On Jan 8, 2006, at 2:29 PM, Jones Beene wrote:
Horace
What happens to the angular momentum? This seems to deny
conservation of angular momentum.
No problem there. 1 - 1 = 0 All balances before and after pair
formation.
That doesn't look like a proper cross product, or else I don't
understand the full situation.
Conservation of angular momentum is conservation of the vector *sum*
of the constituants of a system.
You have studied this more than me, obviously, but I was under the
impression that as a psuedovector there would be no such additive
cancellation. However, being mildly dyslexic I often get these
kinds of spin things confused, so please correct this line of
reasoning. Angular momentum is a pseudovector. Often, the
distinction between vectors and pseudovectors is overlooked, but it
only becomes important in understanding the effect of symmetry on
the solution to physical system interactions. A pseudovector is a
quantity that transforms like a vector under a proper rotation, but
gains an additional sign flip under an improper rotation (a
transformation that can be expressed as an inversion followed by a
proper rotation which is what we have here with two electrons - an
improper rotation). It follows that any improper rotation
multiplies the cross product by -1 compared to a true vector.
My take on the bottom line of this is that the angular momentum
cancellation you seem to be basing this premise on cannot happen in
normal physics.
...or did I get dyslexic again ?
Jones
You are making the simple complex. Since before and after the
proposed superposition the electrons share the same axis, view the
electron angular momenta along a single axis. You don't need to
think in vector addition terms then, just simple addition. The
moments before superposition are +mu and -mu respectively. +mu - mu
= 0 Net momentum of the system is zero. Afterwards the angular
momentum is still zero. The net momentum of two counter-spinning
gyros is zero.
Horace Heffner
