Author: David Tong.

Summary:

As of 2019, the more formal name for particle physics, which is notably missing general relativity to achieve the theory of everything.

cds.cern.ch/record/799984/files/0401010.pdf The Making of the Standard Model by Steven Weinberg mentions three crucial elements that made up the standard model post earlier less generalized quantum electrodynamics understandings

TODO it would be awesome if we could de-generalize the equations in 2D and do a JavaScript demo of it!

Not sure it is possible though because the curl appears in the equations:

One problem popped up about one year after having bought the blinds in 2019: the blind won't stay still except at the most closed position. Anywhere above it started to slowly go up by itself.

It is not super serious as it covers the two main use cases: full closed and fully open, but it is a bit worrying.

Also, we've had some mold grow on the window, so it is something to look out for, and add some mold spray as it comes up. The fact that the window is dark makes the mold harder to spot.

The layered one.

This is basically how quantum computing was first theorized by Richard Feynman: quantum computers as experiments that are hard to predict outcomes.

TODO answer that: quantumcomputing.stackexchange.com/questions/5005/why-it-is-hard-to-simulate-a-quantum-device-by-a-classical-devices. A good answer would be with a more physical example of quantum entanglement, e.g. on a photonic quantum computer.

Remember: having more than one natural language is bad for the world.

The wave equation contains the entire state of a particle.

From mathematical formulation of quantum mechanics remember that the wave equation is a vector in Hilbert space.

And a single vector can be represented in many different ways in different basis, and two of those ways happen to be the position and the momentum representations.

More importantly, position and momentum are first and foremost operators associated with observables: the position operator and the momentum operator. And both of their eigenvalue sets form a basis of the Hilbert space according to the spectral theorem.

When you represent a wave equation as a function, you have to say what the variable of the function means. And depending on weather you say "it means position" or "it means momentum", the position and momentum operators will be written differently.

This is well shown at: Video "Visualization of Quantum Physics (Quantum Mechanics) by udiprod (2017)".

Furthermore, the position and momentum representations are equivalent: one is the Fourier transform of the other: position and momentum space. Remember that notably we can always take the Fourier transform of a function in $L^2$ due to Carleson's theorem.

Then the uncertainty principle follows immediately from a general property of the Fourier transform: en.wikipedia.org/w/index.php?title=Fourier_transform&oldid=961707157#Uncertainty_principle

In precise terms, the uncertainty principle talks about the standard deviation of two measures.

We can visualize the uncertainty principle more intuitively by thinking of a wave function that is a real flat top bump function with a flat top in 1D. We can then change the width of the support, but when we do that, the top goes higher to keep probability equal to 1. The momentum is 0 everywhere, except in the edges of the support. Then:

Bibliography:

Molecules that are the same if you just look at "what atom is linked to what atom", they are only different if you consider the relative spacial positions of atoms.