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The ground state of a quantum/classical mechanical system is its lowest-energy state; the energy of the ground state is known as the zero-point energy of the system. When a quantum system has infinite possible ground states, it is gapless with massless modes; if a quantum system has finite ground states, it is known as gapped and potentially topologically ordered. The ground state of a quantum field theory is usually called the vacuum state or the vacuum.

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My simple version of the answer: because for the energy to be zero, time must be stopped I'm sorry I don't know how to state that in the maths you're looking for, perhaps someone else can, I suspe …
answered Jun 21 '17 by Mr.President