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

[vanhees71]

I agree that he strawmans Copenhagen. But to be fair, I don't know any textbook which carefully distinguishes situations without intermediate outcomes from real sequential measurements off the top of my head.

But in this case he is wrong. A measurement means that you have let the system interact with an apparatus with outcomes for pointers that are in one-to-one correspondence with the value of the measured observable (I don't talk about incomplete measurements here; that's another interesting story of quite recent research on what measurement means in quantum theory), but this is not the case in the neutron interferometer experiment described in Ballentines book.

 

[vanhees71]

What he shows there is that in this case there cannot be a state reduction. Exactly as described by stevendarryl. Do you disagree with that?

Ballentine indeed does show that in his setup there's no state reduction. The only problem with this argument is that even a proponent of the collapse hyposis wouldn't claim that a state reduction has happened since in this setup the spin components at points B and C are not measured.

 

[zonde]

To see that the separation by itself is not a measurement, I could redirect both streams back together into a single stream, and then no measurement of spin would ever be performed.

I have no suggestion about "correct" terminology, however I see no contradiction between the idea that SG apparatus changes the spin state of particle and the fact that two beams can be recombined in a way that restores original spin state.
In order to observe interference we have to preserve relative phase between spin modes and have to make it matter by recombining beams. And interference is responsible for restoration of the original spin state.
If relative phase plays no role in later manipulations we of course can drop spatially separate part of the beam from description by projection.
Production of measurement record necessarily destroys any relative phase relationship as in this process the system interacts with one or more particles which are necessarily removed from experimental setup and do not participate in any later manipulations. But then it has little to do with spin or any other property of the particle (except position of course as we place detectors at certain spot).

 

[Boing3000]

Step 3 is different because there's also the screen which allows the experimenter to make an observation.

OK the screen is a different apparatus. There is only one screen, and it is after step4. I recognize that. The screen interact with the position observable.

If you have only a single electron and use a Stern Gerlach apparatus to put it in a superposition of flying to the right with spin up and flying to the left with spin down you cannot say anything definite about its spin.

Of course, if there is not "spacial/position" screening... and there is only one electron...

So you shouldn't call this a measurement.

OK fine, I'll not call it a measurement, even though every single one of the electron are known to have been prepared/picked up from the left beam. Which seem to me to be identical to having put a screen with a hole only on the left path.

Yet if you perform a measurement located somewhere to the right of the SG apparatus, you know that if the electron arrives there, it definitely has spin up. This is why it is sensible to call this a preparation for this measurement.

But what I cannot got trough my thick skull (or sick, go figure), is how that differs in any shape of form from the very definition of "measurement".

Listen I found some resource with similar setup that seems to be analysed in detail. I'll read it ten time over and eventually get back to you.

Thank you

 

[vanhees71]

I have no suggestion about "correct" terminology, however I see no contradiction between the idea that SG apparatus changes the spin state of particle and the fact that two beams can be recombined in a way that restores original spin state.
In order to observe interference we have to preserve relative phase between spin modes and have to make it matter by recombining beams. And interference is responsible for restoration of the original spin state.
If relative phase plays no role in later manipulations we of course can drop spatially separate part of the beam from description by projection.
Production of measurement record necessarily destroys any relative phase relationship as in this process the system interacts with one or more particles which are necessarily removed from experimental setup and do not participate in any later manipulations. But then it has little to do with spin or any other property of the particle (except position of course as we place detectors at certain spot).

An SG apparatus without a screen to detect the two partial beams of the silver atom can, however, be seen as a preparation procedure for definite spin states, i.e., you get an entanglement between position and spin component in direction of the magnetic field (with theoretically arbitrary accuracy), i.e., an atom at one of the clearly distinguished places of the two partial beams has a determined spin component $\pm \hbar/2$. The wave function (a Weyl spinor) is
$$\Psi(x)=\psi_+(x) |\hbar/2 \rangle + \psi_{-}(x) |-\hbar/2 \rangle,$$
where the $\psi_{\pm}$ have (FAPP) no overlap.

At this point, however, the spin component has not yet been measured, i.e., to know the spin component of a single atom that run through the magnet you have to register at which position it ends up at a screen or something equivalent. Only then you have done a measurement, and this measurement will distroy the relative phase between the two partial beams, which occur in the superposition written above for $\Psi$. After such a measurement a "recombination" of the two partial beams in the sense Ballentine writes in his book is not possible anymore. This is due to the decoherence that necessarily occurs through the interaction of the atom with the measurement apparatus.

 

[kith]

But in this case he is wrong.

I don't dispute this. I just don't have access to the book right now and can't comment on the specifics of where I think he went wrong.

 

[kith]

Yet if you perform a measurement located somewhere to the right of the SG apparatus, you know that if the electron arrives there, it definitely has spin up. This is why it is sensible to call this a preparation for this measurement.

But what I cannot got trough my thick skull (or sick, go figure), is how that differs in any shape of form from the very definition of "measurement".

Because of "if the electron arrives there". You don't know if it will arrive to the right or to the left. Only after the measurement to the right has been performed do you know that it arrived there.

 

[Boing3000]

Because of "if the electron arrives there". You don't know if it will arrive to the right or to the left. Only after the measurement to the right has been performed do you know that it arrived there.

But the preparation consist of taking only the electron from the left path ! Every electron used after that first "preparating" "Left of Stern Gerlach" is one of those... There is no uncertainty there, isn't it ? What am I missing that is so obvious for you physicists ?

