Is the collapse indispensable?

[ddd123]

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.

The paper says

Equation (37) can be seen as a consequence of the wave packet reduction postulate of quantum mechanics, since we obtained it in this way. But it is also possible to take it as a starting point, as a postulate in itself: it then provides the probability of any sequence of measurements, in a perfectly unambiguous way, without resorting, either to the wave packet reduction, or even to the Schroedinger equation itself. The latter is actually contained in the Heisenberg evolution of projection operators, but it remains true that a direct calculation of the evolution of $|\Psi\rangle$ is not really necessary.

As for the wave packet reduction, it is also contained in a way in the trace operation of (37), but even less explicitly. If one just uses formula (37), no conflict of postulates takes place, no discontinuous jump of any mathematical quantity; why not then give up entirely the other postulates and just use this single formula for all predictions of results?

This is indeed the best solution for some physicists: if one accepts the idea that the purpose of physics is only to correlate the preparation of a physical system, contained mathematically in $\rho(t_0)$, with all possible sequence of results of measurements (by providing their probabilities), it is true that nothing more than (37) is needed. Why then worry about which sequence is realized in a particular experiment?

If (37) is a postulate that substitutes collapse, why do you say you should be able to derive it without collapse for it to render collapse dispensable?

 

[zonde]

The paper says

Before that the paper says:
Now, just after the first measurement, we can “chop” the state vector into different “slices”, which are each of the terms contained in the sum of (32). In the future, these terms will never give rise to interference effects, since they correspond to different measurement results; actually, each component becomes correlated to an orthogonal state of the environment (the pointer of the measurement apparatus for instance) and a full decoherence will ensure that any interference effect is cancelled.
But this seems wrong. We can split coherent photon beam using PBS and then observe interference effects by jointly measuring two beams with polarizer at 45 deg. Actually this is the usual way how we observe interference: we split coherent beam into two parts and joined measurement of two parts show interference.

 

[ddd123]

But this seems wrong. We can split coherent photon beam using PBS and then observe interference effects by jointly measuring two beams with polarizer at 45 deg. Actually this is the usual way how we observe interference: we split coherent beam into two parts and joined measurement of two parts show interference.

I guess this doesn't count as measurement (edit: got confused).

 

[zonde]

I guess this doesn't count as measurement (maybe because the beamsplitter orientation is one environment state, not two orthogonal ones).

H and V polarizations are orthogonal. If this does not count as measurement then what does?

 

[wle]

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.

Probability theory, by exactly the same token, does not explain why we obtain a particular sequence of results when we throw a die. The best probability theory can do is make (circular) claims along the lines that if we throw a die a large number of times then the frequency of results will approximate the ideal distribution up to some tolerance only with high probability. It's never a guarantee.

On the other hand, MWI has no ergodic principle, and cannot have it, since ergodicity is incompatible with unitary evolution.

I don't find this convincing. The basic idea of branches in MWI is essentially isomorphic to the set (really a tree) of all possible results in probability theory as applied e.g. to textbook QM. If you can state an ergodic theorem for the predictions made by QM then you should be able to translate it into an ergodic theorem for branches in MWI.

 

[ddd123]

H and V polarizations are orthogonal. If this does not count as measurement then what does?

I think I figured it out. By "pointer" he means a "which" information that has been gathered after the splitting. His slices are just all the collapsed possibilities.

 

[kith]

H and V polarizations are orthogonal. If this does not count as measurement then what does?

For all input states, the beamsplitter gives a deterministic output state. Measurements on the other hand yield deterministic output states only if the input state is an eigenstate of the measurement operator. (This is assuming naive collapse for simplicity)

 

[atyy]

If (37) is a postulate that substitutes collapse, why do you say you should be able to derive it without collapse for it to render collapse dispensable?

Because the question is whether unitary evolution alone makes any sense.

 

[ddd123]

Because the question is whether unitary evolution alone makes any sense.

Makes sense in which sense? It's enough to get a probability distribution out of your experimental questions.

 

[atyy]

Makes sense in which sense? It's enough to get a probability distribution out of your experimental questions.

You are not able to get the joint probability or the conditional probablity for sequential measurements.

 

[ddd123]

You are not able to get the joint probability or the conditional probablity for sequential measurements.

Okay I got it. Though Neumaier seems to imply in the OP that if we think collapse is indispensable then we're treating it as objective. For example, in special relativity it can't be objective since the timing depends on the reference frame (unless we're actually talking about "objective collapse theories", which are not Copenhagen of course). So you seem to be saying: it's not something that physically happens but we need it as a formalism.

 

[bhobba]

In MWI observer finds himself in particular world where he observes particular outcomes.

MW does not require an observer.

Thanks
Bill

 

[atyy]

Okay I got it. Though Neumaier seems to imply in the OP that if we think collapse is indispensable then we're treating it as objective. For example, in special relativity it can't be objective since the timing depends on the reference frame (unless we're actually talking about "objective collapse theories", which are not Copenhagen of course). So you seem to be saying: it's not something that physically happens but we need it as a formalism.

