What happens to physics when the speed of light simply equals one
Physicists sometimes declare that the speed of light is exactly 1, with no metres or seconds attached. Einstein's famous equation then shrinks to E = m, because mass and energy become the same currency. Choosing which constants to erase this way gives a whole family of unit systems, each tuned to a different corner of nature.
The trick is called nondimensionalization. Pick a handful of fundamental constants, declare each equal to 1, and the conversion factors they once supplied vanish from the equations. In the most extreme version every dimension collapses, so the constants alone define the units and the laws of physics carry no conversion terms at all. The price is bookkeeping: to get back to ordinary units, you still have to remember which dimensions each quantity really has, since those tell you where to put the constants back.
The idea is older than most people guess. George Johnstone Stoney proposed it in 1874, in a talk to the British Association called "On the Physical Units of Nature". His scheme was built on light speed, gravity, the Coulomb constant and the charge of the electron. It could not include the Planck constant, because nobody had found that yet. Max Planck's own version arrived about three decades later and used gravity, light speed, his new constant and the Boltzmann constant to fix length, time, mass and temperature, though it left electromagnetism out.
Planck units have a special appeal: they are tied to no object or particle, only to the structure of physical law. Light speed and gravity shape spacetime in general relativity, while the reduced Planck constant underpins quantum mechanics, which is why theorists working on quantum gravity and string theory reach for them. Relativists often prefer a leaner geometrized system that sets only light speed and gravity to 1.
Other fields tailor their own. Douglas Hartree devised atomic units so that the hydrogen atom's electron, in its lowest state, has tidy values for its orbit and speed. Particle physicists use a system built on the electron mass, and so-called strong units centre on the proton for nuclear work. Even Erwin Schrödinger has a system named after him, picked out by the physicist Michael Duff.
Source: Natural units
