3 years agoAugust 9, 2011
This is one of the few laws of physics that are named after a woman (in fact, I’m not sure I can name another one). Noether’s theorem, proved by Emmy Noether in 1915, shows (as far as I understand it) that if you have a physical system that obeys certain requirements — requirements that almost all systems studied by physics do obey — if you have symmetry under translation, you must also have a conservation law. This means that if some property of a system doesn’t change when you translate it (a famous example being that the laws of physics don’t change over time), then you get a law about the conservation of that property (like the law of conservation of energy).
This result is very useful in physics. One of the more esoteric uses to which you can put it is to show how perpetual motion would be undesirable. Perpetual motion sounds great: no more energy problems! That’s why people have been trying to create perpetuum mobiles for hundreds if not thousands of years. The problem is that such a machine violates the laws of thermodynamics, including the law of conservation of energy — energy cannot be created or destroyed. Now, the conservation law is a very well-supported physical law. But suppose it didn’t hold. Couldn’t we have perpetual motion then? Noether’s theorem implies that if the laws of physics don’t change over time, the conservation law must hold. And conversely, if the conservation law doesn’t hold, the laws of physics must change over time. If perpetual motion were possible, the laws we discovered Tuesday might not be valid Wednesday. Everything we know about physics would be highly uncertain or wrong! Gravity could invert itself tomorrow! Our assumptions about the future could not be extrapolated from the past!
That’s one steep price to pay for free energy.