On Thu, Feb 13, 2014 at 12:34 PM, Edgar L. Owen <edgaro...@att.net> wrote:
> Liz, > > 'Any point' for observers in different frames is well defined by > relativity theory itself. The very fact that relativity theory can provide > 2 equations, one for each separate frame, for any SINGLE relativistic > scenario requires that to be true. > By "point" do you mean "point in time"? If so, are you saying that even for observers at different points in space, "relativity theory itself" provides a unique definition of which points on their worldlines are at the same "point" in time? This is obviously not true, since there is no preferred definition of simultaneity in relativity theory itself. You may think you can deduce the *need* for some "true" definition of simultaneity in order to make sense of relativity's claims, but objective simultaneity is clearly not a part of the theory itself in the sense that it won't appear in any textbooks on the theory. > That is what I've continually pointed out to Jesse that's gone over his > head, that relativity itself uses a common computational background for all > frames. > It hasn't gone over my head, I have responded over and over again by pointing out that any mathematical statement about relativity has an analogue in a purely geometric scenario involving things like tape measures on a 2D plane. Just as we can describe the twin paradox with different inertial frames that disagree about which pairs of events have the same t-coordinates, we can describe things on the plane using different Cartesian coordinate systems which disagree about which pairs of markings on the measuring tapes have the same y-coordinate. Does your ill-defined terminology of "common computational background" refers to the notion of a unique objective frame-independent analogue of "same t coordinate" (the analogue being 'same p-time')? If so, my point as always is that you *don't* similarly conclude that the different Cartesian coordinate systems in the measuring tape scenario require a "common computational background" in the sense of an objective coordinate-independent analogue of "same y-coordinate". And if a perfectly analogous argument involving coordinate systems in space leads to a conclusion that even you would agree is erroneous, that implies there is something wrong with the logic of your argument involving frames in spacetime. Even though I've asked you over and over again whether you think there's any quantitative fact about SR and different frames' descriptions of the twin paradox scenario which DOESN'T have a direct analogue in the tape scenario, you've never given a yes-or-no answer to this question, let alone pointed to a specific quantitative fact you think has no analogue. From your continued ducking of this question, I guess you probably recognize on some level that this analogy is problematic for your position. > If it didn't it couldn't properly describe relativistic scenarios from the > separate frame dependent views of all involved observers. > Do you think algebraic geometry (i.e. geometry where we describe shapes in the context of a 2D coordinate system) "can't properly describe geometric scenarios from the separate views of all involved coordinate systems"? > > This hidden and unstated assumption of relativity itself is the basis of > p-time. > If it's "hidden and unstated" than it isn't part of "relativity theory itself" in its standard textbook form. It's rather a conclusion that you draw about the implications of the theory. > > The dozen or so examples I've given to Jesse show how to compare different > relativistic frames in a manner completely consistent with relativity > But I've given my own example that shows that your assumptions about p-time lead to a direct contradiction. You objected to the idea that "events which occur at the same point in spacetime must have the same p-time", which was one of the assumptions I used to derive a contradiction, but clearly you had misunderstood what I meant by "same point in spacetime" since in https://groups.google.com/d/msg/everything-list/jFX-wTm_E_Q/GZznkprLuo8Jyou said "I pointed out maybe a week ago with examples why your notion of "a same point in SPACEtime" is not the same as a same point in p-TIME. They are the same is true only when A and B are at the same point in SPACE". But as I explained in my response at https://groups.google.com/d/msg/everything-list/jFX-wTm_E_Q/6NoHUw_x0tsJ , same point in spacetime DOES always include the notion of "same point in SPACE", this is always how I have used "same point in spacetime" and it's obvious this must be true from the operational definition I gave (how could the time for a light signal to reflect off the other observer and return approach zero if the distance wasn't approaching zero too?). So, now that I have clarified that to say events A and B happened "at the same point in spacetime" means that in any relativistic coordinate system they would have identical time coordinates AND identical spatial coordinates, would you now agree that if A and B happened at the same point in spacetime, they must have been at the same point in p-time? If you do agree with that, then this is sufficient to derive a contradiction when combined with your other assumptions (that p-time simultaneity is transitive, that clocks at rest relative to each other in the absence of gravity that are synchronized in their rest frame must be synchronized in p-time too), as I showed with the Alice/Bob/Arlene/Bart example in https://groups.google.com/d/msg/everything-list/jFX-wTm_E_Q/pxg0VAAHJRQJ . So if you would agree that events A and B having the same position coordinates AND the same space coordinates implies they are simultaneous in p-time, please then look over that example and tell me if you disagree with any of the numbered conclusions 1-4 about simultaneity in p-time. 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 everything-list+unsubscr...@googlegroups.com. 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