A Measurement problem in the Ensemble interpretation

[martinbn]

Suppose that we are in the 1920 were theoretical physicists are equipped only with concepts of classical physics, plus relativity, plus "old" Bohr-Sommerfeld-like QM. They don't have modern quantum mechanics, they don't have quantum field theory and they don't have wave functions. And suppose that some lucky experimentalist observes "quantum" correlations by accident, but he nor anybody else knows about their quantum theoretical origin. In your opinion, how would physicists of that time interpret such correlations? Do you think they would conclude that there is some non-local mechanism involved? Or do you think that a different interpretation would look more natural? Do you think that some smart guy could reproduce the laws of modern QM just from this experiment (without Heisenberg's and Schrodinger's insights that are about to appear 5 years later)?

In my opinion they would consider it a big mystery, but I don't think they would think there is a non-local mechanism involved.

 

[Demystifier]

In my opinion they would consider it a big mystery, but I don't think they would think there is a non-local mechanism involved.

Why not non-local? After all, the good old Newton theory of gravity is also non-local. True, in 1920 there is also a better relativistic local theory of gravity, but it is not yet so rigidly encoded in physicists minds to prevent thinking in old Newtonian terms.

 

[martinbn]

Why not non-local? After all, the good old Newton theory of gravity is also non-local. True, in 1920 there is also a better relativistic local theory of gravity, but it is not yet so rigidly encoded in physicists minds to prevent thinking in old Newtonian terms.

It's just my opinion. I don't think they would jump to conclusions, and I don't think they would have a quantative non-local explanation. I think they would consider it an open problem. Probably very important and worth working on.

 

[RockyMarciano]

If you ask me why macro objects look classical, probably the best answer is decoherence. See e.g. the book by Schlosshauer
https://www.amazon.com/dp/3540357734/?tag=pfamazon01-20

If you think that decoherence cannot be the full answer, then try a Bohmian completion:
https://arxiv.org/abs/quant-ph/0112005

Thanks but both approaches skip/ignore/bypass (like you have in this thread, not surprisingly since you are a declared Bohmian) the measurability problem coming from the intrinsic quantum uncertainty that I raised, considering it trivial or nonimportant, or simply due to interactions as if that explained anything(it's like saying that the measurement problem is due to measurements, true but hardly useful).

 

[Demystifier]

Thanks but both approaches skip/ignore/bypass (like you have in this thread, not surprisingly since you are a declared Bohmian) the measurability problem coming from the intrinsic quantum uncertainty that I raised, considering it trivial or nonimportant, or simply due to interactions as if that explained anything(it's like saying that the measurement problem is due to measurements, true but hardly useful).

So, do you have a better explanation? Or do you think it's still an open problem?

 

[Demystifier]

It's just my opinion. I don't think they would jump to conclusions, and I don't think they would have a quantative non-local explanation. I think they would consider it an open problem. Probably very important and worth working on.

Sure, but they would have various working hypothesis, and some of them would be more popular than others. What would be the most popular ones?

 

[martinbn]

Sure, but they would have various working hypothesis, and some of them would be more popular than others. What would be the most popular ones?

I would guess that the most popular one would be hidden variable. (local of course)

 

[RockyMarciano]

So, do you have a better explanation? Or do you think it's still an open problem?

It's an open problem AFAICS, but I'm intrigued about what I see as a neglected angle of the problem, the stability of measurements despite the intrinsic uncertainty in QM. Curiously something similar happens in relativity where perfectly solid rods are impossible and prevent the existence of stable measuring rods in principle. I found a parallelism with your assertion about dynamics(measurements are considered dynamical) and conservation being incompatible.

 

[Boing3000]

I'm intrigued about what I see as a neglected angle of the problem, the stability of measurements despite the intrinsic uncertainty in QM.

I don't follow you. Why are you saying that the solution provided by BM (a random initial "position/hidden variable" distribution) should be called a "neglected problem". Actually the determinism bundled into BM kind of guaranteed that it may be testable. Until then, it is just another interpretation.

