Why the Quantum | A Response to Wheeler's 1986 Paper - Comments

[Boing3000]

I don't understand what you mean.

Maybe because I wrote "no certainty" instead of "no uncertainty" ?(fixed now)

Let me introduce one more step: after the interaction of the electron with the SG apparatus we have a superposition of a state where it flies to the left with spin up and a state where it flies to the right with spin down. If you put a screen as a measurement device to right, you either get a blob or you don't. Getting a blob corresponds to the electron traveling to the right with spin down, not getting a blob corresponds to the electron traveling to the left with spin up.

That is crystal clear.

So only after looking for the presence of the blob, the observer can say anything definite about the spin.

I don't have to look at the blob after preparation. It is sufficient to look at the latest screen, because no electron measure there can be there without having gone trough the left path. I don't see how it is not strictly equivalent to looking at the blob.

Beside, there is even a temporal relationship between electron measure "to be present" even before the first S/G (preparation) and the electron at the final screen result. Electron can be emitted in the beam one per day for example...

 

[A. Neumaier]

Concerning the question of interpretation, Weinberg's book "Lectures on Quantum Mechanics" is even better although I don't agree with his conclusion that there's something unsolved concerning QM and measurements.

The unsolved problem is the measurement problem in the sense of this post:

after the observer has chosen the device (by whatever rule), there remains the pure quantum problem to show that the device actually produces on each reading the numbers that qualify as a measurement, in the sense that they satisfy Born's rule.
This is the measurement problem! It has nothing to do with the observer but is a purely quantum mechanical problem.

namely to show how given the unitary evolution of the system measured plus detector plus environment, the detector actually produces on each reading the numbers that qualify as a measurement.

You write,

Ok, that's true. Of course, it's only possible for very simple cases in a strict way (like the famous analysis of tracks of charged particles in vapour chambers by Mott or the measurement of spin components in the Stern Geralach experiment).

But your statement is not quite true, since these analyses assume Born's rule for measurements and hence assume what is to be demonstrated.

The measurement problem is solved for some special case in the papers by Allahverdian et al., but as discussed here, these make assumptions different from the tradition.

 

[ftr]

So, after such a long thread, does conservation of angular momentum solve the the ERP or not, as the claim is in OP?

 

[stevendaryl]

So, after such a long thread, does conservation of angular momentum solve the the ERP or not, as the claim is in OP?

I don't think there was a claim that it "solves" it, but that the quantum correlations for EPR can be derived by assuming:

• Measurements always result in an eigenvalue ($\pm \frac{1}{2}$ in the spin-1/2 case)
• On the average, some quantity motivated by conservation of angular momentum is zero.

It's sort of interesting, because the weirdest part of the Born interpretation---that you square the amplitude to get the probability--is not assumed.

But I don't think it actually solves the conceptual puzzles with EPR.

I also wonder whether the derivation can be generalized to show that the Born rule, in general, is implied by conservation laws plus discreteness?

 

[ftr]

My understanding is that EPR is not limited to spin. Also position is not discrete.

 

[vanhees71]

I don't think there was a claim that it "solves" it, but that the quantum correlations for EPR can be derived by assuming:

• Measurements always result in an eigenvalue ($\pm \frac{1}{2}$ in the spin-1/2 case)
• On the average, some quantity motivated by conservation of angular momentum is zero.

It's sort of interesting, because the weirdest part of the Born interpretation---that you square the amplitude to get the probability--is not assumed.

But I don't think it actually solves the conceptual puzzles with EPR.

I also wonder whether the derivation can be generalized to show that the Born rule, in general, is implied by conservation laws plus discreteness?

In the usual most simple setup of the EPR argument by Bohm angular momentum is precisely zero and not only on average. The most simple example is to take neutral pions in their rest frame and then look at the (rare) cases, where the pion decays to an electron-positronium pair. The total angular momentum of the pair is precisely 0 for each such decay and not only on average. The spin state is the singlet state
$$|\Psi \rangle=\frac{1}{\sqrt{2}} (|1/2,-1/2 \rangle - |-1/2,1/2 \rangle).$$
I've no clue what you mean by that the Born rule is the "weirdest part of the Born interpretation". There's nothing weird about it at all. It defines the meaning of the quantum state in a concise and simple way.

 

[RUTA]

So, after such a long thread, does conservation of angular momentum solve the the ERP or not, as the claim is in OP? My understanding is that EPR is not limited to spin. Also position is not discrete.

