The Hamiltonian is a central concept in both classical and quantum mechanics, illustrating how perspectives in physics can evolve over time.

The laws of physics are translation invariant, meaning if I move 10 steps to the left, I experience the same laws of physics as if I was here, which corresponds to the conservation of momentum.

If spacetime has symmetries, such as a timelike Killing field, it allows for the definition of genuinely conserved, coordinate-independent energy.

The connection between quantum mechanics and gravity is a major focus in theoretical physics right now, as there are inconsistencies between the two.

The principle of equivalence in general relativity conflicts with the principle of superposition in quantum mechanics, highlighting a fundamental tension between these two theories.

I believe it's possible to unify general relativity and quantum mechanics, as history shows that physics has often moved towards unification, like how Maxwell unified electricity and magnetism.

The strength of geometric algebra lies in its ability to unify various concepts in physics, including quantum mechanics and relativity, potentially offering new insights into quantum gravity.

In quantum mechanics, probabilities are fundamental to the description of nature, differing from classical probability which reflects our incomplete knowledge of a system.

Maxwell's equations are conformally invariant, meaning they depend on the space-time structure independent of scaling.