From chaos to order
In connection with classical mechanics and its formulation in terms of a least action principle there exists a remarkable theorem, the so called Noether theorem. It states:
For every continuous symmetry of a physical system, there exists a conserved quantity.
The reverse of this statement is also true as we will see later.
Continue reading “Noether’s theorem”In this post I will show you how to setup jupyter notebooks with pip under Windows. Also we will go through the process of creating virtual environments with pipenv and adding them to the kernel list in jupyter.
There are two very interesting emails in the Wikileaks archive of Clinton mails, which were leaked and published during the US election in 2016. They shed a different light on the commonly used rhetoric of a civil war in Libya. These emails were also released under the freedom of information act, however this source has already been removed. Continue reading “Leaks on Libya during civil war”
In classical, non-relativistic particle mechanics the action of a system is given by
$$ S[\vec{q}(t)] = \int_{t_1}^{t_2} L(\vec{q}, \dot{\vec{q}}, t) ~ dt $$
which is a functional $S: F^n \rightarrow \mathbb{R}$, i.e. it maps the $n$ functions $\vec{q}(t) = (q_1(t),\dots,q_n(t)) \in F^n$ of some function space $F$ onto the real numbers. Continue reading “The Euler-Lagrange equation and the principle of least action”
This is a nice video series of Numberphile about Gödel’s incompleteness theorem, which states that in every axiomatic system there are statements that cannot be proved. Continue reading “Gödel’s Incompleteness Theorem”