Special & General Relativity Questions and Answers
In the problem of the marshmallow moving at the speed of light, didn't you forget about its kinetic energy?
Sure I did. I only included the rest mass energy because for the real world, it is hard to accelerate large objects to speeds higher than 1/2 the speed of light, and it is only at those speeds that the kinetic energy term becomes important relative to the rest mass. The total energy is just:
2 2 2 E = ( mc^2 ) + (pc) or 2 E = gamma x mc where 1 gamma = ----------------- 1/2 ( 1 - (v/c)^2 )
OK...If you want to suppose that you could accelerate a marshmallow to the speed of light, you end up with a gamma = infinity, and it's for sure that the Earth is a gonner. Then again, to get the marshmallow to that speed exactly, you will have had to 'burn up' the entire universe and then some to give the marshmallow this speed. Even a marshmallow traveling within 1 percent of the speed of light, will have a gamma of only 12.2 ! This is enough to give engineers a headache, and barely enough to cause a medium-sized crater!
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All answers are provided by Dr. Sten Odenwald (Raytheon STX) for the NASA Astronomy Cafe, part of the NASA Education and Public Outreach program.