Is the collapse indispensable?

[A. Neumaier]

I studied lots of points of view, and lots of how physicists actually use quantum mechanics in the applications. I came to the conclusion that there is an objective and a subjective side to quantum mechanics.

The collapse belongs to the subjective side, since it is associated with ''knowledge'' of which nature is ignorant.

''shut up and calculate'' belongs to the objective side. it couldn't work if the collapse were indispensable.

Properly distinguishing between an objective and a subjective side clears up a lot of the confusion prevailing in the foundations of QM.

 

[A. Neumaier]

The best basis to clear up confusions is the (free) book http://www.fisica.net/quantica/Peres%20-%20Quantum%20Theory%20Concepts%20and%20Methods.pdf.

It makes a lot of sense to first read and understand a large part of this book before trying to understand more esoteric interpretations such as MWI. For unless you have a sensible understanding of what everyone agrees upon how quantum mechanics works you'll never get any clarity about more controversial issues.

The book by Peres presents the fundamentals very clearly and completely, without the need for ever invoking collapse. This makes it particularly suitable for beginners, since they are spared some of the weirdness introduced by the collapse.

Collapse is dispensable since it happens on the subjective side of quantum mechanics only - it tells what happens to a system when the observer changes his/her point of view.

Collapse is an intrinsically classical phenomenon. Suppose someone has cast a die. It has a definite value but if you haven't seen it, your probability for every value is 1/6 although its objective value is already determined. Once you know the value, you change your point of view and update the probabilities to 1 for the observed value and 0 for the others. This is the collapse - except that on the classical level, people refer to it by a different name: conditional probability. Exactly the same happens on the quantum level, though the dynamical system is different, hence the formulas look different.

If collapse could be shown to be derived from conditional probability, then it would not be weird. Many have tried to derive it from those considerations. But there are no derivations that are consensus at the moment. Nielsen and Chuang make that comment. I myself have studied a number of those derivations, and I agree with Nielsen and Chuang.

Yes, there is no consensus. How could it be otherwise in the foundations of QM, where conflicting opinions abound for nearly a century, and there is no consensus about anything! The reason why there is no consensus is that the whole context is a bit vague, and since a lot depends on what people are looking for.

Can you please give a precise reference for Nielsen and Chuang?

 

[ddd123]

How do those that believe in collapse frame it within special relativity?

 

[A. Neumaier]

How do those that believe in collapse frame it within special relativity?

It happens of course in the frame of the observer only. This is the way things are reconciled with causality.

Measurement in the context of relativity is discussed in a survey article by Terno and Peres. They write on p.6:
''Dirac (1947) wrote “a measurement always causes the system to jump into an eigenstate of the dynamical variable being measured.” Here, we must be careful: a quantum jump (also called collapse) is something that happens in our description of the system, not to the system itself.''

 

[ddd123]

Haven't we already ruled out collapse as objective? That was short.

Half-joking of course, what I wonder is how its proponents justify it.

 

[bcrowell]

Wavefunction collapse is a feature of the Copenhagen interpretation (CI). It's not present in the many-worlds interpretation (MWI). Anything that appears in one interpretation of quantum mechanics but not in another is purely a matter of philosophy, and can never be tested by any experiment.

Isn't this all well known and not controversial?

 

[A. Neumaier]

Wavefunction collapse is a feature of the Copenhagen interpretation (CI). It's not present in the many-worlds interpretation (MWI). Anything that appears in one interpretation of quantum mechanics but not in another is purely a matter of philosophy, and can never be tested by any experiment.

Isn't this all well known and not controversial?

I think it is not that easy. The MWI is, in my opinion, an interpretation that explains nothing, and hence doesn't qualify in the same way as the Copenhagen interpretation. The MWI doesn't explain why casting a classical die, considered as a quantum system, produces a definite outcome
with a probability of 1/6 for each result. Instead, the MWI says that all worlds coexist, even those which produce sixes upon every cast of the die. If we were in that world, we could still uphold the MWI although our probabilities are very different from those predicted by quantum mechanics. Thus the MWI explains equally well everything, including all things that happen extremely rarely in our world, and hence has no scientific power at all.

Thus saying that anything that does not appear in the MWI can never be tested by experiment is simply not correct.

