This is hard to get on board with. A theory of time is incomplete without a history of clocks? Have I misunderstood?
Some philosophers and other types of scholars would question whether we should cede all sense of reality to that which can be objectively measured. You might say that there's no one "real" time. Perceptual time is real because it matters to the person experiencing it.
I don't think the point is to deny objective time or physics, but just to say that it is incomplete as a way describing lived reality. And probably also that we'll never have an understanding of neurology that's complete enough to let us even fully characterize perceptual time scientifically.
So, we should accept that there is more to time than what physics can tell us.
Perhaps we should use two different word for the "perceived time" and for the "clock time". The good days, when I go to sleep all the night appears to go away in an instant, but it isn't. It's more useful to have a physical defined "clock time" and then explain why the brain is bad estimating durations using the "perceived time".
It seems to just be saying: your theory uses clocks to illustrate it but doesn't include the history of clocks. I don't think that's quite what you're describing.
* Every thing that happens, happens at a time. Let's call those things "events" from now on. It's nonsense to claim that a thing happened, but never (at any point in time) happened.
* Every event happens in a place. It's nonsense to say that a thing happened, but nowhere happened.
* Every event MAY be related to one or more events, called its causes.
* There is an ordering on points in time, so that an event's time-point comes after the time-point of all its causes.
Without these assumptions, how are you going to do experiments, or draw any conclusions about the world? In fact you pretty much need one more, which is that every event has at least one cause (otherwise there's not much point in scientifically investigating it). These basic categories are certainly no replacement for physics. They're just the bare minimum to start an investigation into physics. But if the way you describe your physics contradicts it, then at best there's a communication problem.
Einstein showed us this more than 100 years ago - please keep up.
The points do not imply Newtonian physics, or any kind of physics at all, because they assert only a ordering relation on events. They put no measure on those things, and certainly no absolute measure.
You clearly also did not understand the problem of trying to do experiments, or even to learn from experience at all without assuming these things.
Really, how much clearer could I have made those things?
What is a "time"? Is it a number? A string like "uyeuhwydyjghafjhbhsjahsgg"? Some opaque object? Is it possible to compre the "time" of two different events? If there are two different events, did they happen at the same "time" or at different "time"?
Time is a word, and I'm trying to establish the absolute minimum common sense rules for using that word. Obviously we have to use other words to do that, words like "event", "cause" and "order" (note, not "object"). But that's OK, the point is to explain what we mean by these words in relation to each other.
To answer your questions explicitly:
* Time, in this philosophical, pre-experimental sense, is not a number. It does not have anything like a unit or scale. It's certainly not a gobbeldygook string.
* You can only order the time of two events, and only if one is in the set of causes of the other (or the causes of causes etc. Talking about an ordering implies that, I hope you agree.) If an event A has two causes B and C, all we can say for sure is that the times of B and C are ordered before the time of A, because that's what we mean by these words, time, cause and event.
* No, you can never say for sure that something happened at the same time. You can maybe order the times, if they are in a causal chain - in that case it makes no sense to say they're equal. If they are not in a causal chain with each other, you can say nothing about their order (or equality). We know nothing about the order of B and C.
In Newtonian Mechanics, everyone agree to assign the same time to the same collection of events.
In Special Relativity, the same time is assigned to different collections of events by different observers.
In General Relativity, it's more complicated.
Back to your original comment
>>> *Every event happens in a place.
Does each event get a different place, of places can be shared between events?
> Does each event get a different place, of places can be shared between events?
Why is this even a question? It is obvious from the definition that two events can happen at the same place at different times.
The theory instead (wisely) says nothing about events happening at the same time.
> Why is this even a question?
It's very strange that two events can not share the same "time". This is not the usual definition of time in physics [1]. So it's a natural question if the same strange property apply to "place".
Also, the definition of "time" in a world with special relativity makes it necessary to include (x,y,z) so "time" includes all the information included in "place". Why is it necessary to have both concepts?
[1] I think it gets more complicated in General Relativity, but I never took that course :( .
They perfectly match the idea of events as 4D points in Minkowsky space time. Points 1 and 2 are matched by describing any event by its (x, y, z, t) coordinates in some reference frame. Point 4 is matched by the fact that the Lorrentz transform preserves the ordering by t of events which are timelike separated.
Many seem to forget that even in relativity, all observers agree on the order of events that are close enough together in space. For example, any possible observer agrees that the pyramids are older than Hacker News (though they will disagree on how much older).
What the GP is saying is that this framework definition of time is in fact a series of requirements that any physical theory of time must fulfill to be recognizable as talking about time. That is, any theory that doesn't match those criteria is not talking about the same thing we are when we say time.
Do you know of any completely physically correct theories?