Similar to quantum jump in the Bohr model, but for the Schrödinger equation.

The idea the the wave function of a small observed system collapses "obviously" cannot be the full physical truth, only a very useful approximation of reality.

Because then are are hard pressed to determine the boundary between what collapses and what doesn't, and there isn't such a boundary, as everything is interacting, including the observer.

The many-worlds interpretation is an elegant explanation for this. Though it does feel a bit sad and superfluous.

The most minimal hello world with gnuplot visualization!!! stackoverflow.com/questions/11175694/bullet-physics-simplest-collision-example/36987063#36987063

The term "Logic alphabet" typically refers to the symbols and notations used in formal logic and mathematical logic to represent logical expressions, propositions, and operations. Here are some common components of a logic alphabet: 1. **Propositional Variables**: Often denoted by letters such as \( P, Q, R \), etc., these represent basic propositions that can be either true or false. 2. **Logical Connectives**: These symbols are used to connect propositional variables.

Does not seem to support it unfortunately:

Python library for Bullet Physics.

Became very popular as of result of people using Bullet Physics for reinforcement learning AI training robot simulations.

Website: pybullet.org/

Source code: somewhere inside the main Bullet Physics source tree. Yay.

Notation used in quantum mechanics.

Ket is just a vector. Though generally in the context of quantum mechanics, this is an infinite dimensional vector in a Hilbert space like $L^2$.

Bra is just the dual vector corresponding to a ket, or in other words projection linear operator, i.e. a linear function which can act on a given vector and returns a single complex number. Also known as... dot product.

For example:is basically a fancy way of saying:that is: we are taking the projection of $y$ along the $x$ direction. Note that in the ordinary dot product notation however, we don't differentiate as clearly what is a vector and what is an operator, while the bra-ket notation makes it clear.

The projection operator is completely specified by the vector that we are projecting it on. This is why the bracket notation makes sense.

It also has the merit of clearly differentiating vectors from operators. E.g. it is not very clear in $x\cdot y$ that $x$ is an operator and $y$ is a vector, except due to the relative position to the dot. This is especially bad when we start manipulating operators by themselves without vectors.

This notation is widely used in quantum mechanics because calculating the probability of getting a certain outcome for an experiment is calculated by taking the projection of a state on one an eigenvalue basis vector as explained at: Section "Mathematical formulation of quantum mechanics".

Making the projection operator "look like a thing" (the bra) is nice because we can add and multiply them much like we can for vectors (they also form a vector space), e.g.:just means taking the projection along the $x+y$ direction.

Ciro Santilli thinks that this notation is a bit over-engineered. Notably the bra's are just vectors, which we should just write as usual with $\overrightarrow{v}$... the bra thing makes it look scarier than it needs to be. And then we should just find a different notation for the projection part.

Maybe Dirac chose it because of the appeal of the women's piece of clothing: bra, in an irresistible call from British humour.

But in any case, alas, we are now stuck with it.

Was a closed source project by "Roboti LLC", which was then acquired by DeepMind in October 2021 and open sourced March 2022: www.deepmind.com/blog/open-sourcing-mujoco

This library is quite cool. Feel very brutally lean and mean.

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Teresa Montaruli is an Italian astrophysicist known for her research in the fields of particle astrophysics and cosmology. She has contributed to the understanding of high-energy cosmic phenomena and is associated with various projects related to astroparticle physics. Montaruli has also been involved in the development of observatories and experiments aimed at investigating cosmic rays, neutrinos, and other fundamental particles.

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