Beside, how does it have anything to do with a meter, which is obviously stable given its classical definition (material/temperature). Are you implying that all atoms of a meter are susceptible to tunnel away into another galaxy ? It this that kind of stability that worries you ?

Curiously something similar happens in relativity where perfectly solid rods are impossible and prevent the existence of stable measuring rods in principle

Here also, solid rod aren't prevented by relativity. Perfectly solid rod are prevented by Nature (whatever that word is supposed to mean (within very misguided intuition)) and explained more by accoustic/mechanic/chemical theories than relativity.

 

[vanhees71]

Suppose that we are in the 1920 were theoretical physicists are equipped only with concepts of classical physics, plus relativity, plus "old" Bohr-Sommerfeld-like QM. They don't have modern quantum mechanics, they don't have quantum field theory and they don't have wave functions. And suppose that some lucky experimentalist observes "quantum" correlations by accident, but he nor anybody else knows about their quantum theoretical origin. In your opinion, how would physicists of that time interpret such correlations? Do you think they would conclude that there is some non-local mechanism involved? Or do you think that a different interpretation would look more natural? Do you think that some smart guy could reproduce the laws of modern QM just from this experiment (without Heisenberg's and Schrodinger's insights that are about to appear 5 years later)?

Well, there's progress in science. All the people dealing with the problems of "quantum phenomena" in the years 1920-1925 were well aware that their semiclassical patchwork models were just this, and they were vigorously looking for a consistent description, leading to modern QT. Why should we bother with these quibbles today anymore? It's interesting for the history of science and it's good to know about how the modern theories (and also classical physics by the way) came about to understand the meaning of the modern theory better, but to answer foundational questions you should answer them with the most recent theories we have. The point is that the standard QFT solved all these apparent problems (at least for a physicist interested in phenomenology). The true fundamental problems of modern relativistic QFT are not in these philosophical issues but in the mathematics which are still not completely solved.

 

[Demystifier]

The point is that the standard QFT solved all these apparent problems (at least for a physicist interested in phenomenology).

Good point! But some of us are interested in more than phenomenology.

 

[Demystifier]

I would guess that the most popular one would be hidden variable. (local of course)

And how would non-local correlations be explained by local hidden variables?

 

[vanhees71]

It can't be explained in this way since the Bell inequality (and related theorems) are violated by QT, and experiment shows that QT is right but not local HV theories.

 

[vanhees71]

Good point! But some of us are interested in more than phenomenology.

Yes, and then you leave the realm of the natural science ;-)). At best you do mathematics then, at worst...

 

[Demystifier]

Yes, and then you leave the realm of the natural science ;-)). At best you do mathematics then, at worst...

... I do something I like, publish it in Foundations of Physics, and get payed for that by tax payers.

 

[vanhees71]

Well, you are still on the good side of mathematical physics, and I think here the tax-payers' money is well spent .

 

[RockyMarciano]

there is no law of conservation of length.

I slipped this. Mathematically there is for all our physical models measurements, actually. It is implied by things like metrics, norms, inner products, unitarity, isometries ...and involved in the dynamics. Matching this to randomness and uncertainty which is the opposite of these symmetries is the puzzle I guess.

 

[vanhees71]

Well, to measure a distance with a meter, the length of meter should not change. But there is no law of conservation of length. What we need here is stability, not conservation laws.

Yes, and indeed the idea to just define the metre by a platinum stick in Paris, is not stable enough. That's why for more than 50 years the metre is defined via natural fundamental constants (or at least what we believe are such quantities according to our contemporary models).

The only unit in the SI that is still defined by a prototype (or better said a set of national copies of the prototype) is the kg, and it's a desaster. That's why pretty soon the kg will be redefined once and for all by fundamental constants either:

https://en.wikipedia.org/wiki/Kilogram

 

[Demystifier]

Well, you are still on the good side of mathematical physics, and I think here the tax-payers' money is well spent .

Well, the kind or research I do is neither phenomenology nor mathematical physics. It is foundations of physics. I like to define it as dealing with philosophical questions by using methodology of theoretical sciences (theoretical physics, mathematics and logic).

