Extra Dimensions in Space and Time by Itzhak Bars and John Terning

Extra Dimensions in Space and Time is a wonderful find.  A few months ago, Randy and I talked about Itzhak Bars' 2T theory of space and time for a Physics Frontiers podcast (it's two podcasts up in the editing queue and will come out about a month from when I publish this), and it was one of the hardest this for us to get a handle on.  Randy is really excited about Bars' theory (and not just because he went to USC), but reading the papers he selected left us a little confused about how it worked.  When I saw that Springer had a book by Bars on the subject, I decided to take the $125.00 hit.  Maybe a longer form text would help me figure out what was going on, and maybe choose a couple of different papers for another podcast that were a little more understandable.

And I was pleasantly surprised by this book.

Extra Dimensions in Space and Time is the first in the Multiversal Journeys series, edited by Farzad Nekoogar.  This series of books is fulfilling the purpose of the Multiversal Journeys organization:
making theoretical physics easy for the public.  In that, the two halves of this book are non-technical introductions to their topics.  The first hundred pages, by Itzhak Bars, talks about a theory of particles and interactions that uses two different time-like dimensions. The next sixty pages, by John Terning, discusses what the proliferation of spatial dimensions in string theory means.  And they don't hurt your brain.

In Itzhak Bars' "Two-Time Physics: The Unified View from Higher Dimensional Space and Time," Bars discusses the reasons for his 2T physics.  This includes an insightful development of physics, including string theory itself, building up to the rationale for the second time dimension.  And then he discusses the implications of the theory.

Interestingly, two-time physics was the result of Bars' postulation of a symmetry.  His  postulate is this: there is a phase-space symmetry between different space-time dimensions without affecting the physics.  Any particular direction at any particular event can be swapped with any other.  Furthermore, this works with the energy-momentum tensor.  On top of that, an energy can be swapped with a time and a spatial dimension can be swapped with a momentum component.  Although his figure does not include cross arrows, I'd expect this to be true with the other possible reconfigurations.  He calls this the Sp(2,R) symmetry.

Again, physics does not change when you regard a spatial dimension as being time-like, as long as you switch a time dimension to be space-like.

If this symmetry is indeed a law of nature, like translational or rotational symmetries, then there must be two time dimensions (no more and no less) and four space dimensions (at least, maybe you can have more, I don't remember, but you can't have less) to prevent anomalies like ghost particles -- the real universe is the 4+2 universe.  These two extra dimensions are macroscopic, not the microscopic curled-in dimensions of string theory.  And this leads to all of the interesting physics.  The big, interesting analogy is that the universe you and I reside in, the 3+1 universe, is a holographic shadow of the 4+2 universe.  And it is the way in which 4+2 objects project into 3+1 space-time that determines how we view them.

The eight ways in which Bars had shown these objects to project into our space are as:

1. Dirac Particles 
2. Particles in a Robertson-Walker Universe
3. Massive Particles
4. Particles in Maximally Symmetric Spaces
5. The Hydrogen Atom
6. Particles in a Conformally Flat Space
7. The Harmonic Osciallator
8. Twistors

which isn't everything, but its a lot.

Bars claims for 2T-Physics are the following:

1. Sp(2,R) gauge symmetry of phase space is a fundamental property of nature.
2. 2T-field theory, free of ghosts, has be successfully constructed and applied.
3. Grand unified theories and supersymmetric 2T-field theory have been constructed as 2T-field theories.
4. 2T-physics provides new technical computation tools for 1T-physics.
5. 2T supergravity, 2T strings, 2T branes, 2T M-Theory are only partially constructed in 2T-physics at this time.
6. A deeper phase space formulation of field theory is likely to exist.
7. The extra space and time dimensions in 2T-physics are neither small nor hidden.

John Terning's "Extra Dimensions of Space" is of a similar level, if not anywhere near as weird.  This is because Terning focusses on the strings and branes in M-Thoery, and stays just as far away from the scary math, ending, more-or-less, at the Higgs.  When the book was written, in 2009, the Higgs particle hadn't been discovered at the LHC, but it was expected.  Although nowhere near as detailed and nowhere near as out there as Bars' discussion, Terning does a good job of explaining why you need something like a string theory, and why the string theories that are limits of M-Theory satisfy those issues.  

He builds up from the standard modern physics story, through symmetry and gravity, and then discusses string theory.  How do strings manifest as particles?  How do they interact with each other and with branes?  How do branes deform, and what are the implications of such a deformation?  Those are the questions Terning answers, just a little bit more exactly than you're used to in an equation-free account.

There is also a final chapter for those of you who feel like equation-free is to physics as Diet Pepsi is a Coca-Cola, "The Equations behind the Words."  The thing is, I expect that for most of you that are interested in the exactness that mathematics provides a concept, the equations provided are things you're already familiar with.

But since that's the 13th chapter, you're going to skip it anyway.

So, this is a great book, especially given my expectations from Bars' papers, and I recommend it to people who want a deeper understanding about the theories that require additional dimensionality for the world.  It's a step up from a popular book, and I think it's exactly the sort of thing that someone who listens to our podcast to enjoy.