09 May 2005


I always imagined that this equation would appear somewhere in Einstein's original paper. But not so. Here's the relevant text (he uses V instead of c to denote the speed of light):
If a body gives off the energy L in the form of radiation, its mass diminishes by L/V2. The fact that the energy withdrawn from the body becomes energy of radiation evidently makes no difference, so that we are led to the more general conclusion that:

The mass of a body is a measure of its energy-content;; if the energy changes by L, the mass changes in the same sense by L/9×1020, the energy being measured in ergs, and the mass in grammes.

One thing that struck me is how Einstein's approach today feels dated, belonging to a time (perhaps the last time) when you could do physics without knowing so much math. Or maybe it was just Einstein who could jump to such broad conclusions from one thought experiment involving radiation emitted by a slowly moving object. It's as though he knew the answer all along and just gave us an example to illustrate the point.

For example, today people favor the mathy Lorentz approach because it shows energy and momentum form a covariant 4-vector just like time and position do. So massless particles satisfy E=cp and light carries momentum. But Einstein saw this (and more) immediately with no intervening math! The next (and final) two sentences of the paper are:

It is not impossible that with bodies whose energy-content is variable to a high degree (e.g. with radium salts) the theory may be successfully put to the test.

If the theory corresponds to the facts, radiation conveys inertia between the emitting and absorbing bodies.

[Here's Einstein's first paper on special relativity.

Another old paper worth finding is the one where Born's rule that probability is the absolute value of the wavefunction squared is introduced wrong in the main text, and then later corrected in a footnote. I can't find it online, but the cite is Born, M., 1926a, Zeitschrift für Physik 37, 863; translated in (Wheeler, 1983), pp. 52-55. See also Born, M., 1926b, Zeitschrift für Physik 38, 803. and Born, M., 1927, Nature 119, 354.]

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