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How does light energy become mass if E=mc2 states that energy becomes mass when approaching the speed of light (because mass cannot go the speed of light, the energy pushing it becomes mass) when light itself is going the speed of light. How is that energy converted back into mass?
Answer 1:

This question stems from a common confusion about the very famous equation E=mc2. The answer is that it doesn't really mean that energy becomes mass in the sense that you are asking. What it really means is that mass is a form of energy, with a conversion factor given by the speed of light (which we call c). When physicists talk about mass in the context of relativity, they mean the "rest mass," the mass of the object when it is not moving. Then, for an object with "rest mass" m and momentum p (in non-relativistic physics, we learn momentum is mass times velocity, which becomes "rest mass" times "proper velocity" in relativity -- maybe you can read about relativity and find out what these are!), the energy is E2 = (mc2)2 +(pc)2. So the total energy comes from rest mass and motion (momentum). So you see, when we say light is "massless" we mean its rest mass is zero.
Another feature of this equation comes in when we consider a bound state of two particles (like a hydrogen atom is a proton and electron "bound" together). In this case, if we just look at the hydrogen and forget that it is made up of a proton and electron, we see mass energy from what is really electric energy holding them together.
Relativity is a fascinating subject and I hope you will read more about it it some more advanced science books to learn more!

Answer 2:

Usually I don't think of it as "light" turning into mass.The Special Relativity relationship that applies is E = gamma x m0 x c2 where m0 = the mass of the object at rest and gamma = 1/sqrt(1-(v/c)2)
where v = speed of the object. So the energy of an object divided by its rest energy is equal to this quantity gamma which equals 1 when speed = 0 and goes to infinity as v approaches c.

Light does not have rest mass but photons ("particles of light") do have energy and momentum related to the frequency of the light.
So, for example, it is possible for two high energy photons to interact and "turn into" an electron and a positron (anti-electron) as long as energy, momentum, charge, and another quantity called lepton number are conserved in the process. That these types of things can happen is a property of the four fundamental forces:
electromagnetic, weak nuclear, strong nuclear, and gravity.

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