Measurement problem in the Ensemble interpretation

[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.

 

[vanhees71]

Well, according to QT there's not more knowable about your particle than the probabilities for the outcome of measurements. The probabilities evolve from a given (prepared) initial to the state at the time of detection, and what we get (repeating the experiment with equal preparations) the distribution by measuring the observable we are interested in. According to the standard model of elementary particles the interactions are local. So your point (1-3) are all well included in the standard model: (1) is ensured by the conservation laws: If I prepare, e.g., some particle with a given charge, then at least this charge must exist all the time; (2) is implemented by construction in any local and microcausal relativistic QFT, (3) is just the only way to answer reasonable the "when" question. How else would you define the "time of detection"?

 

[Demystifier]

Well, according to QT there's not more knowable about your particle than the probabilities for the outcome of measurements. The probabilities evolve from a given (prepared) initial to the state at the time of detection, and what we get (repeating the experiment with equal preparations) the distribution by measuring the observable we are interested in. According to the standard model of elementary particles the interactions are local. So your point (1-3) are all well included in the standard model: (1) is ensured by the conservation laws: If I prepare, e.g., some particle with a given charge, then at least this charge must exist all the time; (2) is implemented by construction in any local and microcausal relativistic QFT, (3) is just the only way to answer reasonable the "when" question. How else would you define the "time of detection"?

I don't agree that standard QT ensures 1). The standard QT talks only about probabilities of measurement outcomes. In particular, the conservation of charge in standard QT says that if you measure charge at two times, then you will get the same number at both times. But it does not claim that charge will exist between the two measurements. It is an extra assumption which may or may not be true, but cannot be tested by experiment. It is a reasonable assumption indeed, but it cannot be strictly derived from principles of standard QT.

So, if you want to think in lines of standard QT, I think you should give up 1).

 

[RockyMarciano]

Symmetry principles aren't the goal. The goal is modeling the world. If the world obeys certain symmetry principles, then of course, we should find out what they are, but finding out symmetry principles isn't the goal.
That is the heart of the measurement problem. Why do macroscopic systems have well-defined macroscopic values?

Sorry to get back to this but aren't precisely the symmetry principles-conservation laws what makes macro systems have (approximately) well defined values by preserving measurements(i.e. measurability)?

 

[Demystifier]

(1) is ensured by the conservation laws: If I prepare, e.g., some particle with a given charge, then at least this charge must exist all the time

Another counterargument:
Suppose that we talk about barion charge (not electric charge) and suppose that, due to some GUT effects, there is a very small probability that the charge will not be conserved. The probability can be arbitrarily small, say ##10^{-100}##, but it is not zero. For all practical purposes the charge can be considered conserved. In this case, would you say that charge must exist all the time? Or almost all the time? Or would you say that it comes to existence only when the detector clicks?

 

[vanhees71]

Well, then you could measure that baryon number is not conserved and then you could indeed only give a probability for still finding the same baryon number as you started with.

 

[Demystifier]

Well, then you could measure that baryon number is not conserved and then you could indeed only give a probability for still finding the same baryon number as you started with.

So you (seem to) introduce a step function. If probability of conservation is smaller than 1, then charge does not exist between measurements. If probability of conservation is strictly 1, then charge exists between measurements.

Don't you have a feeling that there should be a continuous transition, that the difference between 1 and 0.99999999 should not be so radical?

 

[Demystifier]

Well, then you could measure that baryon number is not conserved and then you could indeed only give a probability for still finding the same baryon number as you started with.

Another reason why your reasoning doesn't make sense (to me).

You essentially say that
1) Only conserved quantities exist between measurements.
2) Dynamics is local.
But the goal of dynamics is to describe the change, i.e. to describe the behavior of quantities which are not conserved. By 1), this means that the goal of dynamics is to describe the things which do not exist between measurements. So the fact that dynamics is local really means that dynamics of non-existing entities is local. It says nothing about locality or non-locality of existing entities. Therefore the fact that QFT has local dynamics is not an argument that existing entities obey local laws.

