Image courtesy of The Israel Museum, Jerusalem (Click on image for larger version.)

This page is from a section entitled “Equations of Motion of the Material Point.” Einstein shows how the most basic freshman-physics equations must change to fit the new world.

In the bottom paragraph, m is an object’s mass, q its speed, and c is the speed of light in the vacuum. The text, continuing on the next page, reads: “The expression within the brackets on the right plays the role of the energy E of the moving mass point. This expression: [formula 28] grows to infinity when q approaches the value c; thus, it would require an infinite expenditure of energy to impart the velocity c to the body.”

That is why even today’s highest-energy particle accelerators can only push particles to approach — but never equal or surpass — the speed of light.

The old Newtonian formula, gives zero if q is zero. Here, for q=0 the formula reduces to a special case, called rest energy: E=mc².

Click here to download the pdf version of this article.

Click here for the "Logbook" archive.