Consider a quantum particle emitted from a source, such that the associated wave function spreads as a spherical wave front. Assume that at a large distance from the source there is a spherical shell of a very large number of detectors. When the wave front arrives at the shell of detectors, one and only one (randomly selected) detector clicks, and the wave function is said to have collapsed to the location of that detector. The said particle has been localized to the clicked detector and is obviously no longer anywhere else. Therefore, at the instant of collapse, the wave function becomes zero at the location of every other detector. This vanishing of the wave function happens even before any signal (traveling at the speed of light) from the location of the clicked detector can arrive at the other detectors. How does such an influence take place, in apparent violation of the principles of special relativity? This is the puzzle of quantum non-locality. The puzzle can also be highlighted by considering a pair of correlated and entangled quantum particles emitted by a source, and traveling in opposite directions, to be received by two independent detectors (Alice, and Bob) far away from each other. The measurement on the state of one particle instantly causes the state of the other particle to collapse. This ability of one particle to influence the other particle is in violation of the principle of relativistic causality [`an event B can be influenced by event A only if B occurs after a light signal traveling from A has arrived at B’]. This is known as the Einstein-Podolsky-Rosen (EPR) paradox or, equivalently, the quantum non-locality puzzle.
Independently of the EPR paradox, we ask the following question: why does the universe have only one dimension of time, whereas it has three dimensions of space? Could it be that there are in fact three dimensions of time as well, and the two additional dimensions of time are compact and too tiny (in their time-radius) and hence have escaped detection so far? Our ongoing research on unification of forces suggests this to be the case, and hence that our `quantum’ universe has six space-time dimensions. It is only the classical universe which appears to have four spacetime dimensions. The four classical dimensions are curved by gravitation (according to the laws of the general theory of relativity), whereas the two additional timelike dimensions are curved by the weak force (according to the laws of the electro-weak theory). The electroweak symmetry breaking in the very early universe bifurcates the 6D spacetime into two overlapping copies of 4D spacetimes: one is ours, with three spatial and one timelike dimension. The other 4D spacetime has three timelike and one spatial dimension; and the two 4D spacetimes have one space and one time dimension in common.
The presence of the other 4D spacetime provides a novel causal channel for influence to travel from Alice to Bob. This channel, which we may call a `quantum wormhole’, offers a resolution of the EPR paradox, without having to modify the rules of quantum mechanics or of special relativity. Spacetime distances between Alice and Bob, through this other 4D spacetime, are far, far smaller than through our spacetime. The two spacetimes have distinct metrics of their own. A causal signal traveling from Alice, through the quantum wormhole, arrives at Bob almost instantaneously, in comparison to the corresponding signal traveling through our 4D spacetime. Quantum locality is hence restored in the 6D spacetime, and the apparent quantum nonlocality in our 4D spacetime is only an illusion, caused by our lack of knowledge of the additional timelike dimensions. Bell’s inequalities continue to be violated: the reason for their violation is indeterminism. Local hidden variable theories continue to be ruled out, but local indeterministic theories are allowed. This kind of a resolution of the EPR paradox does not work if the additional dimensions are spacelike. The quantum particle mediating the signal through the other 4D spacetime is the so-called massless dark photon predicted by our unification theory; this particle couples to the square-root of mass and should be sought for in laboratory experiments.
References:
1. Time-like extra dimensions: non-locality, spin, and Tsirelson bound, Mohammad Furquan, Tejinder P. Singh and P Samuel Wesley, Universe 11, 137 (2025) https://doi.org/10.3390/universe11050137
2. Does our universe have more than one dimension of time? Tejinder P. Singh, https://www.preprints.org/manuscript/202505.1074/v1
3. Gravi-weak unification in a six-dimensional spacetime with signature (3,3), T.Asselmeyer-Maluga, F. Finster, N. Gresnigt, J. Isidro, A. Marciano, C. Paganini, T.P. Singh and P Samuel Wesley, in preparation (2025).
