Action and amount of movement

[quiet]

Is the gradient of the action equal to the amount of movement?

[Markus Hanke]

11 hours ago, quiet said:

Is the gradient of the action equal to the amount of movement?

I am unsure what you mean by “amount of movement” - you would have to provide an exact mathematical definition of this term.
In general though, you can obtain the equations of motion for a system from its action by plugging the action into the Euler-Lagrange equations. Solving the equations of motion then gives you the “movement” of the system, in the sense of some quantity changing with respect to some other quantity. This general approach is often used for field theories of various kinds.

To answer your original question - no, the relationship between action and “motion” is somewhat more complicated than a simple gradient.

Edited October 28, 2018 by Markus Hanke

[quiet]

5 hours ago, Markus Hanke said:

I am unsure what you mean by “amount of movement”

Sorry. I use the Google translator and some technical terms are translated in colloquial mode, which sometimes does not match the technical mode. I correct:

Is the linear momentun equal to the gradient of the action?

[Markus Hanke]

13 hours ago, quiet said:

Is the linear momentun equal to the gradient of the action?

No, linear momentum is the conserved quantity that arises from spatial translation invariance via Noether’s theorem.

[quiet]

Thans you Markus !