johanfprins wrote:charliem wrote:tomclarke wrote:
This is a loose statement, but yes, if the twins meet up again relative ages depend on there previous movements.
Tom, if I recall correctly you say that Johan's defend the existence of an universal time, and that that doesn't exist.
Doesn't your interpretation implies the existence of privileged FOR?
Brilliant questions. Yes Tom's interpretation is doing exactly this.
See my reply above. There is a natural reference frame since the twins end up and start in the same frame. If you don't use this, then the precise age difference cannot be determined (unless it is 0).
It is really a no-brainer to see that if any inertial reference frame can be used to get the same experimental results, then the time-rate of clocks within all inertial reference frames must be exactly the same.
No-brainer in the sense of brainless. The statement is extremely ambiguous. What do you mean by time-rate of clocks? If you mean local time-rate relative to physical processes in their rest frame the answer is tautologically yes.
If you mean some sort of comparison between clock rates in different frames the answer is in general no - with the caveat that in clocks in different frames cannot have rates compared except relative to some priviledged frame. Note that without specifying the frame (or implying it, since sometimes a canonical frame is obvious) the comparison does not have a definite answer. (There are specific cases when it does, as when the two clocks are measured at the same spatial position and the time difference is zero).
Time can only change with position within a gravity field.
That is a particularly meaningless comment.
(1) Time is a dimension of (scalar function on) a 4D space.
(2) A unique frame-dependent global time is induced by any frame of reference (the time of a clock at rest in teh frame, extended spatially to clocks at any other point in the frame via Einsteinian synchronisation).
(3) Given such a global time, we can give any event a time. We can also consider the set of all events in space at a given time.
(4) Since, given a priviledged frame and such a global time, time and spatial position are orthogonal, the statement makes no sense. It is obvious that the worldline of any moving object shows time changing with position.
Minkowski space is thus the limiting space-time field when there is no gravity; and this demands that time becomes universal. It is really a trivial case of four-dimensional space-time which dertermines gravity when time does actually change with position.
It is true that MS is limiting case with no gravity, which I stated a few posts ago in response to you saying that MS could only exist in presence of gravity! Glad you have changed your mind. You repeat "time changing with position" which does not make sense.
I think you mean "time rate changing with position" which also makes no sense, see below.
Thus, in the case of Special Relativity all clocks within the universe must keep the same time-rate, since there is no gravity that can alter their time-rates to be different at different positions and speeds.
Your idea here of "time-rate" and of "time-rate" depending on position when their is gravity" is understandable - it seems reasonable in a Newtonian world in which time is separate from space, but it is conceptually wrong.
You have no physical way to define "time-rate". Rate with respect to what? Of course you can define "local time" which by definition is the speed clocks tick in a frame. That ties the local time coordinate to physical processes in the frame. It does not imply anything about time in other frames.
Nor can you compare one "time-rate" with another, except by choosing a priviledged frame.
Some time ago you provided what you claimed was a way to do this, synchronising clocks globally in two frames f0 and F1:
(1) You synchronised clocks over all space in F0 (fine).
(2) You synchronised such clocks in F0 with similar in F1 at a given initial time t0.
(2) contains an implicit priviledged frame. You have to decide whether t0 is measured using F0 or F1 clocks. You get different results since instantaneity in one frame does not imply instantaneity in another.
So your whole conceptual framework, which rests on
frame-independent global time, has no physical basis. I await your attempt to mend the above synchronisation experiment with great interest.