On Wed, Mar 5, 2014 at 2:42 PM, Edgar L. Owen <edgaro...@att.net> wrote:
> Jesse, > > Yes, but respectfully, what I'm saying is that your example doesn't > represent my method OR results. > > In your example of A and B separated but moving at the same velocity and > direction, and C and D separated but moving at the same velocity and > direction, BUT the two PAIRS moving at different velocities, AND where B > and C happen to pass each other at the same point in spacetime here is my > result. > > Assuming the acceleration/gravitation histories of A and B are the same > and they are twins; AND the acceleration/gravitation histories of C and D > are the same and they are twins, then A(t1)=B(t1)=C(t2)=D(t2) which is > clearly transitive between all 4 parties. > You earlier agreed that if two observers are at rest relative to each other, then if they synchronize clocks in their rest frame, their clocks will also be synchronized in p-time from then on. In your post at http://www.mail-archive.com/everything-list%40googlegroups.com/msg48404.htmlyou responded to one of my questions in this way: '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?" ' You didn't say anything about their ages having to be equal, or about their needing to have had identical acceleration histories before this. For example, if I and some stranger named Jimbo are at rest relative to each other in an inertial frame in flat SR spacetime (no gravity), and in this frame my 37th birthday is simultaneous with Jimbo's 20th birthday, then if I set my clock to T=0 on my 37th birthday and he sets his clock to T=0 on his 20th birthday, isn't this sufficient to demonstrate that our clocks will be synchronized in p-time from then on (provided we both remain at rest in this frame), regardless of how either of us may have accelerated *before* we came to rest in this frame? (assuming of course that I came to rest before my 37th birthday, and Jimbo came to rest before his 20th) Even if you somehow don't agree with this, I can easily fill in some details about the past history of my example to give A/B and C/D symmetrical accelerations, if you wish--see below. > > We don't know what t1 and t2 are because you haven't specified their > acceleration histories or birth dates, but whatever they are the equation > above will hold. > OK, I don't think it should be necessary to specify acceleration histories or ages if you agree with my statement about me and Jimbo above, but if you disagree with that statement I can give details about each pair's past history, though it makes the example a bit more complicated. Say that in the frame F where A and B are at rest during the period I described, A and B were originally at rest at position x=12.5, with both having the same ages, and let's say that their proper time clocks have been set to read T = -18 years at the moment they were born (it is the custom in their society to have their proper time clock tell how far from voting age they are, so for example when they turn 15 their clock reads T=-3, when they turn 28 their clock reads T=10, etc.). Then each of them simultaneously began to accelerate in opposite directions with a fixed proper acceleration of 1 light year/year^2, and after each had traveled a distance of 6.25 light years from their starting position in this frame, they began to decelerate (i.e. turn their rockets around and accelerate in the opposite direction, lowering their speed in this frame) at the same proper acceleration of 1 light year/year^2. After they each had traveled another 6.25 light years and come to rest in this frame, they stopped decelerating and simply remained at rest. Each of them will have then traveled a distance of 12.5 light years from their original starting position of x=12.5 light years, with A at position x=25 light years, and B at position x=0 light years. Hopefully you agree that because their accelerations are completely symmetrical in the frame where they were originally at rest with the same ages, in this frame identical ages will still be simultaneous after they finish the acceleration/deceleration phase and come to rest. So, let's just say that they come to rest simultaneously at t=-12 in this frame, and at this moment their clocks both read T=-12, meaning they are both turning 6 at the moment they stop accelerating. After this, their x(t) and T(t) functions are just as I described. As for C and D, let's switch over to the frame F' where THEY are at rest during the period I describe, whose coordinates I had previously labeled as x' and t' (and given the Lorentz transformation equations for converting from x,t to x',t'). Say that in frame F', they were both originally at rest at position x'=7.5, again with both having the same ages, and both having their proper time clocks read a time of T which is just their age minus 18. Then each of them simultaneously began to accelerate in opposite directions with a fixed proper acceleration of 1 light year/year^2, and after each had traveled a distance of 3.75 light years from their starting position in this frame, they began to decelerate (i.e. turn their rockets in the opposite direction) at the same proper acceleration of 1 light year/year^2. After they each had traveled another 3.75 light years and come to rest in this frame, they stopped decelerating and simply remained at rest. Each of them will have then traveled a distance of 7.5 light years from their original starting position of x'=7.5 light years, with C at position x'=0 light years, and D at position x'=15 light years. Because their accelerations are completely symmetrical in the frame where they were originally at rest with the same ages, in this