 

[vanhees71]

Yes, and this is a very important constraint! It's based on the, imho, right methodology, namely theoretical physics (which of course implies mathematics and logic with some relaxation of rigorousity) and not wild speculations based on unfounded prejudices as is too often the case when philosophers without an adequate background in theoretical physics try to write about the "foundations of physics".

 

[RockyMarciano]

Yes, and indeed the idea to just define the metre by a platinum stick in Paris, is not stable enough. That's why for more than 50 years the metre is defined via natural fundamental constants (or at least what we believe are such quantities according to our contemporary models).

Even according to our current models those constants are not so fundamental in the sense of stable, they are "running" constants.

 

[vanhees71]

?

 

[RockyMarciano]

?

I thought you were referring to constants like the fine structure constant, and you surely know about "running constants" in QFT.

 

[Demystifier]

I thought you were referring to constants like the fine structure constant, and you surely know about "running constants" in QFT.

"Running constants" do not run just because time passes. Running constants are just a convenient way to describe the fact that directly measurable quantities (like scattering cross sections) depend on energy.

 

[RockyMarciano]

"Running constants" do not run just because time passes. Running constants are just a convenient way to describe the fact that directly measurable quantities (like scattering cross sections) depend on energy.

Exactly, therefore their stability upon measurement is not complete and as you say depends on energy. This is my point.

 

[Demystifier]

Exactly, therefore their stability upon measurement is not complete and as you say depends on energy. This is my point.

I still don't understand what is your main point behind all your posts about stability and measurement.

 

[RockyMarciano]

I still don't understand what is your main point behind all your posts about stability and measurement.

In QT as you now seem to acknowledge(in spite of your demonstrations on the contrary in #106) measurements are not completely stable, uncertainty and coupling constants are constantly adjusted to the relevant energy because of "the fact that directly measurable quantities (like scattering cross sections) depend on energy", my main point was this and also of puzzlement that even with this lack of stability measurements are possible and consistent, and we can matematically model idealized measuring tools that are conserved(intervals, inner products, etc).

 

[Demystifier]

In QT as you now seem to acknowledge(in spite of your demonstrations on the contrary in #106) measurements are not completely stable, uncertainty and coupling constants are constantly adjusted to the relevant energy because of "the fact that directly measurable quantities (like scattering cross sections) depend on energy", my main point was this and also of puzzlement that even with this lack of stability measurements are possible and consistent, and we can matematically model idealized measuring tools that are conserved(intervals, inner products, etc).

So they are not completely stable, but they are quite stable. Isn't that enough for most practical purposes?

 

[martinbn]

And how would non-local correlations be explained by local hidden variables?

I am not sure what you're asking. They would be explained the usual way, pink and green socks always match.

It can't be explained in this way since the Bell inequality (and related theorems) are violated by QT, and experiment shows that QT is right but not local HV theories.

No, because he is considering a hypothetical scenario that we are in 1920 but have QM experimental results, there is no Bell yet.

 

[Demystifier]

I am not sure what you're asking. They would be explained the usual way, pink and green socks always match.

No, because he is considering a hypothetical scenario that we are in 1920 but have QM experimental results, there is no Bell yet.

But Bell theorem, that certain type of correlations cannot be explained by local hidden variables, does not depend on knowledge of quantum mechanics. A good probability theorist could have derived it in the 19th century. One of Bell's points is precisely that such correlations are not like matching socks.

 

[RockyMarciano]

So they are not completely stable, but they are quite stable. Isn't that enough for most practical purposes?

It is, and that's why I keep asking how is the instability kept small in a random quantum context for measurement dynamics so that it is quite stable for practical purposes. You said because of interactions, and in a way I guess the couplng constants are stable enough in practice as they run very slowly for different energies, but I would like to know the mechanism as it doesn't seem to be explained by the quantum axioms and principles.

 

[Demystifier]

and in a way I guess the couplng constants are stable enough in practice as they run very slowly for different energies

Exactly!

