I Is quantum collapse an interpretation?

[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!

 

[tom.stoer]

Well, I think that Bohmian mechanics is attempting something more ambitious, which is to make the classical configurations deterministic.

Yes, that's basically the idea.

What I do not like is the weird ontology: you have classical particles, but in addition you have the quantum wave function. You attribute some observables to the particles (position, momentum), some others to the wave function (spin etc.). For me this is absolutely unsatisfactory; it complicated things instead of simplifying them.

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 Schrodinger's equation, or quantum field theory.

I think I get your point, but my objection regarding ontology remains the same.

 

[Lord Jestocost]

To my mind, the original question "Is quantum collapse an interpretation?“ seems to point to a fundamental paradox. At the end, all interpretations of "quantum mechanics“ need to assume the real existence of measurement instruments but find themselves in the paradoxial situation that "quantum mechanics“ itself is powerless to explain how their existence comes about.

 

[atyy]

May be I misunderstand what your claim is. But to me it seems that you are claiming that such a theory cannot exists, and I don't see anything even remotely resembling a proof. Given that there are attempts as GRW, your claim seems in the need of some justification

The claim is that an uncontroversial derivation does not yet exist within the context of the Everett approach. There are other approaches that are successful in some domains of quantum mechanics at the physics level of rigour, eg. Bohmian Mechanics and GRW, where additional postulates are made, and the Born rule is derived as an excellent approximation.

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?

So let's say we have the Schroedinger equation for a single non-relativistic particle. How do we add the Born rule and maintain unitary evolution at all times?

 

[kith]

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.

They also elicit a lot of approval which is mostly silent. I think your posts in this forum are among the ones with the highest quality and I enjoy reading them.

If the problem is the interaction with a few specific users, you could simple refuse to engage with them or put them on the ignore list.

 

[bhobba]

To my mind, the original question "Is quantum collapse an interpretation?“ seems to point to a fundamental paradox. At the end, all interpretations of "quantum mechanics“ need to assume the real existence of measurement instruments but find themselves in the paradoxial situation that "quantum mechanics“ itself is powerless to explain how their existence comes about.

Yes you have hit on the central issue of QM.

But I would like to make a few points:

1. The formalism without any interpretation other than simply some intuitive idea of probability requires the existence of a macro world that observations occcur in because it's a theory about such observations. So how does a theory that assumes such explain what it assumes? That is indeed a central if not the central issue.

2. It's far too pessimistic to say '"quantum mechanics“ itself is powerless to explain how their existence comes about'. Yes some issues remain but a lot of progress has been made in resolving it - I have recommended Schlosshauer far too many times to post the reference again. He explains in detail what we know and what we do not as well as exactly how far the progress in resolving that has come. It was written a couple of years ago now - this is a fast changing area so something important may have been discovered since the book was written. I seem to recall a post to that effect but could not verify it. We have PBR etc - but I wasn't thinking of that - but something that throws the whole decohenrce program into doubt - if true it's very very important and Nobel worthy so I guess one way or the other its truth will come out. Many people including myself says it has been resolved for all practical purposes. That is of course NOT resolving it fully, but if you are satisfied with FAPP is now the central issue. It has morphed considerably since Einsteins and Bohr's day - we now know they were both wrong:
http://physicstoday.scitation.org/doi/full/10.1063/1.2155755

Interestingly, and perhaps even telling, is that Einstein went onto promote the Ensemble Interpretation which is popular even today while Copenhagen has morphed somewhat with things like Consistent Histories which its adherents say is Copenhagen done right - whether that's a true categorization or not I will leave to Copenhagenists. I never did like Copenhagen with its insistence 'A system is completely described by a wave function ψ, representing an observer's subjective knowledge of the system' (Heisenberg). But I must say I do rather like Consistent Histories (or Decoherent Histories as Gell-Mann calls it). Interesting aside - Feynman was in the audience when Murray gave a lecture on it. At the end he got up - and everyone thought - the two masters are really going to have a ding-dong - but instead he said - I agree with everything that was said - so you could say Feynman was converted to it.

Thanks
Bill

 

[bhobba]

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.

They also elicit a lot of approval which is mostly silent. I think your posts in this forum are among the ones with the highest quality and I enjoy reading them.

Please don't - it would be a great loss - all I can do is reiterate what Kith said. You are a very special part of this forum - something I noticed from day one.