frame identical ages will still be simultaneous after they finish the acceleration/deceleration phase and come to rest. So, let's just say that they come to rest simultaneously at t'=-12 in this frame, and at this moment their clocks both read T=-12, meaning they are both turning 6 at the moment they stop accelerating. If the moments of their stopping their accelerations are x'=0, t'=-12 for C, and x'=15, t'=-12 for D, we can use the inverse version of the Lorentz transformation equations to figure out the coordinates of their stopping their accelerations in the original frame F where A and B are at rest (which I had been using to describe their paths through spacetime). The equations are: x = gamma*(x' + v*t') t = gamma*(t' + (v*x')/c^2) Again we are using units where c=1, and v=0.8 so gamma =1/0.6, meaning the equations are: x = (x' + 0.8*t')/0.6 t = (t' + 0.8*x')/0.6 So if C stopped her acceleration at x'=0, t'=-12 in frame F', then in frame F she must have stopped her acceleration at the following coordinates: x = (0 + 0.8*-12)/0.6 = -16 t = (-12 + 0.8*0)/0.6 = -20 You can easily verify that x=-16, t=-20 lies along the path x(t) = 0.8c*t that I previously gave for C's path in frame F, and furthermore the idea that C's clock reads T=-12 at this point fits with the equation I had given for her proper time as a function of coordinate time in frame F, T(t) = 0.6*t. So, from this point on you can safely assume that C's x(t) and T(t) functions in frame F were the ones I already gave. Meanwhile if D stopped his acceleration at x'=15, t'=-12 in frame F', then in frame F he must have stopped his acceleration at the following coordinates: x = (15 + 0.8*-12)/0.6 = 9 t = (-12 + 0.8*15)/0.6 = 0 You can easily verify that x=9, t=0 lies along the path x(t) = 0.8c*t + 9 that I previously gave for D's path in frame F, and furthermore the idea that D's clock reads T=-12 at this point fits with the equation I had given for his proper time as a function of coordinate time in frame F, T(t) = 0.6*t - 12. Sp. from this point on you can safely assume that C's x(t) and T(t) functions in frame F were the ones I already gave. This should be sufficient to show that if each pair accelerates away from each other symmetrically in the frame where they started at rest at the same position, just as I described, they can end up with the x(t) and T(t) functions I described in frame F, with each person's clock time T being equal to their age minus 18. Do you agree? > > The problem is that your careful analysis simply DOES NOT use MY method > which depends on the actual real physical causes (acceleration histories) > to deternine 1:1 age correlations between any two observers. > Again, you had previously said that being at rest relative to one another with their clocks synchronized in their common rest frame is sufficient to demonstrate their clocks are synchronized in p-time, regardless of acceleration histories before coming to rest in this frame. But if you want to change your position on that, the above elaboration is sufficient to show that both pairs can accelerate symmetrically and end up with the same x(t) and T(t) functions in frame F that I described, with each one's T value just being their actual age minus 18. Unless you disagree with that, then hopefully we can go back to my numbered list of statements and you can tell me which is the first you would disagree with, or if you are forced by the analysis to agree with all of them. Jesse > It uses YOUR method to prove the standard lack of simultaneity between > VIEWS of pairs of actual physical events. This is a WELL KNOWN result of > relativity WITH WHICH I AGREE! > > But for the nth time, my method concentrates on the ACTUAL RELATIONSHIP, > rather than VIEWS of that actual relationship. > > This is a simple, well accepted logical distinction which most certainly > applies here to the ACTUAL age correlations of people.. > > If a man and a wife love each other that is a real actual physical > relationship. The fact that someone else thinks they don't love each other > may well be his real VIEW, but it does NOT change or affect the ACTUAL love > between the man and his wife. > > No matter how many times I state this it doesn't seem to sink in.... > > Edgar > > > > On Wednesday, March 5, 2014 10:36:10 AM UTC-5, jessem wrote: >> >> >> On Wed, Mar 5, 2014 at 8:19 AM, Edgar L. Owen <edga...@att.net> wrote: >> >> Jesse, >> >> First I see no conclusion that demonstrates INtransitivity here or any >> contradiction that I asked for. Did I miss that? >> >> >> No, I was just asking if you agreed with those two steps, which show that >> different pairs of readings are simultaneous using ASSUMPTION 2. If you >> agreed with those, I would show that several further pairs of readings must >> also be judged simultaneous in p-time using ASSUMPTION 1, and then all >> these individual simultaneity judgments would together lead to a >> contradiction via the transitivity assumption, ASSUMPTION 3. I already laid >> this out in the original Alice/Bob/Arlene/Bart post, but since you >> apparently didn't understand that post I wanted to go over everything more >> carefully with the exact x(t) and T(t) functions given, and every point >> about simultaneity stated more carefully. >> >> I thought you would be more likely to answer if I just gave you two >> statements to look over and verify rather than a large collection of them, >> but if you are going to stubbornly refuse to answer the opening questions >> until I lay out the whole argument, here it is in full:</d >> ... > > -- > 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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