A Measurement problem in the Ensemble interpretation

[Mentz114]

It's exactly what Feynman said - nothing more - nothing less:
[..]
Me - I am with Gell-Mann:


Thanks
Bill

If we're down to quoting authority - Steven Weinberg said

Our job as physicists is to see things simply, to understand a great many
complicated phenomena in a unified way, in terms of a few simple principles.

 

[Mentz114]

I think it's good form not use to quote symbols unless you're quoting. It's not fair to ask me to defend a statement that you just made up (such as "symmetries and conserved charges and currents are irrelevant in Physics").

Anyway, according to quantum mechanics, states obey the principle of superposition: If |A\rangle is a state, and |B\rangle is a state, then \alpha |A\rangle + \beta |B \rangle is a state. Are you asking where that rule is stated? It's part of the definition of a Hilbert space.

Apologies, I hope I didn't distort the meaning.

Ok, thanks. A purely mathematical statement then, with no support from any physical principle.

[aside]
To anyone who finds these things interesting I commend this learned paper. I don't claim to have read it all nor agree with everything the author asserts.

http://philsci-archive.pitt.edu/878/1/PSA2002.pdf

Laws, Symmetry, and Symmetry Breaking; Invariance, Conservation Principles, and Objectivity

John Earman
Dept. of History and Philosophy of Science
University of Pittsburgh

 

[bhobba]

If we're down to quoting authority - Steven Weinberg said

But finding those - well let's just say even its greatest exponent, Einstein, hell even slightly lesser lights like Von-Neumann, guys likely even better than Weinberg (and that's saying something) is a slow slow process with a lot of false twists and turns. As Feynman said a trick, like say positivism, used early on by Einstein, works just once - after that everyone knows it and tries it. If it works, which it rarely does again, but if it does progress is made and everything falls away. If it doesn't, and this is usually the case, a different approach is required. Want a Nobel? Figure out the approach that works. Good luck.

But as to your question - the answer is known - symmetry. But to understand it you need quite a bit of study or simply accept what you have been told.

Thanks
Bill

 

[vanhees71]

But the law of large numbers is not just about any situation involving large numbers. It's specifically (from Wikipedia):
If we use a macroscopic device to measure, say, the spin of an electron, the 10^{24} is not the number of times we perform the experiment. So the law of large numbers is not obviously relevant.

Ok, then why do you think classical physics works so well for macroscopic matter? The ensembles you cite are Gibbs ensembles, but the law of large number says that we measure almost with certainty a definite value for a macroscopic variable given the very small relative standard deviation of this variable of order $\mathcal{O}1/\sqrt{N}$. So you can within this relatively negligible uncertainty predict the value for this macroscopic variable. That's how, in my understanding, the apparent deterministic nature of classical physics is principally explained within the statistical interpretation.

If we measure the spin of an electron (within a neutral atom ;-)) in an SG apparatus we measure its position with a photo plate, which is the macroscopic object. What we call "position", is a very coarse grained macroscopic region consisting of very many atoms/molecules. Within that resolution we can say the "electron hit the photoplate at a definite place". That the position is related to the spin observable is due to the entanglement of the spin component determined by the directdion of the magnetic field with position.

 

[stevendaryl]

Ok, then why do you think classical physics works so well for macroscopic matter?

I think the answer is complicated. I think it has to do with the fact that decoherence will spoil interference effects between macroscopic states with different values of macroscopic observables. Without interference effects, we are free to think of quantum probabilities as classical probabilities, reflecting uncertainty about which of several alternatives is actually the case. So that's why Copenhagen (or the minimal interpretation) seems to work so well, because it is consistent to think of macroscopic probabilities as reflecting ignorance in a way that it is not consistent to interpret microscopic amplitudes.

So the whole structure works, to the extent that we can make a clean distinction between macroscopic and microscopic variables. But it's somewhat schizophrenic, since we are applying a different interpretation to probabilities depending on how large the system is.

 

[vanhees71]

Hm, but you can use quantum statistics to calculate the properties of, say, an ideal gas to get the classical results in the limit, where you can approximate the Bose-Eisntein or Fermi-Dirac statistics with the modified classical Maxwell-Boltzmann statistics (with modified I mean the notorious factor $1/N!$ borrowed from the indistinguishability of particles from QT). Even if you keep the full quantum statistics, the macroscopic quantities which are indeed very coarse grained (total energy $U$, temperature, chemical potential(s),...) you get very small fluctuations due to the fact that $N$ is large. Of course you get quantum effects, if the gas becomes degenerate (low temperatures, high densities), among them early achievements of "old quantum mechanics" like the specific heat at low temperatures, the microscopic understanding of the 3rd Law and so on.

