Non-local Realistic theories disproved

DrChinese

In an exciting and important development, a team of respected scientists has just announced the results of a direct test of non-locality using Leggett's Inequality.

An experimental test of non-local realism, by Simon Groblacher, Tomasz Paterek, Rainer Kaltenbaek, Caslav Brukner, Marek Zukowski, Markus Aspelmeyer and Anton Zeilinger (19 April 2007)

Their conclusion: an entire class of non-local realistic theories - that is, theories in which polarization is predetermined but there may be a dependence on the settings of the separated measurement apparati - are ruled out. By my reading (and I am by no means sure of this), this would exclude Bohmian Mechanics as a viable theory.

The critical element of their assumption about Non-local Realistic Theories (using pairs of photons generated by Parametric Down Conversion) is that they MUST obey Malus' Law for all subsets of possible experiments. For those who follow my usual rantings about Bell's Theorem, you will likely be familiar with this idea and others in the following quote from the paper:

The logical conclusion one can draw from the violation of local realism is that at least one of its assumptions fails. Specifically, either locality or realism or both cannot provide a foundational basis for quantum theory. Each of the resulting possible positions has strong supporters and opponents in the scientific community. However, Bell's theorem is unbiased with respect to these views: on the basis of this theorem, one cannot, even in principle, favour one over the other. It is therefore important to ask whether incompatibility theorems similar to Bell's can be found in which at least one of these concepts is relaxed. Our work addresses a broad class of non-local hidden-variable theories that are based on a very plausible type of realism and that provide an explanation for all existing Bell-type experiments.

The theories under investigation describe experiments on pairs of particles. It is sufficient for our purposes to discuss two-dimensional quantum systems. We will hence focus our description on the polarization degree of freedom of photons. The theories are based on the following assumptions: (1) all measurement outcomes are determined by pre-existing properties of particles independent of the measurement (realism); (2) physical states are statistical mixtures of subensembles with definite polarization, where (3) polarization is defined such that expectation values taken for each subensemble obey Malus' law (that is, the well-known cosine dependence of the intensity of a polarized beam after an ideal polarizer).

These assumptions are in a way appealing, because they provide a natural explanation of quantum mechanically separable states (polarization states indeed obey Malus' law). In addition, they do not explicitly demand locality; that is, measurement outcomes may very well depend on parameters in space-like separated regions. As a consequence, such theories can explain important features of quantum mechanically entangled (non-separable) states of two particles (a specific model can be found in Appendix I): First, they do not allow information to be transmitted faster than the speed of light; second, they reproduce perfect correlations for all measurements in the same bases, which is a fundamental feature of the Bell singlet state; and third, they provide a model for all thus far performed experiments in which the Clauser, Horne, Shimony and Holt (CHSH) inequality was violated. Nevertheless, we will show that all models based on assumptions (1)-(3) are at variance with other quantum predictions.

Enjoy!!

Demystifier

It does not exclude Bohmian mechanics (BM). There is a general theorem that BM has identical statistical predictions as standard QM. What their experiment demonstrates is that realism, if exists, must be not only nonlocal, but also contextual. Contextuality means that the value of the measured variable may change by the act of measurement. BM is both nonlocal and contextual, making it consistent with the predictions of standard QM as well as with their experiment. In fact, after Eq. (4), they discuss BM explicitly and explain why it is consistent with their results.

Their "mistake" is their definition of "reality" as an assumption that all measurement outcomes are determined by pre-existing properties of particles independent of the measurement. This is actually the definition of non-contextual reality, not of reality in general. The general definition of reality is the assumption that some objective properties exist even when measurements are not performed. It does not mean that these properties cannot change by the physical act of measurement.

In simpler terms, they do not show that Moon does not exist if nobody looks at it. They only show that Moon, if exists when nobody looks at it, must change its properties by looking at it.

I also emphasize that their experiment only confirms a fact that was theoretically known for a long time: that QM is contextual. In this sense, they have not discovered something new about QM, but only confirmed something old.

DrChinese

I wouldn't call that a "mistake".

