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A friend of mine on Twitter, Aaron (a pseudonym), is an overseas, 16-year old boy, who seriously admires Albert Einstein and wants to become a physicist. He continually writes me (Ted, also a pseudonym) questions about the theory of relativity and related topics, and I am sending answers. In this series of blog posts, those questions and answers are reproduced with modifications. I am not an expert in the fields of physics related to relativity. So, my answers might contain errors. If you find any error, please do not hesitate to write a comment for the benefit, not only of the boy and me, but also of other readers.
Aaron: The object's mass is zero when it is traveling at the speed of light, right? Where does its mass go? Does it turn into energy?
Ted: Surely, what is traveling with the speed of light, i.e., the photon (the quantum of light and all other forms of electromagnetic radiation), has zero mass. It is to be noted that the photon always has zero mass and always flies with the seed of light. This property is known to belong to the photon only.*
Particles with masses different from zero, when they are at rest (rest masses), can be accelerated to speeds fairly close to the speed of light by the use of large accelerators such as the Large Hadron Collider in CERN. When the particle get higher speeds, the mass of the particle does not approach zero, contrary to your supposition, but becomes larger to make the total energy higher. As a result, no body with a nonzero rest mass can be accelerated to reach just the speed of light. This is explained below by the use of a few equations (clicking on the image, you can see a larger one). Thus, the situation in your question that an object with a finite rest mass would reach the speed of light does not happen.
* Neutrinos were once thought to have zero mass, but the experimentally established phenomenon of neutrino oscillation requires neutrinos to have nonzero masses. As for the experiment that suggested the possibility of neutrinos traveling faster than light, mention will be made in a later story of this series.(Originally written on February 28, 2011)