Jesse, BTW, in spite of your claim it can't be done, here is another simple way for any two observers at rest with respect to each other but separated by any arbitrary distance in space to determine their 1:1 age correlation.

If A and B are separated at any distance but at rest with respect to each other A sends B a light message telling B what A's current age is, and B immediately reflects that light message back to A with B's current age reading attached. Because they are at rest A knows that the actual age difference is A's CURRENT age - B's REPORTED age + 1/2 delta c (half the light signal's round trip time). In this way A determines a unique 1:1 age correlation between his and B's age that will hold for as long as they are at rest. B can use the same method to determine his 1:1 age correlation with A. A and B do NOT have to synchronize the signals to do this. This gives both A and B their single correct 1:1 age correlation at any distance which holds so long as they are at rest with respect to each other. Of course other observers may see this differently but IT'S NOT THEIR AGE CORRELATION, IT'S ONLY A'S AND B'S AGE CORRELATION and A and B can determine exactly what that correlation is. Do you agree? I know you will claim it's not valid since other observers may view it differently, but frankly A and B's age correlation is NONE OF THEIR BUSINESS! I'll respond to the rest of your post later when I have more time... Edgar On Tuesday, March 4, 2014 2:19:46 PM UTC-5, jessem wrote: > > > On Tue, Mar 4, 2014 at 2:02 PM, Edgar L. Owen <edga...@att.net<javascript:> > > wrote: > > Jesse, > > You ask me to choose between 1. and 2. > > 1. If B's proper age at this point in spacetime is T, then C's proper age > at this point in spacetime must be T as well (i.e. their proper ages are > "simultaneous" in the sense that they must reach the same age > simultaneously). > > 2. If B and C's worldlines both pass through a specific point in spacetime > P, and B's age is T1 when she passes through P, while C's age is T2 when > she passes through P, then B must be at age T1 simultaneously with C being > at age T2 (i.e. whatever two specific ages they have at P, they must reach > those two ages simultaneously, even if the two ages are different) > > > First I assume that by "passing through the same point in spacetime" you > mean that the worldlines cross at P simultaneously by the operational > definition of no light delay. > > 1. is true only in a SYMMETRIC case. In the symmetric case they would have > the same ages as they pass through the same point P, but in that case they > have the same ages during the WHOLE trip so no big surprise. > > 2. is true in all cases. The actual ages T1 and T2 at which they > simultaneously cross will stand in a 1:1 correlation, but ONLY AT THAT > POINT P because their ages could be different due to acceleration > differences either before or after. > > > > Thanks for the clear answer. So now you hopefully see that you must > retract your claim that there's an "error" in my comments about the > scenario with the two pairs of twins A/B and C/D, since I never asserted > anything remotely resembling #1, my point about ages that occur at the same > point in spacetime being simultaneous in p-time referred SOLELY to #2. > > Now, can you please address the follow-up questions that I asked you to > address if you did agree with #2? I will requote them below: > > 'On the other hand, if you would answer "no, statement #2 is not in error, > I agree that in this case T1 and T2 are simultaneous in absolute terms", > then please have another look at the specific numbers I gave for x(t), > coordinate position as a function of coordinate time, and T(t), proper time > as a function of coordinate time, for each observer, and then tell me if > you agree or disagree with the following two statements: > > For A: x(t) = 25, T(t) = t > For B: x(t) = 0, T(t) = t > For C: x(t) = 0.8c * t, T(t) = 0.6*t > For D: x(t) = [0.8c * t] + 9, T(t) = 0.6*t - 12 > > --given the x(t) functions for B and C, we can see that they both pass > through the point in spacetime with coordinates x=0, t=0. Given their T(t) > functions, we can see that B has a proper time T=0 at those coordinates, > and C also has a proper time T=0 at those coordinates. Agree or disagree? > > --given the x(t) functions for A and D, we can see that they both pass > through the point in spacetime with coordinates x=25, t=20. Given their > T(t) functions, we can see that A has a proper time T=20 at those > coordinates, and D has a proper time T=0 at those coordinates. Agree or > disagree?' > > (if you don't understand the math of how to use x(t) to determine whether > someone passed through a given point in spacetime with known x and t > coordinates, or how to determine their proper time T at this point, then > just ask and I will elaborate) > > > > > There are two equivalent ways they can confirm their actual 1:1 age > correlations in both (all cases) when they cross paths. > > First they can directly observe this 1:1 correlation by simply looking at > each other's clocks as they pass. Normally this is not possible if two > observers have relative motion with respect to each other, but in this case > there is no time delay and the looking only takes a SINGLE MOMENT OF TIME, > so even though the time RATES of each other's proper clocks are dilated in > each other's frames, each can still actually read the correct proper time > on the other's clock as they cross. > > (One might initially think it is impossible to read each others' clocks > correctly due to the dilation of relative motion, or even if they passed > with different accelerations, but this is not true in the case where they > read as they cross. Each proper clock is ALWAYS reading the actual proper > age. The apparent dilation effect is just due to the longer interval it > takes for signals from that clock to reach the observer. But the signals > received always display the real and actual proper age of the clock WHEN > the signals were sent. So in the crossing case where there is only a single > signal with NO time delay the clock reading received = the actual clock > reading when the signal was sent. > > > Yes, I agree that they can verify their respective