 

[vanhees71]

Yes, and in addition you define the coupling constants in question at a definite scale. For $\alpha_{\text{em}}$ in the low-energy regime, as it was defined always. I don't see any problem here. Of course, if one day we find a better theory revealing what's really behind all these constants which manifest our ignorance, it may well be that we have to redefine the definitions of our system of units again. That's indeed the nature of the natural sciences which are based on empirical facts and their theoretical analysis!

 

[martinbn]

But Bell theorem, that certain type of correlations cannot be explained by local hidden variables, does not depend on knowledge of quantum mechanics. A good probability theorist could have derived it in the 19th century. One of Bell's points is precisely that such correlations are not like matching socks.

I see, we are in 1920, there is no QM yet, there are lucky experiments that show the unexplained QM results, and we know Bell's theorem.

Then it will be a very big puzzle for the physicists, but in my opinion they will not find the action at a distance the most popular approach.

I am guessing that is your point, the they must conclude that there is some instantaneous action.

 

[Demystifier]

I am guessing that is your point, the they must conclude that there is some instantaneous action.

Yes.

 

[vanhees71]

Well, and that would immediately tell them that this interpretation is inconsistent with relativistic space-time structure, and since there were very clever people in the past who could not live with such obvious contradictions in the theoretical picture of the world that we have relativistic QFT today and don't use problematic classical prejudices to describe the world.

 

[martinbn]

Well, and that would immediately tell them that this interpretation is inconsistent with relativistic space-time structure, and since there were very clever people in the past who could not live with such obvious contradictions in the theoretical picture of the world that we have relativistic QFT today and don't use problematic classical prejudices to describe the world.

His point is that at the time relativity was relatively new and not so firm in their way of thinking so there would have been at least some who would consider the possibility of action at a distance.

 

[vanhees71]

Don't underestimate our "old heroes" like Einstein who understood their relativity very well (at least after 1908 when Minkowski brought mathematical order into the game)!

 

[Demystifier]

Don't underestimate our "old heroes" like Einstein who understood their relativity very well (at least after 1908 when Minkowski brought mathematical order into the game)!

That leads to another interesting counter-factual question. How would Einstein interpret QM today, after being familiar with Bell theorem and experiments that rule out local hidden variables?

 

[vanhees71]

Well, there are two possibilities:

(a) Einstein maybe could get more and more convinced that Q(F)T might be more complete than he thought when writing the EPR paper
(b) Einstein maybe could think that Q(F)T is even worse than he thought when writing the EPR paper and the more vigorously look for a classical unified field theory, but then knowing that he'd look for a non-local theory, which doesn't simplify the task.

That's of course speculation ;-).

 

[LeandroMdO]

So what can ensemble interpretation say about the measurement problem of single measurements?

Let's pick some simple example, say, measuring a normalized state a|0> + b|1> in the computational basis. There is no repetition, nor are there many identically prepared states. You make the measurement exactly once.

What the ensemble interpretation says is that the Rules of Quantum Mechanics describe the statistical behavior of a conceptual ensemble of identically prepared states. In a fraction |a|² of them the measurement yields |0>, and in a fraction |b|² it yields |1>. Thus, in good frequentist fashion, the probability that a single measurement will yield |0> is |a|².

What this says about a measurement problem depends on what one found problematic about measurements in the first place. In any event, it seems to me that the ensemble interpretation is not an "interpretation" in the same vein that many worlds or Bohmian mechanics are interpretations. It doesn't aim to provide a "classical" underlying model whence the laws of quantum mechanics follow. The goal is to provide a well-defined shut-up-and-calculate recipe. As such, it is compatible with a hidden variable model should one desire one, such as the Bohmian mechanics I believe you favor.

 

[vanhees71]

The ensemble representation simply says that with the probability given by Born's rule you get the corresponding results when measuring the observable, no more no less. Within the ensemble representation, which takes the probabilistic properties of nature according to QT really seriously, it doesn't make any sense to ask, why you get a specific certain outcome for a given single measurement. That you must get a certain outcome is due to the construction of the measurement device. If it wouldn't lead to definite outcomes for measurements, it wouldn't be defining a measurement accurately enough. In this case you have to use some error analysis related to your measurement apparatus, which has nothing to do with the probability inherent in nature due to QT but it's just using a "bad" measurement apparatus.

