We have been taught that the universe has a constant amount of energy but if energy can be converted into matter, how is it constant?
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Energy and matter are really the same thing. Both are completely interchangeable. When we say total energy of universe is constant ( it includes mass energy). You can convert matter into energy and also energy into matter. At the time of Big Bang it was all energy no matter at all. We do this conversion in our labs all the time. The famous example is how the Higgs particle was synthesized and detected at CERN.
