Two particles separated by kilometers change their 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 offers an explanation that restores a finite speed to entanglement but hides it in an extra time dimension.
A shadow on the wall cast by 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 on our four-dimensional brane appears instantaneous. The geometry of this bulk is not arbitrary: it is uniquely fixed by Einstein's equations with a cosmological constant: the warp factor decays exponentially away from the brane.
The collapse of the wave function in this model is described by deterministic nonlinear dynamics, where the hidden variable is replaced by the projection of the bulk field. This builds on the approach of David Bohm and Jeffrey Bub, but with a geometric foundation. 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-correlation between two independent pairs of entangled photons. Its magnitude is proportional to the square of the ratio of the distance within a pair to the distance between pairs. 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 a strict 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, the collapse of the wave function occurs over a finite time determined by the parameter γ. If this parameter were too small, measurements would take forever; if too large, quantum systems would collapse on their own. Existing experiments constrain its value, but the exact magnitude remains unknown.
The idea of additional time resonates with Greg Egan's novel 'Schild's Ladder', where physicists discover a new fundamental structure of spacetime that changes our understanding of causality. The series 'Dark' also plays with the multiplicity of time dimensions, albeit in a different vein.