Wednesday, November 05, 2008

The speed of light

“What are you reading?” she asked me idly in the kitchen.

“I’ve just finished the unit on special relativity and I’m starting on the general relativity unit.”

“Didn’t I see in your latest ‘New Scientist’ that Einstein was wrong about that?”

That tabloid headline had already caused irritation out there in the physics blogosphere. The subject was the role of the speed of light, c, in the Lorentz transformation of special relativity. Generations of students have wondered what the connection is between space-time topology (Minkowski space) and the propagation speed of electromagnetic radiation.

It has been known for many years that the Lorentz transformation requires a constant β in its transformation matrix. This implies a maximum velocity, as explained in the physics blog Backreaction here. It’s then a subsequent piece of inference (from Maxwell’s equations) to identify that velocity with the speed of light (β = v/c). Even the 1996 Open University text I’m studying has a section clarifying this two-step argument.

So it was ludicrous hyperbole for New Scientist to pretend that this thought was new.

“Yes, but it’s a bit of silliness they put in to sell newspapers. Do you remember special relativity?”


I am already doubtful about this, but I launch into a simple version of the discussion above, as she carries some washing out into the utility room. I get to the bit about the Lorentz transformation being a parameterised orthogonal transformation in Minkowski space.

“Why are you following me around?”

“Well, I was just getting to the crucial bit of the argument – why the New Scientist hype was nonsense.”

“I have no idea what you’re talking about. Do yourself a favour. Just stand in the kitchen and continue talking. I really won’t mind.”