## Physics Questions People Ask Fermilab

Speed of Light

You Wrote:

Why can't anything travel faster then the speed of light!!?

Dear Meherdad,

The mathematical formula in the special theory of relativity that gives the energy, E, of a particle in terms of its mass, m, and its velocity, v, is E = mc^2/sqrt(1-v^2/c^2). (c is the speed of light, sqrt means square root, and ^2 means squared.) For a particle with velocity 0, this is just the famous E = mc^2 formula for the rest energy of a material particle. The amount of energy you need to give a particle to accerate it to a velocity v is given by the formula. No matter how much energy you pump into a particle, you make it closer and closer to the speed of light, but it never gets there.

An example of this occurs in high energy accelerators like Fermilab's. We pump energy into protons by passing them through radio-frequency cavities. At the maximum, they have energies of nearly a trillion electron volts, which is a thousand times larger than their rest energies. Their velocities are almost the speed of light to within one part in a million, but they are still smaller than c and would stay smaller no matter how much energy we could add.

Two books on special relativity that might have more information are "Relativity for the Millions", by Martin Gardner, and "The ABC of Relativity", by Bertrand Russell.

Regards,

Paul Mackenzie

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