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RE: Defining time with atomic fountains
Thanks for the nice comment!
time is not an actual existing force that pushes or pulls or physically alters anything at all
No it is not. Time is defined from something and that's it.
To answer the rest of the comment, time is a relative quantity and not an absolute one. For instance, as soon as gravitational effects matter, one needs to account for general relativity corrections. For the same reason we need to measure time very precisely in fact: this will allow us to test general relativity to a very high level of precision. See here for an experiment connected to this :).