From Backreaction: Dear Dr B: If photons have a mass, would this mean special relativity is no longer valid?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 …
- Make time a coordinate rather than a parameter. That produces 4 dimensional space time.
- Call that Minkowski space.
- Require that laws of physics be the same for all observers moving at constant velocity in Minkowski space (inertial observers).
- Mathematically, that means symmetry transformations are required. The group of these transformations is called the Poincaré group.
- The Poincaré group (again, math) has two subgroups. One is translation — all space-time points have same physics. That one is not so interesting.
- 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.