Layman's questions regarding Measurement Problem

[A. Neumaier]

Thank you very much for the references. I'm still not sure though. Those references do not seem to have wordings similar to what you offer: "There is universal agreement that collapse is _observable_ in open systems" .

The wording is mine, but the meaning is the same. An open system is dissipative, and dissipation is just the form an incomplete collapse takes. The equations for open systems and the equations for objective collapse http://en.wikipedia.org/wiki/Ghirardi-Rimini-Weber_theory are essentially of the same form. The main difference is that objective collapse theories believe that collapse happens at the most fundamental level, while the general theory of open systems takes its equations to be just as empirically validated rather than as fundamental, and often derives it under some plausibility assumptions (that are difficult to justify rigorously) from an underlying Schroedinger equation.

Furthermore, everybody emphasizes that the transition from one state to another is fast, but continuous

This just means that the collapse is only approximate, but to a very good approximation. The collapse in the Copenhagen interpretation also happens gradually, in the course of completing a measurement; it is instantaneous only in the unphysical idealization that a measurement takes no time.

What happens during the measurement duration is not specified by the Copenhagen interpretation, and therefore can well be continuous.

(so theoretically there is always a superposition); therefore, the only thing one can say is that under some conditions collapse can be a good approximation.

Just like all claims made in physics - I never heard even a single claim that models used in physics are accurate to infinite number of digits!

No authors of your references seem to claim any experimental deviations from unitary evolution.

The equations used for the quantitatively correct modeling of open system are without exception non-unitary. Unitary evolution is at best claimed for the much bigger, practically unobservable system composed of the actually observed system and its environment.

On the other hand, unitary evolution directly contradicts strict collapse, as defined in the projection postulate.

Well, if you take both unitary evolution and the projection postulate as absolute truth, exact to infinitely many decimal places, you get a contradiction. But it is ridiculous to regard it as that. There have been many measurements of spectroscopic energy levels, but none of them produced an exact infinite decimal expansion of a discrete eigenvalue of the Hamiltonian (normalized to ground state zero) as would be required by the Born rule as typically stated in textbooks. This shows that these postulates must be regarded as approximations.

 

[A. Neumaier]

But what does it mean for a collapse to be "observable"?

I don't know if it is the collapse itself that is observable. I would tend to think it was more like the result of the collapse. So, I see the collapse as more of a mathematical black-box, and the measurement itself (say, position of the electron is between x and y), as the "real" thing.

If you continually observe a 2-state system with eigenvalues 0 and 1 (as in the references given), and you find that the monitored variable changes randomly from 0 to 1 and back, what else are you observing than a randomly repeated collapse? If the term collapse has any meaning at all, it is this, since the Born rule asks for precisely such a behavior.

 

[A. Neumaier]

Wouldn't an open system still be described fundamentally by the Schrodinger equation, hence superpositions all the way?

An open system cannot be described by a Schroedinger equation. It is either described by a Lindblad evolution equation for the density matrix (see http://en.wikipedia.org/wiki/Lindblad_equation ) or on a more detailed level by a stochastic Schroedinger equation (with random collapses), from which one gets the Lindblad equation by averaging.

 

[StevieTNZ]

So the Lindblad equation is like a density matrix equation, which only includes partial information of the quantum system in question.

 

[homeomorphic]

If you continually observe a 2-state system with eigenvalues 0 and 1 (as in the references given), and you find that the monitored variable changes randomly from 0 to 1 and back, what else are you observing than a randomly repeated collapse? If the term collapse has any meaning at all, it is this, since the Born rule asks for precisely such a behavior.

Hmm...

Well, I will give it some thought. I can't muster a good response at the moment. Too much end of the semester pressure.

I am not a physicist by training, just a poor, helpless math grad student who dabbles in it. I have a physics grad student friend who I guess you could say is an atheist with respect to collapse (and some of that probably rubbed off on me), whereas, I am more agnostic, maybe even leaning towards it, but I'm not sure that whether you believe in collapse or not is really the issue at stake here.

