How time and energy are related

Energy and time are two closely related concepts in physics.

What energy represents is in fact the ‘amount’ of change that takes place in a system. And in turn, a physical system changes state and evolves, obviously over the course of time.

What energy makes a system capable of is to do work, or in other words to allow things to change, by modifying the acceleration or equivalently exerting a force on a system and/or its constituents.

In short, energy allows things to happen, to change. Not without reason, the absence of (useful) energy is the equilibrium state of a system, where everything ceases to happen, and time to flow.

Thus forces make changes happen in a system, momentum is the property that is actually changed, and energy measures the extent of this change.

Forces, momentum and energy are thus fundamental and almost axiomatically irreducible concepts in physics.

And time and energy are also linked by Noether’s theorem, which links every symmetry in nature with a respective conserved quantity. Invariance with respect to time translation gives in fact the well-known law of conservation of energy.