Physics teachers have a habit of handing down laws like they are commandments carved into stone tablets. Momentum is conserved. Energy is conserved. Angular momentum is conserved. They tell you that in a closed box—where no matter enters and no heat leaves—these quantities stay frozen, eternal and unchanging. They never really tell you why.
For the longest time, we just accepted it. It was a brute fact of the universe. But the reason these things stay constant isn’t magic. It was figured out by a woman named Emmy Noether, who looked at the messy, leaking equations of General Relativity and realized that the universe cares more about symmetry than it does about our rules.
Energy is NOT conserved in General Relativity at cosmic scales
Here is the thing about General Relativity: it was broken. Or at least, it seemed broken. Einstein was sweating because his equations suggested energy wasn’t being conserved. He tried to patch it, to force a “fix” so the math would obey the old laws. He added a pseudo tensor. Noether looked at it and said, effectively,
“Stop trying to fix it. It’s supposed to be broken.”
She proved that energy is not conserved on a cosmic scale. As the universe expands, space stretches. Light traveling through that stretching space gets pulled apart, its wavelength getting longer and redder. As it redshifts, it loses energy. That energy doesn’t go anywhere. It doesn’t turn into heat. It just vanishes. Gone. The conservation law is violated because the symmetry in time is broken by the expansion of the universe.
This leads to the most beautiful insight in modern physics: Noether’s Theorem.
She realized that conservation is just the mathematical shadow of symmetry!
Continuous symmetries lead to conserved physical quantities
If motion along a straight line does not change the physical properties of a system (translation symmetry), then the corresponding physical quantity (momentum) is conserved.
If you can spin your laboratory on a turntable and the physical properties remain the same (rotational symmetry), then the corresponding quantity (angular momentum) is conserved.
Similarly if there is symmetry across time (time translation symmetry), then energy would be conserved.
But if the stage itself is warping—like in Einstein’s exploding space-time —the symmetry breaks because of the dynamic nature of space-time, and the energy conservation evaporates. She connected the abstract geometry of space-time to the hard numbers of general relativity.
Now, consider the context of this brilliance. Emmy Noether did this work at the University of Göttingen. She wasn’t a professor. She wasn’t even getting a paycheck. She was working for free.
Emmy Noether – The Unpaid Genius
When David Hilbert and Felix Klein tried to bring her on board in 1915, the faculty exploded. The idea of a woman teaching was apparently more terrifying than the collapse of Newtonian mechanics. They argued about bathroom breaks and precedent. They whined that soldiers returning from the war would feel humiliated to learn at the feet of a woman. Hilbert had to snap back with the famous line, “We are a university, not a bathhouse.” He was determined to use the mathematical expertise of Emmy Noether in trying to understand Einstein’s General Relativity.
Even then, she spent four years lecturing under Hilbert’s name, a ghost writer for the laws of reality. It wasn’t until 1919 that she was finally allowed to officially teach and earn a wage.
Think about the sheer waste of that.
We usually talk about women in STEM with polite, corporate phrasing about “diversity of thought” and “equal opportunity.” Forget that. Look at the raw data. Noether laid the groundwork for understanding the conserved quantities in quantum physics using the gauge invariance. Without her, we don’t understand the conservation of charge, color charge, etc in quantum physics. We are stumbling in the dark.
She changed the fundamental architecture of how we understand reality, and she had to do it while fighting for the right to stand in the room. It makes you wonder what we missed. What other theorems were never written because the woman who could have derived them was told she didn’t belong?
We don’t encourage women in research just to be nice or fair. Just like it is a man’s right to chose his profession and passion, so is it a woman’s right too.
The universe is hard to understand, and we are statistically shooting ourselves in the foot by ignoring half the brainpower available to solve it.
Noether was an unsung giant. She saw the symmetry in the chaos, even when the world around her refused to offer her the same courtesy.
