usually abbreviated to the CFL-condition, says that in any time-marching computer simulation, the time step must be less than the time for some significant action to occur, and preferably considerably less.
For example, if we have a computer simulation of a satellite orbiting a planet, the discrete time interval which we use must obviously be less than the orbital period on common sense grounds. We can guess that for the sake of stability, it must be less than one quarter of the orbital period, and in practice we will take a step of about one fortieth of the orbital period.
This poses problems for many-body computer simulations. If two bodies have a close encounter, then we need short time steps to capture the detail of the encounter correctly. However, the bodies spend most of their time far apart from each other, where lots of ultra-short time steps would be inappropriate. Nothing would ever happen!
The CFL condition was originally formulated in the context of compressible fluid flows. If we divide the flow field up into boxes, then we need a time step less than the time taken for a sound wave to cross one of the boxes. If we are trying to simulate flow which is only slightly compressible or practically incompressible, then we will require many very short time steps. In practice we might wish to opt for an incompressible-flow method such as Alexandre Chorin's vorticity-in-Brownian-motion.
Now what about quantum mechanics, where things can go faster than light, and at infinite speed from the point of view of some observers? Surely the CFL condition would be fatal for our prospects of simulating wave-particle duality?
Computer simulations of the Dirac equation pose no problem. The Dirac pilot waves travel faster than light, but whatever they are physically, numerically they are no more than moiré patterns which we can simulate without difficulty.
The problem comes when the envelope of the Dirac wave packet also has to travel at superluminal speed, as it must do in order to allow the illusion that a particle is in two places at once, this being the standard illusion of quantum mechanics. There is an assumed principle that any model of wave-particle duality must not be beaten by the CFL condition. This is of course taking it for granted that computer simulation is the way forward.
Imagine a soil with slight variations in fertility in which we plant and rake in some grass seed. As the grass grows, the appearance of the ground will become greener. Due to the variations in fertility, waves of greenness will appear to move sideways. There is nothing to stop these waves moving at superluminal speed, since they are not physical entities and do not carry information.
The nonlocal natural Vernam cipher proposed on this website may likewise 'seed' space so that the envelope of the Dirac wave packet can travel at superluminal speed without running into trouble with the CFL condition. This remains to be shown. We can certainly say that any less sophisticated idea will run into trouble, so there are no short cuts or easy options. Research continues.