Right, but as you know, the tracks in bubble chambers happen after an interaction that causes the wave function to decay and thus you see a nice, observable path. It is not the only path the electron could have followed, only one of may superposable tracks. Which one it takes is only knowable after the wave function breaks down.
Einstein insisted that, at some level, a particle must "hold" properties which makes its track predictable, although he was talking about "spooky action at a distance". Since this part of the discussion started because one of the group insisted that the mechanism of gravity was known because of Einstein's theory, I think folks should check out the article that was in the NY Times on Tuesday which basically declares that in the battle between Einstein and the Quantum Mechanicals, Einstein has decisively lost.
> >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.
Right, and since the original proposition that I was contesting was that gravity was a product of the geometry of space-time, it's important to point out that at a fundamental level the notion of a universal geometry is unworkable. As you point out, the problems that Quantum mechanics were developed to deal with came to light as a result of experiments that showed the geometry of space-time failing at the level of particles.
> >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.
Right, very cute. The point is that geometry sees a barrier as a barrier and quantum mechanics sees it as *probably* a barrier (but possibly not). To take as much license as you did, in Euclidean geometry two parallel lines *never* intersect. In non-Euclidean geometry two parallel lines *defnitely* intersect. In a Quantum Mechanical "geometry" two parallel lines *probably* intersect, but maybe not.
> 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.
- by violating geometry
> 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?
Well, I think it's understandable. If a genius as great as Einstein whose mind could conceptually re-shape the universe for all humankind couldn't accept the reality of quantized particles, then a definite, geometrical notion of the universe must be pretty appealling.
> 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.
Right, I know this but it is still neat that people have experimentally observed particles travelling at speeds faster than the speed of light. I also think it's interesting for this discussion that the way you measure a particle travelling faster than the speed of light (but not, admittedly, its wave packet) is by forcing it to tunnel (or rather sorting particles that tunnel). When a particle tunnels, it "travels" faster than the speed of light so you have violation upon violation of geometry and the "rules" of space-time. At least they are violations if you insist on thinking the particle follows a knowable geometry rather than its wave packet.
> 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.
All I was saying.
boddi