>It's not that the electrons follow a curved path instead of a straight
>one, it's that they follow a path which is unknowable except
>probabilistically.
>
huh??? what are those tracks in the bubble chambers? chopped liver???
paths are approximately *knowable* (what happened in between the bubbles?), radius of curvature and all, and are probabilistically *predictable*. David Bohm and others wrote extensively on this many years ago.
>Again, quantum mechanics predict (and we observe in
>the world) that a particle can take a path which violates geometry,
>not which adheres to a curved or alternate geometry.
>
this is pointless, without adding the motivations from the early part of last century for us to drop the concept of a precise trajectory for sub-atomic particles. QM is a result of placing position and speed (momentum) one step down in the hierarchy of fundamental attributes. now we have a particle's STATE as fundamental (one level of abstraction deeper than Newton's mechanical universe) -- containing possibilities -- and position and momentum (x,p) are represented differently in the new physics. rather than precise attributes of a distinct trajectory, (x,p) now become, essentially, selectors, picking out one of the various possibilities. this was done on purpose, since holding to the notion of a classical trajectory created grave headaches that wouldnt resolve after a lot of appealing to the classics.
>There's no
>geometric explaination for a particle going through an impenetrable
>barrier,
>
sure there is (only partly tongue in cheek). the barrier is not high or wide enough, so the particle's wave function doesnt decay to zero on the other side sufficiently fast. hence it leaks thru at a (sometimes) fast rate. alpha decay (depleted uranium decay mode) is a tunneling process.
and let us not forget the scanning tunneling microscopes....
http://physics.nist.gov/GenInt/STM/stm.html
http://en.wikipedia.org/wiki/Scanning_tunneling_microscope
which gives us some of the sharpest geometric pictures around.
so why do people insist on the old clockwork picture of the universe (with its attendant position/momentm specified trajectory) as if its more realistic? this kind of realism was deliberately avoided a century ago because experimental results forced us to scatch our heads. even Bell's great foray into questioning local realism forgets this history. why do we insist that realism means we have to see springs and gears and pinions and camshafts and timing belts everywhere we look?
> or going faster than the speed of light
>
individual waves can travel faster than light, but not their wave packets, in vacua. individual "plane waves" representing particles moving in a given direction with a given sharp momentum (commensurate with a speed less than that of light) give finite and uniform probability for finding the particle ANYWHERE in that dimension, so there's no headache. when you add different "momentum waves" together to get a geographically localized particle (and then the momentum smears out), the speed of the wave packet itself drops below the speed of light. this was all asked and answered in the 1920's.
there is some interesting stuff on "faster-than-light" in tunneling experiments:
http://www.aei-potsdam.mpg.de/~mpoessel/Physik/FTL/tunnelingftl.html
>or taking more than one path simultaneously
>
this is true. superposition is a fact of life.
les schaffer