
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=mc^{2}. 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 nonrelativistic
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 E^{2} =
(mc^{2})^{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 m_{0} x
c^{2} where m_{0} = 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 (antielectron)
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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