Measurement Problems in Quantum Mechanics: Wave/Particle Duality

[Rob Field]

Can we distinguish two measurement problems —

1) Why measurement appears to cause a discontinuous change in the wave function for a single quantum entity/system?

As in Schrodinger, "The abrupt change by measurement … is the most interesting point of the entire theory…in the realism point of view, observation is a natural process like any other and cannot per se bring about an interruption of the orderly flow of natural events."​

2) Why measurement appears to cause a change in the behavior of ensembles of quantum objects (e.g, from wave-like to particle-like, as in the which-path experiments)?

As in Feynman, "It always turns out, however, that it is impossible to arrange the light in any way so that you can tell through which hole the thing is going without disturbing the pattern of arrival of the electrons…. If an experiment is performed which is capable of determining which alternative is taken, the probability of the event is changed…. That is, you lose the interference."​

Or should we understand these issues as different aspects of the same problem?

 

[PeterDonis]

Your #2 isn't an example of the QM measurement problem at all. It's an example of different measurements giving different results. The double slit experiment with no detection of which alternative is taken is a different measurement from the double slit experiment where there is detection of which alternative is taken. That's why they give different results.

 

[Rob Field]

Your #2 isn't an example of the QM measurement problem at all. It's an example of different measurements giving different results. The double slit experiment with no detection of which alternative is taken is a different measurement from the double slit experiment where there is detection of which alternative is taken. That's why they give different results.

Interesting, thanks. How would you characterize the measurement that is made when there is no detection of which path? (I am thinking of Schrodinger's criterion that there be a repeatable physical process that generates the same result under the same conditions.)

 

[PeterDonis]

How would you characterize the measurement that is made when there is no detection of which path?

A measurement of the pattern at the detector.

 

[Rob Field]

I see, so you are saying that the two different measurements are which-path plus pattern or arrival or just pattern of arrival. (Since the pattern of arrival gets measured in all cases.) I need to think about that, thank you

 

[PeterDonis]

the two different measurements are which-path plus pattern of arrival or just pattern of arrival

Yes.

 

[Rob Field]

Is it safe to say that the one measurement (path plus arrival) generates more information than the other (arrival only)? I am guessing the answer is obviously yes, but in this area, it seems like it's best to proceed carefully...

 

[bhobba]

Or should we understand these issues as different aspects of the same problem?

OK let's start from the beginning. I have a coin heads up and flip it. What causes it to discontinuously change or not change?

I can give my answer but thinking it through for yourself is better. A hint is, although not as widely known as interpretations of QM there are in fact different interpretations of probability. There is a strong connection:
http://math.ucr.edu/home/baez/bayes.html

Thanks
Bill

 

[Rob Field]

Maybe the realist would answer that the flip puts the coin into superposition, and then what causes the discontinuous change from superposition is either measurement, or some alternative such as spontaneous collapse of the wave function (GRW), the coin's interaction with the pilot wave (Bohm hidden variables), etc.?

And the instrumentalist might say it doesn't discontinuously change, just our knowledge does?

I'll take a look at that link but maybe another hint would help?

 

[bhobba]

I'll take a look at that link but maybe another hint would help?

You got the answer. I will now expand on it.

First you have to understand what QM is at a formal level:
https://www.scottaaronson.com/democritus/lec9.html
https://arxiv.org/pdf/quant-ph/0101012.pdf

Now in QM the arch-typical situation is as per figure 1 in the above paper. As that paper and the one before it explains, QM is a slight modification of probability theory to allow complex numbers so as to allow going continuously from one pure state to another. One can use the powerful methods of calculus to describe how pure states change. That's all QM is formally. But just like ordinary probability theory we do not know what causes a particular outcome.

All the arguments about QM are is arguments about how to look at that, exactly the same as ordinary probability theory. We have exactly the same problems, plus others. Some think it's not an issue, some like me don't particularly care one way or other, to others its a central problem - you can read all about various interpretations and make your choice. But until someone can figure some way of testing it experimentally its simply an interesting exercise in the myriad of ways you can look at it.

My personal view? Well just so you know my view I like lot of people hold to the Ensemble interpretation of Einstein. But its no better or worse than any other. Of the early pioneers I side with Dirac who is generally thought to be of the Copenhagen school - but really wasn't - he was more like Einstein:
http://philsci-archive.pitt.edu/1614/

Since then we have learned a lot more of course - exactly as Dirac's view suggests would happen.

The answer to your first question is even if there is some kind of discontinuous change is up for grabs. We simply do not know. But as Dirac looks at it - research is ongoing - which likely is the way it always will be.

Thanks
Bill

 

[atyy]

Maybe the realist would answer that the flip puts the coin into superposition, and then what causes the discontinuous change from superposition is either measurement, or some alternative such as spontaneous collapse of the wave function (GRW), the coin's interaction with the pilot wave (Bohm hidden variables), etc.?

And the instrumentalist might say it doesn't discontinuously change, just our knowledge does?

I'll take a look at that link but maybe another hint would help?

I'm not sure that is correct. A realist view (that quantum mechanics is incomplete, because of the subjective division of events into measurements and non-measurements) is consistent with an instrumentalist view of the Copenhagen interpretation. Thus if an instrumentalist view is that nature does not discontinuously change, but only out knowledge does, then a realist can say the same thing. However, it is by no means clear that an instrumentalist would say that - it might be better to say that an instrumentalist is agnostic about which part of the change is due to nature and which is due to our knowledge.

 

[Strilanc]

1) Why measurement appears to cause a discontinuous change in the wave function for a single quantum entity/system?

Measurement is not a discontinuous process. Or, well, I guess it would be more appropriate to say that there is no evidence pushing us to conclude that measurement is necessarily discontinuous.

Measurement can be fast, but my understanding is that when you look in detail at what's going during a measurement (or a "quantum jump", another claimed instantaneous thing) there's a continuous process that takes non-zero time to complete. You can stop the process halfway through, and you still get something meaningful. Half of a measurement? That's basically a weak measurement. Half of a quantum jump? The electron is in a superposition of being in either orbital.

 

[atyy]

Measurement is not a discontinuous process. Or, well, I guess it would be more appropriate to say that there is no evidence pushing us to conclude that measurement is necessarily discontinuous.

Measurement can be fast, but my understanding is that when you look in detail at what's going during a measurement (or a "quantum jump", another claimed instantaneous thing) there's a continuous process that takes non-zero time to complete. You can stop the process halfway through, and you still get something meaningful. Half of a measurement? That's basically a weak measurement. Half of a quantum jump? The electron is in a superposition of being in either orbital.

Yes, that is true in some sense. However, it is important to note that these subtleties do not do away with the measurement problem, and in the standard theory, measurement is fundamentally "discontinuous" in some sense. It is true that one can model part of the measurement apparatus as a quantum system, with interaction with the main quantum system over some time. However, finally, one must still apply the Born rule to the apparatus, so that a real outcome is obtained. It is because of the fundamental status of measurement in quantum theory that the measurement problem arises, and this does not go away as long as one uses an orthodox formulation.