TL;DR – The most complete version of Hamiltonian mechanics lives on the extended phase space that includes position, momentum, time and energy. In this post we look at the most complete version of Hamiltonian mechanics. It is kind of a shame that this is not the version taught because it is the one that works …
TL;DR – Hamiltonians are not invariant: they change as the time component of a covector (i.e. covariant component) in phase space. In the previous post we saw how momentum varies as covariant components and that keeps the Hamiltonian equations unchanged under coordinate transformations. We have also seen, though, that under coordinate transformations that mix time …
TL;DR – The laws of physics are the same for all observers because nature couldn’t care less what coordinate system we use. I recently met someone who had some slight misconceptions about the principle of relativity. “Is it true that time and space are relative concepts?” “That contemporary events for you may not be contemporary …