Jesse, Good, we agree it's a valid method for determining 1:1 age correlations in a common inertial frame in which they are both at rest. I claim that frame is the correct one to determine the actual age correlation because it expresses the actual relation in a manner both A and B agree, is transitive among all observers, AND is the exact same method that gives the correct answer WHEN A AND B MEET and everyone, even you, agrees on the 1:1 age correlation.
Our disagreement over choice of frames is spinning its wheels and not getting anywhere. It's a matter of how to INTERPRET relativity, rather than relativity itself. And I have given very convincing reasons why a privileged frame that preserves the actual physical facts that affect age changes is appropriate. You just don't agree with them. As to your example claiming to prove my method leads to a contradiction, just give me the bottom line, a simple synopsis. I don't have the time to wade through a detailed example only to find the only disagreement is over choice of frames again. On the other hand if you ASSUME privileged frames the way I do and think my method of using them leads to a contradiction that isn't just another disagreement over choice of frames that were assumed, then give me a simple example, the simplest you can come up with. Edgar On Tuesday, March 4, 2014 4:37:32 PM UTC-5, jessem wrote: > > > > On Tue, Mar 4, 2014 at 4:04 PM, Edgar L. Owen <edga...@att.net<javascript:> > > wrote: > > 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 is a valid method for determining what ages are simultaneous in the > inertial frame where they are both at rest. But there is no basis in > relativity for judging this frame's views on simultaneity to be any more > valid than another frame's. > > > > 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. > > > Again, you present no argument for why this is the "single correct" > correlation, you just assert it. > > > > > 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? > > > > No. You already agreed in an earlier post that for an inertial observer to > label the frame where they are at rest as "their own frame" is purely a > matter of HUMAN CONVENTION, not an objective reality that is forced on them > by nature. So even if we ignore these "other observers", there is nothing > stopping A and B from using a different convention to define "their own > frame", such as the inertial frame where they both have a velocity of 0.99c > along the x-axis. > > > > > 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! > > > Again, you are conflating observers with frames, even though you earlier > acknowledged that any link between particular observers and particular > frames is just a matter of convention. > > > > > > I'll respond to the rest of your post later when I have more time... > > > OK, thanks. Please prioritize my latest post discussing the scenario with > A/B and C/D and statement #1 vs. statement #2, since it seems that your > original argument for an "error" in my analysis was based on falsely > imagining I was asserting statement #1 rather than statement #2. Since the > analysis really only depends on #2 which you seem to agree with, I would > like to proceed with the analysis of this scenario to see if you can find > any other reason to object to any other step in the reasoning--if you > can't, then presumably you will have no basis for denying the final > conclusion that two different ages of the same observer A would have to be > simultaneous in p-time, according to your own rules. > > Jesse > > > > 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> 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 > > ... -- 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.
