3 ms·
I would love to hear a good relatively-plain-English retelling (assuming some good undergrad physics knowledge) of how to understand these statements? > Time t
by supernova87a 4y ago
I would love to hear a good relatively-plain-English retelling (assuming some good undergrad physics knowledge) of how to understand these statements?
> Time translation symmetry gives conservation of energy; space translation symmetry gives conservation of momentum; rotation symmetry gives conservation of angular momentum, etc
Something about how if you see that processes can be step-wise played forwards or backwards, it implies the certain quantity is conserved? How?
- davidkunz 4y agoI'm not sure if it makes sense to explain physics in English because it tends to get really imprecise and unclear. That being said, suppose you have a theory which describes physical processes. Given that this theory must hold true for every variation of some parameters (rotation, translation, time, ...) then you can derive some things which are constant (angular momentum, linear momentum, energy, ...). Now one can spend many hours thinking about the relation between energy and time with fuzzy philosophical definitions or one can just accept that the math turns out that way (given some assumptions of that theory).
- funcantor 4y agoI guess very roughly you can say that if you describe a system with some set of parameters, which when changed in particular ways leave the system's quantities (energy, momentum, etc..) unchanged then you have a connection between symmetry and conserved quantities.
- Koshkin 4y agoBut note that this can be misleading (as could be any hand-wavy “explanation”). For example, a time shift does not affect the system’s angular momentum, but that does not mean that the conservation of the latter follows from the symmetry alluded to by the former.
- mhh__ 4y agoAn example: The statement that it does not matter whether I do my (thought) experiment today or tomorrow, can be used mathematically deduce the conservation of some quantity which we can intuit is the mechanical energy. More technically it's a differentiable symmetry: we can do the experiment a day, a week, a year in the future - this time can be varied smoothly. If you know calculus read the first few chapters of Landau and Lifshitz book on classical mechanics.
- aqwsde 4y agoJust wanted to recommend the Landau and Lifshitz book as well. It's pretty dense but elegant.