We'll see if I have any time to think about quantum mechanics over the break. It's probably fairly unlikely, given the academic pressure that is on me right now (trying to graduate/publish/teaching difficulties--I'm about to explode under the pressure).

 

[akhmeteli]

Dear A. Neumaier,

Thank you very much for the reply.

The wording is mine,

That’s what I thought:-)

but the meaning is the same.

And, with all due respect, I cannot accept such unpublished (as far as I know) wording, as it’s clearly arbitrary and maybe misleading. I can also offer the following wording: “There is universal agreement that collapse is an artifact of noise”, but you don’t have to accept such wording, although the meaning is pretty much the same.

An open system is dissipative, and dissipation is just the form an incomplete collapse takes. The equations for open systems and the equations for objective collapse http://en.wikipedia.org/wiki/Ghirardi-Rimini-Weber_theory are essentially of the same form. The main difference is that objective collapse theories believe that collapse happens at the most fundamental level, while the general theory of open systems takes its equations to be just as empirically validated rather than as fundamental, and often derives it under some plausibility assumptions (that are difficult to justify rigorously) from an underlying Schroedinger equation.

Precisely:-) So my problem with your wording is that it is not clear from it that it is just “empirically validated rather than ... fundamental”, and that is why your wording may be misleading.

This just means that the collapse is only approximate, but to a very good approximation. The collapse in the Copenhagen interpretation also happens gradually, in the course of completing a measurement; it is instantaneous only in the unphysical idealization that a measurement takes no time.

As far as I understand, there are several modifications of the Copenhagen interpretation, and in some of (most popular of) them the collapse is actually defined by the projection postulate, where measurement time is not mentioned at all, as far as I know. I fully agree with your emphasis on the nonzero duration of measurement, but typically it is not mentioned at all, so there is a good chance (or a bad chance, if you wish:-)) that your wording will be taken out of context.

What happens during the measurement duration is not specified by the Copenhagen interpretation, and therefore can well be continuous.

Precisely:-), so it can well be zero in that interpretation:-)

Just like all claims made in physics - I never heard even a single claim that models used in physics are accurate to infinite number of digits!

I fully agree, but again, we need to draw the distinction between “fundamental” and “empirically validated”, in particular, “fundamental” and “empirically validated” models. Let me explain. Classical mechanics is a fundamental model, and there is no irreversibility in such a model, whereas thermodynamics is “empirically validated” in some sense, and it assumes irreversibility. Is classical mechanics accurate to infinite number of digits? Certainly not, but within classical mechanics as a model, the recurrence theorem holds, which requires accuracy to (for all practical purposes - FAPP) infinite number of digits. The same is true about quantum theory. Unitary evolution is fundamental, furthermore, there is no experimental evidence of deviations from unitary evolution. Again, within unitary evolution as a model, the quantum recurrence theorem holds, which requires accuracy to (FAPP) infinite number of digits. There is, however, an additional problem in quantum theory, as compared with classical mechanics: many people perceive collapse (e.g., projection postulate) as fundamental, whereas I think it is not fundamental, it is just an approximation, as you say.

The equations used for the quantitatively correct modeling of open system are without exception non-unitary. Unitary evolution is at best claimed for the much bigger, practically unobservable system composed of the actually observed system and its environment.

I insist, nevertheless, that “No authors of your references seem to claim any experimental deviations from unitary evolution.” If you claim such experimental deviations, please say so. (If you say that there are deviations in the presence of noise, well, I have to agree, but such a statement is pretty much tautological.) Thermodynamics is extremely useful, but its success is no evidence of deviations from (say, classical) mechanics, although thermodynamics assumes irreversibility, whereas, strictly speaking, there is no irreversibility in mechanics

Well, if you take both unitary evolution and the projection postulate as absolute truth, exact to infinitely many decimal places, you get a contradiction. But it is ridiculous to regard it as that.