The Bell basis states giving rise to the Tsirelson bound could in principle represent conservation other than angular momentum, as stated in the arXiv version of the paper https://arxiv.org/abs/1807.09115. Now, does conservation per no preferred reference frame, as explained in the paper/Insight, resolve the mystery of EPR-Bell?

Well, that depends on what you require for "explanation" in this case. If you need a 'causal mechanism' or hidden variables to explain the QM correlations violating Bell's inequality, then the answer is "conservation per no preferred reference frame does not resolve the mystery of EPR-Bell." Conservation per no preferred reference frame is different than conservation in classical mechanics (CM). In CM for conservation of angular momentum, you would have two opposing angular momentum vectors (one for Alice's particle and one for Bob's particle) canceling out. Bob and Alice would be free to measure the angular momentum of their particles along any direction they liked, thereby measuring something less than the magnitude in general. In that situation, the direction along which the two angular momentum vectors were anti-aligned would be a "hidden variable" and constitute a "preferred direction in space" for that particular trial (see my post #33). In an entangled quantum exchange of momentum, Bob and Alice always measure +1 or -1, never any fractions. And, both can say their measurement directions and outcomes were "right" while the other person's measurement outcomes along their directions were only "right" on average. That kind of "frame-independent conservation" constitutes a deep explanation of the QM correlations violating Bell's inequality ... for me, anyway.

So, for me, the constraint (conservation per no preferred reference frame) is compelling enough that I don't require any additional 'causal mechanisms' or hidden variables to explain the constraint. In CM, of course, you can explain the conservation of angular momentum dynamically -- it occurs when the net torque on the system is zero. But, apparently, in QM no further explanation for the constraint is required (or even possible), the constraint itself is (necessarily) the "last word." [The use of constraints rather than dynamical laws as fundamental explanans throughout physics is the leitmotif of our book, "Beyond the Dynamical Universe." So, I'm very biased :-)]

As we elaborate in the paper, the light postulate (LP) of SR is an excellent analogy. There, time dilation and length contraction both follow from the fact that "the speed of light c is the same in all reference frames." At the time Einstein postulated it, everyone was looking to explain the LP, not use it to explain other things. The LP was a mystery itself, so many people did not accept the use of one mystery to explain others. Likewise, the frame-independent manner of QM conservation is itself a profound mystery for many people. So, for those people, it cannot be used to explain the QM correlations violating Bell's inequality.

 

[RUTA]

In the usual most simple setup of the EPR argument by Bohm angular momentum is precisely zero and not only on average. The most simple example is to take neutral pions in their rest frame and then look at the (rare) cases, where the pion decays to an electron-positronium pair. The total angular momentum of the pair is precisely 0 for each such decay and not only on average. The spin state is the singlet state
$$|\Psi \rangle=\frac{1}{\sqrt{2}} (|1/2,-1/2 \rangle - |-1/2,1/2 \rangle).$$

Conservation of angular momentum gives rise to that Bell basis state, yes, but how do the actual measurement outcomes along any direction conform to conservation of angular momentum? Only on average, as I explain. This should come as no surprise, since we know QM gives rise to CM on average. The only surprise is that QM's version of conservation is very different from CM in that it requires no 'causal mechanism' or hidden variables. Indeed, after decades of argument, one could reasonably conclude that QM conservation is not compatible with a 'causal mechanism' or hidden variables. But, I'm sure dBB advocates would not agree :-)

 

[slufoot]

hay everyone this is way to complicated natural things are simple

 

[stevendaryl]

In the usual most simple setup of the EPR argument by Bohm angular momentum is precisely zero and not only on average.

Did you read the article?

I've no clue what you mean by that the Born rule is the "weirdest part of the Born interpretation".

Oh, well. I don't know how to help you, there.

 

[stevendaryl]

My understanding is that EPR is not limited to spin. Also position is not discrete.

Well, that's why I was asking whether the derivation of quantum probabilities extended to things other than spin.

