There is action at a distance notwithstanding the vanishing commutators

The theorem

Strong locality can be understood as saying that the outcome at one detector is independent of both the settings of the remote detector, and the outcome of the remote measurement. If the outcome at one detector is independent of the outcome (but not the axes setting) of the remote measurement, that is not enough for strong locality to hold.


The doubt

Is the independence of the measurement in Boston on results in Alaska flawed? Has this nothing to do with locality? Would the proposed law say that no correlations can ever exist in the whole Universe, except perhaps correlations between two objects which sit exacly at the same place, which is really hard to achieve?

This would be obviously wrong. It’s wrong in classical physics, too. When you create a pair of Bertlmann’s socks, their colors are also (negatively) correlated. To use the term “strong locality” would appear as nonsensical.

The complete explanation of the inequality

Yes, such simplistic doubt makes perfectly sense (for a beginner), the term “strong locality” could appear as “nonsensical” because the description is a bit vague regarding the classical case of the pair of socks with different colors. They are negatively correlated. Let me assume that Nature is like a computer executing an algorithm, that can only use local data. The program can say: Alice’s measurement is red or Alice’s measurement is yellow if deterministic (but we know it is not) or there is 20% of being red, 80% of being yellow. The “problem” is that the program can not say: Alice’s measurement is the opposite of Bob’s measurement (because they’re possibly spacelike separated and the computer responsible to produce the result of Alice’s measurement can not know about the other results). The “problem” being that a couple of such “local computers” (even though non deterministic) – trying to reproduce Nature’s results observed by the two detectors for different axes settings – would not violate Bell inequality (extract from a too kind reply to an intolerant racist, stubborn wannabe physicis).

Carlo Rovelli’s point of view

Carlo Rovelli wrote an article about locality.

The founding postulate of RQM stipulates that we shall
not deal with properties of systems in the abstract, but
only of properties of systems relative to one system. In
particular, we can never juxtapose properties relative to
different systems.

Some questions for him:

How do you exactly explain the correlations and the consistency between the distinct descriptions of the world if they’re so irreducible one into the other?

Why can’t we juxtapose those properties just to answer a mathematical (or counterfactual) question?

Is this approach – in terms of explaining the nonlocality of the entanglement – just the equivalent of Copenhagen interpretation “shut up and compute”?

Addendum about non-locality

This paper demonstrates that the Copenhagen, de Broglie-Bohm and sum-over-paths interpretations in their current form do not provide a local interpretation for quantum marginals.

This fact is obscured by the existence of the no-signaling property, which is often used as proof that the marginals are local. In the case of spatial entanglement, the no-signaling property does not sufficiently remove the configuration space effects arising in the marginal probabilities.

in conclusion

There is a complete dissociation between the tensor product structure of the wavefunction and the local propagation of information into quantum subsystems.

Geometry of space

It is surely worth reading a review of the interactions between mathematics and quantum physics.

Recent ideas from quantum gravity and string theory challenge the fundamental concepts of geometry at an even deeper level. Physical intuition tells us that the traditional pseudo-Riemannian geometry of space–time cannot be a definite description of physical reality. Quantum corrections in the theory of gravity will change this picture at distances of the order of the Planck scale. Familiar fundamental properties such as locality only appear at much larger scales. In fact, there is now much evidence within string theory—usually referred to as ‘holography’—that in the end geometry itself is an emergent quantity.

That finally leads us to the more likely underlying phenomenon to explain the non-locality of entanglement: ER=EPR is a conjecture stating that entangled particles are connected by a wormhole.

The authors pushed this conjecture even further by claiming any entangled pair of particles — even particles not ordinarily considered to be black holes, and pairs of particles with different masses or spin, or with charges which aren’t opposite — are connected by Planck scale wormholes.

The conjecture leads to a grander conjecture that the geometry of space, time and gravity is determined by entanglement

In the words of Leonard Susskind

Evidently the nonlocal feature of quantum mechanics that we ordinarily call interference can be a special case of the nonlocality of entanglement. If we believe in the ambitious form of ER=EPR, this implies the presence of an Einstein-Rosen bridge connecting the superposed wave packets for a single particle.

Non-realism doesn’t explain non-locality

I completely agree with the following comment. It’s embarrassing that many wannabe physics don’t understand this

even if we accept subjectivity, a theory still has to provide some sort of explanation why some observer experiences a result and not another

Extra dimensions of spacetime explain the non-locality of the entanglement

From a comment of Charles Stromeyer Jr.

This paper in PRL by a postdoc at MIT shows via AdS/CFT that the creation of nonlocal quantum entanglement yields wormholes:

Also, this paper published in Nature Physics is just one of multiple different papers which show that nonlocal quantum entanglement must originate outside of or beyond 4D spacetime.

Notice, incidentally, that neither Cumrun Vafa nor Nima Arkani Hamed ever wrote a word about entanglement.



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