I am not sure it is ridiculous, if we are talking about the fundamental level, otherwise, e.g., the recurrence theorem is ridiculous, whereas I believe it is an important result, which helps us to understand the true place of thermodynamics in physics. Similarly, “if you take both unitary evolution and the projection postulate as absolute truth, exact to infinitely many decimal places,” you obtain a useful result: the contradiction, which proves that unitary evolution and the projection postulate cannot be both absolute truth. My bet is unitary evolution is fundamental, whereas the projection postulate is not. I guess you agree at least with the latter statement, as you admit that “the collapse is only approximate”. You may say, of course, that I am nitpicking, but I don’t think so. Indeed, the Bell theorem is an extremely important result, but it does exactly what you call “ridiculous”, i.e. takes “both unitary evolution and the projection postulate as absolute truth”, as both of them are required to prove that the Bell inequalities are indeed violated in quantum theory. Approximations are not enough, as there is no such thing as “approximate nonlocality” (I consider this issue in my published article http://www.akhmeteli.org/akh-prepr-ws-ijqi2.pdf , using other people’s arguments; there are some improvements in another published article http://akhmeteli.org/wp-content/uploads/2011/08/JMAPAQ528082303_1.pdf and later preprints).

Let me emphasize that I am not trying to say that unitary evolution will agree with experimental results to infinitely many digits. I am saying that, as of today, unitary evolution is fundamental, and there is no experimental evidence of deviations from unitary evolution. If and when such deviations (e.g., objective collapse) are discovered, I will have to adapt my views accordingly.

There have been many measurements of spectroscopic energy levels, but none of them produced an exact infinite decimal expansion of a discrete eigenvalue of the Hamiltonian (normalized to ground state zero) as would be required by the Born rule as typically stated in textbooks. This shows that these postulates must be regarded as approximations.

That does not mean that unitary evolution is an approximation (as of today). While there are indeed discrete transition frequencies in elementary quantum mechanics, there are no such discrete frequencies, if you take into account natural line width (using QED).

Just a few general words in conclusion. It looks like we pretty much agree on the facts, but disagree on their interpretation. What you say may be OK at the empirical level, but this thread is about “layman’s questions”, and it seems that OP is interested in philosophical implications of quantum physics, rather than in its applications, so maybe we should discuss the fundamental level. And again, at the fundamental level, "no positive experimental evidence exists for physical state-vector collapse" (Schlosshauer)

 

[lauchlan]

and it seems that OP is interested in philosophical implications of quantum physics, rather than in its applications, so maybe we should discuss the fundamental level. And again, at the fundamental level, "no positive experimental evidence exists for physical state-vector collapse" (Schlosshauer)

Indeed you guys lost me some time ago.

Not sure if you noticed my earlier post saying that i strangely met one of the most prominent quantum physicists in the UK the other day? Anyway, it would be great if you guys could elaborate a little on the single and multi universe theory as regards wave function collapse. David seemed to explain it pretty quickly from that standpoint, though after thinking about it i am still slightly confused about something.

From a multi universe standpoint it is easy for me to understand that actually the electron is not spread out all over the place, and that when the wave function collapses we see just one of the outcomes, in our one slice/dimension.

But regardless of weather or not there is one or many universes, our observing the electron in this universe still does something to it? And it is this this that i don't understand.

I am not interested in the philosophical implications of this effect, but just really interested in what i perceive as reality and trying to understand more about it. Also, it seems to me that what we do here must affect other dimensions because let's say for example sake that there are 100 dimensions with 100 options for the electron to choose from, well if we do something here and it uses on of its options in our dimension, then that means it only has ninety-nine options left. So if its potential is checked in those dimensions then it would now be 99 instead of 100? Meaning it has been affected there too. Would be great if you could shed some light on this.

I have to say thank you again for your discussion here. Being an engineer most of this is above my station but i have managed to hang on by a thread and think i understand a lot of what you guys have shared.

 

[thedeester1]

Ill spell it out...You put a cat in a box...No matter what experiment you perform it will become agitated due to claustrofobia!


All experiments with cats prove is that they hate boxes! if they are put in them...On the other hand a cat will sleep in a box at every given opportunity...unless you put it in the box yourself...go figure that...:)

 

[lauchlan]

Sorry but i don't understand what you are saying?

