TL;DR – Subjective experiences, like consciousness, are outside of what can be experimentally tested. I was at a bar, tired from a long day, when a person started pestering me with questions: “Doesn’t the brain process electrical signals, which is ultimately explained by quantum physics?” “Doesn’t quantum physics say that things happen only because we …
TL;DR – Statistical quantities (e.g. averages) and angles (e.g. direction of spin) are measurable quantities but are not associated with linear operators, eigenkets and eigenvalues. When studying quantum mechanics you learn about observables, how to each you associate a Hermitian operator, how the value is only defined on the eigenstates of that operator and how, …
TL;DR – Complex numbers should really be called rotation numbers. Whenever they are used in physics and engineering, some type of 2D vector and related rotation is lurking and begging to be understood. In the past posts we went through a lot of insights in classical mechanics and I want to start doing the same …
TL;DR – Statistics can only study correlations between populations and are blind to the effect on individuals. Since I moved to the United States of America, I have met people with very strong views about religion and science. One would say: “the bible says the world was created 10,000 years ago.” Another would say: “science …
TL;DR – States are identified by position and momentum because this is the space that allows us to define coordinate-invariant densities. As we saw in many of our posts, Hamiltonian mechanics describes the deterministic and reversible evolution of states. This leaves one question: why are states fully described by position and momentum? Why not only …
TL;DR – Inverting the direction of time and space is equivalent to inverting the direction of the parametrization. In previous posts we have seen the classical equivalent for anti-particles. Here we see something that looks similar to the CPT theorem. Naturally, it’s not a complete analogue because we are not really looking at fields at …