An imaginary coefficient in heat equation ensures no special direction in time?
Clash Royale CLAN TAG #URR8PPP up vote 9 down vote favorite In Pauli(1973): Wave Mechanics (Pauli lectures on physics Volume 5) he derives on page 4 the Schrödinger equation (similar to Tong: Lectures on QFT, p. 42) $$ nabla^2 psi' + i frac2mhfracpartial psi'partial t - frac1c^2fracpartial^2 psi' partial t^2 = 0 $$ (the last term vanishes in the limit $c rightarrow infty$) and makes the following peculiar remark: Aside from the imaginary coefficient, it corresponds to the equation of heat conduction. The imaginary coefficient assures that there is no special direction in time; [2.11] is invariant under the transformation $t rightarrow -t, psi' rightarrow psi'^*$, whereby $psi^*psi$ remains unchanged. What does he mean by "the imaginary coefficient assures there is no special direction in time"? Does the real heat equation without imaginary coefficient have a special direction in time? What does direction mean? Forward or backward? Or a d...