Putting cats in boxes? Maybe i can't read because if that is "spelling it out" then clearly i don't know my ABCs.

 

[A. Neumaier]

And, with all due respect, I cannot accept such unpublished (as far as I know) wording,

Wording on PF is generally unpublished unless one quotes something explicitly.

Precisely:-) So my problem with your wording is that it is not clear from it that it is just “empirically validated rather than ... fundamental”, and that is why your wording may be misleading.

Pull your own ears! You use Schlosshauers conclusions in the same unqualified way, where it is not clear from the quote that it is just fundamentally postulated rather than empirically validated. Pull your own ears!

The same is true about quantum theory. Unitary evolution is fundamental, furthermore, there is no experimental evidence of deviations from unitary evolution.

Actually, strictly speaking, there is no experimental evidence in favor of unitary evolution, as all observed processes are dissipative. It is only when you neglect dissipation that you get somenthing unitary. Thus unitarity is a purely theoretical idealization.

 

[akhmeteli]

Wording on PF is generally unpublished unless one quotes something explicitly.

I was not implying that you were breaking the PF rules. I just opined that you offered your own interpretation, and your references do not seem sufficient to warrant this interpretation, it requires a leap of faith as well. I just said I was not ready for such a leap.

Pull your own ears! You use Schlosshauers conclusions in the same unqualified way, where it is not clear from the quote that it is just fundamentally postulated rather than empirically validated.

I respectfully disagree. It is absolutely clear from the words "experimental evidence" in the quote that it is not "just fundamentally postulated". Schlosshauer's work (to a large part) is actually a review of experiments.

Pull your own ears!

I regret that I happened to irritate you. I can only assure you that I am not your enemy. However, one more personal attack like this, and I'll have to conclude that discussing anything with you is not in my best interests.

Actually, strictly speaking, there is no experimental evidence in favor of unitary evolution, as all observed processes are dissipative. It is only when you neglect dissipation that you get somenthing unitary. Thus unitarity is a purely theoretical idealization.

Then there is no experimental evidence of anything - there are always some idealizations:-) Why do I think though that unitarity's experimental status is much better than that of collapse? Because each time there is an apparent deviation from unitarity, one can always find a specific source of this deviation:
"(i) the universal validity of unitary dynamics and the superposition principle has been confirmed far into the mesoscopic and macroscopic realm in all experiments conducted thus far;
(ii) all observed ‘‘restrictions’’ can be correctly and completely accounted for by taking into account environmental decoherence effects;"
(Schlosshauer, ibid.)
On the other hand, you yourself admit that collapse is an approximation.

 

[A. Neumaier]

On the other hand, you yourself admit that collapse is an approximation.

It is exactly the same sort of approximation as unitarity. Both help to have simpler models than if one takes everything into account that affects experiments.

 

[akhmeteli]

It is exactly the same sort of approximation as unitarity. Both help to have simpler models than if one takes everything into account that affects experiments.

Again, I respectfully disagree. As of today, there are no unaccountable deviations from unitarity (on the other hand, there is no positive experimental evidence of collapse). If and when such deviations are found, we will be able to call unitarity "an approximation". And even then we won't be able to say that collapse " is exactly the same sort of approximation as unitarity", - for example, we cannot say that thermodynamics "is exactly the same sort of approximation as" (say, classical) mechanics, as thermodynamics is just a superstructure with respect to mechanics, which superstructure, strictly speaking, is in contradiction with mechanics. Boltzmann's H-theorem was a great achievement, but it is not "exactly the same sort of approximation as " mechanics, it is an approximate superstructure with respect to mechanics.

You just cannot turn a superposition into a mixture without some noise or something similar. And results of averaging over noise just cannot be as fundamental as the underlying theory.

 

[fbs7]

Ill spell it out...You put a cat in a box...No matter what experiment you perform it will become agitated due to claustrofobia!


All experiments with cats prove is that they hate boxes! if they are put in them...On the other hand a cat will sleep in a box at every given opportunity...unless you put it in the box yourself...go figure that...:)

Haha :^)