Introduction
There are $2$ systems $1$ and $2$. Let the Hamiltonian of system $1$ be $H_1$ and let it be in an energy eigenstate:
$$ \hat H_1|E_m \rangle = E_m |E_m \rangle $$
Now, a measurement is done (forcing the system to a momentum eigenstate):
$$ \hat p |p_j \rangle = p_j |p_j \rangle$$...
In this paper1 on the history of functional analysis, the author mentions the following example of an infinite system of linear equations in an infinite number of variables $c_i = A_{ij} x_j$:
\begin{align*}
\begin{array}{ccccccccc}
1 & = & x_1 & + & x_2 & + & x_3 & + & \dots \\
1 & = & & &...
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The Ehlers–Geren–Sachs theorem, published in 1968 by Jürgen Ehlers, P. Geren and Rainer K. Sachs, shows that if, in a given universe, all freely falling observers measure the cosmic background radiation to have exactly the same properties in all directions (that is, they measure the background radiation to be isotropic), then that universe is an isotropic and homogeneous FLRW spacetime, if the one uses a kinetic picture and the collision term vanishes, i.e. in the so-called Vlasov case or if there is a so-called detailed balance. This result was later extended to the full Boltzmann case by ...
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