Which physical quantity's conservation follows from time invariance, with the joule as its SI unit?

• A. Momentum
• B. Energy
• C. Mass
• D. Power

Answer: (B)

If the laws of physics don’t depend on the moment in time, the total energy of a closed system stays the same. That time-invariance means you can’t create or destroy energy just by waiting; instead, energy simply shifts between forms like kinetic, potential, and internal energy without changing the total amount. A classic illustration is a frictionless pendulum: as it swings, kinetic and potential energy trade off, but their sum remains constant.

The joule is the SI unit for energy, defined as the work done when a force of one newton acts over a displacement of one meter. This makes joules the natural way to quantify the capacity to do work, which is exactly what energy measures.

Other quantities aren’t tied to time symmetry in the same way. Momentum conservation arises from spatial translation symmetry, not time, so it’s not the conservation law linked to time invariance. Mass is a separate property that can vary in relativistic or particle-physics contexts, not the conserved quantity associated with time. Power is the rate of energy transfer, not a stored quantity that remains constant in time.