 

[wle]

I think there are so-called "stochastic collapse" interpretations where the idea is that wavefunction collapse is an objective process that occurs at random time intervals (independent of the presence of observers). Otherwise, wavefunction collapse is considered subjective in the interpretations of quantum physics that I'm aware of.

 

[bcrowell]

I think it is not that easy. The MWI is, in my opinion, an interpretation that explains nothing, and hence doesn't qualify in the same way as the Copenhagen interpretation.

No interpretation of quantum mechanics explains anything. They're just little fables we tell ourselves.

The MWI doesn't explain why casting a classical die, considered as a quantum system, produces a definite outcome
with a probability of 1/6 for each result. Instead, the MWI says that all worlds coexist, even those which produce sixes upon every cast of the die. If we were in that world, we could still uphold the MWI although our probabilities are very different from those predicted by quantum mechanics. Thus the MWI explains equally well everything, including all things that happen extremely rarely in our world, and hence has no scientific power at all.

Thus saying that anything that does not appear in the MWI can never be tested by experiment is simply not correct.

As you say yourself, your argument is an argument about classical physics, not quantum mechanics, and therefore it tells us nothing about the advantages of one interpretation of quantum mechanics over the other.

 

[A. Neumaier]

I think there are so-called "stochastic collapse" interpretations where the idea is that wavefunction collapse is an objective process that occurs at random time intervals (independent of the presence of observers). Otherwise, wavefunction collapse is considered subjective in the interpretations of quantum physics that I'm aware of.

The stochastic collapse theories are not interpretations of the standard quantum mechanics but variations of it that make testable predictions different from the main stream quantum mechanics.

On the other hand, there are similar quantum jump models that do not claim to be fundamental or have interpretational value but are thought to describe approximations to a more fundamental unitary dynamics.

 

[A. Neumaier]

As you say yourself, your argument is an argument about classical physics, not quantum mechanics, and therefore it tells us nothing about the advantages of one interpretation of quantum mechanics over the other.

You misunderstood my argument.

Standard quantum mechanics predicts that a classical die gives probabilities 1/6 for each particular result (since rigid body theory can be deduced via statistical mechanics, and the classical behavior of a die follows from it). A world in which we only throw sizes is incompatible with these predictions with probability arbitrarily close to 1. Whereas such a world is fully compatible with MWI.

 

[bcrowell]

Standard quantum mechanics predicts that a classical die gives probabilities 1/6 for each particular result (since rigid body theory can be deduced via statistical mechnaics, and the classical behavior of a die follows from it). A world in which we only throw sizes is incompatible with these predictions with probability arbitrarily close tp 1. Wheras such a world is fully compatible with MWI.

You're just repeating your argument. I understand your argument, but I don't agree with it for the reason given in #9. It's a thought experiment about randomness in general, not about quantum randomness.

 

[A. Neumaier]

about randomness in general, not about quantum randomness.

Whether quantum randomness is or isn't different from randomness in general is a matter of interpretation, and hence wouldn't make a difference, according to your dictum above.

 

[wle]

The stochastic collapse theories are not interpretations of the standard quantum mechanics but variations of it that make testable predictions different from the main stream quantum mechanics.

I'm not sure there isn't wriggle room here. What you say may be true of stochastic collapse models but I think in general the standard textbook account of quantum physics is vague enough that different interpretations could in principle subtly contradict one another. One example I can think of: textbook QM says that the wavefunction collapses when a quantum system is measured but (among other things) is vague about exactly at what time this occurs or even that it's an instantaneous process (as opposed to just very rapid). This could make a difference since textbook QM also says that the wavefunction will continue to evolve according to the Schrödinger equation after this collapse, so different interpretations attempting to model the measurement process more precisely could slightly disagree on how long a quantum state undergoes Schrödinger evolution (or whatever the equivalent of this is in a given interpretation) between measurements.

 

[bcrowell]

Whether quantum randomness is or isn't different from randomness in general is a matter of interpretation

We've been using "interpretation" in a specific technical sense relating to interpretations of quantum mechanics. Maintaining that restriction to that specific meaning of the term, your statement is false.

 

[wle]

Thus the MWI explains equally well everything, including all things that happen extremely rarely in our world, and hence has no scientific power at all.

