Physics and Felines: The ‘Purr-fect’ Analogy to Understanding Noether’s Theorem with Emmy the Cat

It’s time to get our paws wet in the complex world of Noether’s theorem, inspired by my favorite feline, Emmy!

It’s time to get our paws wet in the complex world of Noether’s theorem, inspired by my favorite feline, Emmy!

Emmy Noether, my cat’s namesake.

Emmy Noether was a groundbreaking mathematician, credited with crucial contributions to abstract algebra and theoretical physics. She was a fierce pioneer in her field, navigating a male-dominated academic world to leave an indelible mark on mathematics and physics. Noether’s theorem, arguably her most famous work, is a fundamental part of our understanding of the physical world.

Emmy, my adorable calico.

I name my calico cat after her, a tribute to Emmy Noether’s strength, intelligence, and ingenuity. Just as Noether’s work was characterized by an astonishing depth and breadth of originality and understanding, so too does my calico Emmy exhibit a profound depth of character, curiosity, and a penchant for pushing boundaries — often onto tables and countertops!

Emmy Noether’s theorem states that every differentiable symmetry of the action of a physical system has a corresponding conservation law. A bit of a mouthful, right? But it’s an important pillar of theoretical physics and Emmy (the cat) can help us out.

Imagine Emmy tracking the movement of a laser pointer. She’s so focused that she exhibits a purr-fect symmetry — no matter where I aim the laser, she’ll always mirror its movements. This is akin to the “differentiable symmetry of the action” in the system. Noether’s theorem tells us that this symmetry results in a conservation law — in our case, the conservation of momentum.

Emmy sometimes just outright steals laser pointers, not merely tracks them.

No matter how much Emmy leaps, sprints, or changes direction in pursuit of the red dot, the total momentum in our little system (Emmy + red dot) remains conserved. It’s as if she’s playing out an impromptu physics experiment for us, maintaining her ‘pounce’-mentum no matter what!

But let’s make things a little hairier. If I were to spin the laser dot around in a circle, Emmy would chase it in a similar circular pattern. This rotational symmetry corresponds to the conservation of angular momentum. No matter how frantically Emmy might chase her tail, the total angular momentum stays the same. Just as well — any more spin and we might all end up dizzy!

Emmy chasing a laser that automatically spins in circles.

Finally, let’s think about time symmetry. Whether it’s 2am or 2pm, Emmy treats every hour as playtime, proving that she doesn’t care about the passage of time. This symmetry leads to the conservation of energy. It doesn’t matter how much time passes, Emmy (and therefore, our system) can’t create or destroy energy. She’ll just switch between being kinetic energy on the prowl, or potential energy during her cat-naps.

Emmy demonstrating conservation of energy by being at rest at a place of high gravitational potential energy, the top of a bookshelf.

So, you see, my dear Emmy (the cat), in her endless quest to chase laser dots, maintain her disregard for appropriate playtimes, and pursue tail-chasing, is the purr-fect example of Noether’s theorem in action. It just goes to show, physics can be feline and fabulous!