Two particles separated by kilometers change states in concert, as if there were no distance between them. This is called quantum entanglement, and since its discovery it has baffled physicists: no known carrier can travel faster than light, yet correlations appear instantaneously. Marco Pettini proposes an explanation that restores a finite speed to entanglement but hides it in an extra time dimension.
The shadow of an object moving across a room can travel faster than the object itself. Similarly, in a five-dimensional spacetime with two time axes, a massless field propagates at finite speed, but its projection onto our four-dimensional brane appears instantaneous. The geometry of this bulk is not arbitrary: it is uniquely fixed by Einstein's field equations with a cosmological constant: the warp factor decays exponentially away from the brane.
The collapse of the wave function in the model is described by deterministic nonlinear dynamics, where the hidden variable is replaced by a projection of the bulk field. This builds on the approach of David Bohm and Jeffrey Bub, but with a geometric justification. Previously, entanglement looked like an instantaneous correlation without a carrier; now it appears as the propagation of a field through hidden time at finite speed.
The main result is the prediction of cross-correlations between two independent pairs of entangled photons. Its magnitude is proportional to the square of the ratio of the intra-pair distance to the inter-pair distance. For a tabletop experiment with a base of 1 m and 10 m, a correlation of order 10⁻² is expected, requiring about 10⁴ coincidence events — achievable with modern photonic setups. Standard quantum mechanics gives exactly zero here.
If the predicted correlation is detected, it would be a strong argument for extra time dimensions. The shadow on the wall would cease to be an illusion — behind it would lie a depth we do not yet see.
In the Bohm–Bab model, wave-function collapse takes a finite time set by the parameter γ. If this parameter were too small, measurements would take forever; too large, and quantum systems would collapse on their own. Existing experiments constrain its value, but the exact number remains unknown.
The idea of extra time echoes Greg Egan's novel 'Schild's Ladder', where physicists uncover a new fundamental structure of spacetime that reshapes our view of causality. The series 'Dark' also plays with multiple time dimensions, albeit in a different vein.