Is quantum collapse an 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.

 

[tom.stoer]

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

I agree.

Mixing collapse and probability is not a good idea; I should have been more careful.

 

[akvadrako]

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.

I would like to point out that the many derivations of the Born rule require some additional assumptions and those are the controversial aspect. They either assume $\psi$ can be interpreted as probability in some general sense or that it represents the density of worlds/reality. I can't image how it would ever be possible to derive it without some way to connect a mathematical object to the physical world.

So I would like to ask, what could an uncontroversial derivation of Born's rule in EQM even look like?

 

[vanhees71]

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!

I think that you put meaning into my words which contradict exactly what I'm saying, and this is for me a typical sign that one leaves the realm of the natural sciences and enters the discussion culture of philosophy which is not helping understanding each other but confusing the subject. This thread is imho at this point.

 

[vanhees71]

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.

Again, with this latter point I strongly disagree, and so far I've not heard any convincing (physics!) argument against the view that the classical behavior of macroscopic systems, and that's what I think you mean by "macro/micro distinction", is understood within quantum theory as an approximation valid for sufficiently coarse-grained ("macrcosopic") observables. The application of QT to many-body systems from condensed-matter to relativistic heavy-ion collisions and astrophysics (to put it in order of increasing energy) is pretty convincing evidence for this point of view. So what's "consistently wrong" with just observing this success of quantum statistical methods to explain the macroscopic systems and its "classical" behavior?

 

[vanhees71]

I would like to point out that the many derivations of the Born rule require some additional assumptions and those are the controversial aspect. They either assume $\psi$ can be interpreted as probability in some general sense or that it represents the density of worlds/reality. I can't image how it would ever be possible to derive it without some way to connect a mathematical object to the physical world.

So I would like to ask, what could an uncontroversial derivation of Born's rule in EQM even look like?

I've no clue. For me, Born's rule is among the basic postulates that cannot be derived from the other postulates, which are more or less just providing the framework to formulate Born's rule, which is the key of the (minimal!) interpretation of QT necessary to apply the formalism to real-world experiments/observations. As any fundamental natural law it has been "derived" from a subtle interplay between empirical findings and theoretical/mathematical developments. Now it appears on half a page in any good QM 1 textbook, but it has developed within an amazingly short time of about 26 (from 1900 when Planck introduced the naive "old quantum mechanics" to Heisenberg/Born/Jordan (matrix mechanics), Schrödinger (wave mechanics), and Dirac (representation free approach, then called "transformation theory") and now forms "modern quantum theory".

 

[tom.stoer]

I think that you put meaning into my words which contradict exactly what I'm saying

Sorry if I misinterpreted your post, but ...

... and this is for me a typical sign that one leaves the realm of the natural sciences and enters the discussion culture of philosophy ... This thread is imho at this point.

If you like it if not - I know that you don't like it - interpretation of science is not pure science but - at least partially - philosophy. So yes, the thread is in the realm of philosophy from the very beginning.

The whole discussion whether Everett's approach is of any value for physics is deeply related to the philosophical demand to insist in a realist position regarding physics. So if you do not care about or if you are satisfied with a non-realist position then Everett's approach and nearly every discussion beyond an instrumentalist position is of no value for you.

 

[tom.stoer]

For me, Born's rule is among the basic postulates that cannot be derived from the other postulates, ...

Yes, for you. Others may have a different opinion.

I think none of the attempts to derive Born's rule use only the two postulates mentioned earlier (Hilbert space vector plus unitary tine evolution) but are based on further assumptions. This is rather obvious b/c otherwise it should be possible to derive Born's rule in the context of vacuum electrodynamics as well ;-)

Even the Hartle frequency operator or Gleason's theorem do not derive Born's rule. The conclusion of these approaches is not "Born's rule" but that "if one wants to introduce a probabilistic interpretation then it must comply with the probability measure given by Born's rule".

... which are more or less just providing the framework to formulate Born's rule, which is the key of the (minimal!) interpretation of QT necessary to apply the formalism to real-world experiments/observations.

I think everybody will agree that the minimal interpretation does work in that restricted sense. But that does not automatically mean that everybody is happy with this minimal interpretation. Some of us are not, therefore we are discussing these questions.

As any fundamental natural law it has been "derived" from a subtle interplay between empirical findings and theoretical/mathematical developments. Now it appears on half a page in any good QM 1 textbook, but it has developed within an amazingly short time of about 26 (from 1900 when Planck introduced the naive "old quantum mechanics" to Heisenberg/Born/Jordan (matrix mechanics), Schrödinger (wave mechanics), and Dirac (representation free approach, then called "transformation theory") and now forms "modern quantum theory".

That's why Born's rule is (and will always be) important. But that does by no means support the statement that it must be fundamental.

 

[tom.stoer]

I would like to point out that the many derivations of the Born rule require some additional assumptions and those are the controversial aspect.

I agree.

So I would like to ask, what could an uncontroversial derivation of Born's rule in EQM even look like?

I don't have any clue.

I think Everett's original idea is just a motivation. Wallace's reasoning is - for me - too complicated. I should check Carroll, but as far as I remember it seems to be not fully satisfying, either.

 

[akvadrako]

I don't have any clue.

Well, what about the current proofs/assumptions is unsatisfying to you? Obviously it's impossible to have a proof connecting EQM to reality with zero additional assumptions, but just assuming the wave-function has some kind of probabilistic interpretation is already pretty weak.

Perhaps it's possible by just assuming deterministic outcomes match reality. Would that be satisfying enough?

 

[tom.stoer]

... just assuming the wave-function has some kind of probabilistic interpretation is already pretty weak.

I don't think that will work.

The fundamental problem we have to solve is the emergence of probabilities p and 1-p for two (infinite dimensional) subspaces. Given these two subspaces, why should a pre-factor have any probabilistic meaning in a fully deterministic theory? We should at least have a frequentist approach in the sense of "counting subspaces".

As I said the problem is not to derive which probability measure has to be used (this is unique) but why we should interpret some mathematical structure as probability at all.

 

[atyy]

Even the Hartle frequency operator or Gleason's theorem do not derive Born's rule. The conclusion of these approaches is not "Born's rule" but that "if one wants to introduce a probabilistic interpretation then it must comply with the probability measure given by Born's rule".

Actually, as bhobba has pointed out many times, it must be even more subtle than that, because determinism is a subset of probability (ie. delta measure). In the context of Copenhagen and Gleason, the additional assumption is usually non-contextuality.

 

[akvadrako]

I don't think that will work.

The fundamental problem we have to solve is the emergence of probabilities p and 1-p for two (infinite dimensional) subspaces. Given these two subspaces, why should a pre-factor have any probabilistic meaning in a fully deterministic theory? We should at least have a frequentist approach in the sense of "counting subspaces".

As I said the problem is not to derive which probability measure has to be used (this is unique) but why we should interpret some mathematical structure as probability at all.

I do agree the issue is about introducing probability in the first place, but I also think it's clear that can never be done without some additional assumption. However that assumption doesn't need to reference p and 1-p. You can get close to the the approach of "counting subspaces" if you first decompose your state into equal-weight subspaces. That's how Zurek and Carroll generalise from the case of equally likely outcomes to arbitrary ones.

 

[PeterDonis]

Thread closed for moderation.