Survey of two-time physics

Two-time physics (2T) is a general reformulation of one-time physics (IT) t hat displays previously unnoticed hidden symmetries in IT dynamical systems and establishes previously unknown duality,type relations among them. This may play a role in displaying the symmetries and constructing the dynamics of little understood systems, such as M-theory. 2T-physics describes vario us IT dynamical systems as different d-dimensional 'holographic' views of t he same 2T system in d + 2 dimensions. The 'holography' is due to gauge sym metries that tend to reduce the number of effective dimensions. Different I T evolutions (i.e. different Hamiltonians) emerge from the same 2T-theory w hen gauge fixing is done with different embeddings of d dimensions inside d + 2 dimensions. Thus, in the 2T setting, the distinguished IT which we cal l 'time' is a gauge-dependent concept. The 2T-action also has a, global SO (d, 2) symmetry in flat spacetime, or a more general d + 2 symmetry in curv ed spacetime, under which all dimensions are on an equal footing. This symm etry is observable in many IT-systems, but it remained unknown until discov ered in the 2T formalism. The symmetry takes various nonlinear (hidden) for ms in the IT-systems, and it is realized in the same irreducible unitary re presentation (the same Casimir eigenvalues) in their quantum Hilbert spaces . 2T-physics has mainly been developed in the context of particles, includi ng spin and supersymmetry, but some advances have also been made with strin gs and p-branes, and insights for M-theory have already emerged. In the cas e of particles, there exists a general worldline formulation with backgroun d fields, as well as a field theory formulation, both described in terms of fields that depend on d + 2 coordinates. All IT particle interactions with Yang-Mills, gravitational and other fields are included in the d + 2 refor mulation. In particular, the standard model of particle physics can be rega rded as a gauge-fixed form of a 2T-theory in 4 + 2 dimensions. These facts already provide evidence for a new type of higher-dimensional unification.