The Relativistic Energy of Light

Weirdly enough, the final pages (section 8) of Einstein’s 1905 relativity paper, relate to the energy of light.  Miller observes (page 309) that these three pages are Einstein’s tour de force:

In the three pages of section 8, Einstein deduced the energy of a light complex (a relativistic blob of light – not explicitly a light quantum), and then solved exactly the problems of determining the characteristics of plane waves incident on a perfectly reflecting surface that is in inertial motion with velocity v, and of calculating the pressure of light on this surface.

And that’s not all, as Miller notes on page 311, he also notes how the energy of the light complex relates to other spacetime frames and that the ratio of wavelength (frequency) to energy is always the same.

Of course, Einstein had already proposed the light quantum in another paper (on the photo-electric effect) in 1905.  A similar notion occurs in this section of the relativity as the relation between different pulses of light so he briefly covers the same ground (of light energy) from a slightly different, less “revolutionary” angle.  Einstein regarded the light quantum as the more “revolutionary” of the two proposals and he seems to have been right.  The core group of particle physicists had accepted relativity by 1911, but the light quantum was not generally accepted until the late 1920s even by that core group.  So relativity was accepted in six years and the light quantum – not for around 20 years. For that matter, General Relativity was accepted around a decade before the light quantum.  I hope not to go much into General Relativity – I’m hoping to head into the light quantum as soon as relativity and the aether are eased into their relatively final historical roles  — one steadily replacing the other phenomenologically in the experimental realm.

Since, within a few more posts, this blog (hopefully) will reach Minkowski’s rigorous (1908-1909) 4-dimensional mathematics of special relativity  ( and the 4-vector – noted by Sommerfeld in reviews of Minkowski’s work in 1910) this might be a good time to offer a look at Einstein’s section 8 in terms of light cones.

First the light cone as a pulse (with the future going up the page and the causal past down the page):

And the light cones of two different pulses with the ellipsoidal shape of their comparative relations in spacetime: