Jesse, The only thing we are interested in is whether A and B THEMSELVES can establish an UN-ambiguous 1:1 correlation of their actual ages. At this point we don't care about any other observers or how they may view this.
In the symmetric case we merely take the common point of departure and meeting as the origin of a coordinate system oriented so that the trips are symmetric. You may point out that we could choose another coordinate system in which the trips were not symmetric. Sure but we can ENSURE an absolute frame independent notion of symmetry by having the twins undergo exactly equal accelerations and gravitational encounters so we want to choose a coordinate system that reflects that symmetry since that symmetry is real and actual just as the ages are real and actual. That's the coordinate system whose origin is at the stationary departure and meeting point in space and oriented so the trips are symmetrical, their worldlines are mirror images. In this case the twins can establish an UN-ambiguous 1:1 correlation of actual ages throughout the trip because they know that they both underwent exactly equivalent accelerations and gravitational encounters and thus their actual ages progressed in synch during the entire trip. The choice of coordinate system must reflect these real actual physical facts. When we do that there will be an UN-ambiguous 1:1 correlation of actual ages throughout the trip. So we must choose a coordinate system that properly reflects the real actual accelerations and gravitational encounters being symmetric. Can you agree to this at least? And if you are an objective participant it would be fair if you find some some quibble or poor or ambiguous wording on my part to just tell us how to correct it to make the example work in expressing what I'm sure you know what i want to get at, instead of embarking on another unnecessary tangent. In other words if you are truly interested in determining IF an UN-ambiguous 1:1 correlation of actual ages between any two observers that those two observers THEMSELVES can agree to is possible and in what cases, then you should first assume it might be possible and try to come up with the best examples you can to prove it instead of just picking away at terminological ambiguities. That's how fair objective persons usually evaluate new theories. Edgar On Wednesday, February 26, 2014 7:40:24 PM UTC-5, jessem wrote: > > > > On Wed, Feb 26, 2014 at 7:27 PM, Edgar L. Owen <edga...@att.net<javascript:> > > wrote: > > Jesse, > > Forget about coordinate systems, that isn't really the issue. > > The point is that each twin has A REAL ACTUAL AGE at every point on its > world line no matter what its relativistic circumstances.\ > > > Yes. > > > > The point is that it is always possible for each twin to figure out a 1:1 > correlation of the real actual ages of each other, and both twins will > AGREE to that correlation. > > > Not without using a coordinate system, no. The only kind of "1:1 > correlation" you'll find in relativity is looking at which points on their > worldlines occurred at the same coordinate time in some coordinate system, > and then looking at their respective ages at those points. > > > > They can't OBSERVE the real actual age of the other twin in some cases, > but they can always use their knowledge of relativity and logic to figure > out what it is. > > > WHAT "Knowledge of relativity"? There are no equations in relativity that > could be used to define a 1:1 correlation between proper times of separated > observers in a coordinate-independent way, and you haven't presented any. > > Jesse > > > > > > > On Wednesday, February 26, 2014 5:44:33 PM UTC-5, jessem wrote: > > > On Wed, Feb 26, 2014 at 4:50 PM, Edgar L. Owen <edga...@att.net> wrote: > > Jesse, > > A symmetric trip is defined in terms of the symmetric view of two > observers A and B OF EACH OTHER IN TERMS OF THEIR OWN COMOVING COORDINATE > SYSTEMS. > > > If they aren't inertial observers in flat spacetime--and they can't be > inertial if they depart from one another and then reunite later--then > "their own comoving coordinate systems" is a COMPLETELY UNDEFINED PHRASE. > There are an infinite number of DIFFERENT non-inertial coordinate systems > you could design in which they remain fixed at the spatial origin of the > coordinate system (so each one is "comoving" in that sense), and there is > no convention recognized by physicists that "their own comoving coordinate > system" would refer to any particular one of these different possible > systems. DO YOU DISAGREE? > > I have asked variants of this question several times now, once again you > seem to be back to your old habit of refusing to answer simple > agree/disagree questions I ask you, even after you have demanded that I > answer a number of yours. As I said before, this is quite rude behavior, > and if you aren't interested in civil reasoned discourse where you actually > address the other person's arguments and questions, rather than just > haranguing them with the same assertions and expressing incredulity that > they could fail to be convinced, then there's obviously no point to any > further exchanges between us. > > > The proper times of both twins A and B have a 1:1 correlation and are > equal at start and finish of the trip. > > > Although it's true in a frame-independent sense that their proper times > are equal at the end when they reunite, any 1:1 correlation of proper times > DURING the trip can only be defined relative to a particular coordinate > system, and there's no physical reason why using the system where their > velocities are symmetrical is more "correct" than using any other > coordinate system. As I just said in my last post: > > 'It isn't a 1:1 correlation between the proper times of A and B without > qualification, it's a 1:1 correlation between the proper times of A and B > RELATIVE TO THEIR REST FRAME. If you use a different frame, there is a > different 1:1 correlation between the proper times of A and B, RELATIVE TO > THAT OTHER FRAME. Nothing in the phrase "1:1 correlation between the proper > times of A and B" by itself tells us what frame to use.' > > Do you disagree with the above? > > > > PROPER clocks always run at the same rate in the same relativistic > conditions. > > > "Run at the same rate" has no coordinate-independent meaning in > relativity. You won't find any relativity textbo > > ... -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. 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