### In Search of the Least Mass …

I got to wondering a couple of weeks ago, what is mass? What is the smallest possible amount of mass that theoretically could exist?

It is thought the least massive particles we are aware of are the lightest of the 3 “flavors” of neutrino, in the range of 1/2 to 1 electron-volt.

Then in the pool tonight I got to wondering about E=mc^2. If a photon’s rest mass is 0 (since its frame of reference is the speed of light, its mass must be 0), what is the energy of a photon that would collapse its time-space neighborhood to a black hole?

That turns out to be satisfyingly straightforward — the least possible wavelength is a planck length, whose energy corresponds to a planck mass. This energy bundle would be the smallest possible black hole, having a Schwarzschild radius of 1 planck length. (I say would be, because it’s not clear how such a photon could be created.)

This doesn’t bring any light to the question about the least mass. But at least it’s worth pursuing, as there is a Clay Institute million dollar Millenium Prize attached to a mathematical description of the solution.