Comments on: Refuting nonlocal realism?

By: Howard Wiseman

Howard Wiseman — Sat, 26 May 2007 00:11:59 +0000

p.s. sorry for not formatting the above correctly. believe it or not it is the first time I submitted a blog comment. Also I think I meant modulus, not mod-squared.

By: Howard Wiseman

Howard Wiseman — Fri, 25 May 2007 19:03:55 +0000

Thanks for your analysis of Leggett's paper and the experimental paper, Matt. We also discussed these in my group recently, and I thought I'd share my thoughts. To understand better Legget's restriction, I had to generalise it from photon polarization to arbitrary systems and observables. Using (as in Bell's convention) a,b for observables (i.e. settings) and A,B for outcomes, and c for the preparation procedure, Legget's condition in general should be that p[AB|abc] = \int d\psi \int d\phi p(\psi,\phi | c) \int d\lambda p(\lambda|\psi,\phi) p(A|\lambda,a,b) p(B|\lambda,a,b) where the ps on the RHS are arbitrary probability distributions, restricted by the following two conditions: \int d\lambda p(\lambda|\psi,\phi) p(A|\lambda,a,b) = P(A|a\psi) \int d\lambda p(\lambda|\psi,\phi) p(B|\lambda,a,b) = P(B|b\phi) Here P(A|a\psi) is the *Quantum Mechanical* probability for the outcome A given a measurement of a on some pure state parametrized by \psi. P(B|b\phi) is defined similarly. In the photon case, these are all polarization vectors, and P(A|a\psi) equals the mod-square of dot product of the vectors a and \psi. As Matt said, the functional dependence of p(A|\lambda,a,b) and p(B|\lambda,a,b) shows that Leggett is considering a class of theories that are outcome-independent, but not parameter independent. The two conditions Leggett places are necessary to get something different from QM, since without them the first equation just describes an arbitrary (outcome-independent) nonlocal hidden variable theory, which can always replicate any QM prediction. If you stare at Legget's two conditions for long enough you might convince yourself that they are reasonable. However, it must be the case that Leggett does NOT require that \int d\lambda p(\lambda|\psi,\phi) p(A|\lambda,a,b) p(B|\lambda,a,b) = P(A|a\psi) P(B|b\phi) otherwise Legget's first equation just reduces to the assumption of local realism (i.e. Bell-locality). I think that once one realises that this last equation must NOT hold, the reasonableness of Legget's two conditions diminishes considerably. My conclusion: Legget is clever to have found reasonable-looking equations that give a restriction weaker than local realism but stronger than QM. However on closer examination there is nothing compelling about his assumptions. The class of nonlocal hidden variables the experiment rules out doesn't really tell us much about the world as far as I can see. All of the nonlocal hidden variable theories which people take seriously (e.g. Bohmian mechanics) are *interpretations* of QM so can never be ruled out by an experiment that agrees with QM.

By: Ulrich Mohrhoff

Ulrich Mohrhoff — Tue, 15 May 2007 13:27:41 +0000

“To be is to be measured.”
This means that no property or value is possessed unless its possession, by a system or by an observable, is indicated by (or can be inferred from) an actual event or state of affairs — a “measurement” in the broadest sense of the term. It means that a system or observable has a property or value only if, only when, and only to the extent that it is actually “measured” (in the broadest sense of the term). This is not the only possible way of making sense (or nonsense, depending on your ideology) of the mathematical formalism of quantum mechanics, but it’s certainly better than stories about what happens or is the case between measurements, since such stories can neither be confirmed nor ruled out empirically, however ludicrous they may be. It is also in excellent agreement with all existing experiments and analyses of quantum-mechanical probability assignments.

By: Matthew Leifer

Matthew Leifer — Mon, 14 May 2007 15:07:24 +0000

Where does that quote come from? In any case, it is not justified by quantum theory. It is true that quantum theory only predicts probabilities rather than telling you the exact outcome that will occur in an experiment. Some people jump to hasty conclusions when they learn about this and start spouting a lot of pseudo-philosophical/spiritual nonsense, including a good many physicists who should know better. The fact of the matter is that there are consistent interpretations of quantum theory which prove that many of the weird things you’ll hear people saying about quantum theory are not inevitably true.

Thermal equilibrium does not have much to do with measurement, although there are certain similarities between the process of decoherence, which is relevant for understanding measurement, and the approach to thermal equilibrium. Thermal equilibrium is a particular distribution of physical variables (e.g. positions and velocities) appropriate when you have a large number of degrees of freedom, e.g. a large number of particles, all interacting with each other. It explains why thermodynamics can be used to relate the macroscopic variables, e.g. pressure, volume and temperature, of such a system. The canonical example is a container full of gas, which can usually be thought of as a large number of molecules distributed according to the Maxwell-Boltzmann law.

