Ciro Santilli @cirosantilli 35

Proprietary extension to Mozilla rr by rr lead coder Robert O'Callahan et. al, started in 2016 after he quit Mozilla.

TODO what does it add to rr?

Proportionality factor in the Planck-Einstein relation between light energy and frequency.

And analogously for matter, appears in the de Broglie relations relating momentum and frequency. Also appears in the Schrödinger equation, basically as a consequence/cause of the de Broglie relations most likely.

Intuitively, the Planck constant determines at what length scale do quantum effects start to show up for a given energy scale. It is because the Plank constant is very small that we don't perceive quantum effects on everyday energy/length/time scales. On the ${\lim }_{h\to 0}$, quantum mechanics disappears entirely.

A very direct way of thinking about it is to think about what would happen in a double-slit experiment. TODO think more clearly what happens there.

Defined exactly in the 2019 redefinition of the SI base units to:

Some sources say that this is just the part that says that the norm of a $L^2$ function is the same as the norm of its Fourier transform.

Others say that this theorem actually says that the Fourier transform is bijective.

The comment at math.stackexchange.com/questions/446870/bijectiveness-injectiveness-and-surjectiveness-of-fourier-transformation-define/1235725#1235725 may be of interest, it says that the bijection statement is an easy consequence from the norm one, thus the confusion.

TODO does it require it to be in $L^1$ as well? Wikipedia en.wikipedia.org/w/index.php?title=Plancherel_theorem&oldid=987110841 says yes, but courses.maths.ox.ac.uk/node/view_material/53981 does not mention it.

There are infinitely many primes with a neighbor not further apart than 70 million. This was the first such finite bound to be proven, and therefore a major breakthrough.

This implies that for at least one value (or more) below 70 million there are infinitely many repetitions, but we don't know which e.g. we could have infinitely many:or infinitely many:or infinitely many:or infinitely many:but we don't know which of those.

The Prime k-tuple conjecture conjectures that it is all of them.

Also, if 70 million could be reduced down to 2, we would have a proof of the Twin prime conjecture, but this method would only work for (k, k + 2).

Followup to the Shelter Island Conference, this is where Julian Schwinger and Richard Feynman exposed their theories to explain the experiments of the previous conference.

Julian made a formal presentation that took until the afternoon and bored everyone to death, though the mathematics avoided much questioning.

Feynman then presented his revolutionary approach, which he was unable to prove basic properties of, but which gave correct results, and people were not very happy.

The first working one in 1947 by John Bardeen and walter Brattain in Bell Labs Murray Hill.

People had already patented a lot of stuff before without being able to make them work. Nonsense.

As the name suggests, this is not very sturdy, and was quickly replaced by bipolar junction transistor.

Uses photons!

The key experiment/phenomena that sets the basis for photonic quantum computing is the two photon interference experiment.

The physical representation of the information encoding is very easy to understand:

TODO find/create decent answer.

I think the best answer is something along:

A basic non-precise intuition is that a good model of reality is that electrons do not "interact with one another directly via the electromagnetic field".

A better model happens to be the quantum field theory view that the electromagnetic field interacts with the photon field but not directly with itself, and then the photon field interacts with parts of the electromagnetic field further away.

The more precise statement is that the photon field is a gauge field of the electromagnetic force under local U(1) symmetry, which is described by a Lie group. TODO understand.

This idea was first applied in general relativity, where Einstein understood that the "force of gravity" can be understood just in terms of symmetry and curvature of space. This was later applied o quantum electrodynamics and the entire Standard Model.

From Video "Lorenzo Sadun on the "Yang-Mills and Mass Gap" Millennium problem":

Bibliography:

Respect, big respect to those people.