A new paper revives a hero from physics’s past
, or “thought experiments”, conducted in imaginary versions of the real world. He used them to test ideas that observation could not confirm. But it is also possible to do imaginary experiments in worlds which are themselves imaginary, and thus to illuminate reality in a novel way. This was a particular skill of another 20th-century physicist, George Gamow, who explained his subject to the laity via a Mr Tompkins and his adventures in alternative wonderlands.
In the first of these tales Mr Tompkins dreams of a place where the speed of light is about that of a bicycle. How would a cyclist in such a world look to a watching pedestrian? Gamow’s answer was that the cyclist would shrink from back to front, and the faster he travelled the more slowly his pedalling feet would revolve. Gamow’s cyclist is compressed by an effect called the Lorentz contraction and his pedalling is affected by a slowing of the clock known as time dilation.
The first modification to Mr Tompkin’s dream came in 1959, two decades after his debut. A British mathematician called Roger Penrose calculated that he would actually have seen approaching cyclists as being elongated along their direction of motion, contracting only as they receded. Yet more peculiarly, as they drew abreast of him they would appear rotated, as if somehow cycling sideways with their backs turned to him.
The Doppler effect is a velocity-dependent change in frequency which makes light from an approaching object appear bluer than it would were its source stationary, and that from a receding object redder. So, not only will a cyclist approaching our hero be unfeasibly elongated, he will also be blueshifted so far as to be invisibly ultraviolet. He will thus appear as a black silhouette looming out of the landscape.
This article appeared in the Science & technology section of the print edition under the headline "Cycling tricks"
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