3 ms·
It directly follows from the assumptions that space is isotropic and homogeneous. I recall that there was a short and elegant proof of this link in Landau and L
by dpq 7y ago
It directly follows from the assumptions that space is isotropic and homogeneous. I recall that there was a short and elegant proof of this link in Landau and Lifshits vol 1; you may want to look it up.
- fferen 7y agoIndeed, it is at the start of the book. It also relies on the assumption that the Lagrangian is invariant up to a total time derivative under Galilean transformations, which leads to `dL/d(v^2)` being a constant (1/2 m). This is, I believe, the most fundamental way to look at it. Otherwise you could ask why the Lagrangian can't have other terms like v^4.