Distances in our world (classically at least) can be defined by considering our world to be a model for the Euclidean normed three dimensional space. But how can we set the notion of time on a firm footing? What are the first principles here?
Because almost everywhere in physics, we want to see how a system evolves with “time”. But when I think about it, I can’t find a clear understanding of what time is.
I’m not talking of “the arrow of time”, just time.
Before relativity also, physicists worked with time rates. But how can we be sure that a ticking device is measuring time linearly? As far as I can see, there must be a guaranteed (local, for relativity) existence at every place in the universe of some time keeping mechanism which is infinitely accurate and can be accessed by the observer to read off the time differences between events he observes.
What guarantees such existence?
Basically what I’m asking is against what the rate of time flow is measured. Or asking it is nonsense?
Is there some different way to firmly define this notion?
This is NOT the same question as the marked question, here.
Here, I ask how do we assure that a time keeping device ticks at “equal” intervals? How do we measure these “equal intervals” with? We surely can’t rely on our perception for it.
It is much like (to me) the problem of defining temperature in classical thermodynamics. We have to resort to statistical theory for a firm definition of it. We just can’t say that temperature is proportional to the height of mercury column in a thermometer. Because we’ll, it just isn’t...