 

[morrobay]

So, after such a long thread, does conservation of angular momentum solve the the ERP or not, as the claim is in OP?

https://arxiv.org/pdf/quant-ph/0407041.pdf

These authors believe so.
@RUTA
Does your Frame independent conservation apply in this paper and how so

 

[vanhees71]

Conservation of angular momentum gives rise to that Bell basis state, yes, but how do the actual measurement outcomes along any direction conform to conservation of angular momentum? Only on average, as I explain. This should come as no surprise, since we know QM gives rise to CM on average. The only surprise is that QM's version of conservation is very different from CM in that it requires no 'causal mechanism' or hidden variables. Indeed, after decades of argument, one could reasonably conclude that QM conservation is not compatible with a 'causal mechanism' or hidden variables. But, I'm sure dBB advocates would not agree :-)

I think we've discussed this already. The only thing QT tells you in this state is that if you measure the components of the electron and the positron in the same direction you get always opposite results since the total angular momentum is of course 0. This is what it means that anglar momentum is precisely conserved for any single event. If you measure the components in different direction you have only probabilities, as it must be in view of the uncertainty relation for angular-momentum components in different directions.

 

[stevendaryl]

If you measure the components in different direction you have only probabilities, as it must be in view of the uncertainty relation for angular-momentum components in different directions.

The whole point of the article is to derive the probabilities for measurements in different directions.

 

[ftr]

My elementary understanding is that conservation law is not enough, since both particles are in superposition of up and down before measurement. So conservation law makes it even more mysterious if anything, as if both particles are linked all the time. Am I saying this wrong.

 

[RUTA]

I think we've discussed this already. The only thing QT tells you in this state is that if you measure the components of the electron and the positron in the same direction you get always opposite results since the total angular momentum is of course 0. This is what it means that anglar momentum is precisely conserved for any single event. If you measure the components in different direction you have only probabilities, as it must be in view of the uncertainty relation for angular-momentum components in different directions.

Then you believe Unnikrishnan's result is a mere coincidence? That's a pretty amazing coincidence, but you are free to believe that!

 

[RUTA]

https://arxiv.org/pdf/quant-ph/0407041.pdf

These authors believe so.
@RUTA
Does your Frame independent conservation apply in this paper and how so

I'm presenting his result and cited the published version of that paper in my Insight:

10. Unnikrishnan, C.S.: Correlation functions, Bell’s inequalities and the fundamental conservation laws, Europhysics Letters 69, 489–495 (2005).

I've been in correspondence with him and he would say "perspective invariance" rather than "no preferred reference frame." Essentially, I'm using his result to answer a question in the QIT community, "Why the Tsirelson bound?" The frame independence approach is in response to QIT's desire to answer their question a la the light postulate of SR. It is supremely ironic that Unnikrishnan's result can be used to answer QIT's question precisely per their desideratum while Unnikrishnan himself does not subscribe to "no preferred reference frame." In another twist, Unnikrishnan doesn't believe Bell's paper should be related to the EPR paper at all. So, right now I'm trying to convince him to let me use his result to answer their question anyway. We'll see.

 

[RUTA]

Well, that's why I was asking whether the derivation of quantum probabilities extended to things other than spin.

The result generalizes to the conservation of anything represented by a Bell basis state, as we show in the corresponding paper https://arxiv.org/abs/1807.09115. Unnikrishnan showed likewise. In his own words

The results I proved are the following: Assuming the conservations laws are valid over the ensemble and the observables are discreet valued, there is unique correlation function independent of the nature of the theory. This coincides with what we derive from quantum mechanics. Any correlation function that deviates from this violates conservation laws. Local hidden variable theories are in this class, since all of them have a different correlation (not only less, but linear functions, at lest in parts ). Thus, Bell's inequalities deals with unphysical theories and are redundant. Testing the inequalities is naive physics, akin to trying to build perpetual machines. The result that deviation marks unphysical theories applies both ways. The correlation is exactly what is predicted by conservation laws, not less, not more. Given a state, conservation law over ensemble gives the quantum correlation. For mixed state correlation can approach classical correlation, but obeying the conservation laws (the correlation reduced only because there is a mixture of angular momentum states - by classically averaging over the mixture you can get the correct quantum correlation.).

 

[morrobay]

The result generalizes to the conservation of anything represented by a Bell basis state, as we show in the corresponding paper https://arxiv.org/abs/1807.09115. Unnikrishnan showed likewise. In his own words

Both you and Unnikrishnan show that the correlation functions for QM and the conservation laws, P(a.b,)_QM = P(a,b,)_C = - a.b. = - cosθ.
How is superposition of entangled spin 1/2 particles 1/2 (|ud} - |du}) and photons 1/2 (|H}₁ |V}₂ ± |V}₁H}₂)
in accord with conservation laws in the context of the question by @ftr above in post #345 ?