This is pretty well standard definition of realism, as the entire point is that reality (if it exists) is supposed to be observer independent. Certainly, there may be "contextuality" but I don't consider that to be equivalent to "realism". Neither do the authors of this paper, as they make clear.

Clearly, if the context matters - as is implied in QM as you point out - then the question is: how does one meaningfully assert that there was a pre-determined value prior to the observation, which has been "changed" as a result of that observation? Certainly, this paper's result implies that no greater specification of the system is possible using a non-local theory.

Careful

The implementation of Mallus' law is the weak point in their reasoning (that is equation (1) and (2)); and the entire paper hinges on that. In other words, there is no need to assume that a photon (entangled with another photon) has a definite spin orientation at a coarse grained level classically either (that is: taking the average of the spin over the interaction time of the photon with the stern gerlach apparatus should result in a more or less zero net result). This pretty much destroys the rest of the paper, there is no need to assume a preferred (net) spin direction on the level of the ``entangled'' individual photons (which should be visible for the SG apparatus).

DrChinese

You may not believe that Malus' Law is completely valid with entangled photons, especially if you believe that Bell tests themselves are flawed due to "fair sampling" and other issues. There are local realists that give predictions somewhat at variance with Malus. But for anyone who believes that the QM prediction is in fact accurate, I believe they will see merit in the paper's line of reasoning. Clearly, all signs point to the cos^2 theta relationship - and they always have.

Careful

???? Euh, I am not doubting the validity of Mallus' law at all! All I say is that for an entangled state, it is meaningless to speak about polarization of a single photon in the first place (I said *implementation* of Mallus' law). In other words, I am saying that assumptions (1) and (2) on the second page (left column) are not necessary at all for realistic theories. In other words, Mallus' law is forced upon an ensemble of two particle systems where it should not be in the first place, which should have been clear from my previous post.

DrChinese

OK, I thought you were doubting it for entangled photon pairs. But why does that assumption seem out of place? I mean, it seems pretty reasonable to me to require that observed results match for all subsets too.

Careful

??? What I say is that polarization of an ``entangled'' photon is not well defined, so Mallus' law as it stands there is irrelevant. Neither do outcomes of experiment need to be independent of the measurement and nor do entangled states correspond to ensembles with definite polarizations.

JesseM

Any local realistic theory will need assumption 1 -- "all measurement outcomes are determined by pre-existing properties of particles independent of the measurement (realism)" -- in order to explain how the results show 100% correlation whenever both detector settings are used, with the measurement-events having a spacelike separation. In this case, since FTL coordination of the particles' behavior is assumed impossible, a local realistic theory must assume that the particles were originally created in correlated states such that, given both the particle's complete state and a particular choice of detector setting, the outcome of the measurement is predetermined.

Careful

We were speaking here about NON-LOCAL hidden variable theories, locality (in the sense that *nothing* can go FTL) is probably hard to maintain. But there is something to say for what you say, although FTL is needed anyway (unless you accept superdeterminism) if you want to explain the entanglement correlations.

Demystifier

The realism is observer independent in the sense that there is only one reality even if there are many observers. However, realism may depend on measurement as the process of measurement is a physical process that involves interactions. You should distinguish between the notions of observer and measurement. Observer is a metaphysical concept, measurement is a physical one.

I never said that contextuality is equivalent to realism. Instead, realism may be either contextual or non-contextual. QM allows only contextual realism.

Concerning your question "how does one meaningfully assert that there was a pre-determined value prior to the observation, which has been "changed" as a result of that observation?", I note that BM provides a possible answer. But I emphasize again, the word "observation" is misleading, so one should use the word "measurement" instead. The crucial point is that measurement is a physical process in which the total wave function (describing both the measured degrees of freedom and the degrees of freedom of the measuring apparatus) CHANGES even at the level of Schrodinger evolution, i.e., even without assuming a "wave-function collapse".

vanesch

I would like to chime in with others in this thread: it is impossible to observationally falsify Bohmian mechanics without, at the same time, falsifying quantum theory itself, given that both are empirically exactly equivalent.

