# Perspective

Nature Physics 6, 151 - 153 (2010)

doi:10.1038/nphys1619

Subject Category: Quantum physics

## Dynamical quantum non-locality

Sandu Popescu^{1}

This is an important article - here are some excerpts:

"That nature is non-local, in the sense of so-called Bell-inequality violations, is by now well known. That is, quantum physics allows correlations between distant particles that are stronger than allowed classically: for classical systems to show such correlations they would need to communicate faster than light. Understanding this kind of non-locality and using it is one of the greatest achievements of quantum information science. The non-locality discovered in the AB effect, however, is completely different. Bell-inequality violations follow from the Hilbert-space structure of quantum mechanics; they are purely kinematic. On the other hand, the AB type of non-locality is dynamic — it is the non-locality of the quantum equations of motion."

How quantum wave interference is qualitatively different from classical wave interference:

"Let us first consider waves on water, with the two-slit screen being a dam with two openings in front of the beach. Two observers on the dam, one next to each opening, could both observe and record the phase of the wave, by simply measuring how high the water is as a function of time. They could then find the relative phase by calculating the difference of the phases. So not only can the relative phase be observed, but the individual phases as well.

On the other hand, quantum mechanically *α*_{1} and *α*_{2} cannot be observed. Indeed, quantum mechanically an overall phase is unobservable."

Enter quantum dynamical nonlocality in the relative phase shift operator:

"We thus arrive at a first significant conclusion: the information about the interference is contained in the average of the shift operator, not in the averages of any power of position or momentum. It is therefore this operator that is the relevant one. Without a better understanding of its properties we have no way of actually understanding quantum interference.

### New dynamics ahead?

To summarize, quantum interference is not the benign phenomenon that it is generally considered to be. It is fundamentally different from classical interference. The relevant observables are non-local and they obey non-local equations of motion.

...

The implications are dramatic. On the one hand, the analysis described here sheds new light on the mystery of interference, to the extent that it should change the whole discourse. Rather than focusing on what happens at the screen — wavefunction collapse and so on — one should go back and revisit the notion that an electron, while passing through one slit, cannot know what happens to the slit not taken. It certainly can know, if the physics is non-local. But the implications do not stop here, at the subject of 'interpretations of quantum mechanics'. It is much more than that.

The entire quantum evolution is subject to dynamical non-locality, so we should be able to see its consequences in various quantum effects, regardless of their interpretation. ...

Conceptually however we are almost there. That non-local interactions exist and do not conflict with causality is only possible under the umbrella of quantum uncertainties. This, if we turn the table around, may give a whole new meaning to the reasons that uncertainties exist in the first place — so that nature may be non-local."

Popescu's theory is consistent with Bohm's ontological theory. The former may be easier to make special relativistic than the latter.