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

[vanhees71]

I haven't missed the point. You have failed to convince me that there is a point. There's nothing non-trivial derived in your paper, and it's written in a way that one has to guess what you want to tell and there's a lot of off-topic ballast in it. Excuse me for being harsh.

 

[RUTA]

I haven't missed the point. You have failed to convince me that there is a point. There's nothing non-trivial derived in your paper, and it's written in a way that one has to guess what you want to tell and there's a lot of off-topic ballast in it. Excuse me for being harsh.

If you don't understand the conundrum, then you won't appreciate Unnikrishnan's solution and my qualification thereto. I did revise the manuscript according to my efforts to explain it to you, so these exchanges did prove useful :-)

 

[vanhees71]

Well, I've just looked up the following paper by Unnikrishnan:

DOI: 10.1209/epl/i2004-10378-y

He got the issue with the conservation law correct, i.e., precisely as I stated several times. Maybe it helps to sharpen also your manuscript if you use his explanation on pages 490 and 491 in his paper, particularly the statement on the conservation law directly under item 2) on page 491. Then it becomes really a non-trivial and interesting issue which sheds further light on Bell's inequality in showing that there's no local deterministic HV theory that obeys the angular-momentum-conservation law on average. This is weaker than to assume the conservation law to be valid for any individual system as is the case for quantum theory for the spin-singlet state.

 

[RUTA]

Well, I've just looked up the following paper by Unnikrishnan:

DOI: 10.1209/epl/i2004-10378-y

He got the issue with the conservation law correct, i.e., precisely as I stated several times. Maybe it helps to sharpen also your manuscript if you use his explanation on pages 490 and 491 in his paper, particularly the statement on the conservation law directly under item 2) on page 491. Then it becomes really a non-trivial and interesting issue which sheds further light on Bell's inequality in showing that there's no local deterministic HV theory that obeys the angular-momentum-conservation law on average. This is weaker than to assume the conservation law to be valid for any individual system as is the case for quantum theory for the spin-singlet state.

Here is his item 2:

The theory of correlations obeys the conservation of angular momentum on the average over the ensemble, and for the case of singlet state,STotal = 0, there is rotational invariance. Note that this is a weak assumption, since we do not insist on the validity of the conservation law for individual events.

He says, immediately thereafter

The second criterion is the main assumption, physically well motivated, in the proof that follows. Since the main assumption is applied only for ensemble averages and not for individual events, I do not make any explicit assumption on locality or reality.

That is exactly the point I make when I say Bob can't satisfy conservation of angular momentum on a trial-by-trial basis when he and Alice make measurements at different angles. He can only satisfy the conservation principle an average in such cases. [Of course, he can say the same about Alice.] The correlation function obtained per Unnikrishnan's conservation principle is not satisfied by "instruction sets," which is the Mermin equivalent of saying Unnikrishnan's conservation principle cannot be satisfied by any "local deterministic HV theory." Again, did you read Mermin's paper?

 

[vanhees71]

But you didn't make the point clear! Unnikrishnan does. Even under the assumption of angular-momentum conservation on average, which is less than what's the case for QT, where angular-momentum conservation holds on an event-by-event basis, he can show that there's no local deterministic HV model which leads to the violation of Bell's inequality as predicted by QT. I've not read Mermin's paper, but I don't think it's necessary, because in Unnikrishnan's paper everything is clear.

 

[RUTA]

But you didn't make the point clear! Unnikrishnan does. Even under the assumption of angular-momentum conservation on average, which is less than what's the case for QT, where angular-momentum conservation holds on an event-by-event basis, he can show that there's no local deterministic HV model which leads to the violation of Bell's inequality as predicted by QT. I've not read Mermin's paper, but I don't think it's necessary, because in Unnikrishnan's paper everything is clear.

What I had in the paper was just Unnikrishnan's summary paragraph. Obviously, I can't include all the explication he provides in his paper after that summary, but I didn't think it necessary since his summary was very clear to me. Apparently, it wasn't clear to you, so I revised the paper here replacing his summary with my "no preferred reference frame" argument for his conservation of angular momentum on average. My argument is just another way of looking at his argument or just another way of looking at Boughn's argument here. However you justify it, the key insight of Unnikrishnan is to use conservation of angular momentum on average to provide $\overline{BA+}$ and $\overline{BA-}$ in the correlation function (see post #386). That gives you the quantum correlation function without ever using quantum mechanics. This is akin to deriving the Lorentz transformations from the light postulate (in more ways than one, as I will point out).

As for articulating the fact that Unnikrishnan's result rules out "local HV theories," that's trivially clear from the fact that his conservation principle reproduces the quantum correlation function which rules out local HV theories (I have included that very statement in the paper). In the Mermin paper (had you bothered to read it), he goes to great lengths to explain how his "instruction sets" are the equivalent of any local HV theory. As with the Unnikrishnan paper, I can't include Mermin's entire paper in mine, so I must expect the reader to have read the Mermin paper. The Mermin device is a metaphor for the formalism of QM in this particular experimental set-up. So, when Mermin shows that his device cannot be explained with instruction sets, he's showing how QM rules out local HV theories. The conundrum of the Mermin device is then, "If it doesn't work via instruction sets, how the hell does it work?" Since Unnikrishnan's conservation principle gives the quantum correlation function responsible for the mysterious outcomes of the Mermin device, his conservation principle invoked as a constraint (as with the light postulate) then answers that question, i.e., resolves the conundrum of the Mermin device. However, ...

As I point out, Unnikrishnan's conservation principle only resolves the conundrum of the Mermin device if you can accept the conservation principle as a constraint on the distribution of outcomes in space and time with no `deeper mechanism' to account for the constraint proper. In other words, you have to accept the conservation principle as a constraint in and of itself without further explanation. Prima facie the conservation of angular momentum on average sounds like a perfectly reasonable constraint. But, this constraint does not provide a `deeper mechanism' at work on a trial-by-trial basis to account for the average conservation. So someone might still say, "But, what mechanism is responsible for the conservation? How do the particles `know' how to behave in each trial so as to contribute properly to the ensemble? Each particle has `no idea' what the outcomes were at both locations in preceding trials, nor does it `know' what the other device setting is in their particular trial. How the hell does this average conservation pattern in space and time get created?"

And that leads us to the other analogy with the light postulate. Even Michelson of the Michelson-Morley experiment said, "It must be admitted, these experiments are not sufficient to justify the hypothesis of an ether. But then, how can the negative result be explained?" In other words, even Michelson required some `deeper mechanism' to explain why "the speed of light c is the same in all reference frames." In general, if one cannot accept a constraint or postulate in and of itself as the fundamental explanans, that constraint or postulate is just as mysterious as the explanandum. That's the point of my paper and that is the point of our book, "Beyond the Dynamical Universe." So, my paper is just another argument for constraint-based explanation as fundamental to dynamical/causal explanation.