So any (silly) claim that the Bohmian view on QM has been rejected experimentally by I don't know what contrived reasoning, is fundamentally flawed. The same applies btw to "proofs" or "rejections" of MWI...

Demystifier

True, but not absolutely true.
BM has identical statistical predictions as standard QM as long as the predictions refer to measurements of observables defined by hermitian operators and as long as the quantum equilibrium hypothesis is satisfied.
Some measurable quantities such as time in nonrelativistic QM and particle position in relativistic QM are not described by hermitian operators, in which case it is not clear what the predictions of standard QM are, while BM may give predictions even in these cases. Also, BM suggests that quantum equilibrium may not be satisfied in the early universe, which may have physical implications on quantum cosmology of the early universe.

Even MWI may have observable predictions that differ from the "standard" ones, for example if the linear Schrodinger equation is generalized to a non-linear one. In this case, MWI predicts that parallel worlds may interact with each other.

vanesch

I agree. However, I would consider these predictions as predictions from NEW theories, which have been inspired by specific interpretations of (current, standard) quantum theory. It is not because these new theories are empirically endorsed/falsified, that the original interpretation of current standard quantum theory is endorsed/falsified (although it would be a non-rigorous argument in that direction, of course).

DrChinese

I don't know about the silly part...

I have heard some BMers - at various points - say words to the effect: IF all particle positions were known (including those non-local to a particle), THEN outcomes would be seen as deterministic. However (they say), such positions cannot be known and that leads to the indeterminancy we see. I am not asserting this as true, mind you, nor am I asserting this is an accurate representation of the Bohmian position (I am not qualified for that - I think Demystifier, ttn and others can do a much better job). However, if it were, this seems to me to be exactly the kind of non-local realistic theory that the paper is addressing. I am aware of the claimed "equivalence" of BM and QM as to predictive results (by claimed I mean to say that there may be some objections by some that the equivalence is not total). Of course, QM does not claim that a greater specification of the system is possible.

As I see it, we are being led into an observer-dependent view in keeping with the application of the HUP (& possibly discontinuous wave function collapse as well). It does not seem to matter whether the hidden variables are local or not - they do NOT exist in a fashion which would allow one to say that "there is a more complete specification of the system possible."

vanesch

Yes, but if that's known, then BM is not equivalent in its predictions to QM ; while, when one takes on the "quantum equilibrium hypothesis", which I consider as being part of "standard" BM (that is, we take as initial probability distributions of the positions of the BM particles, the position probabilities as given by QM), then the only numbers that come out of BM that are comparable to experimental results, are probability distributions of observations which are exactly equivalent to the same probability distributions as calculated with standard QM. So no number comes out of standard BM, and that is comparable to experiment, that contradicts a number that comes out of standard QM. As such, I don't see (even without reading the paper) how one could ever, in principle, claim that this or that experimental result has falsified standard BM (without at the same time falsifying standard QM).

The equivalence is easily established. I don't have a reference handy, but it can be shown that an ensemble of a set of particles, with initial probability distribution as given by |psi|^2, and following the BM dynamics, has then, at any later time, a distribution given by |psi|^2.

As this is the only thing we can compare to a measurement (every measurement can ultimately be considered as a position measurement, be it of a pointer on a measurement device, or ink particles on a publication of results), there's no way to distinguish experimentally between predictions from both views.

DrChinese

I want to be clear that the paper nowhere makes the claim that Bohmian Mechanics has been falsified. I hope I didn't leave that impression. However, I think that it may be necessary for the BM camp to clarify their position such that the "pre-determined" (and realisitic) element of the interpretation is dropped. I do not believe this claim can continue to be made (of course that is only my opinion).

So my interpretation - assuming the paper stands - is that one would say:

i) A QM interpretation must be non-realistic (i.e. reality is dependent on subsequent observations).
ii) There are no hidden variables, and there is no predetermination.
iii) Reality must be contextual (more specifically, "Bell Reality" is denied).
iv) No greater specification of the system is possible, even in principle.
v) Wave function collapse (whatever that is) is instantaneous.
vi) There is no evidence that signals can be transmitted faster than c.