On Sun, Feb 9, 2014 at 3:57 PM, Edgar L. Owen <[email protected]> wrote:
> Jesse, > > My answer to your last paragraph is yes, as I understand it... > > For transitivity ignore my first post on that, and just read the second > that concludes there IS transitivity.. > > Edgar > OK, then in the scenario I described, please tell me if you disagree with any of the conclusions 1-4 about which events are simultaneous in p-time: Start by considering their initial positions, velocities and clock times in a coordinate system where Alice and Bob are at rest. At coordinate time t=0 in this frame, Alice is at position x=0 light-years, Bob is at position x=25 light years, and their clock readings are T(Alice)=0 years, T(Bob)=0 years. Meanwhile at the same coordinate time t=0, Arlene is at position x=0 light years--her position coincides with that of Alice--and her clock reads T(Arlene)=0 years, and Bart is at position x=9 light years and his clock reads T(Bart)=-12 years. In this frame, Arlene and Bart are both moving in the +x direction at 0.8c. So 20 years later in this frame, they both will have moved forward by 20*0.8=16 light-years, so at t=20 Arlene is at position x=16 light-years while Bart is at position x=25 light years. Their clocks are running slow by a factor of 0.6 in this frame, so in a span of 20 years they tick forward by 12 years, meaning at t=20 Arelene's clock reads T(Arlene)=12 years and Bart's clock reads T(Bart)=0 years, so this event on Bart's worldline is simultaneous in his own frame with the event on Arlene's worldline where her clock read T(Arlene)=0 years and her position coincided with that of Alice (the fact that these events are simultaneous in the Arlene/Bart rest frame is easily proven using the Lorentz transformation, I can supply the details if needed). But since Bart is at x=25 light years at this moment, his position coincides with that of Bob who has remained at rest at x=25 light years, and whose clock is keeping pace with coordinate time so his clock reads T(Bob)=20 years. Summing it all up, if we use BOTH the rule that a pair of clocks at rest relative to one another and sychronized in their rest frame must also be synchronized in p-time, AND the rule that events which coincide at the same point in spacetime must happen at the same p-time, we get the following conclusions: 1. The event of Bob's clock reading T(Bob)=0 and the event of Alice's clock reading T(Alice)=0 must be simultaneous in p-time, since they are simultaneous in the Alice/Bob rest frame. 2. The event of Alice's clock reading T(Alice)=0 and the event of Arlene's clock reading T(Arlene)=0 must be simultaneous in p-time, since they happen at the same point in spacetime. 3. The event of Arlene's clock reading T(Arlene)=0 and the event of Bart's clock reading T(Bart)=0 must be simultaneous in p-time, since they are simultaneous in the Arlene/Bart rest frame. 4. The event of Bart's clock reading T(Bart)=0 and the event of Bob's clock reading T(Bob)=20 years must be simultaneous in p-time, since they happen at the same point in spacetime. > > > > On Sunday, February 9, 2014 3:22:28 PM UTC-5, jessem wrote: >> >> >> >> On Sun, Feb 9, 2014 at 3:02 PM, Edgar L. Owen <[email protected]> wrote: >> >> Jesse, >> >> 1. is correct. There is an objective truth that past events are >> simultaneous in p-time. Recall I also gave the exact same answer yesterday >> or the day before. >> >> >> Thanks. So how about the issue of transitivity? If event A and event B >> were objectively simultaneous in p-time, and event B and event C were >> simultaneous in p-time, does this necessarily imply A and C were >> simultaneous in p-time, or not? >> >> >> >> >> It will always be able to determine what clock time t in one frame >> occurred at the same p-time of any t' in another frame, but the actual >> values of those t's and t''s will depend on the conditions in the preceding >> paragraph, on the choice of frames. Which is what I said at least several >> separate times in the preceding days. >> >> >> By "clock time" you mean the actual physical reading on a clock, not any >> other notion of coordinate time, right? Say one event is clock 1 reading >> t=50 seconds, and another event is clock 2 reading t=30 seconds. These >> events either ARE or AREN'T objectively simultaneous, correct? There can't >> actually be different, equally valid answers to that question that depend >> on one's "choice of frames", so when you say it will "depend on the >> conditions in the preceding paragraph, on the choice of frames", do you >> just mean that there are rules that tell us the objective truth about >> p-time simultaneity should match some PARTICULAR frame's definition of >> simultaneity, but that the particular frame that must be used depends on >> the physical details of the objects involved, like whether the two clocks >> are at rest relative to one another (in which case the rules say you *must* >> use their rest frame's definition of simultaneity to determine p-time >> simultaneity, you don't have any "choice" in the matter). Is this right or >> am I still misunderstanding your wording? >> >> Jesse >> >> >> >> >> >> >> >> Edgar >> >> On Sunday, February 9, 2014 2:42:43 PM UTC-5, jessem wrote: >> >> >> >> On Sun, Feb 9, 2014 at 1:44 PM, Edgar L. Owen <[email protected]> wrote: >> >> Jesse, >> >> No, "the