Measurement problem in the Ensemble interpretation

[Demystifier]

Are you referring only to classical theory? Because this doesn't seem to be a valid assertion in the quantum realm, at least if we go by its theoretical principles. A solid meter is most likely made up of atoms joined by chemical bonds that act as springs with a ground state energy that fluctuates, the corresponding uncertainty in the length of the spring makes the separation between atoms at each step not well defined so that they shouldn't add up to a fixed and stable expected distance between marks on the meter and therefore it can't justify a robust measure remaining stable independently of how and when it is used as a measuring tool.

Of course in practice these shortcomings are overcome by obtaining a measurement that gives a defined distance that allows to introduce an idealized meter and the atomic fluctuations only produce a minor blurring for the position of each atom(for instance in x-ray scattering). You would have to show from first principles how the meter is stable taking into account the ground state energy fluctuations.

Fluctuations are not necessarily a threat to stability. Stability does not mean that fluctuations do not exist. Stability means that initial small fluctuation remain small. Indeed, if you write down a periodic wave function for crystal lattice (which can be found in all solid state textbooks) you will see that position uncertainties of atoms are much smaller than the size of the crystal as a whole. This means that quantum fluctuations are small, which corresponds to stability.

 

[Demystifier]

@Demystifier , I have the feeling that, at least in part if not fully, the problem you have is because of overuse of the term "non-local". Have you tried to explain it by giving the exact same argument but using a different word and never mentioning "non-local"?

The term "non-local" is standard, but sometimes the term "non-separable" is used instead. Indeed, some physicists hold that QM is non-separable but not non-local. That makes sense because non-locality and non-separability are not the same. In fact, non-separability is a purely technical (i.e. mathematical) concept and there is nothing controversial about the fact that QM is non-separable. But if I was talking only about non-separability, that would mean that I only talk about the mathematical structure of QM and not about its meaning. That would not be satisfying because it is precisely the meaning that I want to talk about.

Perhaps one should invent a new term, different from both non-locality and non-separability? Perhaps! But on the other hand, it could create even more confusion.

 

[RockyMarciano]

Fluctuations are not necessarily a threat to stability. Stability does not mean that fluctuations do not exist. Stability means that initial small fluctuation remain small. Indeed, if you write down a periodic wave function for crystal lattice (which can be found in all solid state textbooks) you will see that position uncertainties of atoms are much smaller than the size of the crystal as a whole. This means that quantum fluctuations are small, which corresponds to stability.

Yes, I referred to this when I wrote about how this is dealt with in practice. But my question was how are these fluctuations kept small, why don't the errors at each atom add up, how are they prevented from cumulating dynamically to a big final error in the absence of conservation of any quantity.
Of course for a periodic wave function for a lattice crystal with a particular pattern it is trivial but I thought you were claiming that measurements are intrinsically aperiodic, and without a conserved pattern and in any case it should not depend on the size of a particular crystal.

 

[Demystifier]

why don't the errors at each atom add up

Even when errors do add up, it is typical for most statistical systems that errors add up as ##\sqrt{N}##, which is small relative to the number ##N## of the constituents when ##N## is big. Intuitively, the reason why errors do not add up as ##N## is the fact different errors can also cancel each other.

 

[RockyMarciano]

Even when errors do add up, it is typical for most statistical systems that errors add up as ##\sqrt{N}##, which is small relative to the number ##N## of the constituents when ##N## is big. Intuitively, the reason why errors do not add up as ##N## is the fact different errors can also cancel each other.

Hmm, but the error remains the same for any N particles for any size of the crystal, while ##\sqrt{N}## grows as ##N## gets larger. So for statistical systems it may be that error adds up slower than N changes, but for quantum objects it doesn't add up at all. Each atom seems to be aware of the location it ought to be if it were a classical particle, in the absence of uncertainty, and it only experiences its quantum uncertainty in relation to this position. It also seems to be aware of the size of the lattice to adjust its uncertainty to it.

 

[Demystifier]

Hmm, but the error remains the same for any N particles for any size of the crystal, while ##\sqrt{N}## grows as ##N## gets larger. So for statistical systems it may be that error adds up slower than N changes, but for quantum objects it doesn't add up at all. Each atom seems to be aware of the location it ought to be if it were a classical particle, in the absence of uncertainty, and it only experiences its quantum uncertainty in relation to this position. It also seems to be aware of the size of the lattice to adjust its uncertainty to it.

Indeed, in this case the errors do not add up at all. That's because atoms are not mutually independent. They interact with each other by attractive interaction. The only free quantities are position ##x## and momentum ##p## of the macroscopic body as a whole, and uncertainties of those satisfy
$$\Delta x \Delta p \sim \hbar$$
which does not depend on ##N##.

 

[vanhees71]

The term "non-local" is standard, but sometimes the term "non-separable" is used instead. Indeed, some physicists hold that QM is non-separable but not non-local. That makes sense because non-locality and non-separability are not the same. In fact, non-separability is a purely technical (i.e. mathematical) concept and there is nothing controversial about the fact that QM is non-separable. But if I was talking only about non-separability, that would mean that I only talk about the mathematical structure of QM and not about its meaning. That would not be satisfying because it is precisely the meaning that I want to talk about.

Perhaps one should invent a new term, different from both non-locality and non-separability? Perhaps! But on the other hand, it could create even more confusion.

It's very simple: Remember that the Standard Model of particle physics is a local relativistic QFT, and it's clear what local means here. It's (a) microcausality and (b) that the Lagrangian and thus the Hamiltonian is written as a polynomial in local field operators (i.e., operators transforming under the Poincare group as the analogous classical fields) and its (first) space-time derivatives at one spacetime point.

Of course, as any QT also relativistic local QFT admits long-range correlations described by entangled states. Einstein called this "non-separability" in a single-author paper concerning the unfortunately more famous EPR paper which in fact he didn't like, because of exactly this point: His quibble was more about non-separability than anything else, but with this quibble he was wrong since nowadays indeed it's demonstrated with high precision that the strong correlations encoded in entangled states are indeed what's observed.

 

[Demystifier]

It's very simple: Remember that the Standard Model of particle physics is a local relativistic QFT, and it's clear what local means here. It's (a) microcausality and (b) that the Lagrangian and thus the Hamiltonian is written as a polynomial in local field operators (i.e., operators transforming under the Poincare group as the analogous classical fields) and its (first) space-time derivatives at one spacetime point.

Of course, as any QT also relativistic local QFT admits long-range correlations described by entangled states. Einstein called this "non-separability" in a single-author paper concerning the unfortunately more famous EPR paper which in fact he didn't like, because of exactly this point: His quibble was more about non-separability than anything else, but with this quibble he was wrong since nowadays indeed it's demonstrated with high precision that the strong correlations encoded in entangled states are indeed what's observed.

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)?

 

[RockyMarciano]

Indeed, in this case the errors do not add up at all. That's because atoms are not mutually independent. They interact with each other by attractive interaction. The only free quantities are position ##x## and momentum ##p## of the macroscopic body as a whole, and uncertainties of those satisfy
$$\Delta x \Delta p \sim \hbar$$
which does not depend on ##N##.

So your answer to my question is interactions. That much we know, how about elaborating on how do quantum interactions(that are themselves subject to the HUP) achieve macroscopic objects as a whole satisfying ##\Delta x \Delta p \sim \hbar##, this is after all the core of the "measurement problem".

 

[Demystifier]

how about elaborating on how do quantum interactions(that are themselves subject to the HUP) achieve macroscopic objects as a whole satisfying ##\Delta x \Delta p \sim \hbar##, this is after all the core of the "measurement problem".

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

 

[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.