Alex,
****1. Particle tunnels because it ALREADY IS outside the barrier. You just sometimes find it outside, sometimes inside according to its wave function. So, this is INCORRECT example. No violations of 1st law seen.****
I'm talking about *before* the particle 'tunnels' and what subsequently happens after. For example, in alpha decay the particles can escape from the nuclei even though they are restrained by the strong force. If all the alpha particles were already outside grasp of the strong force of the nuclei, then alpha decay would happen instantaneously, right? But, alpha decay happens at a computed rate - which is in line with what we would expect if a particle tunnels through the potential. That is, as the state of the alpha particle evolves in time there is a finite probability that the particle will exist outside the potential well. This contradicts Newton's first law in that there is a force acting to keep the particle within the nuclei and *no force* holding the particle within the nuclei, yet the particle *escapes* anyway.
****2. delta p/delta t operator is exactly the analog of force in quantum mechanics, F = delta p/delta t. So, indeed second Newton law is still valid.****
Does delta p/delta t - F = zero? Yes or no.
*3***Every action in QM has exactly opposite reaction. It can't be othervise, because it follows from symmetry of space (x is the same as -x). As a consequence, momentum conserves. I never heard that momentum does not conserve in QM.****
Yeah, I should have mentioned the standard model (not QM). The creation of massive particles (e.g., the W particle) temporarily doesn't conserve momentum (i.e., masses of the particles are temporarily not conserved). Although, if I remember correctly, Feynman's path integral seems to suggest that particles take every possible path - even paths that do not conserve momentum unless all the paths are considered as a whole. Maybe I have that wrong?
http://www2.slac.stanford.edu/vvc/theory/virtual.html
Warm regards, Harv |