A Quantum theory of Gravity may require alternative way of reporting.
The experiment: A ball is thrown vertically upwards. Conventional reporting: If 'up' is treated as the positive y axis, then an observer standing on the ground would first report the velocity as positive but decreasing ( constant negative acceleration) and then as it begins to fall the velocity is reported as negative but increasing (constant negative acceleration again). In mathematical parlance the velocity and acceleration time graphs both describe 'smooth' curves. Alternative reporting: If an observer were riding in the ball, the observer would report the velocity as always being positive but first decreasing ( constant negative acceleration) and then increasing (constant positive acceleration). The reporting of the observer is akin to the passenger of a car _reading_ the speedometer. In this case a plot of the reporting reveals a quantum-like discontinuity at the moment of maximum altitude. In mathematical parlance velocity-time graph describes a 'piecewise smooth' curve and the acceleration-time graph describes a 'jumps discontinuity'. See my 60k pdf file: http://web.ncf.ca/eo200/alternative.pdf for graphical aids. Harry Veeder
