Hello Don,
You have stimulated my interest in the Uncertainty principle, which I wish you luck in its modification or overthrow. I am not really keen in joining that desirable task but I may chip in my thoughts. The following are excerpts on the subject from Wikipedia:
"the uncertainty principle actually states a FUNDAMENTAL property of quantum systems, and is not a statement about the OBSERVATIONAL success of current technology. It must be emphasized that measurement does not mean only a process in which a physicist-observer takes part, but rather any interaction between classical and quantum objects regardless of any observer"
"A nonzero function and its Fourier transform cannot both be SHARPLY LOCALIZED"
"For any two conjugate variables like position and momentum--the more precisely one is known, the less precisely the other can be known"
Heisenberg wrote: It can be expressed in its simplest form as follows: One can never know with perfect accuracy BOTH of those two important factors which determine the movement of one of the smallest particles--its position and its velocity. It is impossible to determine accurately BOTH the position and the direction and speed of a particle at the same instant. Heisenberg imagines an experimenter trying to measure the position and momentum of an electron by shooting a photon at it. If the photon has a short wavelength, and therefore, a large momentum, the position can be measured accurately.
MY QUESTION: How accurately can ONE, not both ever be measured? In particular, how *sharply localized* can position be determined? Can position be accurately measured beyond the Planck dimension, 10^-35m which has no further part? If position cannot be localized beyond this, does the uncertainty relation not then imply that the imprecision or uncertainty is actually limited by this Planck limit and not necessarily because of any relationship between conjugate variables? Note the Planck value as well in the uncertainty equation seems to indicate this limit.
Take note that I am not expert in these matters
Pls. I am copying Gordon Watson whose turf is on Bell's inequalities proposition and whose judgement one can possibly trust. A proposition which I now see arose from attempts to resolve difficulties brought about by what to make of the Uncertainty relation and the initial EPR Paradox attempts to modify it.
Regards,
Akinbo
