Exploring von Neumann's View of Quantum Measurement

[DrChinese]

And to explain their correlations then, we introduce still faster luckyons ?

Let us not forget that we're talking about an effect which is perfectly well described by current quantum theory, so it is a bit strange that we should be introducing concepts which are not present in current quantum theory to explain them... That's BTW why I'm an advocate of an MWI view on these things (until we have some other theory): it works with what we have on our hands right now. Nothing stops us from speculating about theories that will replace quantum theory, but first of all, we don't have them, and second, there's no point in trying to find theories that explain only EPR. EPR is a particularly spectacular example of the measurement problem, but it is present in about all applications of quantum theory. It just limits the kind of solutions to it.

cheers,
Patrick.

I thought chanceons were faster than luckyons.

I totally agree with you about EPR and its example as a measurement problem. It definitely let's you see how difficult it is to construct alternative theories that explain the effect. It is clear that both chanceons, luckyons, etc have a lot of severe problems. After all, where are they and why don't they show up anywhere else?

These are what I call "ad hoc" hypotheses... and for my money, the cure is worse than the disease. In trying to restore a "physical" mechanism to QM, you introduce new components to QM that add absolutely no new predictive power (as you pointed out). Yet, one also needs to add even more elements just to explain why the new physical mechanism is hidden.

 

[vanesch]

Isn't this (a manifestation of) the (measurement)
problem -- that the details of what produces the
correlations aren't *well described* -- that the
physical reason(s) for why the projection works
aren't articulated in qm?

Of course. But in Newtonian theory, the "details of what produces the force of gravity" aren't well described either ; the difference is only that Newtonian gravity gives us a much cleaner mental picture than QM (of which I maintain that in its unmodified, standard version, you cannot escape a MWI vision in one way or another). It might be that QM is not a universally valid theory but will be replaced by something else (and will be a limiting case of that something else). In that case, all interpretational problems of QM are then shifted to whatever that new theory does, and it might give us a much cleaner view. But I would like to stress that the fact that it is not because we haven't gotten a clean view on QM (apart from MWI and some consciousness-related items, which, I consent, is not particularly clean), that necessarily we need to have another theory.
The analogy with Newtonian theory is there: ok, there IS indeed a more general theory of gravity than Newtonian theory, but one can hardly say that this was mainly necessary because of the fact that "we didn't know the details of what produces the force of gravity". The reason for introducing GR was an incompatibility of fundamental principles between non-relativistic classical physics and electromagnetism (afterwards confirmed by experimental results). However, within general relativity, all metaphysical considerations of explanations of "what were the details of what produces the force of gravity" (angels pushing on planets ?) simply became an irrelevant pondering. Nevertheless, GR has its own metaphysical problems :-)

In the same way, it is not because "we don't know the physical reasons of why the projection works" in QM that this _necessarily_ means that we need a more general theory. Only, if ever we have such a more general theory, probably all our metaphysical pondering about the measurement problem in QM will become irrelevant ... just to be replaced by other metaphysical issues in the new theory.

But maybe we will NOT have such a more general theory for centuries to come. I don't want to take one or other side as long as there is a much more urgent problem to solve: GR vs QM ! It might, or it might not, have something to do with the issue. Nevertheless, the apparent incompatibility between the superposition principle (QM) and general covariance (GR) gives us a feeling of deja-vu...

cheers,
Patrick.

 

[selfAdjoint]

Patrick, is it correct to say that QM is unitary evolution plus Born, and does not include projection at all? And that projection is just conjectured because we can't really observe the output of Unitarity-Born, a probability? MWI is then a way to have probability with single datum observation, by splitting the cases into separate "observational sectors".

 

[Nicky]

... Let us not forget that we're talking about an effect which is perfectly well described by current quantum theory, so it is a bit strange that we should be introducing concepts which are not present in current quantum theory to explain them...

I thought that was just the point Einstein et al. were trying to make in identifying the EPR "paradox". ... that QM is incomplete and needs extension or replacement with a new theory to adequately explain the results.

 

[DrChinese]

I thought that was just the point Einstein et al. were trying to make in identifying the EPR "paradox". ... that QM is incomplete and needs extension or replacement with a new theory to adequately explain the results.

No, it is not - that was a different issue, now settled.

EPR demonstrated (at least for the time, and in their opinion) an argument that local hidden variables existed. The alternative, they argued, was that there was NOT "simultaneous reality to non-commuting operators". Their case was in fact convincing - if you follow their actual and literal logic and ignore this "extra" assumption they add by hand in final paragraph.