 

[RockyMarciano]

The ensemble representation simply says that with the probability given by Born's rule you get the corresponding results when measuring the observable, no more no less. Within the ensemble representation, which takes the probabilistic properties of nature according to QT really seriously, it doesn't make any sense to ask, why you get a specific certain outcome for a given single measurement. That you must get a certain outcome is due to the construction of the measurement device. If it wouldn't lead to definite outcomes for measurements, it wouldn't be defining a measurement accurately enough. In this case you have to use some error analysis related to your measurement apparatus, which has nothing to do with the probability inherent in nature due to QT but it's just using a "bad" measurement apparatus.

Ok, but the what is hard to understand is that the probability ineherent in nature due to QT has nothing to do with the error analysis of the measuring apparatus when one starts from the premise that measurements apparatus are part of nature and are therefore also quantum, and also when the Born rule is as much about probability as about measurements and doesn't distinguish measuring devices from other objects. , so why would one separate quantum measurements from the costruction of the measurements devices, are these devices not quantum perhaps, is there something in their construction or their functioning that scapes QT?

 

[vanhees71]

Of course, measurement devices are as quantum as any matter. Nothing in what I said above implies something else.

 

[RockyMarciano]

Of course, measurement devices are as quantum as any matter. Nothing in what I said above implies something else.

You said that defining a measurement accurately enough to be of use(measurement uncertainty) has nothing to do with the probability inherent to nature in QT, why is this if measurement devices are as quantum as anything else? Measurements are a kind of interactions, are these interactions not quantum?

 

[vanhees71]

Of course the measurment device, the measured obeject, and their interaction are all described by QT, but where is in your opinion a principle problem with being able to construct a measurement apparatus that measures, e.g., the position of an electron very accurately?

 

[RockyMarciano]

where is in your opinion a principle problem with being able to construct a measurement apparatus that measures, e.g., the position of an electron very accurately?

I wouldn't formulate the question in such classical terms, as they can be very misleading by suggesting small balls and trajectories. I don't see any problem in principle to have a measurement apparatus that can measure a quantum field configuration that localizes its strength to an accuracy corresponding to the energy employed, much like colliders do.

But this is not related to my question why would quantum measurement uncertainty have nothing to do with the inherent quantum uncertainty/probability.

 

[vanhees71]

The uncertainty relation is not about an uncertainty in measurements but about the uncertainty in being principly unable to prepare a system in a state in which two incompatible observables take accurate values. E.g., the position-momentum uncertainty relation, $\Delta x \Delta p_x \geq \hbar/2$ tells you that you cannot find a state, for which both the standard deviations of position components and momentum components (in the same direction) become arbitrarily small. Of course, you can find states with arbitrarily small $\Delta x$, but then $\Delta p_x$ must be at least as large as given by the uncertainty relation (and vice versa).

 

[RockyMarciano]

The ensemble in the ensemble interpretation can be phenomenologically adscribed to the uncertainty relations or to the measurement uncertainty, no?

 

[RockyMarciano]

Exactly!

But my quible was that no matter how small the instability or the drift is it should build up with time for the measuring tools, increasing the error instead of kipping it constant since it would be a systematic error, at least according to Schrodinger's equation. Instead of that quantum statistical mechanics mixes this uncertainty with the random error inherent to the statisitical atomic theory and cancels out the uncertainties so that they are not distinguishable from the randomization in classical statistical mechanics except for the different distributions that are obtained in the cases with spin.
So as a matter of fact between measurements the uncertainty and the dispersion increases in a deterministic and systematic way as shown in the Schrodinger equation and its dispersion relations, and we are left with the not for well known less puzzling situation that if we don't look the uncertainty builds up regardless of the considerations of quantum statisitical mechanics but if we look(performing consecutive measurements) the uncertainty is stable and keeps a stable macroscopic picture.