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 (XM,PM). 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 AdS5 x S5 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.