  The quantum space-time model which accounts material Reference Frames (RF)
quantum effects considered for flat space-time and ADM canonical gravity. As
was shown by Aharonov for RF - free material object its c.m. nonrelativistic
motion in vacuum described by Schrodinger wave packet evolution which modify
space coordinate operator of test particle in this RF and changes its
Heisenberg uncertainty relations. In the relativistic case we show that Lorentz
transformations between two RFs include the quantum corrections for RFs
momentum uncertainty and in general can be formulated as the quantum space-time
transformations. As the result for moving RF its Lorentz time boost acquires
quantum fluctuations which calculated solving relativistic Heisenberg equations
for the quantum clocks models. It permits to calculate RF proper time for the
arbitrary RF quantum motion including quantum gravity metrics fluctuations.
Space-time structure of canonical Quantum Gravity and its observables evolution
for RF proper time discussed in this quantum space-time transformations
framework.