 

[vanhees71]

The whole point of the article is to derive the probabilities for measurements in different directions.

Fine, I've no problems with that. It only doesn't mean that angular momentum isn't conserved exactly on an "event-by-event basis". It was a very old error by Kramers and Bohr to assume that the conservation laws only hold on average. It was ingeniouly disproven by Walther Bothe with his coincidence measurement method (here applied to Compton scattering). He got the Nobel prize for this method.

 

[vanhees71]

Then you believe Unnikrishnan's result is a mere coincidence? That's a pretty amazing coincidence, but you are free to believe that!

No, he simply has proven that theories obeying the "realism postulate of EPR" and Bell's inequalities are not compatible with precise angular-momentum conservation, as is predicted by QT. As far as I know, so far nobody has ever found the fundamental conservation laws violated in any quantum experiment. So I choose to use QT describing the empirical facts rather than using a theory obeying a strange notion of "realism" a la EPR, which is disproven by the Bell experiments with overwhelming significance.

 

[stevendaryl]

Fine, I've no problems with that. It only doesn't mean that angular momentum isn't conserved exactly on an "event-by-event basis". It was a very old error by Kramers and Bohr to assume that the conservation laws only hold on average. It was ingeniouly disproven by Walther Bothe with his coincidence measurement method (here applied to Compton scattering). He got the Nobel prize for this method.

But in the case where you measure spins along different axes, it's not possible for the vectorial sum of the two measured angular momenta to be zero exactly.

 

[RUTA]

Both you and Unnikrishnan show that the correlation functions for QM and the conservation laws, P(a.b,)_QM = P(a,b,)_C = - a.b. = - cosθ.
How is superposition of entangled spin 1/2 particles 1/2 (|ud} - |du}) and photons 1/2 (|H}₁ |V}₂ ± |V}₁H}₂)
in accord with conservation laws in the context of the question by @ftr above in post #345 ?

Sorry, I haven't been able to keep up with the discussion lately. If I understand your question correctly (and that in #345), the QM conservation at work here is different than in classical mechanics (CM). I tried to explain in the Insight and in other posts here, so I won't repeat all that. The major difference is that in CM there is a "true" value for the angular momentum $\vec{L}$ for each of the two particles and Alice and Bob measure some component (and therefore fraction) of $\vec{L}$ for their respective particles. In QM what Alice and Bob measure is always +1 or -1, no fractions. That means they have conservation of angular momentum only on average (unless they choose to measure along the same direction in which case they get exact cancelation). Of course, as pointed out by ftr, that leaves a mystery for the person who wants to know what makes the particles behave properly on a trial-by-trial basis, i.e., there is no hidden variable or 'causal mechanism' to account for conservation on average. So, this conservation principle leaves a mystery for those who demand dynamical explanation. That's the point of the Insight. Are you happy with the 4D constraint (conservation on average) as the fundamental explanation? Or, do you demand a dynamical/causal explanation? As with the many examples in my blockworld series, dynamical thinking creates a mystery that is resolved by blockworld constraint-based thinking.

 

[RUTA]

No, he simply has proven that theories obeying the "realism postulate of EPR" and Bell's inequalities are not compatible with precise angular-momentum conservation, as is predicted by QT. As far as I know, so far nobody has ever found the fundamental conservation laws violated in any quantum experiment. So I choose to use QT describing the empirical facts rather than using a theory obeying a strange notion of "realism" a la EPR, which is disproven by the Bell experiments with overwhelming significance.

So, it sounds like you're happy to accept the 4D constraint (conservation on average) as a sufficient explanation of Bell-inequality-violating QM correlations. No need to look for hidden variables or 'causal mechanisms'. In that case, we're in agreement.

 

[vanhees71]

But in the case where you measure spins along different axes, it's not possible for the vectorial sum of the two measured angular momenta to be zero exactly.

Of course, but here the minimal interpretation again solves this apparent quibble. The state with its probabilistic meaning refers to an ensemble. To empirically check, whether angular momentum is conserved, you prepare an ensemble and for each member you measure the spin components of both particles in the same direction. Then you'll find with 100% probability (i.e., for each event) a sum of 0, i.e., angular momentum in this direction is conserved. You can repeat the measurement as often as you like in an arbitrary direction.

Of course, the quantum state implies more statistical properties than that, namely the correlations for measurements of spin components of the two particles in different directions, among them choices, where Bell's inequality is predicted (and empirically found with high significance for e.g., polarization-entangled photon pairs) to be violated, disproving the possibility of local deterministic hidden-variable models.

