the causality problem and tunneling?
Tunelling is a quantum effect which consists in the existence of a non zero probability of that a point particle with energy E passes through a finite width potential barrier V(x)>E .
The causality of physical phenomena states that the effect cannot precede the cause.In classical dynamics,causality is questioned whenever forces that depend of the acceleration derivatives wrt to time appear.I would infer you to the analysis of the Abraham-Lorentz equation in the classical electrodynamics (can be found in Jackson...)
still unclear on the tunneling I am not fimilar with non zero probability (do u mean of being in a location?) and finte width potential Barrier
Classically,the particle has no chance to penetrate that potential barrier,as its energy is less than the barrier's.But QM proves that this becomes possible (has a non zero probability (do u know what probabilities are...?)) once the system is quantized.Yes,the probability of passing through could be seen as the probability of finding the particle anywhere in the semiinfinite interval between the point at which the particle exits the potential barrier and the +infinity on the axis describing the direction of movement.I assumed the particle comes from -infinity.That's why the potential barrier must be finite,both as width and as height.If it wasn't finite along the "x" axis (if it didn't have a finite width),we would not be speaking about the tunnel effect.If it were infinitely hight,we would not speak about tunnel effect,but about "delta potential problem".
I hope it's clear.
Separate names with a comma.