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[T-(t), T+(t)] != 0 ?

Is the time operator non-communitive? In other words, is the operation that allows time to go forward non-communitive with the operation for when time goes backward?

Normally, we absorb the operator into the variable t and then just not worry about it. But given a space-time coordinate, is the operator that moves t communitive? Space seems to be, but time's a bit screwy, and it may not be. I'm not sure yet; if [T-(t), T+(t)] != 0, then I think I have an experiment in mind that can test if it is true...


Speaking of time related subjects, I actually saw the use of dt/dt in practice this week. It turns out that the relativistic time skew experienced by satellites in orbit is a measurable parameter that one of the instruments on the satellite that I'm working on reports. Therefore, one of the outputs of a program provided to me is labeled "clockskew (s/s)".