On Thu, Feb 13, 2014 at 8:15 PM, Edgar L. Owen <[email protected]> wrote:
> Jesse, > > You agree "It is true that they both agree on an overview which says > things along the lines of "In frame 1, X is true, in frame 2, Y is true"" > > Presumably what you mean by that is that both A and B agree on (1) A's > calculation of B's t' in A's frame AND (2) B's calculation of A's t in B's > frame. Is that correct? They both can know each other's relativistic > calculations of their own clock times. Correct? > > Yes or no? > Yes. > Question 1: Do you agree those 2 frames are mathematically correlated? > > Yes, or no? > Yes. > > 2. Do you agree that each frame contains the variable t (A's reading of > his own clock) and t' (B's reading of his own clock), that each frame gives > a relationship between those two variables? > > Yes or no? > Do t and t' refer to proper times for A and B (defined only along each one's worldline), or coordinate times in the rest frame of A and B (coordinate times have a well-defined value for arbitrary events, and will agree with the proper time for the observer that's at rest in whichever coordinate system we're talking about)? If proper time, I don't know what you mean by "relationship between those variables", unless you're just talking about what pairs of readings are simultaneous in each frame. If coordinate time, then my answer is yes--the relationship between the coordinate time of an event in one system and the coordinate time of the same event in another system is just given by the Lorentz transformation equations for time: t' = gamma*(t - (vx/c^2)) t = gamma*(t' + (vx/c^2)) where gamma = 1/sqrt(1 - (v/c)^2), and v is the velocity of B's frame as measured in A's frame (with the assumption that we set up our coordinate axes so that B is moving along A's x-axis). > > 3. Do you agree that A's frame gives a value of t' in terms of t? And B's > frame gives a value for t in term's of t'? > > Yes or no? > If t and t' are proper time again I'm not sure what you mean, though if you're just asking if A's frame tells us what values are simultaneous in A's frame then yes. If coordinate times then yes, see the two equations above. > > 4. Do you understand that if we have equations for t' in terms of t in A's > frame, and t in terms of t' in B's frame, that we can always establish a 1: > 1 correlation between t in A's frame and t' in B's frame? > > Yes or no? > If you are talking about proper times, no, each frame disagrees about what pairs of proper time readings are simultaneous so I see no way to use that to generate a single 1:1 relationship between proper times. If you're talking about coordinate times, then yes, but that 1:1 relationship only relates the coordinates each system assigns to a SINGLE event, for example if that single event is A's clock reading a proper time of 10, it would tell us that this event has coordinates t=10 in A's frame, and t'=gamma*10 in B's frame. It doesn't give us any sort of 1:1 relationship between DISTINCT events, like the event of A's clock reading a proper time of 10 and the event of B's clock reading some proper time. Do you agree? Yes or no? > > To your last question I provided nearly a DOZEN numerical examples, and > procedures of how the above works in specific examples, apparently none of > which seems to have registered with you. > You provided some examples (using variables whose meaning wasn't always clear, rather than specific numbers) of how you think absolute simultaneity works in certain cases, but you simply ASSERT that it works this way, you never derive your conclusions from standard relativistic equations like the Lorentz transformation equations I mentioned above. That's why I said you never "show how the fact that they agree on each frame's description allows them to derive a unique truth about simultaneity"--the emphasis there is on the "how". > > > Lastly, once more, for the nth time, your spatial coordinates point is > just equivalent to saying you can use an arbitrary clock time coordinate > system which is trivially true. But the fact you can get arbitrarily > different clock times or location on a measuring tape that way does NOT > change the fact that we are talking about REAL actual, exact and fixed age > differences. > Yes, and the measuring tape example involves a REAL, actual, exact and fixed difference in path lengths along the tapes from the first crossing-point to the second, exactly analogous to the difference in proper time lengths along the worldlines of the twins from the first meeting-point to the second. Can you picture a spacetime diagram for the twins, and see how it looks like two different curves (or one curve and a straight line) between the same pair of points, exactly like a drawing of two measuring tapes which have different paths through space between two crossing-points? Do you understand that just as the number of markings on a measuring tape between the two crossing-points measures the ACTUAL PHYSICAL DISTANCE ALONG THE PATH between the two points that the tape was laid along, so the number of ticks on a twin's clock between the two meetings measures the actual physical proper time along their worldline between the two meetings? > > You seem obsessed with this tape analogy which has NOTHING to do with the > discussion. > > You are continually harping on a point to which I agree (assuming you > won't try switching the goal posts again). That it's possible in relativity > to assign arbitrary coordinate systems for either space OR CLOCK TIME. > However that has nothing to do with the fact of real age differences which > is the only REAL clock here, the biological clocks. > No, I'm not just talking about "arbitrary coordinate systems", the number of markings along the tape between the crossing points is meant to be directly analogous to the number of ticks on a clock between the meeting points of the twins--both are physical measures of path length that are COORDINATE-INDEPENDENT. Coordinate systems only enter into my example if the tapes are laid on a sheet of graph paper with Cartesian coordinate axes drawn on (or if a transparent Cartesian graph is laid on top of the measuring tapes), the tapes themselves have nothing to do with defining any coordinate system. Jeez Edgar, I asked you over and over again if you thought there was anything in the twin paradox example that didn't have a direct analogy