  Ions in channels have been imagined as hard balls in a macroscopic mechanical
model, for a very long time. Hard balls interact by collisions in such models,
randomly knocking each other on and off `binding' sites in thermal motion. But
ions have large charge, and the hard balls of classical models do not. The
electrodynamics of charge guarantee strong correlations between the movements
of ions on all time scales, even those of atomic scale thermal motion.
Correlations are present whenever Maxwell's equations apply, so they are
present in individual trajectories, not just averages. Indeed, in a series
system like an idealized narrow channel, the correlation is perfect (within the
accuracy of Maxwell's equations) because of conservation of total current (that
includes Maxwell's displacement current, the ethereal ${\varepsilon
}_0{\partial \boldsymbol{\mathrm{E}}}/{\partial t}$).The ethereal component of
current prevents spatial variation of total current in a series system. The
stochastic complexity of spatial thermal motion disappears for current }in a
series system. Total current does not depend on location in a series system
like a narrow ion channel on any time scale. Spatial variables are not needed
in the description of total current in a one dimensional channel on any time
scale, according to the Maxwell equations. Removing the spatial dependence of
total current should dramatically simplify theories and simulations, one might
imagine.