 

[Mentz114]

I don't see anything confusing or incorrect on page 5, 6. What do you mean exactly?

Ballentine is not confusing me - atyy is !

 

[vanhees71]

I don't see anything confusing or incorrect on page 5, 6. What do you mean exactly?

Me neither. There's nothing incorrect on pages 5, 6 in Ballentine's book, where he discusses an SG experiment with neutrons. Also there, however, he doesn't measure the spin components before recombining the "partial beams", i.e., there's no decoherence and that's why the recombination leads back to the original state.

Nevertheless, Ballentine is among the best QM textbooks I know of.

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. What's unsolved is the lack of a consistent quantum description of the gravitational field, but it's not measurement within standard QM and QFT, where the great success of QT describing the empirical findings shows that in fact there's no problem from the point of view of physics. Maybe there's a puzzle for philosophers about reality and such things, but that's philosophy, not physics.

 

[kith]

But the preparation consist of taking only the electron from the left path ! Every electron used after that first "preparating" "Left of Stern Gerlach" is one of those... There is no certainty there, isn't it ? What am I missing that is so obvious for you physicists ?

I don't understand what you mean. 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. So only after looking for the presence of the blob, the observer can say anything definite about the spin.

 

[stevendaryl]

I don't like the equation of measurement with state reduction or terminology like "a measurement has occurred". State reduction neither fully captures what happens in a measurement (it leaves out the outcome) nor is it exclusively used for measurements (it's also used for convenience in situations where the observer doesn't obtain any knowledge).

That's true. For the purposes of the interpretation of quantum mechanics, I think what's important is not measurement, specifically, but interactions that cause a microscopic quantity to become correlated with the results of an irreversible macroscopic change. Such interactions are not actually measurements, because we might not actually learn anything from them.

For modeling purposes, one of these examples of interactions leading to decoherence and macroscopic entanglement can often be thought of as a measurement followed by forgetting the result of the measurement. That sounds like that combination should be the same as doing nothing, but it isn't, in combination with the Born rules.

 

[atyy]

Not again this wrong statement. You cannot admit at the same time that the classical behavior is derivable from QT and then claim that there is a cut. That's a contradictio in adjecto!

OK, let's try this again, since we seem to agree on the error in section 9.5 of Ballentine's book. Here is LL stating explicitly that classical concepts are needed in the formulation of QM postulates, and that it is also true that classical mechanics is a limit of quantum mechanics. Here are some relevant quotes from p2-3 of the English translation.

"A more general theory can usually be formulated in a logically complete manner, independent of a less general theory which forms a limiting case of it. ... It is in principle impossible, however, to formulate the basic concepts of quantum mechanics without using classical mechanics."

"By measurement, in quantum mechanics, we understand any process of interaction between classical and quantum objects ..."

"Thus quantum mechanics occupies a very unusual place among physical theories: it contains classical mechanics as a limiting case, yet at the same time it requires this limiting case for its own formulation."

 

[kith]

Landau and Lifshitz does. They are careful to say that a measurement produces an irreversible macroscopic mark, [...]

By "carefully distinguish" I mean a tangible discussion of both types of situations: an experiment, where the observer actually gets multiple outcomes and an experiment, where state reduction is used for convenience because certain parts of the state aren't relevant for future measurements. And ideally also how one can modify an experiment such that it falls into the other class.

which is nowadays often called a "definite outcome" following Schlosshauer's influential review.

What passage exactly do you have in mind? In his 2004 paper, he talks about the possibility of "subjective definiteness" so his notion of "definite outcome" seems to be more general to me.

In any case, I think that the word "outcome" should be avoided if one doesn't speak about the perception of a person. It is loaded language which blurrs the boundary between what is independent of the observer and what isnt.

 

[atyy]

By "carefully distinguish" I mean a tangible discussion of both types of situations: an experiment, where the observer actually gets multiple outcomes and an experiment, where state reduction is used for convenience because certain parts of the state aren't relevant for future measurements. And ideally also how one can modify an experiment such that it falls into the other class.

Yes, I've never seen that explicitly discussed in a textbook. I think I realized it sometime after reading LL (which is the first book from which I understood quantum mechanics because of its explicit mention of the classical measuring apparatus), and not just the formal postulates. It also helped by explicitly seeing how this is played out in the indirect measurements formalism with a quantum ancilla, and showing that the reduced density matrix is the same as that after a projective measurement in which information about the result is not retained. However, I still did not know it in every specific situation. For example, I did not know about the unitary description of a polarizer until @Cthugha pointed it out to me here on PF many years after I had already learned QM.

What passage exactly do you have in mind? In his 2005 paper, he talks about the possibility of "subjective definiteness" so his notion of "definite outcome" seems to be more general to me.

Nothing so specific, just his general term "definite outcome", eg. https://arxiv.org/abs/quant-ph/0312059 has a whole section II.B headed "The problem of definite outcomes".

BTW, I realized my memory of LL was faulty, and even they do not state the idea of an "irreversible macroscopic outcome" so clearly. It must be something I picked up with their help.

The concept of irreversibility is mentioned more clearly in Haag's 1996 "Local Quantum Physics" on p304: "In Bohr's discussion the time asymmetry appears as obvious. For instance: "The irreversible amplification effects on which the registration of the existence of atomic objects depends reminds us of the essential irreversibility inherent in the very concept of observation" [Bohr 58]."

 

[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.