Henrique Mello

Hey, guys What are the arguments that show the invariance of the First and Third laws under the galilean transforms?

You're right Actually I'm asking the scale LHC reached in its research. I mean: we know how physics works at 10^-n meters. I want to know this "n". But thanks for trying to help me

What is the scale (in meters) that LHC have already reached?

Can I say that the conjugate momentum defined by p_\phi \equiv \frac{\partial L}{\partial \dot{\phi}} is a covariant quantity?

Thank you, guys

But my doubt is, for example: The shortest distance between two points in Earth is the arc a great circle. But we actually have two possiblities: To travel from New York to Madrid directly (crossing Atlantic Ocean) or go through Japan, Russia etc until arrive at Spain. The geodesics just says that the path is a great circle, but doesn't say which path is the shortest. You know what I mean?

The Euler-Lagrange equation just guarantees that the integral is stationary. In the calculation of geodesics, how do I know that the path I found is actually the shortest distance between two points?

I'm reading a paper and the author uses some "Lagrangian techniques" to go from ds^2 = -(1-\frac{2M}{r})dt^2 + (1-\frac{2M}{r})^{-1} dr^2 + r^2(d\theta^2 + sin^2\theta d\phi^2) to 2L = -(1-\frac{2M}{r})\dot{t^2} + (1-\frac{2M}{r})^{-1} \dot{r^2} + r^2(\dot{\theta^2} + sin^2\theta \dot{\phi^2}), where L is the Lagrangian. Can someone explain what the step between these two equations? PS: I don't know how to make the latex code work here.

Thanks, elfmotat. I'll work on this problem here and if I can't do it I call for help here

Guys, does anyone know which affine parameter should I use to study spacelike geodesics? I mean, for timelike curves we use the proper time. I've read somewhere that I should use the proper distance. Is it correct? And why (or why not)? Thanks to all.