You don't have to agree with everyone but you are always respectful and full of insight.

And to be frank you keep some of my ramblings in check. I would hate to loose that balance.

Thanks
Bill

 

[atyy]

Interestingly, and perhaps even telling, is that Einstein went onto promote the Ensemble Interpretation which is popular even today while Copenhagen has morphed somewhat with things like Consistent Histories which its adherents say is Copenhagen done right - whether that's a true categorization or not I will leave to Copenhagenists. I never did like Copenhagen with its insistence 'A system is completely described by a wave function ψ, representing an observer's subjective knowledge of the system' (Heisenberg). But I must say I do rather like Consistent Histories (or Decoherent Histories as Gell-Mann calls it). Interesting aside - Feynman was in the audience when Murray gave a lecture on it. At the end he got up - and everyone thought - the two masters are really going to have a ding-dong - but instead he said - I agree with everything that was said - so you could say Feynman was converted to it.

Just to clarify: Einstein's Ensemble Interpretation was basically a hidden variable interpretation. Bohmian Mechanics is an example of a hidden variable interpretation. Einstein did not like Bohmian Mechanics, but given the Bell inequalities, we now know that his objections hold no water.

The modern Ensemble interpretation, when done right, is just a flavour of Copenhagen. Copenhagen remains the only uncontroversial interpretation of quantum mechanics, and is the standard interpretation.

 

[bhobba]

Just to clarify: Einstein's Ensemble Interpretation was basically a hidden variable interpretation.

Yes that's true, as basically was Ballentine's 1970 paper - although you had to read it a bit more carefully. However as presented in his book it's a bit more subtle and I would say its modern version is agnostic ie it can be hidden variable or not.

Thanks
Bill

 

[bhobba]

The modern Ensemble interpretation, when done right, is just a flavour of Copenhagen. Copenhagen remains the only uncontroversial interpretation of quantum mechanics, and is the standard interpretation.

Yes and no - it comes down to what you mean by 'flavor'. One has a more Bayesian view of probability, the other is more frequentest. I will not come down on any side of this argument except to point out what John Baez said:
http://math.ucr.edu/home/baez/bayes.html
'It turns out that a lot of arguments about the interpretation of quantum theory are at least partially arguments about the meaning of the probability!'

Its obvious John is of the Bayesian view but in practice I tend to be a frequentest personally, as I think a lot of people into things like probability models eg queuing theory etc, usually are. But the probability sub-forum is the place to discuss that - not here.

Thanks
Bill

 

[atyy]

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?

That the pure state represent complete knowledge of a single system is, of course, standard Copenhagen. Additionally, the full knowledge is probabilistic and specified by the Born rule. Under a frequentist interpretation of probability, we get a statistical interpretation of quantum mechanics, in which we only get predictions about ensembles of systems. As you point out, the standard interpretation requires a macroscopic/microscopic distinction - so yes, vanhees71 is consistently wrong on this issue.

 

[atyy]

Yes and no - it comes down to what you mean by 'flavor'. One has a more Bayesian view of probability. the other is more frequentest. I will not come down on any side of this argument except to point out what John Baez said:
http://math.ucr.edu/home/baez/bayes.html
'It turns out that a lot of arguments about the interpretation of quantum theory are at least partially arguments about the meaning of the probability!'

Its obvious John is of the Bayesian view but in practice I tend to be a frequentest personally, as I think a lot of people into things like probability models eg queuing theory etc, usually are. But the probability sub-forum is the place to discuss that - not here.

Thanks
Bill

I include both Bayesian and Frequentist interpretations of probability as being Copenhagen. The Bayesian view recovers the Frequentist practice under the assumption of exchangeability. Traditional Copenhagen is Bayesian in rhetoric, and Frequentist in practice (eg. Landau and Lifshitz, Messiah).

So both are correct. The one "Ensemble" interpretation that is not acceptable is Ballentine's since he omits state reduction.

 

[bhobba]

I include both Bayesian and Frequentist interpretations of probability as being Copenhagen. The Bayesian view recovers the Frequentist practice under the assumption of exchangeability. Traditional Copenhagen is Bayesian in rhetoric, and Frequentist in practice (eg. Landau and Lifshitz, Messiah). So both are correct. The one "Ensemble" interpretation that is not acceptable is Ballentine's since he omits state reduction.

Yes I agree - a lot of this stuff is just a semantic quibble and semantics would have to be one of the silliest things there is to argue about - especially in science.

