Pedestrian Physics 6

Einstein and the Mass/Energy relation

Following his first paper on relativity, Einstein came out swinging. Shortly after his magnum opus he published the paper that secured his immortality.

In a few terse paragraphs he

established that kinetic energy contributed to
the mass of a moving body

established the value of this contribution

stipulated that what was true for kinetic energy
should be true for all forms of energy

suggested that “the new radium salts” might offer a
means to test these hypotheses.

To call this paper “earth-shattering” would not be a metaphor.

*********
Einstein proved that two supposedly identical photons, leaving in opposite ditection from a moving body, had unequal momentum, He postulated that the speed of the photons would have the same value c both systems. To explain their difference in momentum he assigned them different intrinsic energy (i.e frequency) values, It is a tough sell but he closed the deal.

**********
According to Ritz,the velocities are uneven and the photons unchanged: Let m represent the hypothetical mass of the photon. The two photons have the momenta m(c+v) and m(c-v). The difference is 2mv, The conservation law requires that the emitting body must have lost an equivalent momentum. Since its speed is unchanged it must be perceived as having lost mass.

The lost kinetic energy of the source is e = mv². The total energy of the departing photons is

0.5 m(c+v)² + 0.5 m(c-v)² = mc² + mv² .

Hence, the lost (non-kinetic) mass from the body represents an energy

e = mc²

At first blush it appears that the Ritz derivation has an aesthetic advantage. It avoids Einstein’s fudge factor: “Neglecting magnitudes of fourth and higher orders”

There is a catch, though. The term e = mv² for kinetic energy is an approximation. We were not supposed to know that ahead of time; an iteration is necessary.

The relativistic mass correction is ƒ. The kinetic energy lost by the body is

m(ƒ- 1)c².

The total energy delivered to the photons is mƒc². The difference, mc² , is the energy equivalent of the residual (non-kinetic) mass lost by the source.

The significant insight is that the magnitude of the momentum vector implies a loss of mass at the source. However the vector is parsed, the result is the same.

Einstein’s axiom is a thing of beauty. I want it to be perfect without hidden flaws in any shape or form; least of all with a rounding error. Ritz looks better to me, the more I see of him.

Ritz’s argument is reversible. Return the photon to the body and it will repay the borrowed mass. I have not been able to run Einstein’s thought experiment in reverse.