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If energy is only found in discrete amounts what happens when the amount of energy falls below the minimum individual unit? does it have a floor or ceiling function or does it matter what type it is?

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The answer is that it's impossible. If energy is quantized then the smallest you can have is some amount of energy $\epsilon$, and any measurement you make will give a result equal to $n\epsilon$ where $n$ is some integer. If we measured an energy less than the smallest quanta, then we would either redefine the smallest quanta, or we would reconsider our current understanding.

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