that the states of the environment that correspond to different states of the system are almost orthogonal. The environment, then, is said to “continually measure” the system and it is stressed that such “measurement” does not require a human observer of any sort.

Now let us see how all this works more formally. Suppose we have a quantum system whose initial state is some superposition $\frac{1}{\sqrt{2}} \left( |\psi_1 \rangle + |\psi_2 \rangle \right)$ and we let it interact with its environment, with initial state $|E_0 \rangle$. As a result of what we said above, the evolution will look as follows $$\label{sE}
\frac{1}{\sqrt{2}} \left( |\psi_1 \rangle + |\psi_2 \rangle \right) |E_0 \rangle \xrightarrow{Schrödinger} \frac{1}{\sqrt{2}} \left( |\psi_1 \rangle |E_1 \rangle+ |\psi_2 \rangle |E_2 \rangle \right) ,$$ with $\langle E_1|E_2 \rangle \approx 0$. Next it is argued that, since we are interested in the system, and not the environment, we can trace over the degrees of freedom of the environment and construct a reduced density matrix for the system, $\rho_S$, which contains a complete description of its measurement statistics. The result is $$\begin{aligned}
\rho_S &=& \frac{1}{2} \left\{ |\psi_1\rangle\langle\psi_1|+|\psi_2\rangle\langle\psi_2|+|\psi_1\rangle\langle\psi_2|\langle E_2|E_1 \rangle+|\psi_2\rangle\langle\psi_1|\langle E_1|E_2 \rangle\right\} \nonumber \\
&\approx& \frac{1}{2} \left\{|\psi_1\rangle\langle\psi_1|+|\psi_2\rangle\langle\psi_2|\right\} .\end{aligned}$$ What we obtain, then, is 