Yes, I mean we need collapse as formalism. Whether it is real or not is unknown.

Even in special relativity collapse may be real. Since all operational predictions are the same whether it is real is not, we cannot use special relativity to say that collapse is not real.

 

[atyy]

H and V polarizations are orthogonal. If this does not count as measurement then what does?

We do not usually consider the beam splitter to be conscious, so it is not necessarily a measurement. If a measurement is made, but the outcome is discarded or not retained by the conscious observer, then there is no need for collapse.

To support this, the beamsplitter can be modeled using unitary evolution. http://arxiv.org/abs/quant-ph/0305007 (section 4.1)

If one doesn't like the term "conscious", one can replace it with the term "classical".

 

[akhmeteli]

ergodicity is incompatible with unitary evolution.

Could you please give a reference to this statement?

 

[naima]

You can discuss at length about the collapse of one particle. It will have no physical content if you neglect the no cloning theorem.

 

[zonde]

We do not usually consider the beam splitter to be conscious, so it is not necessarily a measurement. If a measurement is made, but the outcome is discarded or not retained by the conscious observer, then there is no need for collapse.

To support this, the beamsplitter can be modeled using unitary evolution. http://arxiv.org/abs/quant-ph/0305007 (section 4.1)

If one doesn't like the term "conscious", one can replace it with the term "classical".

If using BPS does not count as measurement then what does? Please give real example.

 

[zonde]

MW does not require an observer.

I don't see how this is possible. Predictions are made for observer. And correspondence principle requires observer.

 

[bhobba]

I don't see how this is possible. Predictions are made for observer. And correspondence principle requires observer.

Its based of the concept of history the same as decoherent histories:
https://www.math.rutgers.edu/~oldstein/papers/qts/node2.html

Thanks
Bill

 

[vanhees71]

We do not usually consider the beam splitter to be conscious, so it is not necessarily a measurement. If a measurement is made, but the outcome is discarded or not retained by the conscious observer, then there is no need for collapse.

To support this, the beamsplitter can be modeled using unitary evolution. http://arxiv.org/abs/quant-ph/0305007 (section 4.1)

If one doesn't like the term "conscious", one can replace it with the term "classical".

Well, if something is unobservable for physics it is totally unimportant which other properties (being realistic or not is one such property) it may have. It's simply not part of physics, because physics is about objectively observable facts about Nature.

Conceptually the objectivity of a collapse is, however, highly problematic in the context of the relativistic space-time structure and causality. This doesn't matter much either, because the collapse is not observable and thus one doesn't need to introduce it. In this sense collapse is a short-cut description of what we mean when we say we prepare a system in a certain (pure or mixed) state. It's of course much more natural to describe the quantum-theoretical state simply by the description of a preparation procedure. Then you can make a model in terms of quantum theory for this state, i.e., you assume a statistical operator and then make measurements on an ensemble of such prepared systems to check whether the probabilistic predictions of quantum theory with the postulated description in terms of the statistical operator are correct or not. That's all, what's behind "collapse". One should not speak about it as if it were a real process in the sense of an instantaneous change of the state due to the interaction of the system with the measurement apparatus. According to the best working quantum theory, i.e., local relativistic quantum field theory there is no such instantaneous interaction and no violation of the relativistic causality structure!

 

[ddd123]

In this sense collapse is a short-cut description of what we mean when we say we prepare a system in a certain (pure or mixed) state. It's of course much more natural to describe the quantum-theoretical state simply by the description of a preparation procedure. Then you can make a model in terms of quantum theory for this state, i.e., you assume a statistical operator and then make measurements on an ensemble of such prepared systems to check whether the probabilistic predictions of quantum theory with the postulated description in terms of the statistical operator are correct or not. That's all, what's behind "collapse".

Could you point me to an article or a book which explains how this and collapse are equivalent? Thanks.

 

[vanhees71]

No, that's just the conclusion I came to when thinking about the meaning of collapse.

 

[zonde]

Well, if something is unobservable for physics it is totally unimportant which other properties (being realistic or not is one such property) it may have. It's simply not part of physics, because physics is about objectively observable facts about Nature.

If something is part of the model that makes testable predictions, then it matters and it is part of the physics.

 

[rkastner]

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.