in the measuring-tape example, why didn't you just answer this question by answering something like "the fact that there is a real coordinate-invariant difference in ages between the twins when they reunite has no analogy in the measuring tape"? Then I could have set you straight that the number of markings on each tape between their two crossings was a coordinate-invariant fact that measures the actual physical length of each path, and is analogous to the difference in ages of the twins. It would have saved us both a lot of time! Please don't use the fact that you think you "know where I'm going" with an argument as to not bother answering the questions I ask you--often you are wrong about where I'm going with an argument. And even when you're right, I ask that you still do me the courtesy of indulging my questions and giving them specific answers, as you can see I am quite willing to do with your own questions. Jesse On Thursday, February 13, 2014 4:55:13 PM UTC-5, jessem wrote: > > > > On Thu, Feb 13, 2014 at 4:38 PM, Edgar L. Owen <[email protected]> wrote: > > Jesse, > > 4 questions: > > 1. Do you agree that for every relativistic scenario involving 2 > relativistic observers A and B, that relativity provides a description of > how each observes the other's clock time vary relative to their own clock? > That it provides 2 descriptions, both consistent with relativity theory? > > Yes or no? > > > Yes. > > > > 2. Do you agree that A can always know what B's view of him is, and that B > can always know what A's view of him is? Both A and B understand relativity > theory so they can, right? > > Yes or no? > > > Yes. > > > > 3: Do you agree that this means that the two views taken together are > something both A and B agree on? That both A and B always have an agreed on > frame independent OVERview of their whole relativistic relationship that > consists of knowledge of both frames? > > Yes or no? > > > No, although this is just a matter of terminology--that's not what > physicists mean by "frame independent", they mean a particular physical > variable whose value is the same regardless of what frame you use to > calculate it, like the proper time between two events on a specific > worldline. It is true that they both agree on an overview which says things > along the lines of "In frame 1, X is true, in frame 2, Y is true". > > > > 4. Do you see how this mutual agreed on understanding of how each's clock > time varies in the other's frame always allows each to correlate their own > comoving clock time with the comoving (own) clock time of the other? In > other words for A to always know what B's clock time was reading when A's > clock time was reading t, and for B to always know what A's clock time was > reading when B's clock time was reading t'? > > Yes or no? > > > No. Nowhere have you provided a mathematical explanation or even a > numerical example where you show how the fact that they agree on each > frame's description allows them to derive a unique truth about > simultaneity. Moreover, there is a spatial analogy to each of the > statements 1-3 involving a pair of different Cartesian coordinate systems > and how they each say different things about which markings on two > measuring tapes are at the "same y", yet you would NOT similarly conclude > there must be some coordinate-independent truth about which markings are at > the "same y" (and before you object that spatial examples are irrelevant, > please respond to my questions in the post at https://groups.google.com/ > d/msg/everything-list/jFX-wTm_E_Q/xtjSyxxi4awJ , specifically the one > that asks which of two statements A or B better matches your view about the > logic behind your conclusion of absolute simultaneity). > > Jesse > > > > > > > Edgar > > > > On Thursday, February 13, 2014 3:24:02 PM UTC-5, jessem wrote: > > > On Thu, Feb 13, 2014 at 2:28 PM, Edgar L. Owen <[email protected]> wrote: > > Jesse, > > I haven't seen any book on relativity point this out even though it is > quite obviously what relativity actually does. Do you deny relativity gives > equations for BOTH frames for each single relativistic scenario? That, my > friend, is frame independence.... > > > Sure, it gives equations for both frames, but you haven't given any sort > of mathematical derivation to show how this leads to the conclusion that > there must be a unique "true" definition of simultaneity, or what that > definition would be. In Cartesian geometry we can have different coordinate > systems which have different equations for which markings on different > measuring tapes have the same y-coordinate, but you DON'T conclude that > this implies there must be a unique "true" way of defining something like > "y-equality". > > > > > Answer to second paragraph. Depends on what you mean by "instantaneous > acceleration". There is no such thing yet you are claiming it has an actual > physical effect. > > > See my other recent post where I explained that "instantaneous > acceleration" can be understood either in terms of the limit as a finite > acceleration period gets briefer and briefer, or just an approximation for > an acceleration that's very brief compared to the timescales that we are > considering in the problem. > > Jesse > > > > > > > > On Thursday, February 13, 2014 2:09:29 PM UTC-5, jessem wrote: > > > > On Thu, Feb 13, 2014 at 1:55 PM, Edgar L. Owen <[email protected]> wrote: > > Jesse, > > The same reading in the exact same sense that relativity tells us they do > which I've already explained for the nth time. It's in the same frame > independent sense that relativity is able to meaningfully define 2 frames > for any 1 relativistic scenario. That gives us the frame independent method > to get the answer. That answer is given by relativity theory, not by p-time > theory. > > > > But do you agree that this is your own original conclusion about the > implications of SR that somehow all mainstream physicists have missed, that > no relativity textbook will discuss any "frame independent method" to > determine simultaneity? > > Also, do you agree that your statement "when the relative motion magically > stops, their clocks will still read the same as each other's" would NOT be > true if we were comparing readings in their common rest > > ... -- 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. 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