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with negative energy, was when the theory is telling you,
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hey, there are particles and there are anti-particles,
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and the negative energy when properly interpreted will describe anti-particles.
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So the equations are very smart.
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The way the physics works is
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you will find some laws of motion in mathematical form,
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you put in the initial conditions of whatever,
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you solve the equations, and the answer that comes,
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you have no choice.
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You have to accept the answer,
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but there are new answers besides the one you were looking for.
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You've got to think about what they mean,