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   John Carlos Baez (johncarlosbaez@mathstodon.xyz)'s status on Tuesday, 01-Oct-2024 01:13:57 JST John Carlos Baez

   Imagine grabbing a circle and turning it around a bit. You can turn it around by however much you like, and it will look just the same.

   There are at least two important ways this fact shows up in physics. In neither of these are we literally rotating an object in space, like a steering wheel. Both are more abstract.

   First, in quantum mechanics, there's an abstract way to turn around anything at all, called 'rotating its phase'. The 𝑒𝑛𝑒𝑟𝑔𝑦 of any object is simply the rate at which its phase rotates as time passes.

   Second, electromagnetism involves another way to turn things around. The 𝑚𝑎𝑔𝑛𝑒𝑡𝑖𝑐 𝑓𝑖𝑒𝑙𝑑 says how much anything turns around in this other way when you carry it around a little loop in space. The 𝑒𝑙𝑒𝑐𝑡𝑟𝑖𝑐 𝑓𝑖𝑒𝑙𝑑 is similar, but it involves little loops in spacetime.

   These two ways of rotating something are connected by the concept of electric charge. As time passes, any object will be rotating in the second, electromagnetic way at some rate. If you multiply this rate by the object's charge, you get the object's 𝑒𝑛𝑒𝑟𝑔𝑦 - or more precisely, the part of its energy due to electromagnetism!

   All of this so amazing that if you didn't know better, you might think I'm a crackpot explaining a personal wacky theory. But in fact, this is just ordinary physics, of the sort you'd learn in grad school. For some reason physicists don't talk about it enough. Maybe because people would think they're crazy?

   If you ever wondered what trig was good for, well this is one thing: understanding the essence of physical reality.