What is Special Relativity?

I got issues. Here’s one. I don’t like what people say about special relativity. Because we’re friends, special relativity and I.

I got issues with certain people in particular, those writing popular science books. Sometimes I feel like have to thank every physicist who takes the time to write a book. But, well, I got issues. Also, I got sunglasses and a haircut, see photo.

I presently read “The Universe in the Rearview Mirror” (disclaimer: free copy) and here we go again. Yet another writer who gives special relativity a bad name.

Here’s the issue.

Ask some theoretical physicist what special relativity is and they’ll say something like “It’s the dynamics in Minkowski space” or “It’s the special case of general relativity in flat space”. (Representative survey taken among our household members, p=0.0003). But open a pop science book and they’ll try to tell you special relativity applies only to inertial frames, only to observers moving with constant velocities.

Now, as with all nomenclature it’s of course a matter of definition, but referring to special relativity as being only good for inertial frames is a bad terminology, and not only because it doesn’t agree with the modern use of the word. The problem is that general relativity is commonly, both among physicists and in the pop sci literature, referred to as Einstein’s theory of gravity, rubber sheet and all. Einstein famously used the equivalence principle to arrive at his theory of gravity and that principle says essentially: “The effects of gravity are locally indistinguishable from acceleration in flat space.” With the equivalence principle, all you need to do is to take acceleration in flat space and glue it locally to a curved space, and voila there’s general relativity. I’m oversimplifying somewhat, all right, but if you know a thing or two about tensor bundles that’s essentially it.

The issue is, if you don’t know how to describe acceleration in flat space then the equivalence principle doesn’t gain you anything. So if you’ve been told special relativity works only for constant velocities, it’s impossible to understand all the stuff about angels pulling lifts and so on. You also mistakenly come to believe that to resolve the twin paradox you need to take into account gravity, which is nonsense.

Yes, historically Einstein first published special relativity for inertial frames, after all that’s the simplest case, and that’s where the name comes from. But the essence of special relativity isn’t inertial frames, it’s the symmetry of Minkowski space. It’s absolutely no problem to apply special relativity to accelerated bodies. Heck, you can do Galilean relativity for accelerated bodies! All you need is to know what a derivative is. You can also, for that matter, do Galilean relativity in arbitrary coordinate frames. In fact, most first semester exercises seem to consist basically of such coordinate transformation, or at least that’s my recollection. So don’t try to tell me that the ‘general’ of relativity has something to do with the choice of coordinates.

So yes, historically special relativity started out being about constant velocities. But insisting – more than 100 years later – that special relativity is about inertial frames, and only about inertial frames, is like insisting a telephone is a device to transfer messages about cucumber salad, just because that happened to be the first thing that ever went through a phone line. It’s an unnecessarily confusing terminology.

Since special relativity is busy boosting your rocket ships with laser cannons and so on, on her* behalf I want to ask you for somewhat more respect. Special relativity is perfectly able to deal with accelerated observers.

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*German nouns come in three genders: male, female and neuter. Special relativity, or theory in general, is a female noun. Time is female, space is male. The singularity is female, the horizon is male. Intelligence is female, insanity male. Don’t shoot the messenger.