Of course, decoherence is also an important point. Here you can even get semiclassical behavior of microscopic objects when interacting with macroscopic objects, as was already realized in Mott's famous article on why $\alpha$ prticles in a clould chamber seem to run on straight-line trajectories.

 

[zonde]

It should be possible, if measuring devices were treated no differently than microscopic systems, to restate the theory without mentioning measurements or macroscopic systems.

Why do you think it should be possible?
Measuring devices are just bigger more complicated "particles". If you take away Born rule, QM can not say anything about microscopic particles. Why it should say anything about measuring devices?

 

[stevendaryl]

Why do you think it should be possible?
Measuring devices are just bigger more complicated "particles".

That's my point. If measuring devices are just complicated systems, and measurements are just complicated interactions, then the Born rule shouldn't treat measurements differently than any other interactions. But it does: The Born rule says "If you measure a quantity, you get an eigenvalue of the corresponding operator, with such-and-such probability."

 

[zonde]

That's my point. If measuring devices are just complicated systems, and measurements are just complicated interactions, then the Born rule shouldn't treat measurements differently than any other interactions. But it does: The Born rule says "If you measure a quantity, you get an eigenvalue of the corresponding operator, with such-and-such probability."

You apply Born rule to measurements only. You do not apply Born rule to other interactions. At least this is my understanding.

And my point is that Born rule treats microscopic reality differently too. Before you apply Born rule you don't describe particles. You describe modes not particles.

 

[AlexCaledin]

As long as ensemble interpretation refuses to talk about single measurements, it cannot say anything about the measurement problem.

- but what if the EI is applied to the whole spacetime-universe? Then, there is the Ensemble of "prepared" universes, each one having its definite observable history (Bohmian trajectory) - quite definite past and future - but "we" are uncertain as to what universe we are in - and we are in the process of getting knowledge about that - and then every measurement is simply a little increment of our knowledge.

 

[vanhees71]

If you want to derive macroscopic behavior you also use Born's rule, using an appropriate statistical operator like the usual equilibrium operators (microcanonical, canonical, grand canonical).

 

[stevendaryl]

You apply Born rule to measurements only. You do not apply Born rule to other interactions. At least this is my understanding.

And my point is that Born rule treats microscopic reality differently too. Before you apply Born rule you don't describe particles. You describe modes not particles.

Okay, I guess I agree with that.

 

[stevendaryl]

If you want to derive macroscopic behavior you also use Born's rule, using an appropriate statistical operator like the usual equilibrium operators (microcanonical, canonical, grand canonical).

But that's not the same. In the case of a macroscopic measurement, each measurement produces an eigenvalue of the operator corresponding to the observable being measured. In the case of an ensemble, you're talking about averages, not properties of individual systems.

An ensemble average is a kind of macroscopic observable. So again, it seems that QM treats macroscopic systems differently than microscopic systems.

 

[vanhees71]

The point is that the pointer states have very small (relative) standard deviations, so that you can treat them as if they were determined as in classical physics.

 

[atyy]

The point is that the pointer states have very small (relative) standard deviations, so that you can treat them as if they were determined as in classical physics.

That is not true. The standard deviation of the pointer states depends on the observable that is measured.

 

[Demystifier]

The point is that the pointer states have very small (relative) standard deviations

That is so only after the information update (not to use the dirty c-word). But update needs measurement, and measurement needs "classical" pointers states, so the whole explanation becomes circular.

 

[vanhees71]

What? If I measure something, of course the apparatus has interacted with the measured object, and you get a clear pointer reading. The pointer position is a macroscopic observable and should have a small standard deviation as any macroscopic observable. No dirty c needed, just statistics ;-).

 

[Lord Jestocost]

That is so only after the information update (not to use the dirty c-word). But update needs measurement, and measurement needs "classical" pointers states, so the whole explanation becomes circular.

As I am new in "PhysicsForum": What the heck is the "dirty c-word"?

 

[Demystifier]

As I am new in "PhysicsForum": What the heck is the "dirty c-word"?

Collapse.

 

[Demystifier]

If I measure something, of course the apparatus has interacted with the measured object, and you get a clear pointer reading.

