Re: [Phys-L] Status of Superstring and M Theory?

[John Denker <jsd@av8n.com>]

On 3/13/19 9:18 AM, Don asked:

> 1) Is superstring or M theory now well accepted by most theoretical
> physicists, so we do, in fact, have a theory of everything?  

The word "theory" has many different meanings, depending on
context.  Superstrings in general and M-theory in particular
are theories in the weakest sense of the word.  They're lots
better than nothing, but they are still works in progress.

> Or is superstring/M theory still the only consistent mathematical
> development which can both quantize gravity and integrate it with the
> other forces but still lacks firm experimental verification?

There is no proof that any of these theories are even theoretically
self-consistent.  Plausible, yes, interesting, yes,proven, no.  On
top of that, they are notorious for the lack of experimentally-
testable predictions.
 
> 2) Is there an "undergraduate" level "explanation" of superstring/M
> theory somewhere in the middle between Pythagorean theorem level mathematics
> and the full blown complex mathematics required for complete understanding?

Here's a hands-on model to consider.  Start with a Shive torsion
wave machine:
  https://www.youtube.com/watch?v=DovunOxlY1k
or the home-made backyard version:
  https://www.youtube.com/watch?v=eY265Ml7ZGM

Then modify it so the arms are very lopsided, so they are pendulums,
with a strong gravitational restoring force on each arm, and a
relatively weak torsional coupling from arm to arm.  You can still
propagate waves along such a machine.  Assume /fixed/ boundary
conditions at each end.
  https://www.youtube.com/watch?v=J4LcJ4vwXbk

The buzzword here is sine-Gordon wave equation.  The name is
partly an homage to Klein-Gordon wave equation, but I digress.

Now (!) apply a 360° rotation to one boundary.  This creates a
/soliton/.  In fact it is a /topologically conserved/ soliton.
You can cause the soliton to move from place to place, but you
cannot destroy it (not without changing the boundary conditions).
  https://www.youtube.com/watch?v=SAbQ4MvDqEE

You can however create (or destroy) *pairs* i.e. particle-
antiparticle pairs, by grabbing an arm somewhere in the
middle and flip it over 360°.

This exhibits the idea that you can sometimes use /topology/
to explain conservation laws.  This idea is one of the main
foundations of string theory.

I'm not saying this will be an easy lesson.  It will take a
ton of explaining beyond what I've said here.  For starters,
keep in mind that the students probably have no clue what the
word "topology" means.  Or what the word "soliton" means.

OTOH there is tremendous upside if you can make this work.
It will reinforce and expand their understanding of what a
wave is, and of what "conservation" means.

For extra credit, note that the topological idea is easiest
to visualize using one or more /extra dimensions/.  The model
is one dimensional, in the sense that the wavefunction is a
function of one variable, but topological conservation applies
to something that is going on in a perpendicular dimension,
i.e. the torsional angle.  Extra dimensions are a famous
feature of string theories.

This is the best tradeoff I can come up with, combining some
teachability and learnability with some faithfulness to the
fundamental physics.