Recent content by DarthVader

The Euler-Lagrange equations are the foundation for variational calculus. So, their derivation can be found in many calculus of variations/theoretical mechanics books. The standard derivation is also given in the Wolfram Mathworld encyclopedia...

Just to clarify, my original issue was that 2 spatial dimensions are used in the derivation, not that well-established facts (such as the Pythagorean theorem) are used in the derivation. I'm a little confused by this statement. Once you have time dilation, can you not use the fact that speed...

Yes, I made a mistake on that point. The action is minimized but the negative sign in front of the integral means that the integral must actually take a maximum. It is probably not as intuitive to prove this as I first thought (due to the differing signs in the square root), but the solution is...

When integral(ds) is minimized, S is also minimized since the two are proportional. Note that S has to be a local minimum (not maximum) according to the principle of least action. The expression sqrt( c ^ 2 * dt ^ 2 - dx ^ 2 - dy ^ 2 - dz ^ 2) represents the length of a small path taken in...

Thank you very much to all. I knew there had to be a way of deriving gamma in 1+1 D but I was not sure how.

Hello, It kind of bothers me that the derivation for the Lorentz transformation relies on two dimensions of space. (Here I am referring to the standard derivation where one person is using a vertical light clock in a trolley traveling horizontally at speed v, and an observer outside is...

A world-line is a path through space-time (generally speaking, this is a coordinate system with one time dimension and three space dimensions). In one-dimensional space, a world-line is a simple position-time graph. The last equation in your question simply states that a free particle will...

Hello. A problem I have given my physics class states, "The distance between two crests in a wave is 1.5 m, and two crests pass a pole each second. What is the speed and period of the wave?" I believe the proper solution should be v = 3 m/s, and T = 0.5 s. In order for two crests to pass a given...

I know that the curvature of space-time around an uncharged mass is different from that around a charged mass (specifically, one situation is characterized by the Schwarzschild metric and the other by the Reissner-Nordstorm metric). But consider an uncharged particle in each situation. Wouldn't...