definition of p-time simultaneity itself depends on the >> arbitrary "choice of coordinate system" is NOT true. I clearly stated >> otherwise and explained why. Please reread if it isn't clear. >> >> >> >> Rereading doesn't help, I just don't understand what you mean since I >> can't think of another way to interpret "Yes, the PARTICULAR 1:1 >> relationship only exists with respect to some arbitrary coordinate system >> (which I stated as just some other clock). The choice of that coordinate >> system is of course arbitrary." >> >> Perhaps another question would help. Say it's true in some sense that a >> meteor impact on Mars happens at the "same p-time" as a lightning strike on >> Earth. Does either of these capture your view on how p-time works? >> >> 1. The fact that these events are "simultaneous in p-time" is an >> objective truth by itself, it requires no context of a particular reference >> frame (though there may still be a rule for determining this objective >> truth that refers to reference frames, like "two events happening to >> objects that share the same rest frame are objectively simultaneous in >> p-time if and only if they are simultaneous in the time coordinate of their >> mutual rest frame). >> >> 2. It is an objective truth that these events are "simultaneous in >> p-time" in the context of one frame, and "not simultaneous in p-time" in >> the context of another frame, but there is no frame-independent objective >> truth about which events are simultaneous in p-time. >> >> If either of these does capture your view, please point out which >> one...if neither does, then perhaps in trying to explain your view to me >> you could keep in mind that these are the only two options *I* can imagine >> at the moment, so perhaps you could explain how your third alternative >> would differ from each of these two in turn. >> >> >> >> >> >> As for your last example, establishing past p-time simultaneity across >> multiple frames is NOT transitive >> >> >> So does "p-time simultaneity across multiple frames" mean that p-time >> simultaneity is frame-dependent, as suggested in option 2 above? If not I >> don't know how to interpret that phrase. >> >> >> >> >> (in your sense of using the same intermediate frame t value). You can >> only establish it between any two frames (at a time) in general because the >> relativistic differences between multiple frame relationships as in your >> example are not transitive. >> >> However take clocks A, B and C. You can always determine same past >> p-times between A and B, and between B and C IN TERMS OF their clock time >> relationships as calculated by standard relativity theory. However you >> cannot in general say that because B's t' = A's t, and B's t' = C's t'' >> that t and t'' were at the same p-time. Relativity doesn't work like that >> as I'm sure you know. >> >> >> >> Relativity doesn't talk about p-time at all, so not sure what you mean. >> Perhaps you would take my option 1 above, but you would just say that >> although there are objective truths about p-time simultaneity, these truths >> aren't transitive? In other words you could be saying that there is a >> frame-independent objective truth that events A and B are simultaneous in >> p-time, and a frame-independent objective truth that events B and C are >> simultaneous in p-time, but this does not imply that A and C are >> simultaneous in p-time. Is that right or am I still misunderstanding your >> view? >> >> Jesse >> >> >> >> On Sunday, February 9, 2014 12:47:49 PM UTC-5, jessem wrote: >> >> >> >> >> On Sun, Feb 9, 2014 at 11:19 AM, Edgar L. Owen <[email protected]> wrote: >> >> Jesse, >> >> Same thing as I'm saying. My other clock time is just a clock centered in >> your coordinate system. It's the same idea. If you look at the equations of >> relativistic clock time they are always of the general form dt'/dt = f( ). >> I just note that the dt with respect to which dt' is calculated is another >> clock. You simply note that other clock is some coordinate system. Exactly >> the same. MY clock is the clock at the origin of YOUR coordinate system. >> The equations are exactly the same. The concept is exactly the same. You >> are talking about the exact same thing as I am. >> >> Yes, the PARTICULAR 1:1 relationship only exists with respect to some >> arbitrary coordinate system (which I stated as just some other clock). The >> choice of that coordinate system is of course arbitrary. That's irrelevant >> because with EVERY choice of a coordinate system there will be some such >> 1:1 relationship on the basis of which clock times can be used to determine >> the same points in p-time. Depending on the choice of coordinate system >> those clock times will of course be different but there will be such a >> relationship that defines the clock times in ANY two relativistic systems >> such that a same point in p-time can be defined in terms of a 1:1 relation >> between those clock times. >> >> >> Are you saying that the definition of p-time simultaneity itself depends >> on the arbitrary "choice of coordinate system"? I thought p-time >> simultaneity was supposed to be an objective matter, so the question of >> whether any two past events were simultaneous in p-time could have only one >> TRUE answer. 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