Jesse, Before I go the trouble of answering your 4 questions on your example could you please tell me if you agree with the 3 examples I provided, and the p-time simultaneities I stated there?
I gave simpler examples to make p-time simultaneity easier to understand, so it makes no sense to address your slightly more complex examples until we agree on my 3. Also in general it would be useful if you could let me know what you do agree with that I say about p-time. Your MO is just to continually ask question after question without usually indicating what answers of mine you agree with or don't. To conduct an objective discussion it helps to know what we agree with as well as what we don't. Don't you agree? Edgar On Sunday, February 9, 2014 5:45:07 PM UTC-5, jessem wrote: > > > > > On Sun, Feb 9, 2014 at 3:57 PM, Edgar L. Owen <edga...@att.net<javascript:> > > 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 <edga...@att.net> 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 <edga...@att.net> 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" > > ... -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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