## The Special Beards of Relativity

I’ve recently moved on to the part about Special Relativity in my module on Mechanics and Special Relativity and this afternoon I’m going to talk about the Lorentz-Fitzgerald contraction or, as it’s properly called here in Ireland, the Fitzgerald-Lorentz contraction.

The first thing to point out is that the physicists George Francis Fitzgerald and Hendrik Lorentz, though of different nationality (the former Irish, the latter Dutch), both had fine beards:

One of the interesting things you find if you read about the history of physics just before Albert Einstein introduced his theory of special relativity in 1905 was how many people seemed to be on the verge of getting the idea around about the same time. Fitzgerald and Lorentz were two who were almost there; Poincaré was another. It was as if special relativity was `in the air’ at the time. It did, however, take a special genius like Einstein to crystallize all that thinking into a definite theory.

Special relativity is fun to teach, not least because it throws up interesting yet informative paradoxes (i.e. apparent logical contradictions) arising from  that you can use to start a discussion. They’re not really logical contradictions, of course. They just challenge `common sense’ notions, which is a good thing to do to get people thinking.

Anyway, I thought I’d mention one of my favorite such paradoxes arising from a simple Gedankenerfahrung (thought experiment) here.

Imagine you are in a railway carriage moving along a track at constant speed relative to the track. The carriage is dark, but at the centre of the carriage is a flash bulb. At one end (say the front) of the carriage is a portrait of Lorentz and at the other (say the back) a portrait of Fitzgerald; the pictures are equidistant from the bulb and next to each portrait is a clock.The two clocks are synchronized in the rest frame of the carriage.

At a particular time the flash bulb goes off, illuminating both portraits and both clocks for an instant.

It is an essential postulate of special relativity that the speed of light is the same to observers in any inertial frame, so that an observer at rest in the centre of the carriage sees both portraits illuminated simultaneously as indicated by the adjacent clocks. This is because the symmetry of the situation means that light has to travel the same distance to each portrait and back.

Now suppose we view the action from the point of view of a different inertial observer, at rest by the trackside rather than on the train, who is positioned right next to the centre of the carriage as the flash goes off. The light flash travels with the same speed in the second observer’s frame, but this observer sees* the back of the carriage moving towards the light signal and the front moving away. The result is therefore that this observer sees the two portraits light up at different times. In this case the portrait of Fitzgerald is lit up before the portrait of Lorentz.

Had the train been going in the opposite direction, Lorentz would have appeared before Fitzgerald. That just shows that whether its Lorentz-Fitzgerald contraction or Fitzgerald-Lorentz contraction is just a matter of your frame of reference…

But that’s not the paradoxical thing. The paradox is although the two portraits appear at different times to the trackside observer, the clocks nevertheless display the same time….

*You have to use your imagination a bit here, as the train has to be travelling at a decent fraction of the speed of light. It’s certainly not an Irish train.

### 4 Responses to “The Special Beards of Relativity”

1. Wyn Evans Says:

Good though the beards of Fitzgerald & Lorentz are, I think those of Wilhelm Rontgen & Ludwig Boltzmann are still more luxuriant

2. You can simplify this down to saying that clocks that appear to be synchronized in the carriage FoR are not synchronized in the trackside FoR, and vice-versa.
…Of course, the disadvantage of this simplification is that you lose out on those fine beards 😄

3. “Emission theory, also called emitter theory or ballistic theory of light, was a competing theory for the special theory of relativity, explaining the results of the Michelson–Morley experiment of 1887…The name most often associated with emission theory is Isaac Newton. In his corpuscular theory Newton visualized light “corpuscles” being thrown off from hot bodies at a nominal speed of c with respect to the emitting object, and obeying the usual laws of Newtonian mechanics, and we then expect light to be moving towards us with a speed that is offset by the speed of the distant emitter (c ± v).” https://en.wikipedia.org/wiki/Emission_theory

Banesh Hoffmann, Einstein’s co-author, admits that, originally (“without recourse to contracting lengths, local time, or Lorentz transformations”), the Michelson-Morley experiment was compatible with Newton’s variable speed of light, c’=c±v, and incompatible with the constant speed of light, c’=c:

“Moreover, if light consists of particles, as Einstein had suggested in his paper submitted just thirteen weeks before this one, the second principle seems absurd: A stone thrown from a speeding train can do far more damage than one thrown from a train at rest; the speed of the particle is not independent of the motion of the object emitting it. And if we take light to consist of particles and assume that these particles obey Newton’s laws, they will conform to Newtonian relativity and thus automatically account for the null result of the Michelson-Morley experiment without recourse to contracting lengths, local time, or Lorentz transformations. Yet, as we have seen, Einstein resisted the temptation to account for the null result in terms of particles of light and simple, familiar Newtonian ideas, and introduced as his second postulate something that was more or less obvious when thought of in terms of waves in an ether.” Banesh Hoffmann, Relativity and Its Roots, p.92 https://www.amazon.com/Relativity-Its-Roots-Banesh-Hoffmann/dp/0486406768