I have lately been concerned with time and whether or not it is an illusion. For argument's sake let's assume it is. Then time should stand on its own.
Can anyone describe, (or point me to a paper that describes) time without referring to something else.
For example, defining time without the mention of a measuring device.
Can anyone describe, (or point me to a paper that describes) time without referring to something else.
No. Nobody can. However I can point you to Presentism, and to A World Without Time: The Forgotten Legacy of Godel and Einstein. I can also point out that relativity accurately models our world using spacetime and worldlines and geometry, but that the map is not the territory, and that we live in a world of space and motion, not a block universe. I can also point you towards a clock, and tell you that the inner workings of that clock are quite aptly called a movement. I can then point out the patent blatant fact that a clock clocks up some kind of regular cyclical motion and shows you a cumulative display that we call the time. Whether it's a mechanical clock with a spring-driven rocker, a grandfather clock with a pendulum, a quartz wristwatch with a vibrating crystal, or any other kind of clock, that clock "clocks up" some kind of regular cyclical motion and shows you a cumulative display called the time. The big hand moves, and the little hand moves. That's no illusion. But it doesn't literally measure the flow of time like some magic cosmic gas-meter gizmo. Moreover I can hold my hands up a foot apart. Can you see that gap, that space between them? Yes. Now watch as I waggle my hands. Can you see that motion? Yes. Because space and motion are empirical. But can you show me time? No. You cannot. Nor can anybody else.
You've probably read Minkowski's introduction to Space and Time. He said "space for itself, and time for itself shall completely reduce to a mere shadow, and only some sort of union of the two shall preserve independence". I would venture to volunteer that had Minkowski lived longer, if he hadn't died before his time, he would have ended up writing a new paper. Called space and motion.
Can anyone describe, (or point me to a paper that describes) time without referring to something else.
The principal relevant description is surely the one which Einstein put at the foundation of the (special) theory of relativity:
"[... that instead] of ``time´´ we substitute ``the position of the little hand of my watch´´."
[Punctuation marks as in the German original: Ann. Phys. 17, 891 (1905)]
Note that the mere appearances and the distinguishability of "positions of the little hand" of some particular participant's watch, or generally: of "indications" of some particular participant, does not imply any particular durations, or duration ratios, between pairs of such indications. Consequently, Einstein's quoted description doesn't mention or involve any "measurment device" (such as any "ideal clock" whose construction is presented in MTW, §16.4).
In turn, this is of course an acknowledgement that "time" can be described only in referring to any particular identifiable participant (MTW Box 13.1 chose the description "principal identifiable point"); i.e. not exactly "naked".
p.s.
Unfortunately, IMHO, Einstein missed the opportunity to likewise dispense as plainly and rigorously with the notion of "naked place(s)", e.g. by substituting "you", or "me", or any particular participant ("just as you and me", at least for the purpose of thought-experimental description).
