Conservation laws are supported by two reinforcing pillars: a deep mathematical proof that links every conservation law to a symmetry of nature, and centuries of experimental measurements that have never found a violation. Together, these make conservation laws some of the most rigorously tested statements in all of science.
The Mathematical Foundation: Symmetry
The strongest theoretical evidence comes from a result known as Noether’s theorem, published by mathematician Emmy Noether in 1918. The theorem proves that whenever the equations governing a physical system have a certain symmetry, a corresponding quantity must be conserved. This isn’t an approximation or a guess. It’s a logical consequence of the mathematics that describes how systems evolve.
The connections are specific and concrete. If the laws of physics don’t change when you shift everything forward or backward in time (time-translation symmetry), then energy is conserved. If the laws don’t change when you move everything to a different location in space (spatial-translation symmetry), then momentum is conserved. If the laws don’t change when you rotate everything by some angle (rotational symmetry), then angular momentum is conserved. Each symmetry produces exactly one conserved quantity, and the theorem tells you precisely what that quantity is.
This means that conservation laws aren’t separate rules bolted onto physics. They emerge automatically from the structure of physical laws themselves. Any theory that obeys these symmetries will produce conservation of energy, momentum, and angular momentum whether or not the physicist writing the theory intended it.
Conservation of Mass: Lavoisier’s Careful Weighing
The earliest systematic experimental evidence for a conservation law came from chemistry. In the late 1700s, Antoine Lavoisier performed a series of reactions while meticulously weighing every reactant and product. His signature technique was comparing the total weight before and after a reaction. When he heated mercuric oxide (a red powder), chemists already knew it produced liquid mercury that weighed less than the original powder. Lavoisier’s innovation was collecting the gas released during the reaction and showing that the mass of the mercury plus the mass of the gas roughly balanced the mass of the original oxide.
In another experiment synthesizing water from hydrogen and oxygen, he recovered about 5 gros of water, which corresponded closely to the combined weight of the two gases he started with. By accounting for all reactants and all products, including gases that previous chemists had ignored, Lavoisier provided strong evidence that mass is neither created nor destroyed in chemical reactions. This principle held up for over a century until nuclear physics revealed that mass can convert into energy, upgrading the law to conservation of mass-energy.
Conservation of Energy: Joule’s Paddle Wheel
In the 1840s, James Prescott Joule set out to prove that mechanical work and heat are different forms of the same thing, and that converting one to the other never gains or loses any. His most famous apparatus was a paddle wheel submerged in water, turned by falling weights. The gravitational energy of the weights became the rotational energy of the paddles, which became heat in the water. Joule measured the temperature rise with thermometers he could read to about 0.005°F, aiming for increases of just 0.5 to 2°F.
He ran five series of experiments using different materials: brass paddles in water, iron paddles in mercury, and solid iron wheels rubbing against each other. The results were remarkably consistent. Series 1 gave 772.692 foot-pounds per British thermal unit. Series 2 gave 772.814. The other series fell between 773 and 776. His final published value was 772 foot-pounds of mechanical work to raise one pound of water by 1°F. The fact that completely different physical setups, friction in water, friction in mercury, friction between solids, all yielded nearly the same number was powerful evidence that energy transforms from one form to another at a fixed rate, with nothing lost along the way.
Conservation of Momentum and Angular Momentum
Momentum conservation is tested every time physicists smash particles together in an accelerator. The total momentum of the debris always matches the total momentum of the incoming particles, down to the precision of the detectors. This has been confirmed in billions of collisions spanning decades of experiments.
Angular momentum conservation shows up dramatically in astrophysics. When a massive star collapses into a neutron star, its core shrinks from thousands of kilometers across to roughly ten. Because angular momentum must be conserved, the shrinking core spins up enormously, the same principle that makes an ice skater spin faster by pulling in their arms. Astrophysicists modeling neutron star births assume angular momentum conservation and then predict the resulting spin periods. Their models indicate that iron cores rotating with periods of around 50 to 100 seconds before collapse should produce neutron stars with the rotation periods actually observed in young pulsars (tens to hundreds of milliseconds). The match between prediction and observation serves as evidence that angular momentum is conserved even through violent stellar explosions.
Conservation of Electric Charge
Electric charge conservation has been tested to extraordinary precision. If charge were not conserved, electrons could decay into lighter particles like photons and neutrinos. Physicists have searched for exactly this decay using ultra-sensitive germanium detectors. One experiment by the Heidelberg-Moscow collaboration monitored a 591-cubic-centimeter germanium detector for over 3,000 hours and found no evidence of electron decay, setting a lower limit on the electron’s half-life of 1.63 × 10²⁵ years. That’s roughly a quadrillion times the current age of the universe. The fact that no experiment has ever caught an electron disappearing is strong evidence that electric charge is strictly conserved.
Conservation of Baryon Number
Protons are the lightest baryons, so if baryon number conservation were ever violated, the most likely sign would be a proton decaying into lighter, non-baryon particles. The Super-Kamiokande detector in Japan, a tank holding 50,000 tons of ultra-pure water lined with thousands of light sensors, has watched for proton decay for years. It has found nothing. The current lower limit on the proton’s lifetime is 2.4 × 10³⁴ years for one of the most commonly predicted decay paths. That astonishing number, trillions of trillions of times the age of the universe, represents the strongest experimental bound on baryon number conservation.
Some theories in particle physics actually predict that protons should eventually decay, which would mean baryon number conservation is only approximate. The fact that experiments keep pushing the lifetime limit higher and higher without finding a single decay either confirms the conservation law or tells us that any violation is vanishingly rare.
Mass-Energy Conservation in Nuclear Reactions
When physicists first measured nuclear reactions precisely, they discovered something unsettling: the products of a reaction sometimes weighed slightly less than the original ingredients. This “mass defect” isn’t a violation of conservation. The missing mass has been converted into energy, exactly as Einstein’s equation E = mc² predicts. Each type of atomic nucleus has its own binding energy, the energy that was released when its protons and neutrons came together. That released energy corresponds to a tiny but measurable loss of mass.
In nuclear fission, a heavy nucleus splits into lighter fragments whose combined binding energy is greater than the original. The difference shows up as kinetic energy of the fragments and radiation. In fusion, light nuclei merge into a heavier one with the same kind of energy release. Every nuclear reaction ever measured confirms that the total mass-energy before and after is the same, once you account for the energy carried away by radiation and moving particles.
Where Conservation Gets Complicated
In everyday physics and even particle physics, conservation laws hold with extraordinary precision. But general relativity introduces genuine subtleties. The expanding universe, modeled by Friedmann-Robertson-Walker spacetimes, is neither static nor the kind of simple geometry where energy conservation has a clean definition. The mathematics of general relativity gives a local conservation statement: energy and momentum are conserved in any small patch of spacetime. But defining the total energy of the entire universe runs into trouble because you can’t straightforwardly add up energy contributions at different points in a curved spacetime.
Some physicists argue that the energy lost by light as it redshifts in an expanding universe becomes gravitational energy. Others say the concept of total energy simply doesn’t apply to the universe as a whole. This isn’t evidence against conservation laws. It’s a recognition that the concept of “total energy” requires careful definition, and some definitions break down when spacetime itself is changing shape. In every laboratory and every astrophysical system where energy can be cleanly defined, it is conserved.