I have proposed an experiment to test the ideas discussed in the previous pages. The details of my proposed experiment can be found in this published paper, or in this preprint. An earlier version of the experiment (published in 2008) can be found in this preprint, and a simplified summary or a “proof of concept” can be found in this preprint (published in 2015).
The central goal of the proposed experiment is to test the hypothesis that quantum correlations are a consequence of—or a measure of—the torsion at each point in our physical space:
This upper bound is derived in the last appendix of this paper (see also this paper). The experiment can be performed either in the outer space or in a terrestrial laboratory. In the latter case the effects of gravity and air resistance would complicate matters, but it may be possible to choose experimental parameters carefully enough to compensate for such effects.
With this assumption, consider a “bomb” made out of a hollow toy ball of diameter, say, three centimeters. The thin hemispherical shells of uniform density that make up the ball are snapped together at their rims in such a manner that a slight increase in temperature would pop the ball open into its two constituents with considerable force. A small lump of density much greater than the density of the ball is attached on the inner surface of each shell at a random location, so that, when the ball pops open, not only would the two shells propagate with equal and opposite linear momenta orthogonal to their common plane, but would also rotate with equal and opposite spin momenta about a random axis in space. The volume of the attached lumps can be as small as a cubic millimeter, whereas their mass can be comparable to the mass of the ball. This will facilitate some possible spin directions for the two shells, whose outer surfaces can be decorated with colors to make their rotations easily detectable.
Now consider a large ensemble of such balls, identical in every respect except for the relative locations of the two lumps (affixed randomly on the inner surface of each shell). The balls are then placed over a heater—one at a time—at the center of the experimental setup, with the common plane of their shells held perpendicular to the horizontal direction of the setup. Although initially at rest, a slight increase in temperature of each ball will eventually eject its two shells towards the observation stations, situated at a chosen distance in the mutually opposite directions. Instead of selecting the directions and for observing spin components, however, one or more contact-less rotational motion sensors—capable of determining the precise direction of rotation—are placed near each of the two stations, interfaced with a computer. These sensors will determine the exact direction of the spin angular momentum (or ) for each shell in a given explosion, without disturbing them otherwise so that their total angular momentum would remain zero, at a designated distance from the center. The two interfaced computers can then record this data entirely locally, in the form of a 3-dimensional map of all such directions, at each observation station.
Once the actual directions of the angular momenta for a large ensemble of shells on both sides are fully recorded, the two computers are instructed to randomly choose a pair of reference directions, say for one station and for the other station—from the two 3-dimensional maps of already existing data—and then calculate the corresponding pair of numbers and . The correlation function for the bomb fragments can then be calculated as
where n is the number of experiments performed. According to Bell’s reasoning [which amounts to setting in Eq. (1)] the calculation done in Eq. (2) would not yield correlation stronger than
where is the angle between the vectors and . On the other hand, if my reasoning is correct and quantum correlations are indeed a consequence of the torsion in our physical space as I have hypothesized [cf. equation (1) above], then we expect the correlation function (2) to yield
The plot below shows the difference between the correlations predicted by functions (4) and (5):
Undoubtedly, there would be many different sources of errors in a macroscopic experiment of this nature. However, at least according to David Wineland the proposed experiment is “doable.”
PS: I have recently won the 10,000 Euros offered by Richard Gill for theoretically producing the 2n angular momentum vectors, and , appearing in the above equations. He had foolishly claimed that it was mathematically impossible to construct such 2n vectors and had challenged me to produce them as a “proof of concept” for my proposed experiment. I defeated his challenge in May and June of 2014 by explicitly producing the 2n vectors in these four simulations: (1), (2), (3), and (4), which reproduce the strong correlations purely local-realistically. This suggests that my proposed experiment will be a spectacular success. It will reproduce the strong correlations exactly as I have predicted in several of my papers, for example in Appendix C of this paper where I have given a proof of the strong correlation.
PPS: In the above experiment I have used two hemispheres of an “exploding” ball as a convenient means to illustrate the physical scenario. But in practice a spherically asymmetric hemisphere would wobble violently because of all sorts of inertial effects. A much better system would be something like two flexible squashy balls, squeezed together initially, and then released as if they were parts of a single bomb. This will retain the spherical symmetry of the two constituents after the “explosion” and reduce the inertial effects to near zero. For this system, however, it may be harder to maintain the singlet nature of the composite system (i.e., to maintain the vanishing total spin angular momentum of the composite system).
PPPS: In the published version of the paper the following two paragraphs have been added:
PPPPS: With the bomb made out of two squashy balls (instead of a single ball) which rapidly reshape to perfectly round spheres, the determination of spin directions would be easier, since the spin and rotation axes for each sphere would then be the same. It would still be important to eliminate aerodynamic effects before the final shapes are stabilized. A good quality check of the setup would be to compare how accurately the spins are anti-parallel, thus making sure that the singlet property for each pair of the measured spins is maintained.