__Two-Time
Physics (2T-physics)__

Starting with the 1998
formulation of Two-Time Physics (2T-physics), which was inspired by 2T notions in
earlier papers since 1995, evidence has been mounting that the ordinary
formulation of physics, in a space-time with three space and one time
dimensions (1T-physics), is insufficient to describe our world.

A one-page summary of the
concepts of 2T-physics can be found in this diagram (not up to
date) with related narrative below. For technical information please refer to
my original papers.

According to the body of work
in 2T-physics,
there is more to space-time than can be garnered with 1T-physics. 2T-physics
introduces additional one space and one time dimensions, which can coexist with
the familiar 3+1 dimensions as well as extra space dimensions of tiny sizes
known as Kaluza-Klein-type dimensions, but the new ones have
very different properties. First of all, the extra 1+1 dimensions in 2T-physics
are not small. However, there are gauge symmetries that effectively reduce
2T-physics in 4+2 dimensions to 1T-physics in 3+1 dimensions without any Kaluza-Klein remnants. The reduction is not unique because
there is an infinite variety of 3+1 embeddings in 4+2 dimensions (more
generally (d-1)+1 in d+2), and this is what is
non-trivial and rich in emergent space-times and 1T-physics content.

To help grasp the relation
between 1T-physics and 2T-physics, consider the many possible shadows of a 3
dimensional object projected from different perspectives on the surrounding
walls of a 3-dimensional room. A flatlander that can crawl and measure only on
the surface of the walls would think that the shadows of different shapes are
different “beasts” and move differently. Similarly, even though according to
2T-physics a unique dynamical system in 4+2 dimensions generates a large
variety of 1-time “shadows”', 1T-physics presents these “shadows” in 3+1
dimensional space-times as different dynamical systems in terms of different
Hamiltonians (different times).

In this way 1T-physics misses
the underlying relationship between the “shadows” as well as the underlying
properties (e.g. symmetries) of the higher dimensional space-time. Actually, it
turns out that each “shadow” is a holographic image that retains all the
information of the d+2 structure. This information takes the form of hidden
symmetries, dualities and other non-trivial structures, which are hard to
notice by the 1T physicist that investigates the “shadows” (i.e. different dynamical
systems). But he/she could in principle discover the hidden information.
2T-physics provides the missing information to the 1T physicist who can verify
by experiment or computation that indeed the d+2 structure of space-time
governs all levels of physics, from macroscopic to microscopic scales, in
classical and quantum systems, including the fundamental physics of quarks,
leptons and force particles described by the Standard Model of Particles and
Forces, and beyond.

The permitted motions in 4+2
phase space are highly symmetrical, as they are constrained by a Sp(2,R) gauge symmetry that makes momentum and position *indistinguishable
at any instant*. Such Sp(2,R) symmetric motions in
4+2 dimensions are completely compatible with the way physics is perceived in
3+1 dimensions. In particular, there are no problems with causality or unitarity because the extra 1+1 space-time (chosen in
distinguishable ways from the point of view of 1T-physics) is removable by the
gauge symmetry.

The two timelike
dimensions were not introduced whimsically “by hand”. As mentioned above,
2T-physics is based on gauging the symplectic
transformations Sp(2,R) acting on phase space (X^{M},P_{M}).
One of the fundamental results of this new gauge principle is that, in order to
be nontrivial, it requires the theory to be formulated in a spacetime
having at least two times. While taking exactly two timelike
dimensions produces a coherent theory, investigations of alternatives with more
than two times have been done (including alternatives to Sp(2,R)).
So far such possibilities are ruled out because of problems with ghosts and unitarity, and this seems to confirm the special status of
2T-physics.

Recently, a field theoretic
description of 2T-physics has been established. Amazingly, the best understood
fundamental theory in Physics, the Standard Model of Particles and Forces (SM)
in 3+1 dimensions, is reproduced as one of the “shadows” of a parent field
theory in 4+2 dimensions. But even more amazing is that this *emergent SM*
has better features than the ordinary SM in 1T-physics. Among the successes of
the emergent SM is the resolution of the strong CP problem of QCD due to the
more constraining structure of the underlying 4+2 theory. This suggests that
the so far elusive axion need not exist at all, since the issues in the
fundamental theory are resolved with the gauge mechanisms of 2T-physics. The
emergent SM agrees with all aspects that actually work experimentally so far in
the usual SM.

The field theoretic studies
of 2T-physics have been generalized to supersymmetric field theory with N=1,2,4
supersymmetry. It is expected that the more
constraining structure of the underlying 4+2 theory has phenomenological
consequences that would be relevant to distinguish 2T-physics from other
approaches in experiments at the LHC starting in 2008, if supersymmetry
is found experimentally at the TeV scale.

The field theory version of
2T-physics suggests new emergent principles in field theory. These have been
enunciated in a paper
that explores dual field theories in (d-1)+1
emergent spacetimes from a unifying field theory in d+2 spacetime.

Prior to recent success in
field theory, the work on 2T-physics since 1998 had mostly concentrated on the worldline formalism of particles, and had demonstrated that
2T-physics stands above 1T-physics as a structure that encompasses and explains
phenomena which appear very surprising from the point of view of 1T-physics.

The prior work on 2T-physics
during 1998-2004 extended the initial concepts in several directions, including
spinning
particles, supersymmetry, and interactions of particles with background
fields (electromagnetism, gravity, and all higher spin fields). Covariant
quantization of 2T systems led to field
theoretic equations of motion but without an action principle, and a non-commutative
approach was developed for 2T-field theory in phase space. There was also some
limited work on the world-sheet or world volume level for the 2T-physics
formulation of strings
and branes. Some hidden 10+2 or 11+2 structures in supergravity and
M-theory, in the AdS_{5}
x S^{5} and other compactifications, were
also identified and explained as features of 2T-physics.

After some excursions into
String Field Theory during 2001-2004 to explore non-commutative aspects,
extensive research on 2T-physics resumed in 2004-2005. This was sparked by the twistor
superstring and its relation to the twistor gauge of 2T-physics. New
unifying roles for twistors were discovered and a new approach to spinning
particles led to a new hidden SU(2,3) duality symmetry that includes conformal
symmetry SU(2,2).

These older results, along
with the more recent field theory successes mentioned above, have established
that 2T-physics is a structure that correctly describes, at least in principle,
all the physics we have understood up to now. But 2T-physics emerged also as a
unification scheme that suggests the existence of new relationships and new
phenomena that are not even hinted by 1T-physics and which remain so far
largely unexplored both theoretically and experimentally.

This 2T-physics point of view
provides new mathematical tools and new insights for understanding our
universe. It also suggests a new paradigm for the construction of a
fundamental theory that is likely to impact on the quest for unification.

For systems that are already understood, 2T-physics tells us that the
description of dynamics via the usual 1T-formalism should be interpreted as
emergent dynamics that holographically represents an
image of a deeper higher dimensional structure in one extra space and one extra
time. A lot more work awaits to be done in this
direction to reveal the hidden dimensions in various 1T systems, including in
the field theory formalism. Ultimately we expect 2T-physics to be useful not
only for insights into the deeper structures, but also as a calculational
tool that takes advantage of the dualities
and hidden symmetries in 1T-physics field theory.

For systems that are not yet understood or even constructed, such as M-theory,
2T-physics points to a possible approach for a more symmetric and more
revealing formulation in 11+2 dimensions that can lead to deeper insights,
including a better understanding of space and time. The 2T approach could be
one of the possible avenues to construct the most symmetric version of the
fundamental theory.