  The concept and subsequent experimental verification of the proportionality
between pulse amplitude and detector transit time for microchannel plate
detectors is presented. This discovery has led to considerable improvement in
the overall timing resolution for detection of high energy gamma photons.
Utilizing a 22Na positron source, a full width half maximum (FWHM) timing
resolution of 138 ps has been achieved. This FWHM includes detector
transit-time spread for both chevron-stack type detectors, timing spread due to
uncertainties in annihilation location, all electronic uncertainty, and any
remaining quantum mechanical uncertainty. The first measurement of the minimum
quantum uncertainty in the time interval between detection of the two
annihilation photons is reported. The experimental results give strong evidence
against instantaneous spatial-localization of gamma photons due to
measurement-induced nonlocal quantum wave-function collapse. The experimental
results are also the first that imply momentum is conserved only after the
quantum uncertainty in time has elapsed [H. Yukawa, Proc. Phys. -Math. Soc.
Japan, 17, 48 (1935)].
