Question

The law of conservation of energy states that energy can neither be created nor destroyed. What does “conservation” mean in this law?

Answer 1

In this law, “conservation” means that the total amount of energy in a closed (isolated) system does not change with time. Energy may move from one place to another and may change form (kinetic → potential → thermal → electromagnetic, etc.), but if you add up all forms of energy for the whole isolated system the sum remains constant.

Key points:
- For a closed system: ΔE_total = 0 (or dE_total/dt = 0). Energy is conserved globally.
- For a subsystem that exchanges energy with its surroundings, energy of that subsystem need not be constant because energy can flow in or out.
- Conservation can be expressed locally by a continuity equation for energy density u and energy flux S: ∂u/∂t + ∇·S = 0 (no sources or sinks).
- The deep reason is symmetry: by Noether’s theorem, conservation of energy follows from the invariance of the laws of physics under shifts in time.
- Caveat in general relativity and cosmology: defining a single global energy for the whole expanding universe is subtle; however, local conservation of stress–energy (∇μTμν = 0) still holds.

Simple examples: a swinging pendulum converts between kinetic and potential energy but the total (neglecting air resistance and friction) stays the same; friction converts mechanical energy into heat, but that heat is still energy — it’s not destroyed.