Science › Classical physics
Conservation of energy
1847· Idea
ProvenTested many times; part of working physics.
The rule that the total energy of an isolated system never changes; it only shifts between forms.
See it on the Science map →How it works
Energy comes in many forms: motion, heat, chemical bonds, electric charge, mass. It converts between them: a dam turns falling water into electricity, a body turns food into heat and movement. The total stays fixed. The principle was established in the 1840s by Julius Robert Mayer, James Joule and Hermann von Helmholtz (1847). Einstein's E = mc² added mass to the list of forms.
Why it matters
It is the most useful bookkeeping rule in science and engineering, and it rules out perpetual-motion machines for good.
Think of it like
Like a property's cash-flow statement: money moves between operating, reserve and capital accounts, but every dollar is accounted for.
How we know
Joule's paddle-wheel experiments (1840s). In 1930 Wolfgang Pauli predicted the neutrino to save energy conservation in radioactive decay; it was detected in 1956. No verified violation has ever been seen in a lab.
Still a mystery
In an expanding universe, energy conservation has no simple global meaning: light stretched by cosmic expansion loses energy, and physicists debate how to account for it.
Connections (4)
▸Thermodynamics: energy and heat is built on Conservation of energyProven
The relationship
The first law of thermodynamics is conservation of energy applied to heat: energy added to a system equals the rise in its internal energy plus the work it does. Every engine efficiency calculation starts by balancing this energy budget. Recognising heat as a form of energy, not a substance, made the law possible.
How the link was found
Mayer (1842), Joule (1843–1850) and Helmholtz (1847) established energy conservation; Clausius and Kelvin made it the first law around 1850–1851.
Why it's proven
Joule measured a fixed exchange rate between mechanical work and heat. No machine has ever put out more energy than it took in.
Open questions and mysteries
On cosmic scales, in an expanding universe, energy conservation lacks a simple global form; how to account for it is still discussed.
▸Noether's theorem: symmetry means conservation explains why we have Conservation of energyProven
The relationship
Noether's theorem says that if the laws of physics are the same at every moment (a time symmetry), one particular quantity must stay constant. That quantity is energy. Conservation of energy is therefore not a separate rule of nature but a consequence of the laws not changing over time.
How the link was found
Emmy Noether proved it in 1918 while helping David Hilbert and Felix Klein with energy questions in general relativity.
Why it's proven
It is a mathematical theorem. Experiments confirm both that lab physics is the same over time and that energy is conserved.
Open questions and mysteries
The expanding universe is not the same at all times, so cosmic energy conservation has no simple form; physicists differ on how to describe it.
▸Conservation of energy was widened by E = mc²Proven
The relationship
Energy conservation said energy is never created or destroyed, while chemistry said mass is never created or destroyed. E = mc² merged the two rules: mass is a form of energy. Only total energy, mass included, is conserved. A hot object weighs very slightly more than a cold one; a nucleus weighs less than its parts.
How the link was found
Conservation of energy was established by Mayer, Joule and Helmholtz in the 1840s. Einstein linked mass to it in September 1905.
Why it's proven
Nuclear reactions show exactly the predicted mass loss as energy release. Particle collisions create new particles from energy and the books always balance.
Open questions and mysteries
In an expanding universe, total energy conservation becomes hard to define; how to account for it cosmically is debated.
▸A zero-energy universe squares creation with Conservation of energySpeculative
The relationship
Conservation of energy says totals never change. A universe from nothing seems to break that rule, going from zero to a vast amount of energy. If gravity's negative energy exactly cancels matter's positive energy, the total stays at zero throughout, so creation needs no outside input. The books balance at every moment, including the first.
How the link was found
Pascual Jordan suggested in the 1940s that a star could arise from nothing this way. George Gamow recalled that when he told Einstein, Einstein stopped in the middle of a street. Tryon applied it to the universe in 1973.
Is it proven?
Plausible but unproven. In general relativity, energy conservation holds locally, but a total for the whole universe is defined only in special cases, so 'zero' may be a definition rather than a discovery.
Open questions and mysteries
Creation from nothing needs every conserved total to start at zero, not just energy. Electric charge seems to, but matter far outnumbers antimatter: was that excess made later, as baryogenesis theories propose?