On Sun, Feb 9, 2014 at 11:19 AM, Edgar L. Owen <edgaro...@att.net> 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. Is that not correct? > > > Yes is the answer to your question "if two clocks are at rest relative to > one another and "synchronized" according to the definition of simultaneity > in their mutual rest frame, do you automatically assume this implies they > are synchronized in p-time?" > > I already stated that several times in my posts of yesterday and even gave > concrete examples in which it was true, so I'm surprised you accuse me of > not answering it. > Thanks for giving a clear answer. I understand that you think that some of your statements in previous posts were answering it, like "A and B in deep space. No gravity. Their clocks, t and t', are synchronized. They are in the same current p-time moment and whenever t = t', which is always their clock times confirm they are the same current p-time as well as the same clock time." But I think there is still potential for ambiguity in that statement, because "synchronized" could mean synchronized in p-time which might not agree with relativistic synchronization in their rest frame--that's why in my own question I said 'synchronized according to the definition of simultaneity in their rest frame. If you can just quote a question I ask and respond directly to the quote, as you did above, it'd be appreciated, since this would avoid any possible ambiguities that might occur to me but wouldn't occur to you. In any case, now that I understand your answer, let me elaborate on what I meant when I said earlier that such a rule for p-time simultaneity will "run into major problems if you consider multiple pairs of clocks where each member of a pair is at rest relative to the other member of the same pair, but different pairs are in motion relative to another". Suppose we have two pairs of observers, with each member of a pair being at rest relative to the other member of the same pair, but the two pairs in relative motion. Call the first pair Alice and Bob, and the second pair Arlene and Bart. Assume that in the Alice/Bob rest frame, Alice and Bob's clocks are synchronized, and likewise assume that in the Arlene/Bart rest frame, Arlene and Bart's clocks are synchronized. 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. Thus if simultaneity in p-time is transitive, we can put these all together and arrive at the conclusion that the event of Bob's clock reading T(Bob)=0 is simultaneous in p-time with the event of Bob's clock reading T(Bob)=20! I am sure you would not accept such a conclusion, but it is an unavoidable consequence of the two rules for p-time simultaneity I listed above, so if you want to avoid the conclusion you have to either ditch one of the rules or say that p-time simultaneity is not transitive (which I guess would be possible if you don't think there's a single objective truth about p-time simultaneity and that it depends on the context of the frame we are using, see my question about this above). Jesse > > Edgar > > > > > > > On Sunday, February 9, 2014 10:51:32 AM UTC-5, jessem wrote: >> >> >> On Sun, Feb 9, 2014 at 9:49 AM, Edgar L. Owen <edga...@att.net> wrote: >> >> Jesse, et al, >> >> A Propros of our discussion of determining same past moments of P-time let >> me now try to present a much deeper insight into P-time, that illustrates >> and explains that, and see if it makes sense. I will show how relativity >> itself implicitly assumes and absolutely requires P-time to make sense. >> >> >> Every relativistic calculation of clock times consists of some equation >> describing how one clock time varies with respect to another clock time. >> >> >> No, every relativistic calculation of clock times consists of an equation >> describing how one clock time varies with coordinate time in some >> coordinate system. There is no coordinate-independent way of defining how >> "one clock time varies with respect to another time" when they are at >> different points in space (aside from apparent visual rates, but that >> involves things like the Doppler effect, and in terms of p-time it would >> also involve delays due to the time for light signals to cross from one to >> the other, so I assume you're not just trying to talk about apparent visual >> rates here). >> >> >> >> And likewise we can get the total elapsed clock time differences along >> the worldlines by integrating along them until any dt'/dt = f( ). >> >> >> >> Total elapsed time for a clock with a known path is found by integrating >> clock rate as a function of time in some coordinate system, which can be >> defined as a function of v(t), velocity as a function of time in that >> coordinate system. The actual integral can be seen towards the bottom of >> the page at http://math.ucr.edu/home/baez/physics/Relativity/SR/ >> TwinParadox/twin_spacetime.html for example (part of a useful larger >> series on different conceptual approaches to understanding the twin paradox >> in relativity at http://math.ucr.edu/home/baez/physics/Relativity/SR/ >> TwinParadox/twin_paradox.html ). >> >> >> >> This establishes a 1:1 relationship between the clock times, t and t', at >> every point along the worldlines. >> >> >> If you agree with my statements above, you can see that the 1:1 >> relationship only exists within the context of a particular choice of >> coordinate system. If you disagree, and think there is a >> coordinate-independent way to define "how one clock time varies with >> respect to another clock time" (and which is also more than just a >> statement about apparent visual rates), then you are just expressing a >> basic misconception of how calculations are done in relativity. >> >> Also, as usual you ignored the direct question I asked to