Ciro Santilli @cirosantilli 37

Relates particle momentum and its wavelength, or equivalently, energy and frequency.

The wavelength relation is:but since:the wavelength relation implies:

Particle wavelength can be for example measured very directly on a double-slit experiment.

So if we take for example electrons of different speeds, we should be able to see the diffraction pattern change accordingly.

Notably, convolution can be implemented in terms of GEMM:

In 1962 Brian Josephson published his inaugural paper predicting the effect as Section "Possible new effects in superconductive tunnelling".

In 1963 Philip W. Anderson and John M. Rowell published their paper that first observed the effect as Section "Possible new effects in superconductive tunnelling".

Some golden notes can be found at True Genius: The Life and Science of John Bardeen page 224 and around. Philip W. Anderson commented:

As part of the course Anderson had introduced the concept of broken symmetry in superconductors. Josephson "was fascinated by the idea of broken symmetry, and wondered whether there could be any way of observing it experimentally."

Once upon a time, this must have been a nice covered market.

But as of 2020, it is completely surrounded by extremely poor people, to the point that it makes you scared if you stand out in any way by showing any kind of middle/upper class wealth, or being a foreigner.

The market is basically a touristic spot that no person in Sao Paulo will ever go to (unless they are young, single, and can just walk in there by themselves) in the middle of this surreal environment.

In 2020 Ciro was there with his wife on a touristic visit. Living in Europe at the time, he felt even more privileged. So they went to a fruit stand, and the man started giving his wife amazing free samples of very exotic fruit, some of which Ciro had never tasted himself, without saying the price. It did feel like he was giving out too much for free. Then Ciro decided of course to buy some more fruits to pay for the show, which was a nice show. Then while buying, it came out a bit more expensive than would have been reasonable, but Ciro was too dazzled by the speed and noises, and he paid for it. Later on, he told his wife about it, and how he felt that they had added some ultra-expensive bulk fruits that were of a clearly lower level than the gold nuggets of the free samples (especially for Brazil's cost standards). The presenter was an extremely crafty con artist, and Ciro felt like they had specifically preyed on Ciro Santilli's self perceived compassionate personality, because it was apparent that those men were underprivileged and fighting for their living day by day with those over-expensive fruits. This was an extremely valuable lesson, Ciro was glad that it was learnt at a relatively low cost on that occasion.

Web of Stories 1997 interview playlist: www.youtube.com/playlist?list=PLVV0r6CmEsFxKFx-0lsQDs6oLP3SZ9BlA

The way this dude speaks. He exhales incredible intelligence!!!

In the interviews you can see that he pronounces names in all languages amazingly, making acute effort to do so, to the point of being notable. His passion for linguistics is actually mentioned on Genius: Richard Feynman and Modern Physics by James Gleick (1994).

Maybe this obsession is partly due to his name which no English speaking person knows how to pronounce from the writing.

This passion also led in part for his names to some physics terminology he worked on winning out over alternatives by his collaborators, most notably in the case of the naming of the quark.

A suggested at Physics from Symmetry by Jakob Schwichtenberg (2015) chapter 3.9 "Elementary particles", it appears that in the Standard Model, the behaviour of each particle can be uniquely defined by the following five numbers:

E.g. for the electron we have:

Once you specify these properties, you could in theory just pluck them into the Standard Model Lagrangian and you could simulate what happens.

Setting new random values for those properties would also allow us to create new particles. It appears unknown why we only see the particles that we do, and why they have the values of properties they have.

Given a matrix $A$ with metric signature containing $m$ positive and $n$ negative entries, the indefinite orthogonal group is the set of all matrices that preserve the associated bilinear form, i.e.:Note that if $A=I$, we just have the standard dot product, and that subcase corresponds to the following definition of the orthogonal group: Section "The orthogonal group is the group of all matrices that preserve the dot product".

As shown at all indefinite orthogonal groups of matrices of equal metric signature are isomorphic, due to the Sylvester's law of inertia, only the metric signature of $A$ matters. E.g., if we take two different matrices with the same metric signature such as:and:both produce isomorphic spaces. So it is customary to just always pick the matrix with only +1 and -1 as entries.

Intuitive definition: real group of rotations + reflections.

Mathematical definition that most directly represents this: the orthogonal group is the group of all matrices that preserve the dot product.

The degree of some algebraic structure is some parameter that describes the structure. There is no universal definition valid for all structures, it is a per structure type thing.

This is particularly useful when talking about structures with an infinite number of elements, but it is sometimes also used for finite structures.

Examples:

Demo under: nodejs/sequelize/raw/many_to_many.js.

NO way in the SQL standard apparently, but you'd hope that implementation status would be similar to UPDATE with JOIN, but not even!

The problem of deletionism is that it removes users' confidence that their precious data will be safe. It's almost like having a database that constantly resets itself. Who will be willing to post on a website that deletes the content they created for free half of the time thus wasting people's precious time?

The best example to look at first is the penalty kick left right Nash equilibrium.

Then, a much more interesting example is choosing a deck of a TCG competition: Magic: The Gathering meta-based deck choice is a bimatrix game, which is the exact same, but each player has N choices rather than 2.

The next case that should be analyzed is the prisoner's dilemma.

The key idea is that:

An impossible AI-complete dream!

It is impossible to understand speech, and take meaningful actions from it, if you don't understand what is being talked about.

And without doubt, "understanding what is being talked about" comes down to understanding (efficiently representing) the geometry of the 3D world with a time component.

Not from hearing sounds alone.

The Klein-Gordon equation directly uses a more naive relativistic energy guess of $p^2+m^2$ squared.

But since this is quantum mechanics, we feel like making $p$ into the "momentum operator", just like in the Schrödinger equation.

But we don't really know how to apply the momentum operator twice, because it is a gradient, so the first application goes from a scalar field to the vector field, and the second one...

So we just cheat and try to use the laplace operator instead because there's some squares on it:

But then, we have to avoid taking the square root to reach a first derivative in time, because we don't know how to take the square root of that operator expression.

So the Klein-Gordon equation just takes the approach of using this squared Hamiltonian instead.

Since it is a Hamiltonian, and comparing it to the Schrödinger equation which looks like:taking the Hamiltonian twice leads to:

We can contrast this with the Dirac equation, which instead attempts to explicitly construct an operator which squared coincides with the relativistic formula: derivation of the Dirac equation.

Where derivation == "intuitive routes", since a "law of physics" cannot be derived, only observed right or wrong.

TODO also comment on why are complex numbers used in the Schrodinger equation?.

Some approaches:

The derivative of a function gives its slope at a point.

More precisely, it give sthe inclination of a tangent line that passes through that point.