What do you think these Weak Measurement, Quantum Uncollapse Tests. Re-write QM??

Demystifier

Why not? Why reality could not change when the context is changed? After all, classical physics is also contextual, i.e., even classical properties may change by the act of measurement. The only essential difference between classical and quantum contextuality is that the latter is nonlocal.

Why not? If the performed measurement is a WEAK measurement, then the measurement has not induced a decoherence. If decoherence has not happened, then it is not a problem to re-assemble probability waves back into a superposition after a measurement is performed. Are you familiar with the theory of decoherence (which is an experimentally verified interpretation-independent phenomenon)?

Demystifier

Maybe Bohm was not so influential in the past, but it seems that it changes now.

Demystifier

Perhaps you would agree with Sculy et al that Bohmian trajectories are not realistic but surrealistic. Namely, they have shown that Bohmian trajectories differ from trajectories obtained by weak measurements, from which they have concluded that Bohmian trajectories are surreal. However, Bohmians (as well as some theoretical experts for weak measurements) disagree with such a conclusion. If you think more carefully what a weak measurement really is, you should realize that a weak measurement is not a true measurement, but an indirect (and somewhat naive) conclusion about some not-really-measured variable from a true (strong) measurement of some other variable. In fact, Bohmians could argue that weak values are the ones which are not realistic but "surrealistic".

And again, as I have already stressed, if weak values are to be taken seriously (which I think they shouldn't), then SOME weak measurements may be used as an experimental verification of the Bohmian interpretation.

Demystifier

DrChinese, this paper itself is enough to explain why weak measurements should not be taken very seriously. One only needs to read carefully (and critically) the explanation around Eq. (3). In particular:

1) They say
"... this gives an operational way of defining what the value of A is ..."
The crucial word is DEFINING. This definition is somewhat arbitrary. True, it may look intuitively appealing to someone, but the Bohmian definition of velocity may also look appealing to someone. Anyway, this definition is based on measuring AVERAGE values of something, and average values, in general, do not need to be a good estimate of the actual values (unless the standard deviation is small, which is often not the case when beam splitters are present.)

2) The weak value expressed by Eq. (3) does not even need to be a real number. How would you interpret that?

3) If the operator A in Eq. (3) is the velocity operator (i.e., momentum operator divided by mass) and if |phi> is the position eigenstate |x>, then real part of Eq. (3) is nothing but the Bohmian velocity. Would you be ready to take such a weak measurement of particle velocity at a given position as an experimental verification of the Bohmian theory?

DrChinese

2. They specified that only the real part was to be considered.

3. Sure I would. There better be a lot of experimental support for Bohmian theory or else we're all wasting a bunch of time. Of course that would not be expected to support BI over oQM due to quantum equivalence hypothesis.

Demystifier

But if oQM is correct (and almost nobody doubts that it is), then the experiment will CERTAINLY "confirm" the Bohmian interpretation.
You may be surprised that, for me, it would not be an experimental support for Bohmian theory at all.
Nevertheless, I would be happy if someone would make such an experiment (I have no doubts on the result) and publish it in Nature, Science, or Physical Review Letters. I would be happy because it would certainly increase the interest of physicists for the Bohmian interpretation, even if that interest would be initially caused by a wrong reason. (Just as it is equally wrong to interpret some different (already existing) weak measurements as experimental support against the Bohmian theory.)

By the way, what do you mean by the quantum equivalence hypothesis? The equivalence between oQM and BM? I cannot overemphasize that it is not a hypothesis but a theorem (valid for "ideal" strong measurements).

Demystifier

Fine, but don't you find it slightly artificial to simply discard a part of a complex number simply because you have no idea how to interpret it?
I'm just trying to convince you how illusive and unnatural weak measurements are.

Demystifier

Further arguments against weak measurements:

1. By a suitable choice of the post-selected state, the weak value can be made ARBITRARILY large. In particular, the title of the first (PRL) paper on weak measurements reads:
"How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100"
I don't think that such arbitrariness (made by experimentalists!) should be viewed as a measurement of a true value existing out there in nature itself.

If this is not convincing enough, then the following should:

2. The resolution of the original Hardy paradox with electrons and positrons is based on a NEGATIVE number of particles obtained by a weak measurement. What, for the God sake, a negative number of particles means? It is nothing but a number obtained when some POSITIVE numbers directly obtained by measurements are put into a weird MATHEMATICAL FORMULA supposed to represent a "physical" quantity called "weak value".

