It is incomplete in that it cannot replace older ideas of time in all contexts. It is perfectly valid/complete for use in scientific contexts. But the general population's use the idea of time for other purposes as well where Einsteins purely Relativistic formulation cannot be a stand in replacement is how I read it.
> It is incomplete in that it cannot replace older ideas of time in all contexts. It is perfectly valid/complete for use in scientific contexts.
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.
There is a distance-free notion of time which predates, and necessarily predates, all experimental theories of time. This is (loosely after Kant):
* 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.
Cause or pre-condition? It's simple to state the pre-condition for quantum tunnelling to occur, but as a probabilistic event the cause seems hard to define...
No, none of these points are contradicted by SR or GR.
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.
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"?
Come on! I make a serious effort to be precise here, and you just don't seem to give a damn.
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.
So the idea is to assign a different "time" to each event. It's very different from physics, because physics assigns the "same" time to multiple events.
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?
I agree. In Classic Mechanic "time" an be just t (or an opaque container with t), but in Special Relativity you "time" as defined by the G...P must be (t,x,y,z) (or an opaque container with (t,x,y,z)).
> 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 :( .