I don't see how this, in itself, is different from standard probability theory. In case it's not clear, in MWI there's roughly one branching per measurement, so if an observer observes a six-sided quantum die ten times, the end result is $10^{6}$ observer-correlated-with-die branches, only one, or a fraction $1 / 6^{10}$, of which corresponds to the sequence "all sixes".

From what I know of MWI there are unresolved issues with it, and this might include explaining why we in general perceive the quantum mechanical weight associated with a branch as a probability, but I don't think the problem is quite as simplistic as your summary would imply.

 

[atyy]

Wavefunction collapse is a feature of the Copenhagen interpretation (CI). It's not present in the many-worlds interpretation (MWI). Anything that appears in one interpretation of quantum mechanics but not in another is purely a matter of philosophy, and can never be tested by any experiment.

Isn't this all well known and not controversial?

That is well known and not controversial. What is controversial is whether MWI works (the debate is technical and not a matter of taste).

What I assert is that some version of CI is the only consensus interpretation. So textbook quantum mechanics that is correct is CI, and no other interpretation. All other interpretations are BTSM.

 

[atyy]

Can you please give a precise reference for Nielsen and Chuang?

Just after Eq 2.98, p87:
"According to Postulate 2, the evolution of this larger isolated system can be described by a unitary evolution. Might it be possible to derive Postulate 3 as a consequence of this picture? Despite considerable investigation along these lines there is still disagreement between physicists about whether or not this is possible. We, however, are going to take the very pragmatic approach that in practice it is clear when to apply Postulate 2 and when to apply Postulate 3, and not worry about deriving one postulate from the other."

 

[ddd123]

In fact collapse is not dispensable because without it, one cannot recover the classical conditional probability.

Could you expand on this? Thanks.

 

[atyy]

Could you expand on this? Thanks.

There is a way to "avoid" collapse, but one needs a new postulate - the generalized Born rule. The generalized Born rule is rarely stated in full generality, but an example of the the generalized Born rule is Eq 37 of http://arxiv.org/abs/quant-ph/0209123.

The usual Born rule plus collapse is equivalent to the generalized Born rule. If there is no collapse, that is equivalent to claiming that the axioms of QM with the usual Born rule but without collapse are sufficient to derive the generalized Born rule. As far as I know, that has not be done.

 

[A. Neumaier]

Just after Eq 2.98, p87:

of which paper? I need a link!

 

[atyy]

of which paper? I need a link!

http://www.cambridge.org/sg/academi...-quantum-information-10th-anniversary-edition

 

[A. Neumaier]

http://www.cambridge.org/sg/academi...-quantum-information-10th-anniversary-edition

Oh, it is a book. I don't have access to it.

 

[A. Neumaier]

I don't see how this, in itself, is different from standard probability theory. In case it's not clear, in MWI there's roughly one branching per measurement, so if an observer observes a six-sided quantum die ten times, the end result is $6^{10}$ observer-correlated-with-die branches, only one, or a fraction ##1 / 6^{10}$$ , of which corresponds to the sequence "all sixes".

In standard probability theory, you have a single world, and you observe a sequence of 10 results. it is very unlikely to contain 10 sixes. Even if you got 10 sixes by chance, if you repeat this experiment 100 times you are very unlikely to get again 10 sixes.

IN MWI, if you are in one of the worlds where in the past, everything was ordinary, but from now on only sixes are thrown (according to MWI, this world exists, and is populated by people exactly like us, with exactly the same memory, but with a different future) you observe a sequence of 10 results and find 10 sixes. If you repeat this experiment 100 times you get again 10 sixes, each time. This is completely against the predictions of QM, and you conclude that QM, which predicts the opposite, is invalid in your world. The fact that there are other worlds in which other, more ordinary things happen is completely immaterial, as you only experience this particular world and make all your statistics in this particular world.

This is what I mean by saying that MWI is consistent with every conceivable outcome, and hence has zero scientific content.

 

[ddd123]

Oh, it is a book. I don't have access to it.

I just read that part, postulate 3 and postulate 2 in atyy's quote are standard collapse and unitary evolution respectively.

 

[A. Neumaier]

Whether quantum randomness is or isn't different from randomness in general is a matter of interpretation, and hence wouldn't make a difference, according to your dictum above.