ages at the moment they > cross paths just by looking at each other's clocks at this moment, I have > made this point several times before in discussion with you. > > > > Note that this analysis points out that all proper clocks continually show > the actual proper age of the clock when the signal was sent. So that real > actual age is REALLY OUT THERE. Your imaginary 1:1 correlation problem just > doesn't take into proper account the transmission time from the clock to > the receiver. Just subtract the transmission time and you will get the > actual 1:1 age correlation between when any proper age signal was sent and > what proper time it was received.) > > > This doesn't help in establishing a 1:1 correlation in their ages when > they are at DIFFERENT locations in space, since different frames disagree > about the value of the "transmission time from the clock to the receiver". > > > > > > Second they CAN CONFIRM the actual age correlation in ALL cases simply by > exchanging light messages as they cross telling each other their actual > ages which is an equivalent method. As they cross the light signal has no > appreciable delay so whatever actual age they report will correlate to the > actual age the other receives the signal. > > In this way crossing observers CAN UNambiguously determine the 1:1 > correlation of their actual ages even if they are in relative motion. > > > Of course, it was never in dispute that they can unambiguously define > simultaneous ages AT THE MOMENT THEY CROSS PATHS, this is something all > frames agree on. What is in dispute is whether there is any physical basis > in relativity for a unique definition of simultaneous ages when they are at > DIFFERENT points in space. > > Jesse > > > > > > With this understanding your 1. is true of symmetric cases, and 2. is true > of all cases... > > Edgar > > > > > > > On Tuesday, March 4, 2014 12:19:27 PM UTC-5, jessem wrote: > > > > On Tue, Mar 4, 2014 at 8:37 AM, Edgar L. Owen <edga...@att.net> wrote: > > Jesse, > > I'm interested in finding the truth, not in assigning blame. > > The important thing is we both now agree that there IS ALWAYS A > CORRELATION OF ACTUAL AGES between any two observers. > > The difference is I think it's an EXACT correlation, and you think that > it's ALMOST EXACT except for cases of extreme separation or motion. > > I think we have to analyze the age correlation from a POV that preserves > the actual relationship of the accelerations that are the ONLY cause of age > rate differences. Whereas you think we have to consider all possible views > irrespective of whether they properly preserve the relationship of causes > of age rate differences. My method provides an EXACT correlation. Your > method provides an ALMOST EXACT correlation in all but extreme cases. > > > Also now that I have pointed out the error in your Alice, Bob, Arlene, > Bart example do you agree my method does produce consistent, unambiguous > and transitive 1:1 correlations of proper ages among all observers? > > > So you are just going to COMPLETELY IGNORE my response, which pointed out > that your supposed "error" relied on using the ambiguous phrase "B's and > C's proper ages are simultaneous in p-time because they are at the same > place in spacetime" to describe my views, and interpreting it in a way that > I would never had agreed with? Again, this phrase could be interpreted two > possible ways: > > 1. If B's proper age at this point in spacetime in T, then C's proper age > at this point in spacetime must be T as well (i.e. their proper ages are > "simultaneous" in the sense that they must reach the same age > simultaneously). > > 2. If B and C's worldlines both pass through a specific point in spacetime > P, and B's age is T1 when she passes through P, while C's age is T2 when > she passes through P, then B must be at age T1 simultaneously with C being > at age T2 (i.e. whatever two specific ages they have at P, they must reach > those two ages simultaneously, even if the two ages are different) > > Your attempt to show an "error" in the phrase you invented to describe my > views depended on interpreting the phrase as meaning #1, but I never > asserted anything like #1, my position is described by #2. Do you think > statement #2 is still in "error"? PLEASE ANSWER THIS QUESTION YES OR NO. If > your answer is "yes, #2 is still in error" I suspect you are > misunderstanding something very basic about relativity...so if you do > answer "yes", please tell me if you would agree or disagree that in case > #2, the event of B's clock reading T1 and the event of C's clock reading T2 > both satisfy the OPERATIONAL definition of "same point in spacetime" that I > had given earlier involving light signals. > > On the other hand, if you would answer "no, statement #2 is not in error, > I agree that in this case T1 and T2 are simultaneous in absolute terms", > then please have another look at the specific numbers I gave for x(t), > coordinate position as a function of coordinate time, and T(t), proper time > as a function of coordinate time, for each observer, and then tell me if > you agree or disagree with the following two statements: > > For A: x(t) = 25, T(t) = t > For B: x(t) = 0, T(t) = t > For C: x(t) = 0.8c * t, T(t) = 0.6*t > For D: x(t) = [0.8c * t] + 9, T(t) = 0.6*t - 12 > > --given the x(t) functions for B and C, we can see that they both pass > through the point in spacetime with coordinates x=0, t=0. Given their T(t) > functions, we can see that B has a proper time T=0 at those coordinates, > and C also has a proper time T=0 at those coordinates. Agree or disagree? > > --given the x(t) functions for A and D, we can see that they both pass > through the point in spacetime with coordinates x=25, t=20. Given their > T(t) functions, we can see that A has a proper time T=20 at those > coordinates, and D has a proper time T=0 at those coordinates. Agree or > disagree? > > If you would agree with my statement #2 above, and you also agree with > these two statements, then this should be sufficient to show that the event > of B's proper time clock reading T=0 is simultaneous in p-time with th > > ... -- 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. 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