Sunday, May 15, 2016

Special relatively predicts the photon: Minkowski:Poincaré:Lorentz:Boosts from 2 assumptions & math.

From Backreaction: Dear Dr B: If photons have a mass, would this mean special relativity is no longer valid? I learn that while Einstein may have created Special Relativity with light in mind he could have done it in the dark.

To summarize …

  1. Make time a coordinate rather than a parameter. That produces 4 dimensional space time.
  2. Call that Minkowski space.
  3. Require that laws of physics be the same for all observers moving at constant velocity in Minkowski space (inertial observers).
  4. Mathematically, that means symmetry transformations are required. The group of these transformations is called the Poincaré group.
  5. The Poincaré group (again, math) has two subgroups. One is translation — all space-time points have same physics. That one is not so interesting.
  6. The other Poincaré group is called the Lorentz-group. It has rotations and boosts. Rotations in space aren’t so interesting, they just say all directions are the same. Boosts are rotations between space and time. Minkowski:Poincaré:Lorentz:Boosts give us length and time contraction and the like.

and so

Deriving the Lorentz-group …  is a three-liner … it is merely based on the requirement that the metric of Minkowski-space has to remain invariant … the  boosts depend on a free constant with the dimension of a speed. You can further show that this constant is the speed of massless particles.

… if photons are massless, then the constant in the Lorentz-transformation is the speed of light. If photons are not massless, then the constant in the Lorentz-transformation is still there, but not identical to the speed of light…. 

Giving a mass to photons is unappealing not because it violates special relativity – it doesn’t – but because it violates gauge-invariance, the most cherished principle underlying the standard model. But that’s a different story and shall be told another time.

Perhaps (this is me writing) another way of thinking about this is that making time a coordinate, and requiring physics have inertial constancy, gives us, through math, the properties of a massless particle. So if we didn’t already have personal experience with photons, we’d know what to look for. When we found them we’d then say that our science made a great prediction…

I’m really looking forward to Dr. Hossenfelder’s explanation of Gauge-invariance.

PS. OS X insists in quietly auto-correcting photons to photos.

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