Possibly even right

1
Possibly even right

• Noncommutative Geometry
• and the real world

2
According to some strings are not even wrong

• They are at best a mathematical theory without
  any possibly verifiable connection with the real
  world
• Are we like them or can we be wrong?
• Can we be right?
• What do I mean by Noncommutative Geometry?

3
Where do we come from?

• Quantum Mechanics (Heisenberg, Dirac, Von Neumann
  Moyal)
• Mathematics (Gelfand, Connes)
• Strings (Frohlich, Seiberg, Witten)
• Quantum Field Theory- Structure of space time at
  Planck lenght (Doplicher, Fredhenagen, Wess.)

4
Where can we go?

• Mathematics
• There have been lots of successes in mathematics
• This is a noble activity, and apart that it may
  create problems with funding agencies I see
  nothing wrong in doing it
• Or we may do physics

5
Connes standard model

• It is nor really noncommutative, the structure of
  spacetime is unchanged
• It makes predictions testable at LHC

6
?-Minkowski

• It is an Hopf Algebra with a rich structure
• It has non trivial dispersion relations
• They could help explain some astronomical
  observations of ? ray burst
• The dispersion relations depend on the basis!

7
Moyal Plane

• Consider ? as a background tensor
• Most of the effects are a consequance of Lorentz
  non invariance
• Accelerator experiments (Trampetic, Ohl)
• Cosmology. Inflation makes a huge amplification
  of short distance effects (up to 1013 GeV at
  Planck)

8
T-Poincaré

• We still have a (deformed) Lorentz Invariance
• We can study deformations of Gravity (al et Wess)
• Spin Statistics

9
Are we mature enough to make predictions?