There is still no consensus among philosophers and, of course, no empirical evidence of existence of time as a phenomena of the Universe, apart from mental concept which could be derived from this or that physical processes using mathematical modeling. But for math models being proven does not imply existence. There are phenomena we call "mass", and hence phenomena we call forces, there is notion of distance, succession, rate of change, but there is no phenomena of time apart from some physical process observable by a mind. The famous clocks being accelerated is mere a mental construct.
How come that we are so convinced that time exist? Well, suppose you have arrived to some big Tibetan Monastery in Lhasa or Shigatse at the beginning of the last century. You will be overwhelmed by the architecture, paintings, buzzing activities, which all seemingly makes perfect sense for those who performs them. All the rituals, offerings, recitation of scriptures, daily duties, strict hierarchy, etc. Much like MIT nowadays.)
Unless you are questioning everything, trying to reduce everything back to first principles, being skeptical and aware of socially constructed dogmas, you will be convinced very quickly that there are various buddhas and other deities which appear and disappear upon their will, that they hide some scriptures in the past, to be revealed when humanity will be ready for the knowledge. You will study cosmology, reasoning, philosophy of emptiness, as a refinement of crude ancient Indian philosophy (which is the only real marvel Tibetan culture produced) and so on. If you are good student you will become very good rimpoche, expert in all the subtle details of the teachings. I am seasonal guide in Tibet, so I know what I am talking about.)
What do we call notions held firmly by society but which cannot be empirically proven? We call it beliefs. How do we call organized beliefs, supported by social institutions? We call it a religion. Modern quantum physics is nothing but a bunch of religious sects.
BTW, traditional Indian philosophy, which goes back to Upanishads, put the human mind in the center, so it could observe itself, how easily and readily it produces chimeras and dogmas. The two almost unbreakable of these is "myself" and "time". Upanishads were the very first systematic discourses which attempted to prove logically non-existence of these mental concepts. Still, no one managed to refute Upanishads. "A priori" established by Kant is related to that mind - an observer, not to the observed Universe.
Newtonian / Classical Mechanics is an effective theory in the technical sense[0], which means that it is independent (up to some unspecified constants) of the finer underlying details.
Yes, we may be wrong about how we see the world. But wrong is relative. No amount of science or new discovery will make us see the Earth as flat. [1]
[0] https://en.wikipedia.org/wiki/Effective_theory
[1] http://chem.tufts.edu/AnswersInScience/RelativityofWrong.htmWell, you list "rate of change" among your phenomena, but deny time as part of the phenomena. But how can rate of change be a "real" phenomena without time also being "real" in the same sense? "Rate of change" is really "rate of change with respect to time", after all.
When I look at the (often) over engineered (by modern standards) Victorian bridges and such I don't scoff because they didn't understand the tensile strength of the materials like we do now I appreciate the mastery they had at the time.
Beaides which, the pyramids are pretty remarkable from a scientific and mathematical standpoint.