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.
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”
I just started my own WordPress page and came across several different tutorials to use Mathjax and Markdown in my blog.
The easiest and most convenient way to do this is probably the following: