Two time dimensions?

[Startraveler]

There've been a number of physical theories that have toyed around with adding extra spatial dimensions to the universe but this one adds an extra time and an extra space dimension.

AIP:

Time and Time Again

The physics world accepts the idea of spacetime, a combined metrical entity which puts time on the same footing as the visible three spatial dimensions. Further spatial dimensions are added in some theories to help assimilate all physical forces into a unified model of reality. But what about adding an extra dimension of time too? Itzak Bars and Yueh-Cheng Kuo of the University of Southern California do exactly that, and add an extra spatial dimension too.

Bars explains this proposal with a comparison. Just as a projection of a 3D object onto a 2D wall can have many different shapes, and each such shape is incapable of fully conveying all the properties of the 3D object, so the single-time description of dynamics in the standard formulation of physics is insufficient to capture many properties of dynamical systems which have remained mysterious or unnoticed.

The addition of an extra time and an extra space dimension, together with a requirement that all motion in the enlarged space be symmetric under an interchange of position and momentum at any instant, reproduces all possible dynamics in ordinary spacetime, and brings to light many relationships and hidden symmetries that are actually present in our own universe.

The hidden relationships among dynamical systems are akin to relationships that exist between the multiple shadows of a 3D object projected on a 2D wall. In this case the object is in a spacetime of 4 space and 2 time dimensions while the shadows are in 3 space and 1 time dimensions. The motion in 4+2 dimensions is actually much more symmetric and simpler than the complex motions of the shadows in 3+1 dimensions.

Besides the general unification of dynamics described above, what does this addition to one extra time and one extra space dimension (in addition to all those extra space dimensions called for in string theory) accomplish that could not be achieved without it? Bars (bars@usc.edu) says that his theory explains CP conservation in the strong interactions described by QCD without the need for a new particle, the axion, which has not been found in experiments.

It also explains the fact that the elliptical orbit of planets remains fixed (not counting well-known tiny precessions). This “Runge-Lenz” symmetry effect has remained somewhat mysterious in the study of celestial mechanics, but now could be understood as being due to the symmetry of rotations into the fourth space dimension.

A similar symmetry observed in the spectrum of hydrogen would also be accounted for in 2-time physics, and again explained as a symmetry of rotations into the extra space and time dimensions. There are many such examples of hidden symmetries in the macroscopic classical world as well as in the microscopic quantum world, Bars argues, which can be addressed for the first time with the new 2T formulation of physics.

There have been previous attempts to formulate theories with a second time axis, but Bars says that most of these efforts have been compromised by problems with unitarity (the need for the sum of all probabilities of occurrences to be no greater than 1) and causality (maintaining the thermodynamic arrow of time).

The USC theorists have reformulated their model to fit into the ongoing supersymmetry version of the standard model and expect their ideas to be tested in computer simulations and in experiments yet to come. (Physical Review Letters, upcoming article)

[Invader Skoodge]

Very interesting.

There is a text about the connection between the Kepler problem and the SO(4) rotation group on Wikipedia. Now Bars and Kuo have an even more symmetric description by also using an additional time dimension.

I do however not see how this can be a physical theory. I'd rather think it's like, for exaple, eigenvectors with complex-valued components. They're good to simplify the mathematics, but you don't consider them an actual possibility of our physical space.

But no matter if it's physics or maths. It surely will be fun to have more time -- a full dimension more of time to do all those calculations which used to be so complicated.

Now, when will I see the first 2-->4 ephemeris tables?

[Startraveler]

I agree it's difficult to wrap one's mind around how this could be physically true. But you never know what the implications are going to be. it's interesting (given the subject of this thread) that you'd bring up the fact that eigenvectors can take on complex-values because the complex nature of state vectors seems to be some reflection of their time structure. That is, since the time reversal (Wigner) operator turns out to be complex conjugation we start to see new symmetries in time. Related, seemingly unphysical concepts but perhaps there's more going on than meets the eye.

The whole does raise an interesting question that borders more on philosophy than science. How much of the mathematics is just a device and how much actually reflects something physical about the universe? If someone throws in a second time dimension and it makes the physics flow a bit easier does that imply that a second time dimension exists in some sense? Or just that things work as if that were the case?