Nonlocality - fact or fiction?

[ThomasT]

Because these interpretations claim that objective (i.e., existing even without observations) reality does not exist. Of course, these interpretations admit that there are nonlocal correlations (which is only what is truly experimentally proved), but they claim that reality itself is not nonlocal, simply because reality does not exist.

I am not saying that it makes sense to me, I am just saying what they say. :tongue2:

I agree that what you say they're saying doesn't make sense. However, I don't think that what you say they're saying is what they're saying. :uhh:

I don't think that Bohr and Heisenberg would characterize the Copenhagen interpretation as saying that reality doesn't exist. They would say, I think, that if you want the word "reality" to have some physical meaning (rather than using it merely as an honorific and absurdly ambiguous term), then there's no reality (that is, we can have nothing, save speculatory metaphysics, to say about what exists) beyond the level of instrumental behavior.

If one says that there is a hidden reality that exists beyond our sensory apprehensions, then what is this reality? How can we know that it exists. What can we say about it unambiguously?

The essence of the Copenhagen interpretation is that the modern science of physics shouldn't proceed via the path of metaphysical speculation (even though it seems that it sometimes does). The speculatory path is the one taken by, eg., Bohmian mechanics and MWI, so the developers of the Copenhagen interpretation would say that these interpretations are unacceptable adjuncts, unnecessary baggage, with respect to the development of the quantum theory.

As for nature being nonlocal. That's an open question. And, we return to the Copenhagen interpretation with its emphasis on semantics to ask two questions when any claim about nature (such as its nonlocality) is made.
(1) What do you mean?
(2) How do you know?

 

[akhmeteli]

No, it doesn't answer the question at all. My question has nothing to do with what happens a zillion years after the atom decays or doesn't decay (enough time for the system to have a significant likelihood of returning to its initial state), I don't understand why you think that would be relevant--I'm just asking what happens shortly afterwards, say after an hour. At this point, if you take unitary evolution seriously without the projection postulate, the cat should be in a superposition which assigns significant amplitudes to both the "atom decayed and cat is dead" states and the "atom didn't decay and cat is alive" states. So what do you think is the actual physical truth of the matter at this point in time? Do you think the cat is really one or the other, implying that unitary evolution can't be the whole story? Or do you think that since both outcomes are assigned a significant amplitude by the wavefunction, both must be on equal footing as far as 'physical truth' is concerned--and if so, how is this different from the many-worlds interpretation? Or do you suggest some third alternative, and if so what is it?

Sorry, could not reply earlier - was a bit busy.

Ok, so you suggest that we consider the original version of the Schroedinger cat paradox. No objections. I am not sure though that this is a major change from what I wrote. Yes, now we start the measurement in an hour after the start of the experiment. However, the question is how long it takes to perform the measurement. If the measurement takes a very long time, again, the system can switch from one state to the other. The problem is the dichotomy "dead cat/alive cat" may be false: an alive cat can die (if, for example, the measurement provokes a radioactive decay), and a dead cat can become alive, say, as a result of a thermodynamically absurd, but mechanically inevitable process. So I do suspect that both outcomes might be "on equal footing as far as 'physical truth' is concerned", as telling one outcome from the other is not so straightforward. I guess this is quite different from MWI, as there is just one world, but no measurement is ever final.

I am not trying to offer some clearer picture of what happens in the Shroedinger's gedanken experiment, I am just trying to say that the picture that unitary evolution presents is not as absurd as it may seem (although it may seem thermodynamically absurd). Perhaps a clearer picture can be found in the article by Allahverdyan et al. quoted in my post #20 in this thread. They consider an exactly solvable model of spin measurement and show when and how the "Shroedinger's cat's" terms disappear and how this is related to irreversibility. They conclude: "The solution of our model shows that the so-called “measurement problem”, to wit, the fact that the final state... does not seem to be related unitarily to the initial state, has the same nature as the celebrated “paradox of irreversibility” in statistical mechanics,... with additional quantum features." Actually, they derive the Born rule from the unitary evolution, but as an approximation, not as a rigorous result.

I only brought up that link because it seemed to support my memory that in QM when you construct the wavefunction for a multiparticle system, you can use it to assign amplitudes to combinations of measurable outcomes. This is just a question about the mathematics of the theory of QM, you said you were a physicist yourself so I figured you'd know whether my memory on this is right or wrong; if not, then I can go dig up my old textbooks to see if I can find an example of such a multiparticle amplitude. But obviously if it's true that a single amplitude can be assigned to combinations of outcomes, then we can use the Born rule to calculate the probability of measuring such combinations, without the need to worry about the projection postulate discontinuously shifting the wavefunction between measurements.

And I tried to explain that, while it may certainly be important what is written in the link you gave or in your textbooks, another question may be more important for this discussion: why it is written, as it may well be that something is written just on the basis of the projection postulate, and it would not mean that it is downright wrong, but it would mean it is not quite relevant. For example, I would not call a textbook downright wrong just because it states that all processes are irreversible. Irreversibility may be a good approximation, but, strictly speaking, it contradicts mechanics.

Anyway, let us assume for this discussion that "you can use [the wavefunction] to assign amplitudes to combinations of measurable outcomes." But then, to conduct an experiment and test the Bell inequalities, you have to measure correlations, and one typically conducts two separate measurements - on the first and on the second particle, and consequently the projection postulate is used to calculate the probabilities that quantum mechanics is supposed to predict. Again, as I said, while maybe "we can use the Born rule to calculate the probability of measuring such combinations", as the product of spin projections is an Hermitian operator, but in practice the actual measurement consists of two separate measurements. Furthermore, maybe I should admit that I cannot be sure that it is the projection postulate and not the Born rule that generates nonlocality, which does not seem to exist in the rigorous unitary evolution picture, as both the Born rule and the projection postulate are just approximations. However, my bet is the projection postulate is the main culprit.

For combinations of spin measurements it might be that there is no time-dependence in the amplitudes, in which case it wouldn't really matter whether the measurements were simultaneous or not.

And if it does not matter, we may assume that we need two measurements, one after another (anyway, two absolutely simultaneous measurements are an abstraction), and the projection postulate is needed to calculate the prediction of quantum mechanics.

 

[akhmeteli]

You accepted "fair sampling" in neutrino detection but reject it in Bell-type experiments? What gives? How do you think they detect neutrinos in the first place?

Zz.

I admit that I have no clear idea on what form of the fair sampling assumption is used in neutrino detection and what it has to do with the fair sampling assumption in the experiments on Bell inequalities. Furthermore, if it is found tomorrow that neutrinos have zero mass after all, I won't loose any sleep over such development. I'd like also to emphasize that there is not necessarily something wrong with accepting something in one situation and rejecting the same thing in another situation. I both accept irreversibility in thermodynamics and refuse to accept it as a rigorous concept. Another example: the Boltzmann's hypothesis of molecular chaos made possible his outstanding achievements - the kinetic equation named after him and the famous H-theorem. However, strictly speaking, the hypothesis is wrong, as it introduces irreversibility where mechanics is reversible. The analogy with the fair sampling assumption is striking: in both cases some assumptions are introduced which are external with respect to the underlying mechanics, and inevitably such assumptions are, strictly speaking, wrong in both cases. At least that's my understanding.