To address your questions:

1. Yes, of course the choice of "their own frame" is a matter of 
convention. But that does NOT mean that all frames are equal when it comes 
to accurately representing some particular physical fact or relationship.

2. The "their experience" in my symmetric example is the actual physical 
fact that they know their accelerations are symmetric because they 
exchanged flight plans to ensure that. And because their ACTUAL EXPERIENCE 
is the fact that they both can feel their proper accelerations AND time 
them by their own proper clocks to ensure they are in accordance with the 
flight plans they exchanged. By simple logic they then KNOW BEYOND DOUBT 
that their proper times are always in synch. AND they confirm this by 
meeting with the exact same clock readings that they AGREE upon.

It is true "their OBSERVATIONAL experiences" of each other do not reflect 
this 1:1 proper time correlation but they are SMART ENOUGH TO UNDERSTAND 
that these are NON agreed VIEWS which do NOT reflect the actual physical 
FACTS of the relationship on which they DO AGREE and thus which is an 
actual physical fact rather than just views of facts.

3. I DO want to address your '"proof" of non-transitivity. But for the sake 
of clarity and saving time can you please just restate it in the simplest 
possible terms? I'll make it easier by restating my thesis concisely.

I claim:

a. That any two observers can always establish an agreed 1:1 correlation of 
their proper times BETWEEN THEMSELVES.
    (This does NOT MEAN that A's t is always = B's t'. It means there is a 
1:1 correlation that both A and B agree upon.)
b. That this 1:1 relationship will be transitive in the sense that if A's t 
:: B's t', and B's t' :: C's t'', then C's t'' :: A's t.

Assuming my method of establishing the 1:1 correlation what's your proof 
this is incorrect?


On Friday, February 28, 2014 1:28:01 PM UTC-5, jessem wrote:
> On Fri, Feb 28, 2014 at 12:38 PM, Edgar L. Owen <<javascript:>
> > wrote:
> Jesse,
> First I would appreciate it if you didn't snip my proximate post that you 
> are replying to... 
> Anyway we MUST choose a frame that preserves the symmetry because remember 
> we are trying to establish a 1:1 proper time correlation BETWEEN THE TWINS 
> THEMSELVES (not them and anyone else), and it is only a symmetric frame 
> that preserves the facts as EXPERIENCED BY THE TWINS THEMSELVES. ALL we 
> need to do in my p-time theory is demonstrate that each twin can correlate 
> his OWN proper time with that of the other twin.
> But you agreed earlier (in your post at 
> that the idea of calling the comoving inertial frame of an observer 
> "their own frame" is purely a matter of CONVENTION, not anything imposed on 
> them by "reality". So, we could easily choose a different convention--one 
> in which each twin defines "their own frame", or "what they experience 
> themselves", as the inertial frame in which they have a velocity of 0.99c 
> along the x-axis. If they both agreed to define "the facts as experienced 
> by the twins themselves" in this way, by convention, they could also agree 
> on a 1:1 correlation between their proper times, one that would be 
> different from the 1:1 correlation they'd get if they used the comoving 
> frame.
> Do you wish to take back your earlier agreement that phrases like "their 
> own frame", "their view", "what they observe/experience" are only by 
> CONVENTION understood to refer to the comoving inertial frame, that this 
> isn't something forced on us by reality? If you still agree this is a 
> matter of convention, then it seems to me that trying to use something 
> that's merely a matter of human linguistic convention to prove something 
> absolute about "reality" is obviously silly, like trying to prove something 
> about the essential nature of God by noting that according to the spelling 
> conventions of English, "God" is "dog" spelled backwards.
> All the other frames are the views of OTHER observers, not the views of 
> the twins themselves which is all that we need to consider to establish 
> whether the TWINS THEMSELVES can establish a 1:1.
> Obviously if all observers agreed on an invariant 1:1 correlation we never 
> would have to establish the 1:1 on a successive observer pair basis and 
> then try to prove it transitive as I've consistently worked on doing. 
> MY theory establishes this 1:1 correlation BETWEEN THE ACTUAL TWINS 
> THEMSELVES on a pairwise basis, not on the basis of any invariance. 
> Therefore it obviously uses a symmetric frame that is consistent with how 
> those two twins experience their own and each other's realities and doesn't 
> require input from any other frames to do that.
> That isn't obvious at all--I don't see how the symmetric frame reflects 
> their "experience" in any way that isn't purely a matter of convention, 
> they certainly don't "experience" their proper times and velocities being 
> equal at each coordinate time if they don't CHOOSE to use a particular 
> coordinate system. All that they directly "experience" in a way that 
> doesn't depend on coordinate systems is the way that their proper 
> acceleration varied as a function of their proper time.
> MY theory then attempts to prove these correlations are transitive on a 
> pair by pair basis, not by considering all irrelevant frames and trying to 
> establish some invariance that I agree is impossible.
> Does this make it clear what my theory is trying to do? The theory is 
> based on pair wise correlations, not invariance....
> My proof of a contradiction in your ideas about p-time doesn't consider 
> the other frames you consider "irrelevant" either, it is based SOLELY on 
> the following premises:
> 1. If a pair of inertial observers are at rest relative to one another, 
> then events (like clock readings) that are simultaneous in their comoving 
> frame are also simultaneous in p-time
> 2. Any two events that happen at precisely the same position and time 
> coordinate in a particular inertial frame must be simultaneous in p-time
> 3. p-time simultaneity is transitive
> Your only response was to dispute premise #2, but subsequent discussion 
> suggested you were originally misunderstanding what I meant by "same 
> position and time coordinate" and that properly understood, you would most 
> like agree with premise #2 after all. That's why I want you to address my 
> last few questions about the "same position and time coordinate" issue at 
> you promised to address earlier, but have subsequently ignored all my 
> requests to get back to. Once again, if you continue to just ignore the 
> requests, that indicates a lack of respect for me and for the two-way 
> nature of discussions. Here, I'll even repost those questions to save you 
> the time of going back through your inbox to find the original post to 
> reply to:
> <div
> ...

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