If we are tearing matter apart in accelerators, why can't they reverse the process? Apply energy at one end and take matter out of the other. When energy first changed to matter in the Big Bang, matter must have first started as particles and then grew into atoms?
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Possible duplicate of How does rest mass become energy? – Kyle Kanos Nov 27 '15 at 11:30
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It is inaccurate to say that we are "tearing matter apart" in accelerators. We are just changing particles into other particles. If we smash 2 protons, the collision excites various quantum fields and gives rise to multiple other particles. This happens because the energy of the incoming protons is used to create the outgoing particles. Both energies (of the "in" and "out" particles) are the same.
You cannot have "pure energy" and turn this into "matter". You can have particles (which have energy) and change them into other particles (which also have energy).
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1Some people consider matter to be fermions, so pair-production from photons would "generate" mass but this process seems much harder and it doesn't tell us much about small scales. – jinawee Nov 27 '15 at 12:52