popular science - Is there a proof of existence of time?

It seems to me that there is no such thing as time. There is only movement in the universe and we compare our own movement to a different object to have a sense of time. It can be a clock or a atomic vibration.

Does this view of time work within the current framework of phsics?

Do physicists have an explanation/proof about time's existence?

Answer

It's easy to get mixed up between time and the flow of time, and I think you've done this in your question.

Take time first: since 1905 we describe any event as a spacetime point and label it with four co-ordinates ($t$, $x$, $y$, $z$). Saying that time doesn't exist means we can ignore the time co-ordinate and label everything by just it's spatial co-ordinates ($x$, $y$, $z$), which is contradiction with observations. The time co-ordinate obviously exists and be used to distinguish events that happen at the same place but at different times.

Now consider the flow of time: actually this is a tough concept, and relativity makes it tougher. We all think we know what we mean by the flow of time because we experience time passing. To take your example of movement, we describe this as the change of position with time, $d\vec{r}/dt$, where we regard time as somehow fundamental. I'm guessing that this is what you're questioning i.e. whether the flow of time is somehow fundamental.

I don't think there is a good answer to this. To talk about the flow of time you'd have to ask what it was flowing relative to. In relativity we can define the flow of co-ordinate time relative to proper time, $dt/d\tau$, and indeed you find that this is variable depending on the observer and in some circumstances (e.g. at black hole event horizons) co-ordinate time can stop altogether. But then you'd have to ask whether proper time was flowing. You could argue that proper time is just a way of parameterising a trajectory and doesn't flow in the way we think time flows.

At this point I'm kind of stuck for anything further to say. If I interpret your question correctly then you do have a point that just because we observe change of position with time (i.e. movement) this doesn't necessarily mean time is flowing in the way we think. However I'm not sure this conclusion is terribly useful, and possibly it's just semantics.