Indeed, the Bell theorem says essentially that if there are changing entities that exist between measurements, then their dynamics must be non-local. It is compatible with the conclusion above that local QFT dynamics is only dynamics on non-existing entities.

 

[Demystifier]

But the goal of dynamics is to describe the change, i.e. to describe the behavior of quantities which are not conserved.

Let me put this point forward.

As an extreme case, consider the Lagrangian
$$L(q,\dot{q})=0$$
This Lagrangian is invariant under any conceivable transformation, so by Noether theorem everything is conserved in this theory. In other words, in this theory, there is no dynamics at all.

This demonstrates my more general point that conservation laws show that some quantities are not dynamical. But the point of dynamics is to describe quantities which are dynamical. So conservation laws, although very useful, do not describe dynamics. Conservation laws describe non-dynamics; they tell us which of the potentially interesting quantities are not dynamical, so can be excluded from further dynamical considerations.

 

[RockyMarciano]

Let me put this point forward.

As an extreme case, consider the Lagrangian
$$L(q,\dot{q})=0$$
This Lagrangian is invariant under any conceivable transformation, so by Noether theorem everything is conserved in this theory. In other words, in this theory, there is no dynamics at all.

This demonstrates my more general point that conservation laws show that some quantities are not dynamical. But the point of dynamics is to describe quantities which are dynamical. So conservation laws, although very useful, do not describe dynamics. Conservation laws describe non-dynamics; they tell us which of the potentially interesting quantities are not dynamical, so can be excluded from further dynamical considerations.

How would you reconcile this with the fact that measurements must be possible in a dynamical world for science to make sense(for different local measurements to be coherent with one another) which seems to imply that at least there must be conservation laws for dynamical measuring tools?

 

[vanhees71]

So you (seem to) introduce a step function. If probability of conservation is smaller than 1, then charge does not exist between measurements. If probability of conservation is strictly 1, then charge exists between measurements.

Don't you have a feeling that there should be a continuous transition, that the difference between 1 and 0.99999999 should not be so radical?

I've not said what you seem to have understood. All I said was what holds for any unstable particle: You prepare it, and then with some probability it's decayed after a given time. That's all you can know in such cases. I still don't get, what should be a problem with that. To the contrary thanks to Q(F)T we have a theory to describe such decays very well.

If there's a conserved charge, at least you know that it will be there forever in the one or the other form. To be sure that a once prepared particle is always there, of course it must be stable, because if there is only the tiniest probability for its decay, then you can never be sure that it is still there after some time. That's why it's called unstable.

 

[Lord Jestocost]

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).

To my mind, assumptions 1) and 2) are misleading when thinking about quantum phenomena. These assumptions are based on classical conceptions.

Regarding assumption 3), I follow J . Marburger: „We can only measure detector clicks. But when we hear the click we say “there’s an electron!” We cannot help but think of the clicks as caused by little localized pieces of stuff that we might as well call particles. This is where the particle language comes from. It does not come from the underlying stuff, but from our psychological predisposition to associate localized phenomena with particles.“ (J. Marburger, “On the Copenhagen interpretation of quantum mechanics” in Symposium on The Copenhagen Interpretation: Science and History on Stage, National Museum of Natural History of the Smithsonian Institution, 2 March 2002)

 

[Demystifier]

How would you reconcile this with the fact that measurements must be possible in a dynamical world for science to make sense(for different local measurements to be coherent with one another) which seems to imply that at least there must be conservation laws for dynamical measuring tools?

I don't see how this implies a need for conservation laws.

 

[RockyMarciano]

I don't see how this implies a need for conservation laws.

I mean that something must be conserved for measurements being valid regardless where and when they are performed and how(at which energy, etc), i.e. for the physics not to depend on any special factor in a dynamical or changing context.

 

[Demystifier]

I mean that something must be conserved for measurements being valid regardless where and when they are performed and how(at which energy, etc), i.e. for the physics not to depend on any special factor.

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.

 

[RockyMarciano]

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.

how do you maintain this stability without conservation laws in a dynamical context?