Consider a Stern-Gerlach apparatus. It has two detectors, one in the upper position and the other in the lower position. When one particle is sent through the apparatus, only one of the detectors clicks. In this case, did the other detector also interacted with the particle (measured object)?

 

[vanhees71]

Obviously not, because then (taken it as a very good detector with close to 100% detection efficiency) you'd see 2 spots in any experiment with an intensity due to the $|\psi|^2$ distribution. The very fact that this is not the case rules out the original interpretation of the wave function as a classical field describing the (charge) density of the particles by Schrödinger.

 

[Demystifier]

Obviously not, because then (taken it as a very good detector with close to 100% detection efficiency) you'd see 2 spots in any experiment with an intensity due to the $|\psi|^2$ distribution. The very fact that this is not the case rules out the original interpretation of the wave function as a classical field describing the (charge) density of the particles by Schrödinger.

So at what point did the particle decide that it will go to one detector and not to the other? Did it happen at the moment of interaction with the detector, or did it happen before that? Does the question even make sense to you?

 

[vanhees71]

QT tells us that this is just random with probabilities given by Born's rule. It doesn't make sense to ask, how the particle "made a decision".

 

[zonde]

It doesn't make sense to ask, how the particle "made a decision".

The question was not "How?" but "When?"

 

[Demystifier]

QT tells us that this is just random with probabilities given by Born's rule. It doesn't make sense to ask, how the particle "made a decision".

As zonde observed, the question is when the decision is made, not how.

 

[vanhees71]

It's of course made when the detector "clicks" (or writes the information to any kind of storage). I don't know, why this is in any sense "problematic" or "mysterious".

 

[Demystifier]

It's of course made when the detector "clicks" (or writes the information to any kind of storage). I don't know, why this is in any sense "problematic" or "mysterious".

Here is why it is problematic. You simultaneously assume that
1) The measured system (particle) exists even before measurement.
2) The dynamics is local.
3) The random decision happens when the detector clicks (not before).
Indeed, each assumption by itself seems reasonable. But the problem is that they cannot all be simultaneously true. At least one must be wrong. You must give up at least one of them.

Let me explain why they cannot all be true. From 3) and 1) it follows that, immediately before the click, the system exists not only near one detector, but near both of them. But then, puff, at the time of click, the system suddenly ceases to exist near the detector that didn't click. How did this part of the system knew that the click happened near the other part? Since the two parts are spatially separated, there must have been some non-local (even if random) mechanism, which contradicts 2). Hence assumptions 1) and 3) contradict 2), which implies that it is not possible that all three assumptions are true.

And yet, you seem not be ready to give up any of the three assumptions. That's the problem.

Note that the argument above is even simpler than the Bell theorem, because the system studied above does not involve entanglement. The Bell theorem derives a contradiction by assuming 1), 2) and entanglement. The argument above derives a contradiction by assuming 1), 2) and 3).

 

[RockyMarciano]

Here is why it is problematic. You simultaneously assume that
1) The measured system (particle) exists even before measurement.
2) The dynamics is local.
3) The random decision happens when the detector clicks (not before).
Indeed, each assumption by itself seems reasonable. But the problem is that they cannot all be simultaneously true. At least one must be wrong. You must give up at least one of them.

Let me explain why they cannot all be true. From 3) and 1) it follows that, immediately before the click, the system exists not only near one detector, but near both of them. But then, puff, at the time of click, the system suddenly ceases to exist near the detector that didn't click. How did this part of the system knew that the click happened near the other part? Since the two parts are spatially separated, there must have been some non-local (even if random) mechanism, which contradicts 2). Hence assumptions 1) and 3) contradict 2), which implies that it is not possible that all three assumptions are true.

And yet, you seem not be ready to give up any of the three assumptions. That's the problem.

Right. It could even be necessary to give up both 1) and 3) to save 2).

 

[Demystifier]

Right. It could even be necessary to give up both 1) and 3) to save 2).

Not really. To save 2) it is sufficient to give up 3). Example is Bohmian mechanics, which, in absence of entanglement, is local.

EDIT: This is my 7777th post.

 

[RockyMarciano]

Not really. To save 2) it is sufficient to give up 3). Example is Bohmian mechanics, which, in absence of entanglement, is local.

Sure. Sufficient, but I was thinking of necessary if one uses the freedom to change axioms without changing the physics. I think I've read you arguing something like this but maybe it was in a different context.

EDIT: This is my 7777th post.

Nice number. Long ways from the biblical one but still.