I try not to do it - with varying degrees of success.

Thanks
Bill

 

[bhobba]

Correct me if i am wrong but if you do that you end up with a mixed state either |V> or |H>, not just |H>. So you have a measurement problem, how do you get away with only unitary evolution?

Its this FAPP (For All Practical Purposes) thing I mentioned.

Some are satisfied with FAPP others not.

Either way it does NOT resolve it - its simply how you view the situation.

Such things can not be resolved rationally - its a personal preference thing.

I think you know enough of QM to understand the only real value of interpretations is the light they shed on the formalism - apart from that its not really science until something can be decided experimentally. The other advantage is sometimes a certain view can be helpful in solving problems - that happens in probability theory - mostly people tend to think in frequentest terms, but sometimes Bayesian is better and even occasionally a decision theory viewpoint like that used in many worlds seems more natural.

Thanks
Bill

 

[tom.stoer]

Back to the title

Is quantum collapse an interpretation?

I would say, no, the collaps is not an interpretation by itself but is is an essential ingredient in some interpretations. In all non-collapse interpretations it remains an essential phenomenon, an apparent collapse, that has to be explained based on the postulates.

 

[tom.stoer]

To my mind, the original question "Is quantum collapse an interpretation?“ seems to point to a fundamental paradox. At the end, all interpretations of "quantum mechanics“ need to assume the real existence of measurement instruments but find themselves in the paradoxial situation that "quantum mechanics“ itself is powerless to explain how their existence comes about.

I don't agree.

Everett approach - upgraded by decoherence - is a venture to explain the measurement instruments, the measurement process including its observation and the disturbance by uncontrolled and unobserved environmental degrees of freedom entirely based on quantum mechanical rules without a collapse postulate.

Besides the philosophical implications this has physical consequences.

Whereas in other interpretations the collapse postulate could or could not be independent of the other postulates, in Everett's approach it must to be derived, otherwise the whole venture has failed. So in that sense Everett's claim is much more ambitious b/c it requires the math to work, not only words. Decoherence is also very demanding. The math has to work in all cases, in accordance with experiments; it cannot be replaced by hand-waving arguments.

In that sense Everett's approach was - and still is - a scientific program with concrete issues where it may fail.

 

[tom.stoer]

The one "Ensemble" interpretation that is not acceptable is Ballentine's since he omits state reduction.

That's interesting.

One often finds the statement that the ensemble interpretation is a non-collapse interpretation. Are you saying that this is not correct? (besides the fact that obviously it is not a realistic interpretation at the fundamental single-particle level)

 

[atyy]

That's interesting.

One often finds the statement that the ensemble interpretation is a non-collapse interpretation. Are you saying that this is not correct? (besides the fact that obviously it is not a realistic interpretation at the fundamental single-particle level)

Ballentine's interpretation is a non-collapse interpretation. However, it is definitely wrong.

Think about it this way: Copenhagen is already an ensemble interpretation, because it asserts that the only predictions we can make are probabilistic. Under the usual frequentist interpretation of probability, Copenhagen is an ensemble interpretation. Can we remove the state reduction from Copenhagen? As far as I know the answer is no - unless we do BM or MWI.

If Ballentine were right, we would not need BM or MWI or Copenhagen.

 

[martinbn]

The claim is that an uncontroversial derivation does not yet exist within the context of the Everett approach.

So? Is there a non controversial derivation of the fifth postulate in Euclid's geometry.

So let's say we have the Schroedinger equation for a single non-relativistic particle. How do we add the Born rule and maintain unitary evolution at all times?

It seems that your objection is not that it is not derived, but that there is no prove that it is compatible. If there was such a prove, would it matter whether it is an independent axiom or a theorem that follow from the rest?

 

[tom.stoer]

It seems that your objection is not that it is not derived, but that there is no prove that it is compatible. If there was such a prove, would it matter whether it is an independent axiom or a theorem that follow from the rest?

As we explained a couple of times there is a simple proof that it explicitly incompatible.

 

[martinbn]

As we explained a couple of times there is a simple proof that it explicitly incompatible.

So there is a proof that the Born rule is incompatible with Everett's interpretation? Then why is the interpretation still popular, and why some people still try to derive the rule within the interpretation?

 

[atyy]

So? Is there a non controversial derivation of the fifth postulate in Euclid's geometry.

