If I move one watch, put it higher, and wait a little bit... with very good clocks, and today we can... you bring it [back] down, and this [the clock that was higher] is ahead, this [the clock that remained lower] is behind. ...The clock up, has measured more time than the clock down. And it's not just a matter of clocks. Everything, ...if you are high ...a flower would blossom more, a machine would do more cycles ...more things happening up than down. Of course, the difference is small, otherwise we would have noticed it ...earlier.
Italian physicist
Carlo Rovelli (born May 3, 1956) is an Italian physicist and cosmologist working in the field of quantum gravity. In 1988, Carlo Rovelli, Lee Smolin and Abhay Ashtekar introduced a theory of quantum gravity denoted loop quantum gravity.
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What is then the physical content of a solution of Einstein's equations..? ...[C]onsider what is actually measured in general relativistic experiments. ...Consider a clock at rest on ...Earth and a clock on a satellite in orbit around the Earth. ...Call T<sub>1</sub> and T<sub>2</sub> the readings... Each measures the along its own worldline, in the Earth gravitational field. ...the theory predicts the value of T<sub>2</sub> that will be associated to each value of T<sub>1</sub>. Or vice versa.
GPS... gets messages from satellites. On those satellites are clocks... The satellites broadcast the times and your little device use the time to tringulate wherever you are... [W]hen this was built the physicists told the [engineers] that were putting up the system, "Careful, up there... your clocks are going to run faster..." ...The entire project was controlled by the American army ...supervised by the generals ...[who] didn't believe it. So the first satellites were put up there with a switch... and of course it does not work if you do not take this into account. ...You would crash the car against the wall, driving with the navigator if we didn't [take] this into account ...
While non-relativistic time is the observable quantity measured (or approximated) by physical clocks, in general relativity clocks measure s along their worldline, not t. The relativistic... t is a freely chosen label with no direct physical interpretation. ...The physical content of a solution of Einstein's equations is not in its dependence on t, but ...in what remains once the dependence on t (and x) has been factored away.
Intuitively (and imprecisely) speaking, time "flows", we can never "go back in time", we remember the past but not the future, and so on. Where do all these very peculiar features of the time variable come from? ...[T]hese features... emerge at the thermodynamical level. ...[T]hese are all features that emerge when we give an approximate statistical description of a system with a large number of .
[I]n general relativistic observations there is no preferred independent time variable. What we measure are a number of variables, all on equal footing, and their relative evolution. ...[I]t can be equally read it as the evolution of the variable T<sub>1</sub> as a function of the variable T<sub>2</sub>, or viceversa. Which of the two is the independent variable here?