This is a common assumption, but it is not necessarily true. In fact I have argued that this assumption is part of the longstanding problem in interpreting QM. In a direct-action theory of quantum fields, you DO get collapse as an objective, physical process.
This is what the transactional interpretation (TI) is based on. I argue in my published research that this solves the measurement problem by providing a physical account of 'measurement' that is not observer-dependent. Also, if there are non-unitary collapses in nature, this would also explain where the 2nd Law of thermodynamics comes from. Non-unitary collapse is an irreversible process and would constitute the 'seed' of irreversibility that is ubiquitous in micro-processes. For example, under TI, thermal interactions are non-unitary collapses in which energy is exchanged between gas molecules.
In my view the big mistake in QM interpretation has been assuming that all QM dynamics must be unitary. See my (peer-reviewed) papers and books for presentation of the TI alternative. Yes, the direct-action theory has been ignored and marginalized for quite some time, but there is nothing wrong with it. In fact John Wheeler was enthusiastically endorsing it in 2003, see e.g.: http://www.ijqf.org/archives/2004

 

[vanhees71]

If something is part of the model that makes testable predictions, then it matters and it is part of the physics.

How is the "collapse of the state" observable? I'm not aware of any example.

 

[A. Neumaier]

See my (peer-reviewed) papers

Just point to one, if possible in an arXiv version. (You can place it there if it isn't already there.)

 

[eltodesukane]

Whether the wavefunction collapses into an (unpredictable) specific state in of the Copenhagen interpretation, or whether the wavefunction branches into an (unpredictable) specific world in the many-worlds interpretation (MWI), it is really the same thing, the same problem. Why the collapse into some state? Why the branch into some world?

 

[MarkPercival]

>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.

I don't understand why QM needs a subjective side.

"Objectivity" usually is taken to mean something like "Any observer stationed *here* will observe *this* under *these* conditions". That is to say, there's something going on that will look the same to anyone who happens to be there looking at it., and it will do so in the same way even if there's nobody there looking at it which must be the case for all possible observers to see the same thing. To put an ever finer point on it, reality is real in and of itself- it doesn't require an audience to be real.

This strongly implies that non-conscious physical entities (particles, fields, macroscopic objects) are valid observers of each other and don't need us to validate them.

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

A philosophical assumption. How can Nature be ignorant? Every subatomic particle in existence, even the virtual ones, "knows" its own state(s) and the state(s) of its environmental variables (field vectors and strengths) to which it couples. If this were not the case physics couldn't happen. I'm not arguing "hidden variables" mind you- I'm simply restating objectivity. All of the allegedly infinite possible outcomes of every quantum interaction that has ever happened and that are happening right now unfailingly unitarily add up to what we observe. Each particle collapses the eigenstates of its environmental variables constantly.

What we see when we look at them depends solely on how we choose to look at them. Isn't that what quantum eraser experiments are about? How are they different from imposing constraints all of the possible paths from here to there and then being surprised when the outcome changes?

>''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.

I think the whole concept of subjectivity needs to be put on trial to justify its existence.

 

[A. Neumaier]

I don't understand why QM needs a subjective side.

It may not need one, but given the history of the subject, it obviously has one, as can be seen empirically from the discussions.

 

[atyy]

"Objectivity" usually is taken to mean something like "Any observer stationed *here* will observe *this* under *these* conditions". That is to say, there's something going on that will look the same to anyone who happens to be there looking at it., and it will do so in the same way even if there's nobody there looking at it which must be the case for all possible observers to see the same thing. To put an ever finer point on it, reality is real in and of itself- it doesn't require an audience to be real.

That is the point. We don't know whether the moon exists if nobody looks at it.

In QM it is difficult to assert "Nature doesn't care what we like", since there is no model of "Nature" that exists apart from "us".

 

[Jilang]

MarkP, QM only has a subjective side. It is totally silent on the objective side.

 

[rkastner]

MarkP, QM only has a subjective side. It is totally silent on the objective side.

That's a matter of interpretation. The appeal to subjectivity only arose because no one could provide a physical account of collapse.
You get the latter in TIQM. See eg http://transactionalinterpretation....tivistic-and-non-relativistic-quantum-theory/

 

[rkastner]

Just point to one, if possible in an arXiv version. (You can place it there if it isn't already there.)

An introduction to the basic principles of TI and to my extension of it is here:

http://transactionalinterpretation....tivistic-and-non-relativistic-quantum-theory/

 

[rkastner]

Whether the wavefunction collapses into an (unpredictable) specific state in of the Copenhagen interpretation, or whether the wavefunction branches into an (unpredictable) specific world in the many-worlds interpretation (MWI), it is really the same thing, the same problem. Why the collapse into some state? Why the branch into some world?

The Born Rule gives the probability that one outcome occurs. So clearly, either there really has to be 'collapse' to that outcome, or we have a many worlds situation (which doesn't work, as I've noted here: http://arxiv.org/abs/1406.4126 )
The problem has been accounting for collapse in physical terms. In a direct-action theory, this can be done (through the transactional picture). I discuss other benefits of the direct-action theory here: http://www.ijqf.org/archives/2004

 

[strangerep]

MarkP, QM only has a subjective side. It is totally silent on the objective side.

Not true.

Proof: The half-integral spectrum of quantum angular momentum is independent of the observer, hence objective. But that spectrum arises from representing rotational symmetry on a Hilbert space. Hence the Hilbert space is not subjective. $\Box$