5 ms·
I think "symmetry" is actually not a great way to think about F=ma. The reason is that Newton's laws still work even if your system is non-symmetric with non-co
by millstone 7y ago
I think "symmetry" is actually not a great way to think about F=ma. The reason is that Newton's laws still work even if your system is non-symmetric with non-conserved dynamical quantities.
Consider releasing a rock and calculating how long it takes to hit the ground. In this system, the rock's momentum increases in time, and is therefore not conserved.
Consider a charged particle in an oscillating electric field. In this system, the particle oscillates, and so energy is not conserved.
What about Noether's theorem? In the first example the Lagrangian has a height dependence, and in the second one there's a time dependence. So the theorem does not apply.
Yet F=ma still works. So F=ma does not come from symmetry.
You might object that these quantities are conserved globally. But the point is that F=ma allows us to use model systems as affected by external forces; this is a very powerful simplifying technique.
- Skunkleton 7y agoMomentum is always conserved. You just have to draw the boundaries correctly.
- chupasaurus 7y agoRead about the mass defect.
- poelzi 7y agom is derived as m = P_S / c² * V_fohs P_S and V_fohs do not exist in the standard model. The gravitational microcuviture of protons/neutrons cause changes in the P_S (static vacuum pressure) that therefor changes the mass. P_S is around 1.3 * 10^26 N/m². This is from the Basic Structures of Matter - Supergravitation Unified Theory model, not the standard model.
- millstone 7y agoBUT you don't have to. You CAN re-express whole systems as partial systems with external forces. A ball falling to earth has a time-independent Lagrangian because you neglect the earth's acceleration. The electron orbiting the hydrogen nucleus moves in a fixed potential for the same reason. "Draw the boundaries correctly" and you can't do physics.
- Skunkleton 7y agoSure, but you cant turn around and say that momentum isn't conserved "because gravity".
- dr_dshiv 7y agoThis is great. Can you explain why the oscillating particle doesn't conserve energy?
- jfengel 7y agoOscillating charges emit electromagnetic waves that carry away some energy.