quantized relative of Laplace’s demon. Suppose there were a quantum demon with the unusual capacity to ‘see’ every detail of a closed system, without interacting with the system. (The demon doesn’t need to be physically realizable; this is just a fictional argument to make a vivid point.) The demon leaves the whole system (consisting of the measured system together with the measuring device) undisturbed and only interprets our claims on measurements and compares it with the dynamics it sees.

The demon notes the time intervals $t,u,v,\dots$ between the successive measurements $A,B,C,D,\dots$. What does it see us measure? In the Heisenberg picture, with unlabelled operators at the time of the first measurement, the state of the complete system remains unchanged, and the measurements are those of $A,B(t),C(t+u),D(t+u+v),\dots$. If we use the Heisenberg dynamics and introduce the commuting operators $\Phi_a=\exp(itH/\hbar)$, $\Phi_b=\exp(iuH/\hbar)$, $\Phi_c=\exp(ivH/\hbar)$, we see that the demon sees us measure $A, \Phi_a^*B\Phi_a, \Phi_a^*\Phi_b^*C\Phi_b\Phi_a, 
\Phi_a^*\Phi_b^*\Phi_c^*D\Phi_c\Phi_b\Phi_a, \dots$. (This is quite different from what Wigner asserts in his equation (43), where he assumes an [*additional*]{} Heisenberg dynamics of the operators between the state-reducing measurements.)

Comparing with the above interpretation of , and noting that projectors are Hermitian, we see that the difference between the unproved 