do photons have mass? i always assumed that since they have no rest mass, they have no mass. i wanted to find out so i did a little math.
i took [math]E=hf[/math] and [math]E^2=m^2c^4+p^2c^4[/math] and put them togather. i got [math]m=\frac{hf}{{c^2}{(1+c^2)^{\frac{1}{2}}}}[/math]. when i solved, i found that the mass was zero. i took a closer look and saw that that wasn't true, for if i put 0 in for m, the photon would have 0 energy.
then i decided to put in a stupidly high value for the frequency and i found it DID have mass. it is just so close to 0 at normal frequencys that you don't need to worry about it.
i decided to pick a mass and find the frequency. i chose 1 nanogram. i got 4.07x10^46hz. that brings me to my question.
the highest frequencys i know of are terahertz rays. is there an upper limit on photon frequency?