But Bell showed that this final assumption, which seemed so reasonable, was flawed. I.e. assume there WAS "simultaneous reality to non-commuting operators". This lead to a contradiction with the predictions of QM, and subsequent experiments.

So to summarize: EPR believed local hidden variables accounted for missing elements of theory, but that was later demonstrated not to be the case. As Vanesch points out, there is nothing technically inconsistent or missing from QM other than it seems unsatisfying in certain respects. That does not imply in any way that QM won't be enhanced or improved in the future, so please don't draw that conclusion. The question is really: is QM self-consistent over its domain of applicability?

In many ways, it is a shame that the focus on whether QM is "complete" was unfortunate. In a lot of ways, this really comes back to semantics. People would have been looking for local hidden variables no matter what they thought of QM anyway. Eventually, Bell's Theorem would have been discovered and then the debate would have shifted to why/how there are no local hidden variables (the state today). That is still an interesting subject, more so to me anyway than debating whether or not QM is complete.

 

[vanesch]

Patrick, is it correct to say that QM is unitary evolution plus Born, and does not include projection at all?

I wouldn't say that, it depends on one's viewpoint. QM is for sure unitary evolution. Some think (hardline MWIers) that that is sufficient ; I think that in one way or another, the Born rule is needed in order to calculate probabilities. To the entity for which these probabilities make sense (the "observer"), the projection ALSO makes sense. Indeed, if the global wavefunction is:
|psi> = a |O1> |sys1> |env1> + b |O2> |sys2> |env2> + c |O3> |sys3> |env3>
in a strict unitary view, then in one way or another, observer O can be in states O1, O2 or O3, and (that's the hokus-pokus that gives problems) is only aware of ONE of these states, with probabilities |a|^2, |b|^2 and |c|^2 respectively.

In a von Neumann view, the above state is the result of the "pre-measurement interaction" and the "measurement" gives then rise to a projection: in the case O is in state O2, (which could happen with probability |b|^2), the STATE is now just |O2> |sys2> |env2>. Projection "ontologically" happened.

In an MWI view, the state |psi> remains what it is, but you happen to be observer number 702340 which is associated with the state O2.
However, FOR THAT PARTICULAR OBSERVER, everything happens AS IF the state is now |O2> |sys2> |env2> (on the condition that env2 remains for ever essentially orthogonal to all other |envx> states). So in this case, the projection doesn't really ontologically happen, but it does happen for all practical purposes FROM THE STANDPOINT OF OBSERVER O2, in that this is the only part of the wavefunction he will still have to care about ; he can, if he likes, continue to calculate what happens to his twin observers in other branches but it won't make a difference to him.

There is in fact only a difference between the von Neumann and the MWI view if some ontological status is given to the wavefunction. In both, the projection plays a role, but in the von Neumann view, something "happened" to the wavefunction, while in the MWI view, it is a "trick to only work with the relevant part of the wavefunction from the point of view of an observer".

In a true Copenhagen view (which is often confused with a von Neumann view), things are less clear. In a Copenhagen view, it somehow doesn't make sense to talk about the quantum state of the observer which lives in a classical world. So you cannot talk about a premeasurement evolution in this language, because there is no quantum mechanical description of the observer, or even the macroscopic measurement system. There, the projection somehow happens directly to the microscopic system and it is impossible to analyse deeper the interaction between the measurement apparatus and the system (at least this is how I understand it).

In the viewpoint that the wavefunction does not have any ontological status, then there is no difference between von Neumann and MWI ; however, I think that there is a difference between Copenhagen on one side (which gives ontological status to all "classical" objects, and denies it to all quantum objects) and MWI/von Neumann on the other hand, in which or the wavefunction has an ontological status, or nothing has.

Given that Copenhagen (if I understand it well) doesn't give any ontological status to the wavefunction, I guess that the projection also doesn't mean much: it is just calculational machinery that somehow makes classical measurement apparatus give results.

EDIT: I might try to add the strong points and weaknesses of each viewpoint:

- in von Neumann and MWI, not giving an ontological status of the wavefunction (in which case there is no difference between both) deprives physics in fact of all forms of ontology. We only have observers which know results of measurements, but nothing is really there, because everything is in fact described by a wavefunction. So that's strange: we know results of measurements about nothing.