By: Zach

Zach — Sat, 12 May 2007 00:43:34 +0000

Hello, I just stumbled upon this article and I found it interesting. I’m a senior in high school, with a very limited knowledge on quantum physics. But I just have a few random questions about this quote.

“To be is to be measured.”

The ability to be measured is the ability to be, in other words?

Does “thermal equilibrium” theorize that something can exist without the ability to be measured?

Thanks you in advance.

By: Ulrich Mohrhoff

Ulrich Mohrhoff — Fri, 04 May 2007 02:30:02 +0000

My computer stores all sorts of information in forms I never ever see, when I’m programming in say Java, and the Java universe’s I create seem as viable and well running, as any other universe even thought the creatures in this universe never have access to this hidden information.

What exactly is the uncertainty relation for your Java universe?

By: Matthew Leifer

Matthew Leifer — Thu, 03 May 2007 16:55:40 +0000

Apropos of Bohmian mechanics: Why would Nature use variables and then make sure that they cannot be measured?

It’s a good question. IF I believed in Bohmian mechanics (and the emphasis is on IF) then I would probably believe in Valentini’s version, which doesn’t have this problem, i.e. the universe started out in a state where these variables could be measured, but has relaxed to “quantum equilibrium”. This is analogous to thermal equilibrium, wherein you also can’t measure every quantity associated with a system.

Is the experiment by Simon Gröblacher, Tomasz Paterek, Rainer Kaltenbaek, Časlav Brukner, Marek Żukowski, Markus Aspelmeyer, and Anton Zeilinger isn’t proof enough… If local realism cannot be rule out, then it belongs in the same category as those elastic strings.

For me the Bell experiments are enough to rule out “reasonable” hidden variable theories, i.e. I would like fundamental Lorentz invariance (or diffeomorphism invariance at the GR level) in my theory. This means I’m going to have to adopt a very bizzare ontology and the whole game is to figure out what this should be. On the other hand, if I were to advocate nonlocal hidden-variables, then I see no reason to single out Leggett’s class of theories as the most compelling. Of course, it is interesting that one can rule out some class of nonlocal hidden-variable theories by experiment, and so I think the work is interesting, but I don’t think it significantly changes the interpretational landscape.

I agree, but if one thinks about the question of “where” the information is in the nonlocal hidden variable theory, then I think this sepearation is meaningful, right?

I’m not entirely sure what this means because most of the toy models are pretty unrealistic, i.e. you somehow imagine the photons are carrying around a list of variables with them. “Where” the information is located does not make much sense to me unless we are talking about a realistic physical model. On the other hand, I agree that the separation is meaningful in some contexts, and particularly when we are talking about information processing. For example, it was useful in the Barrett-Hardy-Kent proof of the resilience of quantum key distribution to superquantum eavesdroppers.

By: Dave Bacon

Dave Bacon — Thu, 03 May 2007 16:03:18 +0000

“Why would Nature use variables and then make sure that they cannot be measured?”

I disagree. My computer stores all sorts of information in forms I never ever see, when I’m programming in say Java, and the Java universe’s I create seem as viable and well running, as any other universe even thought the creatures in this universe never have access to this hidden information.

But of course this is my own personal bias!

By: Dave Bacon

Dave Bacon — Thu, 03 May 2007 15:49:03 +0000

“Leggett has proposed to consider theories that maintain the assumption of outcome independence, but drop the assumption of parameter independence. It is worth remarking at this point that the attribution of fundamental importance to this factorization of the locality assumption can easily be criticized. Whilst it is usual to describe the outcome at each site by ±1 this is an oversimplification. For example, if we are doing Stern-Gerlach measurements on electron spins then the actual outcome is a deflection of the path of the electron either up or down with respect to the orientation of the magnet. Thus, the outcome cannot be so easily separated from the orientation of the detector, as its full description depends on the orientation.”

I agree, but if one thinks about the question of “where” the information is in the nonlocal hidden variable theory, then I think this sepearation is meaningful, right?

By: Ulrich Mohrhoff

Ulrich Mohrhoff — Thu, 03 May 2007 05:19:56 +0000

Apropos of Bohmian mechanics: Why would Nature use variables and then make sure that they cannot be measured? One might as well posit strictly unobservable elastic strings to explain Newton’s law of gravity. The only sensible reason why so-called “hidden variables” are hidden is that they do not exist. To be is to be measured. Variables have values only if, only when, and only to the extent that they are actually measured (that is, their values are indicated by some actual event or state of affairs). Is the experiment by Simon Gröblacher, Tomasz Paterek, Rainer Kaltenbaek, Časlav Brukner, Marek Żukowski, Markus Aspelmeyer, and Anton Zeilinger isn’t proof enough… If local realism cannot be rule out, then it belongs in the same category as those elastic strings.