I Is the collapse indispensable?

[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 :-)).

 

[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.