2Tphysics

Two-Time Physics (2T-physics) is a theoretical framework that extends spacetime by introducing a second temporal dimension, yielding a d+2 dimensional arena with two times. Developed by Itzhak Bars, the approach uses an Sp(2,R) gauge symmetry on the phase space of a relativistic particle, with coordinates X^M and momenta P^M. The theory imposes the first-class constraints X^2 = P^2 = X·P = 0. Via gauge invariance these constraints eliminate unphysical degrees of freedom, making the extra time dimension unobservable, and producing a family of one-time (1T) dynamical systems—shadows of the same 2T theory.

The global symmetry in the ambient space is SO(d,2), which becomes manifest as conformal symmetry in the emergent 1T shadows. Depending on the gauge choice, one recovers diverse 1T dynamics in 3+1 dimensions, including relativistic particle motion, nonrelativistic systems, harmonic-oscillator mappings, and certain gravitational models with Weyl invariance. Thus 2T-physics provides a unifying viewpoint in which seemingly disparate theories are connected as different gauge choices of a single higher-dimensional framework.

Beyond particle mechanics, 2T-physics has been developed for field theories and supersymmetric extensions, and has been linked to holographic ideas and dualities. It has yielded insights into hidden symmetries and dual descriptions of physical systems, though it remains speculative and has not made unique experimental predictions.

Critics note that the framework relies on gauge constraints to generate observable physics, while supporters emphasize its potential to illuminate structural relations among theories and to reveal deeper symmetry principles. See also Itzhak Bars, Sp(2,R), conformal symmetry.