We've been using "interpretation" in a specific technical sense relating to interpretations of quantum mechanics. Maintaining that restriction to that specific meaning of the term, your statement is false.

No. According to Bohmian mechanics, every quantum randomness is ordinary randomness. According to the Copenhagen interpretation, quantum randomness is irreducible. Thus, according to you, the difference between ordinary randomness and quantum randomness

is purely a matter of philosophy, and can never be tested by any experiment.

 

[A. Neumaier]

Collapse is an intrinsically classical phenomenon. Suppose someone has cast a die. It has a definite value but if you haven't seen it, your probability for every value is 1/6 although its objective value is already determined. Once you know the value, you change your point of view and update the probabilities to 1 for the observed value and 0 for the others. This is the collapse - except that on the classical level, people refer to it by a different name: conditional probability. Exactly the same happens on the quantum level, though the dynamical system is different, hence the formulas look different.

This is almost certainly wrong. If collapse could be shown to be derived from conditional probability, then it would not be weird. Many have tried to derive it from those considerations. But there are no derivations that are consensus at the moment. Nielsen and Chuang make that comment. I myself have studied a number of those derivations, and I agree with Nielsen and Chuang.
In fact collapse is not dispensable because without it, one cannot recover the classical conditional probability.

Can you please give a precise reference for Nielsen and Chuang?

Just after Eq 2.98, p87:
"According to Postulate 2, the evolution of this larger isolated system can be described by a unitary evolution. Might it be possible to derive Postulate 3 as a consequence of this picture? Despite considerable investigation along these lines there is still disagreement between physicists about whether or not this is possible. We, however, are going to take the very pragmatic approach that in practice it is clear when to apply Postulate 2 and when to apply Postulate 3, and not worry about deriving one postulate from the other."

http://www.cambridge.org/sg/academi...-quantum-information-10th-anniversary-edition

I just read that part, postulate 3 and postulate 2 in atyy's quote are standard collapse and unitary evolution respectively.

But then the comment is empty. I had expected to find a survey jusifying the statement ''Many have tried to derive it from those considerations. But there are no derivations that are consensus at the moment. Nielsen and Chuang make that comment.''

 

[atyy]

But then the comment is empty. I had expected to find a survey jusifying the statement ''Many have tried to derive it from those considerations. But there are no derivations that are consensus at the moment. Nielsen and Chuang make that comment.''

Indeed, it is just that they are "authorities". Anyway, off the top of my head some interesting attempts are:

Ballentine, in his famous 1998 textbook, discussion around Eq 9.26 - 9.28.
Ozawa, http://arxiv.org/abs/quant-ph/9706027 (he tried several times around these years, they are all interesting)
Fuchs, http://arxiv.org/abs/quant-ph/0106166

Fuchs comes very close to making it look like the classical conditional probability, but he also clearly fails to make it identical.

 

[wle]

This is completely against the predictions of QM, and you conclude that QM, which predicts the opposite, is invalid in your world.

No it's not. Quantum mechanics would predict that you can get ten sixes in 100 repetitions of the experiment with probability $1 / 6^{-1000}$. This is very small but not zero and therefore not ruled out. Whatever flaws MWI may have this is one thing, within its worldview, that it gets right: the sequence of all sixes in 100 repetitions, however unlikely, is still possible so MWI has to include a branch corresponding to that possibility.

This is what I mean by saying that MWI is consistent with every conceivable outcome, and hence has zero scientific content.

Exactly the same criticism could be made of textbook QM (or in general any theory using probability theory): any outcome attributed any finite nonzero probability, however small, is still possible and therefore consistent with QM. The only reason we can "test" QM is that we don't accept all results consistent with QM as evidence. In experiments, we require that the results are close to "typical" and, in doing so, we accept a small chance that we might incorrectly reject the theory. Likewise, MWI includes "atypical" branches which would (presumably) include observers who mistakenly think they've experimentally disproved QM.

 

[bhobba]

Wavefunction collapse is a feature of the Copenhagen interpretation (CI). It's not present in the many-worlds interpretation (MWI). Anything that appears in one interpretation of quantum mechanics but not in another is purely a matter of philosophy, and can never be tested by any experiment. Isn't this all well known and not controversial?

