On Mon, Feb 24, 2014 at 6:53 PM, Edgar L. Owen <[email protected]> wrote:
> Jesse, > > Well, I thought I was expressing your own model, but apparently not. > > However IF, and a big if, I understand you correctly then I do agree that "if > two events have the same space and time coordinates in a single inertial > frame, they must also satisfy the operational definition of "same point in > spacetime" I gave earlier? And I would agree this means that the two events > happened at the same p-time?" > > I'm assuming this means we agree that the meeting twins do meet in the > same space and time coordinates of the inertial frame in which they meet, > though obviously NOT in the same time coordinates of their own proper > comoving frames? > Depends what you mean by that. Say that in the original inertial frame we first use to analyze the problem (which may not be the rest frame of either Alice or Bob), the event of Alice turning 30 has the same space and time coordinates as the event of Bob turning 40, i.e. these two events happen at the same point in spacetime. Then the event of Alice turning 30 could be at a time coordinate of t=30 in her own comoving rest frame, but in her comoving frame the event of Bob turning 40 would ALSO be at t=30 (and both events would have identical space coordinates in this frame). And the event of Bob turning 40 could be at a time coordinate of t'=40 in his own comoving rest frame, but in his comoving frame the event of Alice turning 30 would ALSO be at t'=40 (and again the space coordinates would be the identical). So no matter what frame we use, these two events--Alice turning 30, and Bob turning 40--are assigned the same time-coordinates AS ONE ANOTHER in that specific frame, but the actual time coordinate common to both events can differ from one frame to another (in Alice's frame they had a common time coordinate of t=30, while in Bob's frame they had a common time coordinate of t'=40). Is the latter all you meant by "NOT in the same time coordinates of their own proper comoving frames", or would you actually disagree with my claim that if these two events have the same space and time coordinates as one another in some frame, they must still have the same space and time coordinates as one another in any other frame as well? Also, would you agree that crossing through identical space and time coordinates implies satisfying the operational definitions I gave even if they don't actually stop and come to rest relative to each other, but just cross paths briefly while moving at a large relative velocity? That they would still satisfy the operational definition of crossing through the "same point in spacetime" in the sense that if they were sending continuous signals to one another, the time for the signal to be reflected and return would approach zero as they approached the space and time coordinate that both their paths cross through? I can give an example if this scenario isn't clear. 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.
