# Legget's inequality and Bohmian mechanics

1. Nov 13, 2013

### bohm2

Leaving aside the debatable point about whether bell's violation rules out all local theories or just local realism, is there general agreement that if the assumptions are valid, violation of Leggett's inequalities rules out any non-local model that treats properties other than position as real as argued here:
The Foundational Significance of Leggett’s Non-local Hidden-Variable Theories

If this is the case, why is position so privileged toward realism in BM, unlike all other properties? Does it having anything to do with distinguishing the difference between 'measurement' of the position operator versus measurement of the Bohmian particle positions. So in that case, position is, in some sense, not privileged or am I misunderstanding?

2. Nov 13, 2013

### DrChinese

That is a strange statement. By EPR's definition, experimentally observed perfect correlation of entangled photon polarization prove it is quite real. That is because it can be predicted with certainty.

I realize to the Bohmian, spin is not fundamental and that particular point is not proven either way by experiment. But spin and position both share the same experimentally demonstrated "reality", whatever that is. (Bell would say it is not a local reality.)

3. Nov 14, 2013

### Demystifier

See Sec. 2 of
http://lanl.arxiv.org/abs/1112.2034 [Int. J. Quantum Inf. 10 (2012) 1241016] ,
especially
- first paragraph on page 5 (beginning with "An interesting question is ...")
and
- fourth paragraph on page 6 (beginning with "The basic idea is ...")

In short, since wave functions after decoherence are localized in the position space (and not some other space), which is an interpretation-INDEPENDENT fact, measurable predictions with a Bohm-like interpretation can only be reproduced with a privileged role of positions.

4. Nov 14, 2013

### stevendaryl

Staff Emeritus
I think there are two different notions of what it might mean for spin to be "real":
1. Before measurement, there is a definite (although unknown) spin vector associated with the particle at each moment: $\vec{\sigma} = (\sigma_x, \sigma_y, \sigma_z)$
2. Before measurement, for a given setup of the detectors, there is a definite (although unknown) answer to the question: "Will the particle's spin be measured spin-up, or spin-down?"

In the first case, the spin is a property of the particle, and the detector just measures it (or one component). In the second case, the spin is a property of the composite particle/detector system.

In contrast, in Bohm's model, the position of a particle is assumed to be a property of the particle itself, but spin is a property of the composite system.

I'm not 100% positive that this is a meaningful distinction, but it might be.

5. Nov 14, 2013

### audioloop

Regardeless of Bohmians

Foundations and Interpretation of Quantum Mechanics. Gennaro Auletta and Georgio Parisi, World Scientific
"A criticism of experiments on the Leggett–Garg inequality is that they do not really show a violation of macrorealism because they are essentially about measuring spins of individual particles"

example:

Macrorealism from entropic Leggett-Garg inequalities
http://pra.aps.org/abstract/PRA/v87/i5/e052103

"in two spatially separated spin-s particles sharing a state of zero total spin"

-------
Macrorealism is based on (i) the object remains in one or the other of many possible states at all times in decoherence free state and (ii) Non-invasive measurability.

but
Quantum- vs. MacroRealism: What does the Leggett-Garg Inequality actually test?
http://ora.ox.ac.uk/objects/uuid:c2c31bfa-f9d3-4bc6-9853-79fcd79917f7/datastreams/ATTACHMENT1

"A macroscopically observable property with two or more macroscopically distinct values available to it will at all times determinately possess one or other of those values"

"We have seen that macroscopic realism should be understood not as the claim that certain kinds of quantum superposition are not possible, but as the claim that all ontic states are non-contextually value-denite for a macroscopically observable quantity ~ Q. We have shown that macroscopic realism would not be impugned by a Leggett-Garg inequality violation involving measurements of ~ Q Within the notion of macroscopic realism per se we have seen that there are three distinct broad kinds of theories: operational eigenstate macroscopic realism, preparation-support macroscopic realism, and extra-preparation macroscopic realism. It is only the first of these which is unable to account for potential Leggett-Garg inequality violation. Nevertheless, even if Leggett-Garg inequality violation does not refute macroscopic realism, it would still remain an interesting result, since operational eigenstate macroscopic realism follows from macroscopic realism proper when combined with the idea that one is able experimentally (in principle at least) to prepare every possible probabilistic state which the world allows. If macroscopic realism is true, then, Leggett-Garg inequality violation would show that we are subject to fundamental limits in our ability directly to control and manipulate the world"

-------
For a psi-epistemic theory all measurements which do not change the quantum state cannot change the ontic state, and thus for psi-epistemic theories all undetectable measurements are also non-invasive measurements. However for psi-ontic theories this is not the case. Psi-ontic theories allow for the existence of non-invasive measurements

.

Last edited: Nov 14, 2013
6. Nov 14, 2013

### bohm2

This seems reasonable and I naively did not even consider anything else. But cannot one argue as Matthias Egg argues that this is really an empirical question since detection always involve some macroscopic "threshold type" effect (discrete clicks of detectors). Not sure of this would make any difference? Here's what he writes:
P.S. I realize (from reading your previous posts) that you agree with Laudisa who views Leggett's work as nothing new, as they are already ruled out by Kochen–Specker no-go theorem.

Last edited: Nov 14, 2013
7. Nov 15, 2013

### Demystifier

One additional argument for a preferred role of position in BM: Suppose you want to make BM relativistic covariant. Then you need to treat space on an equal footing with time. But you already know that time has a special role in QM, by being a "classical" quantity, not an operator. Then relativity suggests that space should also be a "classical" quantity, not an operator. But this is exactly what the position in BM is.

For a detailed exposition of such a relativistic covariant version of BM see
http://lanl.arxiv.org/abs/1309.0400