- in von Neumann and MWI, giving an ontological status to the wavefunction (which I think is the only sensible thing to do), I think that von Neumann has the advantage of an ontology which corresponds to our observations (measured things really happened), but has the problem of the fact that a measurement by a single individual (what is that ?) changes the objective state of the entire universe, moreover in a non-local way.
MWI has the advantage of implying that a measurement only affects the observer and also that locality is respected, but has two other problems: the first one is that the measurement doesn't correspond to "what is really there" and the second one is that one needs to make a difference between the physical construction of the observer (the body) and his "mind"/"consciousness" which is associated with it ; it being the last one which is in fact the "true observer".

- Copenhagen as such, to me, cries out for a more general theory, in which quantum theory is the limiting case for "microscopic" systems, and classical physics a limiting case for "macroscopic systems". But EPR situations make it damn hard to define what is microscopic and what is macroscopic. it might very well be that Copenhagen is the crude version of what is to come. However, as it is, today, it has the disadvantage of not defining where is this famous boundary between quantum and classical behaviour.
cheers,
Patrick.

 

[selfAdjoint]

This von Neumann view intrigues me. It sounds like the preparation interaction is pre-consciousness, as if it could happen without an observer. True?

 

[vanesch]

This von Neumann view intrigues me. It sounds like the preparation interaction is pre-consciousness, as if it could happen without an observer. True?

Yes, it is exactly the same unitary evolution as in MWI ! And to say that von Neumann wrote that in the 194ies... I take his book from the shelf and read...

On p 418 of his monumental book, we read:

"Let us now compare these circumstances with those which actually exist in nature or in its observation. First, it is inherently entirely correct that the measurement or the related process of the subjective perception is a new entity relative to the physical environment and is not reducible to the latter. Indeed, subjective perception leads us into the intellectual inner life of the individual, which is extra-observational by its very nature (since it must be taken for granted by any conceivable observation or experiment). Nevertheless, it is a fundamental requirement of the scientific viewpoint - the so-called principle of the psycho-physical parallelism - that it must be possible so to describe the extra-physical process of the subjective perception as if it were in reality in the physical world - i.e. to assign to its parts equivalent physical processes in the objective environment, in ordinary space. Of course in this correlating procedure there arises the frequent necessity of localizing some of these processes at points which lie within the portion of space occupied by our own bodies. But this does not alter the fact of their belonging to the world about us, the objective environment referred to above. In a simple example, these concepts might be applied about as follows: we wish to measure a temperature. If we want, we can pursue this process numerically until we have the temperature of the environment of the mercury container of the thermometer, and then say: this temperature is measured by the thermometer. But we can carry the calculation further, and from the properties of the mercury, which can be explained in kinetic and molecular therms, we can calculate its heating, expansion and the resultant length of the mercury column, and then say: this length is seen by the observer. Going still further and taking the light source into consideration, we could find out the reflection of the light quanta on the opaque mercury column, and the path of the remaining light quanta into the eye of the observer, their refraction in the eye lens, and the formation of an image on the retina, and then we would say: this image is registered by the retina of the observer. And were our physiological knowledge more precise than it is today, we could go still further, tracing the chemical reactions which produce the impression of this image on the retina, in the optic nerve tract and in the brain, and then in the end say: these chemical changes of his brain cells are perceived by the observer. But in any case, no matter how far we calculate, to the mercury vessel, to the scale of the thermometer, to the retina, or into the brain, at some time we must say: and this is perceived by the observer. That is, we must always divide the world into two parts, the one being the observed system, the other the observer. In the former, we can follow up all physical processes (in principle at least) arbitrarily precisely. In the latter, this is meaningless.
The boundary between the two is arbitrary to a very large extent. In particular we saw in the four different possibilities in the example above, that the observer in this sense needs not to become identified with the actual body of the actual observer: [...]
Indeed, experience only makes statements of this type: an observer has made a certain (subjective) observation ; and never anything like this: a physical quantity has a certain value.
Now quantum mechanics describes the events which occur in the observed portions of the world, so long as they do not interact with the observing portion, with the aid of process 2 (unitary evolution), but as soon as such an interaction occurs, (a measurement) it reuires the application of process 1. The dual form is therefore justified."

Then, on p 437 - p445 he explains in painstaking detail the "premeasurement" (not his terminology) and the measurement, when he considers I the system, II the apparatus (+ part of the body, eventually brain included) and III the "observer". It is the last one which applies the projection postulate... Hey, this is closer to MWI than I ever thought !

cheers,
Patrick.