It seems that your objection is not that it is not derived, but that there is no prove that it is compatible. If there was such a prove, would it matter whether it is an independent axiom or a theorem that follow from the rest?

Sure, you can try adding it, but how? Just give an example, using a single non-relativistic particle.

 

[atyy]

So there is a proof that the Born rule is incompatible with Everett's interpretation? Then why is the interpretation still popular, and why some people still try to derive the rule within the interpretation?

There is a very good argument by David Wallace, building on David Deutsch's work, that the Born rule can be derived in the context of the Everett interpretation. However, even the author of that derivation is unsure whether it really makes sense.

The attempted interpretation is still popular because it is (i) very beautiful (ii) may lead to a new view of reality (iii) the arguments by Deutsch and Wallace are deeply serious work (unlike the fluffy Ballentine nonsense so often paraded in these forums), even if they may ultimately be flawed.

 

[martinbn]

Sure, you can try adding it, but how? Just give an example, using a single non-relativistic particle.

I don't know how, nor do I know if it is possible. I made no statements about it either way. You are the one who makes the claims. I am only asking you to prove your claims. Otherwise state them as opinions.

 

[martinbn]

...unlike the fluffy Ballentine nonsense so often paraded in these forums...

This kind of attitude makes these discussions unpleasant. If you could be a bit more respectful it would certainly be more interesting and useful to read the threads in this subforum.

 

[atyy]

I don't know how, nor do I know if it is possible. I made no statements about it either way. You are the one who makes the claims. I am only asking you to prove your claims. Otherwise state them as opinions.

Simple: the Born rule applies when there is a measurement. In the Everett interpretation, there is only unitary evolution, and no measurements as fundamental. Hence the Born rule must be derived.

If you want to just add the Born rule, the standard way is incompatible with unitary evolution, ie. either there is unitary evolution or measurement and collapse, but not both at the same time.

 

[atyy]

This kind of attitude makes these discussions unpleasant. If you could be a bit more respectful it would certainly be more interesting and useful to read the threads in this subforum.

Ballentine deserves no respect. He claims standard QM is wrong.

 

[tom.stoer]

So there is a proof that the Born rule is incompatible with Everett's interpretation? Then why is the interpretation still popular, and why some people still try to derive the rule within the interpretation?

Sorry, I was not very precise.

The Born rule is usually formulated as a collection of statements; one is saying that after measuring observable A the system is in an eigenstate |a> of this observable; this is the so-called "collapse of the wave function". It is this collapse-statemement which is incompatible with unitary time evolution.

In Everett's relative state formulation there is no such collapse, therefore the content of Born's rule in Everett's context is different; it's about the measure for a certain subspace, but w/o any collapse of reduction of the state vector to this subspace. The question why this measure has a probabilistic interpretation, so why probability does arise w/o collapse within a deterministic framework is still controversial (see Wallace and Carroll for example), but the question which mathematical probability measure has to be used has been answered from different perspectives and by different authors, e.g. Everett himself, Hartle and Gleason.

 

[atyy]

I don't know how, nor do I know if it is possible. I made no statements about it either way. You are the one who makes the claims. I am only asking you to prove your claims. Otherwise state them as opinions.

I replied to this above, but let me just add: when I say there is no uncnotroversial derivation of the Born rule from unitary time evolution in the context of Everett, I do not mean there can never ever be such a derivation, I mean there is none at present. As I stated, David Wallace, building on Deutsch, has given a strong argument for such a derivation. Earlier in the thread, I was responding to tom.stoer, with whom we have discussed Wallace's work in other threads in these forums, so he would have understood my meaning.

 

[tom.stoer]

Earlier in the thread, I was responding to tom.stoer, with whom we have discussed Wallace's work in other threads in these forums, so he would have understood my meaning.

Yes, I had to learn in a hard school.

I would recommend to forget about "orthodox quantum mechanics" and everything you may have heard about "many worlds". Most people trying to explain "many worlds" are not competent at all, so what you may have in mind about "many worlds" is misleading.

Trust me, it's worth a try.

 

[martinbn]

Sorry, I was not very precise.

The Born rule is usually formulated as a collection of statements; one is saying that after measuring observable A the system is in an eigenstate |a> of this observable; this is the so-called "collapse of the wave function". It is this collapse-statemement which is incompatible with unitary time evolution.

If you mean this then I agree. But for this is von Neuman's reduction postulate not the Born's rule.