Jesse, You are misunderstanding most of my points here!
By standard I just mean any usual analysis that computes the correct answer of the twins' clock time differences when they meet. It seems to me, correct me if I'm wrong, that your coordinate time analysis just comes up with the exact same clock time differences using a different coordinate system. Is that not so? I don't see any way around that no matter what coordinate system you use because there is a single correct answer both twins agree upon and confirm by looking at each other's watches in their common present moment. Of course you need some coordinate system to do relativity calculations. I never claimed you didn't. It wasn't I that said a coordinate time analysis wouldn't give the correct answer. I said it doesn't give any calculation of what the present moment IS in which its calculated results occur which they must have to to make sense. I thought you said, contrary to my thinking, that coordinate spacetime would do that but I don't see it doing it and you agreed that is an independent definition, so I don't see the sense of your diversion into coordinate time since it gives the same answer for the twins that any relativistic analysis does, and it does not calculate a present moment because no relativistic approach does that I'm aware of. Re your last paragraph: First what do YOU mean by proper time? Do you simply mean their clock times on their clocks or some other time? And you say in the last paragraph "then the event of twin A turning 30 is assigned the same t-coordinate as the event of twin B turning 40." Who does this assigning? And what time is the "then" in which the assigning takes place? Is this just some arbitrary assignment after the meeting, in the same sense that you said that the same point in spacetime had to be independently defined? What is "the same t-coordinate in which A turns 30 and B turns 40"? What's the value of that t-coordinate that is not the same as the different clock times? And what type of time coordinate is it? Clock time, coordinate time, proper time? And finally you say "for example both events might be assigned a time of t=50 in some coordinate system". That just seems you are saying that it's possible for the twins to reset and synchronize their clocks after they meet which is obvious. But even if they do that, one twin still is REALLY younger than the other. That real actual time disparity can NOT be reset. There is a real absolute time and age difference that relativity can CALCULATE but relativity CANNOT explain why that time and age difference exists in the same present moment the twins share. So again I don't see the coordinate time approach adding anything to the discussion. It still, correct me if I'm wrong, does NOT calculate the fact that the twins meet up with different clock times in a SAME present moment.. Only the assumption of a separate p-time in my theory explains how that happens..... Edgar On Thursday, February 6, 2014 12:34:25 PM UTC-5, jessem wrote: > > > > On Thu, Feb 6, 2014 at 12:03 PM, Edgar L. Owen <[email protected]<javascript:> > > wrote: > >> Jesse, >> >> Frankly the utility of this approach seems opaque to me. I don't see how >> it differs from just being able to calculate the actual clock time >> differences the twins will have when they meet in 'a same present moment'. >> Because you say we already have to previously define what the same present >> moment they meet in is (means) and do that independently of this coordinate >> time calculation. You first must define, rather than calculate, what a same >> point in spacetime means by the reflected light method which is fine for >> establishing two twins are at the same point in spacetime WHEN they are at >> the same place in space but not otherwise. >> >> You say that (using coordinate time calculations) "For the twins, if you >> know the coordinates they departed Earth and their coordinate speeds when >> they departed, and you know the coordinates of any subsequent accelerations >> (or forces causing those accelerations), you can predict the different >> coordinates where they will reunite, and what proper time their clocks will >> show then." >> >> But that's exactly what the standard equations of relativity give you >> isn't it? Assuming that by the "proper time their clocks will show then >> (when they meet)" is just the t values their clocks read. So I fail to see >> what we get out of this approach that standard relativity calculations >> don't give us. >> > > > What do you mean by "standard relativity calculations"? The standard > calculations *are* done using some coordinate system, I don't know of any > way to make predictions about future behavior given some initial conditions > without making use of a coordinate system. All the equations of relativity > you'll find in an introductory textbook, like the time dilation equation, > will only apply in inertial coordinate systems for example (though more > advanced textbooks will provide different equations that can be used in > non-inertial coordinate systems). If you think there is some way in > relativity to make such predictions without using any coordinate systems at > all, please elaborate. > > > >> Don't they give us the exact same results of two different times in a >> "same point in spacetime" that we've already defined independently of the >> calculations? >> >> If so I repeat my assertion that there is no calculation from coordinate >> time, or relativity in any form, that gives the twins having the exact same >> coordinate time reading on some cryptic clock that proves they are the same >> time as well as the same place when they meet. >> > > And...what is this assertion based on, exactly? Even if you think there is > some other way of calculating what ages the twins will be when they meet > that doesn't make use of coordinate systems, this doesn't in any way imply > that the calculation involving coordinate systems gives the wrong answer, > or doesn't give an answer at all, to the question of what coordinate clock > will be at the same point in spacetime as the meeting of the twins, or what > the reading of that coordinate clock will be. Are you in fact arguing that > a calculation involving an inertial coordinate system will not give the > correct numerical answer to this question? If so, on what basis? > > > > >> >> So again I repeat my assertion that the present moment is locally >> DEFINABLE (via reflected light) but NOT CALCULABLE by a coordinate time or >> any other approach. >> > > So it's the operational definition involving reflected light that you're > concerned with? But of course if you know the initial coordinate positions > and velocities of two observers approaching one another, and you know that > one observer is continually sending out light signals to the other and > measuring the reflections, then you can figure out the coordinate position > and time that each signal is sent out, the coordinate position and time it > gets reflected, and the coordinate position and time it returns to the > sender, and the proper (clock) time interval he will experience between > sending a given signal and receiving back the reflection of that signal. > There should be no problem with showing that this proper time interval > approaches 0 as you approach the coordinate position and time the two > observers meet. And it would work just the same if you replaced one of the > observers by any particular coordinate clock. > > > >> That's what I've always said, but I thought you were telling me that same >> points in spacetime were CALCULABLE with coordinate time, that there was >> some mysterious coordinate time calculation that made the twins' clocks >> come out the same t readings when they met proving that the meeting was at >> the same point in spacetime. >> > > By "same t readings when they met" do you mean that their own clocks > actually show the same proper time when they meet, or do you just mean that > their proper times at the point in spacetime when they meet are each > assigned the same t-coordinate in a coordinate system? I have obviously > been talking about the latter--I repeatedly used the example where, if twin > A is 30 and twin B is 40 when they meet, then the event of twin A turning > 30 is assigned the same t-coordinate as the event of twin B turning 40, for > example both events might be assigned a time of t=50 in some coordinate > system (and both events would also be assigned the same spatial > coordinates, which implies that since all the coordinates were identical > these events must have happened at the same point in spacetime). > > Jesse > -- 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 [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.