you in the >> previous post you are responding to: >> >> 'As I asked before, if two clocks are at rest relative to one another and >> "synchronized" according to the definition of simultaneity in their mutual >> rest frame, do you automatically assume this implies they are synchronized >> in p-time?' >> >> Can you please answer the above question yes or no? If you continue to >> consistently avoid answering simple questions I ask, I'm going to conclude >> you're not really interested in a civil discussion and analysis of >> concepts, but rather are behaving like a lawyer or politician who just >> wants to "win" rhetorically and has no interest in addressing the other's >> concerns in an intellectually honest way. I am happy to answer any >> questions you have for me, I just ask that you extend me the same courtesy, >> at least in cases where the questions are simple ones that don't require a >> lengthy write-up. >> >> Jesse >> >> >> >> >> On Sunday, February 9, 2014 12:05:32 AM UTC-5, jessem wrote: >> >> >> >> On Sat, Feb 8, 2014 at 8:07 PM, Edgar L. Owen <edga...@att.net> wrote: >> >> Jesse, >> >> Consider another simple example: >> >> A and B in deep space. No gravity. Their clocks, t and t', are >> synchronized. They are in the same current p-time moment and whenever t = >> t', which is always their clock times confirm they are the same current >> p-time as well as the same clock time. >> >> >> When you say "synchronized", do you mean they are synchronized according >> to the definition of simultaneity in their mutual rest frame? As I asked >> before, if two clocks are at rest relative to one another and >> "synchronized" according to the definition of simultaneity in their mutual >> rest frame, do you automatically assume this implies they are synchronized >> in p-time? If so you are going to run into major problems if you consider >> multiple pairs of clocks where each member of a pair is at rest relative to >> the other member of the same pair, but different pairs are in motion >> relative to another...I will await a clear answer from you on this question >> before elaborating on such a scenario, though. >> >> >> >> >> Now magically they are in non-accelerated relative motion to each such >> that each sees the other's clock running half as fast as their own. >> >> >> Physics textbooks often consider examples where there are "instantaneous" >> accelerations such that the velocity abruptly changes from one value to >> another, with the objects moving inertially both before and after the >> "instantaneous" acceleration, is that the same as what you mean by >> "magically they are in non-accelerated relative motion"? >> >> >> >> >> During the duration of the relative motion whenever A reads t = n on his >> OWN clock and B reads t'=n on his OWN clock they will be at the same >> current moment of p-time. They can use this method later on to know what >> they were doing at the same present moment. >> >> >> Even if we assume instantaneous jumps in velocity, there are multiple >> ways they could change velocities such that in their new inertial rest >> frames after the acceleration, each would say the other's clock is running >> half as fast as their own. For example, in the frame where they were >> previously at rest, if each one's velocity symmetrically changed from 0 in >> this frame to 0.57735c in opposite directions in this frame, then in each >> one's new rest frame the other would be moving at 0.866c (since using the >> relativistic velocity addition formula at http://math.ucr.edu/home/baez/ >> physics/Relativity/SR/velocity.html their relative velocity would then >> be (0.57735c + 0.57735c)/(1 + 0.57735^2) which works out to 0.866c), and a >> relative velocity of 0.866c corresponds to a time dilation factor of 0.5. >> But likewise, in the frame where they were previously at rest, it could be >> that one twin would remain at rest in this frame while the other would jump >> to a velocity of 0.866c in this frame, and then it would still be true that >> in each one's new rest frame the other is moving at 0.866c. Does your >> statement above that "whenever A reads t = n on his OWN clock and B reads >> t'=n on his OWN clock they will be at the same current moment of p-time" >> apply even in the case of asymmetrical changes in velocity? Are you saying >> all that matters is that in either one's new inertial rest frame, the other >> one's clock is ticking at half the rate of their own? >> >> >> Jesse >> >> >> >> On Saturday, February 8, 2014 5:28:08 PM UTC-5, jessem wrote: >> >> >> >> >> On Sat, Feb 8, 2014 at 4:01 PM, Edgar L. Owen <edga...@att.net> wrote: >> >> Jesse, >> >> Yes, I think there is always a way to determine if any two events happen >> at the same point in p-time or not, provided you know everything about >> their relativistic conditions. >> >> You do this by essentially computing their relativistic cases BACKWARDS >> to determine which point in each of their worldlines occurred at the same >> p-time. >> >> Take 2 observers, A and B. >> >> 1. If there is no relative motion or gravitational/acceleration >> differences you know that every point t in A's CLOCK time was in the same >> present moment as every point t' in B's CLOCK TIME when t=t'. >> >> >> And what if there *are* gravitational differences, if there are sources >> of gravity nearby and they are at different points in s >> >> ... > > -- > 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. > To post to this group, send email to everything-list@googlegroups.com. > Visit this group at http://groups.google.com/group/everything-list. > For more options, visit https://groups.google.com/groups/opt_out. > -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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