On Thu, Feb 6, 2014 at 12:03 PM, Edgar L. Owen <[email protected]> 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.