Perhaps weak values can be best understood through an every-day analogy in the classical world. The physical (i.e., strong) amount of money cannot be negative. Yet, a weak value of the amount of money can be negative. Namely, there is a reasonable MATHEMATICAL formula that in some cases attributes a negative amount of money in certain situations in which the amount of money is not strongly measured. Indeed, we have a standard word for such a negative amount of money - DEBT.

Let me push the analogy further. There is a guy called Bohm who proposed that money exists even when nobody observes it. It is called the Bohmian interpretation of economics. According to this interpretation, the amount of money is allways non-negative. However, weak measurements of money show that the amount of money can be negative. Some economists take this as an indication that the Bohmian theory of money is wrong, or at least that it is highly unnatural.

Nevertheless, the Bohmian theory is very simple and natural. It proposes a double ontology, according to which both money (particles) and human rules of behavior (wave function) separately exist. A "negative amount of money", that is debt, is not really an amount of money, but a part of human rules which say that some humans should give money to other humans whenever certain circumstances take place. We see that money (which is a hidden variable which exists even when nobody observes it) is guided by the pilot human rules. We also see that this hidden variable is highly contextual (although local, or course).

Count Iblis

Because Demystifier, who posts frequently here, is a Bohm fan who has written quite a few academic papers on this subject. So he can explain this topic well to others here and that leads to frequent discussions on this topic.

Demystifier

It may be a part of the reason, but note that it was DrChinese who first mentioned Bohm in this topic in post #8. In my understanding, he is not a fan of Bohm, but admits that it has some merits.

Another, more important reason is that several proponents of weak measurements argue that weak measurements (unlike ordinary strong measurements) are in contradiction with the Bohmian interpretation. Such arguments need to be discussed properly.

DrChinese

You are right about my feelings about the Bohmian interpretation, but I consider myself still a "student" trying to understand more about it. Fortumately for me, you and others here have stepped up to the task of assisting in my (slow) education.

Actually I am quite a fan of Bohm the person, although I don't agree with all of his ideas. (You are probably familiar with the Holographic paradigm.) I consider him instrumental in the development of a lot of important work.

Demystifier

I don't care much about Bohm as a philosopher, including his holographic paradigm.
On the other hand, I care much about the Bohmian interpretation of QM because this interpretation is naturally suggested by the EQUATIONS.

Demystifier

Let me continue with my criticism and demystification of weak measurements.

In most cases, the essence of weak measurements is hidden behind relatively complicated cases considered in practice. So let us consider the simplest (and the most honnest) case in which no final experimental outcomes are discarded. In other words, let us consider the case in which the post-selected state is equal to the pre-selected state. In this case, the weak value in nothing but the well-understood average value
<psi|A|psi>
Is that a good representation of an actual value? As an example, consider a simple experiment with one 50:50 beam splitter and two standard particle detectors. Take A to be the position operator. One expects that the position of the photon should be either in the left arm or in the right arm of the experimental setting. Nevertheless, the weak position of the particle is in the middle between these two arms, where the particle will NEVER be found by a strong measurement.

If it is still not obvious to you that such a weak value should not be taken as an actual value, then the following should convince you. The weak value of the photon position above is completely analogous to the fact (that every American knows) that the average American family has 2.6 children. How can any family have 2.6 children? Of course it can't. This is just the average, that is the "weak value" of the number of children.

You can also make it "more complicated" by postselecting only those families that live in Manhattan, for example. In this case you will not get 2.6 but a smaller number. Nevertheless, it is still clear and trivial: the number you will get (say 1.7) is only an average and does not describe any real family.

An orthodox experimentalist may say: "But that is the number that I've measured, so I am obliged to take it seriously." But he is wrong, he has NOT measured this number. Instead, he has CALCULATED it. He has measured the total number of children Nc. He has also measured the the total number of families Nf. However, the number of children per family (nf) is a result of CALCULATION through a mysterious formula
nf=Nc/Nf

Mysterious? No, trivial! Silly? If you interpret the weak value as an actual value of an individual system, then it is more than silly.

To conclude, in a Ballentine style: A strong measurement reveals a property of an individual system, but a weak measurement only reveals a property of a large STATISTICAL ENSEMBLE of equally prepared systems. A weak measurement says nothing about properties of an individual system. All weirdness of weak values results from attempts to interpret properties of an ensemble (2.6 children) as properties of an individual system (a family).

Therefore, no weak measurement can be taken as an indication against the Bohmian interpretation or any other hidden-variable theory. Essentially, Bohmian interpretation says that children exist even when nobody watches them, and that the number of children in a family is allways an integer. The fact that the average American family has 2.6 children does not contradict the Bohmian interpretation.