  Position and momentum enter at the same level of importance in the
formulation of classical or quantum mechanics. This is reflected in the
invariance of Poisson brackets or quantum commutators under canonical
transformations, which I regard as a global symmetry. A gauge symmetry can be
defined in phase space (X,P) that imposes equivalence of momentum and position
for every motion at every instant of the worldline. One of the consequences of
this gauge symmetry is a new formulation of physics in spacetime. Instead of
one time there must be two, while phenomena described by one-time physics in
3+1 dimensions appear as various shadows of the same phenomena that occur in
4+2 dimensions with one extra space and one extra time dimensions (more
generally, d+2). The 2T-physics formulation leads to a unification of
1T-physics systems not suspected before and there are new correct predictions
from 2T-physics that 1T-physics is unable to make on its own systematically.
Additional data related to the predictions, that provides information about the
properties of the extra 1-space and extra 1-time dimensions, can be gathered by
observers stuck in 3+1 dimensions. This is the probe for investigating
indirectly the extra 1+1 dimensions which are neither small nor hidden. This 2T
formalism that originated in 1998 has been extended in recent years from the
worldline to field theory in d+2 dimensions. This includes 2T field theories
that yield 1T field theories for the Standard Model and General Relativity as
shadows of their counterparts in 4+2 dimensions. Problems of ghosts and
causality in a 2T space-time are resolved automatically by the gauge symmetry,
while a higher unification of 1T field theories is obtained. In this lecture
the approach will be described at an elementary worldline level, and the
current status of 2T-physics will be summarized.