Exactly. We have interpretations that have it, and some that dont. Its not part of the formalism - and quite obviously so. Indeed if you look at the formalism from axioms such as found in Balentine its not even mentioned.

Thanks
Bill

 

[bhobba]

No interpretation of quantum mechanics explains anything. They're just little fables we tell ourselves.

For sure. One of the issues here is even otherwise good books like the following present QM as having it:
https://www.amazon.com/dp/0071765638/?tag=pfamazon01-20

I remember when David released that book he did some posts on science forums I frequented at the time. I pointed out the axioms he used, including collapse, were not required. They could be drastically reduced to two as found in Ballentine. He simply kept repeating they are the axioms and all are necessary. I gave up. It is still a good book though that I often recommend over Griffiths because its much cheaper.

Thanks
Bill

 

[A. Neumaier]

MWI includes "atypical" branches

The difference is that we are in a fixed branch, and observe the probabilities of this branch. MWI has no explanation for the fact that this particular branch that we are in has the desired probabilistic behavior.

In classical statistical mechanics, which has a similar problem, the argument used to solve this is the ergodic principle, that each single classical trajectory comes arbitrarily close to every point in space-time, in a reasonable time frame. This principle (though far from proved in general) guarantees that short time expectations agree with ensemble expectations, hence the probabilities observed on each trajectory (not only the typical ones) agree with those described by the ensemble. Indeed, the need for the ergodic principle to justify thermodynamics is the weakest spot in the foundations of classical statistical mechanics.

On the other hand, MWI has no ergodic principle, and cannot have it, since ergodicity is incompatible with unitary evolution. Thus we cannot argue in the same way as in the classical case, and the observd probabilities depend (a lot!) on which paticular trajectory (i.e., world, branch) our culture finds itself in. One would have to invoke the anthropic principle in its place. But the anthropic principle is far too weak to explain that probabilities are everywhere in the part of the universe observable by us are given by the formulas of quantum mechanics.

 

[zonde]

Wavefunction collapse is a feature of the Copenhagen interpretation (CI). It's not present in the many-worlds interpretation (MWI).

In MWI observer finds himself in particular world where he observes particular outcomes. So the collapse is moved from system side to observer side. This does not remove collapse but just makes it harder to analyze (it makes false impression that it is outside the scope of the theory).
* I hope I'm not mixing up what is collapse and what is Born rule.

And another thing. Because MWI extends QM laws to "classical world" it has MUCH more to do to fulfill correspondence principle (in it's general sense).

 

[naima]

From an information point of view, collapse would be an erasement of an ancient knowledge.Take the case of the famous Young slits: the initial state contains information about the distance between the slits. When you "ask" the position of the particle (with your screen) the collapse point of view is that you get random position outputs and that each of them has no memory of the distance between he slits.
We can have another point of view. There is a no cloning theorem which states that we cannot know the information content of ONE particle. Nothing in nature tells you: believe me this particle is an eigenvector of such operator with such value. If you trust a physicist who prepares many identical states and tells it to you, you can only have a recipe to verify it : you measure the observable. If you get the value given by your friend it is a good thing but you have to repeat this to be sure that it was not only luck.
When you measure something else (say position on the screen) you can look at the first impact and stop the experiment you say that there was a collapse: you are interested only in the position output and the initial information does not matter.
If you go on, you will get a pattern. this mixture allows you to get a very precise value of the distance between the slits. With your bad questions you get the good information carried by the beam of particles. Information was not erased. Collapse has nothing to do with measurement, it is only usefull when you want to prepare states: just ignore the ancient state and neglect the other outputs.

 

[vanhees71]

Wavefunction collapse is a feature of the Copenhagen interpretation (CI). It's not present in the many-worlds interpretation (MWI). Anything that appears in one interpretation of quantum mechanics but not in another is purely a matter of philosophy, and can never be tested by any experiment.

Isn't this all well known and not controversial?

I couldn't agree more. In my opinion, collapse is superfluous. From a pragmatic point of view it boils down to a simple thing such as putting a particle absorber in the way of partial beams in a Stern Gerlach experiment to filter out all the "unwanted" spin states (at an arbitrary precision which only depends on the technical ability in the Stern-Gerlach setup) and keeping the wanted one.

Of course, this is far from non-controversial. There are endless debates about this not only in these forums but also in the literature :-)).