Thank you for all your responses. A further question: (Excuse the MATLAB notation, I don't know latex.)
Transformations of the form {cosh a, -sinh a; -sinh a, cosh a} leaves the Minkowski metric invariant. How are we to determine 'a' from this knowledge? How would I know that 'a' is a function...
I'm learning about special relativity in its differential geometry formulation. I don't understand how special relativistic effects can be derived from the Minkowski metric. It isn't obvious to me where relative velocity comes in, or why this makes things look different. Can somebody explain how...
The wave nature of light involves all 4 equation to derive. The inverse square law confirms the first equation. The second equation has been probed in monopole experiments. The vacuum part of the third and fourth equations are used to determine the speed of light. I haven't seen a convincing...
If the lagrangian has some symmetry, Noether's theorem shows that there is a conserved quantity. I'm not sure the converse holds. That is, if there is a conserved quantity, there must be a lagrangian that has that symmetry. If in fact there is a variational principle which determines the...
Ok I'm actually looking for something else than what I'm getting. I want to know if an arbitrary differential equation of the position of a particle as a function of position,time can be obtained through some variational principle. This means its a classical theory on euclidean 1 dimensional...
I was wondering if anybody could help me crack this one.
Variational principles such as hamilton's principle are used to state the laws of physics. To my knowledge, all of classical theory (including GR) can be stated this way. The resulting DE can then be found using the euler-lagrange...