Ciro Santilli @cirosantilli  40

The "Truth and Beauty" motto hugely coincides with Ciro Santilli's ideas.

Truth is easier somewhat as it is more subjective.

Beauty, like all arts, sometimes you achieve, sometimes you don't.

Searcing beauty is a painful thing. You just keep endlessly looking for that one new insight that will blow your mind.

The key missing point would be "usefulness". See also: Section "Art".

A way to write the wavefunction $\psi (x)$ such that the position operator is:i.e., a function that takes the wavefunction as input, and outputs another function:

If you believe that mathematicians took care of continuous spectrum for us and that everything just works, the most concrete and direct thing that this representation tells us is that:equals:

This operator case is surprisingly not necessarily mathematically trivial to describe formally because you often end up getting into the Dirac delta functions/continuous spectrum: as mentioned at: mathematical formulation of quantum mechanics

One dimension in position representation:

In three dimensions In position representation, we define it by using the gradient, and so we see that

Derived from classical first principles, matches Planck's law for low frequencies, but diverges at higher frequencies.

Video "The Biggest Ideas in the Universe | 17. Matter by Sean Carroll (2020)" at youtu.be/dQWn9NzvX4s?t=3707 says that no one has ever been able to come up with an intuitive reason for the proof.

As mentioned at: physics.stackexchange.com/questions/212726/a-quantum-particle-moving-from-a-to-b-will-take-every-possible-path-from-a-to-b/212790#212790, classical Gravity waves for example also "take all possible paths". This is just what waves look like they are doing.