 

[vanhees71]

So, it sounds like you're happy to accept the 4D constraint (conservation on average) as a sufficient explanation of Bell-inequality-violating QM correlations. No need to look for hidden variables or 'causal mechanisms'. In that case, we're in agreement.

What is the "4D constraint"? As I already said, in this case angular momentum is, according to standard QT, not only on average conserved but strictly for each individual particle pair!

There's no need for new theories if the old ones perfectly work fine. Since QT is causal, as any physical theory must be, there's also no argument against QT from this corner. Many people find QT unsatisfactory, because it's not deterministic. Well, physics is not there to please people's opinions about how Nature should work but it tries to figure out as accurately as one can how Nature in fact works.

Whether there is a deterministic HV theory consistent with all knows facts, I don't know. If there is one, it will be as puzzling as QT since it's for sure non-local, as is shown by the violation of Bell's inequality, and a non-local theory that's consistent with the relativistic space-time structure, will be very mind-boggling. Maybe it's not even possible to construct such a model, but this one cannot rule out yet.

 

[stevendaryl]

Of course, but here the minimal interpretation again solves this apparent quibble. The state with its probabilistic meaning refers to an ensemble. To empirically check, whether angular momentum is conserved, you prepare an ensemble and for each member you measure the spin components of both particles in the same direction. Then you'll find with 100% probability (i.e., for each event) a sum of 0, i.e., angular momentum in this direction is conserved. You can repeat the measurement as often as you like in an arbitrary direction.

That doesn't address the issue of what statistics you get when you measure one particle of a twin pair along one axis and you measure the other particle along a different axis.

Of course, the quantum state implies more statistical properties than that, namely the correlations for measurements of spin components of the two particles in different directions, among them choices, where Bell's inequality is predicted (and empirically found with high significance for e.g., polarization-entangled photon pairs) to be violated, disproving the possibility of local deterministic hidden-variable models.

The point of the Insights article was to try to derive the statistics for measurements in arbitrary directions without assuming the Born rule, and without assuming the mathematics of spin states.

 

[stevendaryl]

Many people find QT unsatisfactory, because it's not deterministic.

That might have been the reason for Einstein, but that is not an accurate explanation for why everyone finds QT to be unsatisfactory. I would say that the measurement problem is the reason most people find the minimal interpretation of QT unsatisfactory.

 

[Lord Jestocost]

That might have been the reason for Einstein, but...

To my mind, Einstein didn't want to accept that "quantum probabilities" are - so to speak - irreducible. In his book “Quantum Reality - Beyond the New Physics” Nick Herbert drops the term “quantum ignorance”:

“Once you get down to the quantum randomness level, no further explanation is possible. You can’t go any deeper because physics stops here. Albert Einstein, no fan of the orthodox ontology, objected to this fundamental lawlessness at the heart of nature when he said that he could not believe that God would play dice with the universe. This new kind of ultimate indeterminism may be called quantum ignorance: we don’t know why an electron strikes a particular phosphor because there’s nothing there to know about. When the dice fall from the cup, on the other hand, their unpredictable outcome is caused by classical ignorance — by our unavoidably partial knowledge of their real situation.”

 

[RUTA]

What is the "4D constraint"? As I already said, in this case angular momentum is, according to standard QT, not only on average conserved but strictly for each individual particle pair!

There's no need for new theories if the old ones perfectly work fine. Since QT is causal, as any physical theory must be, there's also no argument against QT from this corner. Many people find QT unsatisfactory, because it's not deterministic. Well, physics is not there to please people's opinions about how Nature should work but it tries to figure out as accurately as one can how Nature in fact works.

Whether there is a deterministic HV theory consistent with all knows facts, I don't know. If there is one, it will be as puzzling as QT since it's for sure non-local, as is shown by the violation of Bell's inequality, and a non-local theory that's consistent with the relativistic space-time structure, will be very mind-boggling. Maybe it's not even possible to construct such a model, but this one cannot rule out yet.

As we've all been telling you, the only way to get conservation when the measurements are different is on average. That means the conservation principle applies not only between spatially separated outcomes but also between temporally separated pairs of outcomes, i.e., 4D. Hidden variables and 'causal mechanisms' are not required, QM is simply describing the spatiotemporal (4D) pattern of outcomes per conservation of angular momentum.