Abstract:

*A consequence of the quantum mechanical uncertainty principle is that one may not discuss the path or “trajectory” that a quantum particle takes, because any measurement of position irrevocably disturbs the momentum, and vice versa. Using weak measurements, however, it is possible to operationally define a set of trajectories for an ensemble of quantum particles. We sent single photons emitted by a quantum dot through a double-slit interferometer and reconstructed these trajectories by performing a weak measurement of the photon momentum, postselected according to the result of a strong measurement of photon position in a series of planes. The results provide an observationally grounded description of the propagation of subensembles of quantum particles in a two-slit interferometer.*

Also see the press release on this here.

Most astounding part is the path reconstruction shown in Fig. 3.

For the experimentally reconstructed trajectories for our double slit (Fig. 3), it is worth stressing that photons are not constrained to follow these precise trajectories; the exact trajectory of an individual quantum particle is not a welldefined concept. Rather, these trajectories represent the average behavior of the ensemble of photons when the weakly measured momentum in each plane is recorded contingent upon the final position at which a photon is observed. The trajectories resemble a hydrodynamic flow with a central line of symmetry clearly visible:

The authors conclude that what they have observed verifies the Bohmian picture of QM.

Single-particle trajectories measured in this fashion reproduce those predicted by the Bohm–de Broglie interpretation of quantum mechanics (8), although the reconstruction is in no way dependent on a choice of interpretation.

If this is true, then this might be the first evidence that there's something to this interpretation of QM.

Fascinating paper!

Zz.

[1] S. Kocsis et al., Science v.332, p.1170 (2011).

## 2 comments:

It is well known that the "Bohm momentum" (p= grad S for a polar decomposition psi=sqrt{P}exp{iS/hbar} of the wave function), is equal to the "weak value" of the momentum postselected on position. This is a prediction of QM, independent of any interpretation thereof.

The experiment is neat in that it measures this weak value at each of a number of positions with high resolution (note BTW that the weak value is the average of many many measurements, not a single measurement outcome). However, the equivalence to the Bohm momentum is a tautology - any other result would mean that QM is simply wrong.

Hence this paper, while nice experimentally, tells us nothing new about the foundations of QM.

Yup. Bohm's theory is one of those ones that you *CANNOT* have evidence for. Similar to the "gravity is caused by invisible and undetectable little green men pulling on invisible and undetectable strings attached to all objects".

It's mathematically equivalent to standard QM and only adds an unnecessary layer of complexity because there are people who are psychologically bothered by QM's branching.

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