything else! That's the whole point we are discussing in this endless thread and many more of this kind!

 

[stevendaryl]

The wave function is a representation of a vector in Hilbert space. The corresponding ray (or projector) represents a pure state. It's a mathematical description of a preparation procedure. In the lab, I don't find Hilbert-space vectors but, e.g., an accelerator (to prepare particles I want to collide) and a bunch of detectors to measure the outcome of collisions between particles, which are other particles, which I sort with respect to species ("particle ID"), energy and momentum and, sometimes, polarization/spin.

It's certainly consistent to deny the existence of microscopic phenomena, and say that the only thing that exists is macroscopic phenomena (measurements, preparation procedures, detections, etc.) Then quantum mechanics can be viewed as a stochastic theory of such macroscopic phenomena. But you consistently deny that you're making any kind of macroscopic/microscopic distinction. To me, what you're calling the minimal interpretation is actually incoherent and inconsistent. You make claims that have ontological implications, and then deny any ontology.

If someone doesn't want to get into ontology, then it seems to me that they should stick to the shut up and calculate interpretation, and honestly answer "I don't know and don't care" about questions involving the nature of measurement and the nature of the wave function and whether quantum mechanics is nonlocal, and whether it's ontological or epistemological. But people seem to want to have their cake and eat it too.

 

[stevendaryl]

I don't know what' minimal interpretation' means and I don't care. This is just a waste of time because it has nothing to do with physics.

I don't agree with you that it has nothing to do with physics. But you have to make your own judgement about such things.

 

[stevendaryl]

I think there is some misunderstanding here. Let me try again: The maximal possible knowledge about a quantum system is given, if I have prepared it in a pure state.

That doesn't make any sense to me. To me, the use of the word knowledge implies a distinction between what is true and what is known. Without such a distinction, then what does "knowledge" mean?

 

[vanhees71]

I don't know what' minimal interpretation' means and I don't care. This is just a waste of time because it has nothing to do with physics.
But I have enjoyed the discussion up to now. Thank you.

The minimal interpretation is the physics described by the formalism of QT. Everything beyond that leaves the realm of the natural sciences and enters philosophy and speculation.

I strongly disagree with @stevendaryl that this point of view implies that there is a distinction between macroscopic and microscopic phenomena. Everything is discribable with QT. For macroscopic systems, often a very coarse-grained view is sufficient, and this coarse-grained view leads to the validity of the classical description which in these cases is a very good approximation for the behavior of the relevant macroscopic observables.

 

[vanhees71]

That doesn't make any sense to me. To me, the use of the word knowledge implies a distinction between what is true and what is known. Without such a distinction, then what does "knowledge" mean?

This is too philosophical for me. I think the thread is overdue to be closed :-(.

 

[Mentz114]

I don't agree with you that it has nothing to do with physics. But you have to make your own judgement about such things.

Why would it matter if I believed that the WF 'existed' or not ? It makes no difference to the predictions. No physics is affected.
This applies to almost anything in physics. There is no need to assume that things that can't be measured 'exist'.

 

[stevendaryl]

The minimal interpretation is the physics described by the formalism of QT. Everything beyond that leaves the realm of the natural sciences and enters philosophy and speculation.

I strongly disagree with @stevendaryl that this point of view implies that there is a distinction between macroscopic and microscopic phenomena.

It seems to me that your position is just inconsistent. The formalism itself explicitly invokes macroscopic concepts such as "measurement". Now it's possible to explain the formalism in terms of an underlying theory that doesn't make such a distinction, but doing so is going beyond the minimal interpretation.

The minimal interpretation is consistent with "collapse", which treats measurements as special, and it is also consistent with Bohmian mechanics, which does not treat measurements as special. So if you're claiming that measurement isn't special, then you're going beyond the minimal interpretation.

 

[stevendaryl]

This is too philosophical for me. I think the thread is overdue to be closed :-(.

But you're the one who insists on the word "knowledge". That's bringing in philosophy. That's my point--you don't consistently stick to the minimal interpretation.

 

[stevendaryl]

Why would it matter if I believed that the WF 'existed' or not ? It makes no difference to the predictions. No physics is affected.
This applies to almost anything in physics. There is no need to assume that things that can't be measured 'exist'.

The discussion is about the nature of collapse. It's not literally true that the nature of collapse makes no difference to predictions. In practice, it's true that it makes no difference. It's sort of like the question of whether entropy always increases for macroscopic systems. It's not literally true, but we'll never witness a counterexample.

 

[stevendaryl]

I realize that the discussions that I enjoy having on Physics Forums often elicit irritation from a lot of the regulars. I should really take the hint and leave the forum. I can't seem to figure out how to delete my account, but I am realizing how often discussions turn into bickering, and it's unpleasant.

 

[Mentz114]

I realize that the discussions that I enjoy having on Physics Forums often elicit irritation from a lot of the regulars. I should really take the hint and leave the forum. I can't seem to figure out how to delete my account, but I am realizing how often discussions turn into bickering, and it's unpleasant.

I've done my best ( and failed) not to practise bickering and I'm sorry you feel that way.
Believe me it is not as unpleasant as having posts (justifiably) ignored and being called 'incoherent' ( is there an award for that ?)

 

[tom.stoer]

This is too philosophical for me. I think the thread is overdue to be closed :-(.

Strange reflex.

Discussing interpretations of quantum mechanics is always about philosophy; in this thread that begins with the headline and the very first post.

But b/c many physicists contributed to these questions (Einstein, Bohr, Weizsäcker, ...), b/c interpretations are developed and discussed by physicists ( ..., Bohm, ..., Everett, Carroll, Tegmark et al. re "many-worlds", ... GRW, ... Rovelli, ...) this seems to be relevant to many physicists.

So why closing this thread? Think about it!