Jesse,

Just checking but I'm sure you would agree that twins AT REST with respect 
to each other are the same actual age (have a 1:1 proper age correlation) 
even if they are SEPARATED by distance? You just don't agree that if they 
are separated by distance AND in symmetric acceleration that there is any 
correlation of actual ages possible. Is that correct?

Edgar



On Sunday, March 2, 2014 2:37:13 PM UTC-5, jessem wrote:
>
>
>
> On Sun, Mar 2, 2014 at 2:25 PM, Edgar L. Owen <edga...@att.net<javascript:>
> > wrote:
>
> Jesse,
>
> I'll address your points in a later post, but first let me run this simple 
> new case by you.
>
> Imagine the symmetric trips of the twins continually criss cross each 
> other at 1 second intervals (of their own proper clocks) for the duration 
> of the entire trip.
>
> At each 1 second meeting I'm sure you would agree their proper times are 
> in a 1:1 correlation so their proper times are in a 1:1 correlation every 
> second of the duration of the trip and both twins agree on that.
>
> There is a 1:1 correlation of proper age clocks at the criss crosses 
> because they are in "the same point of space and time" by your operational 
> reflected light definition AND they both compute both their 1 second proper 
> time intervals since the last criss cross as the same invariant number as 
> each other, AND they BOTH HAVE AGREED TO CRISS CROSS WHEN EACH OF THEIR 
> PROPER TIMES READS 1 SECOND INTERVALS which in itself ensures the 1:1 
> correlation of proper times.
>
>
> Sure, there is complete agreement about their respective ages at each 
> crossing-point.
>
>
>  
>
>
> Now just take the limit of that and imagine a vanishingly small interval 
> for the criss crosses. If we do that then clearly we can say the twins have 
> a 1:1 correlation of their proper ages at EVERY MOMENT during the entire 
> trip to any limit of accuracy we wish.
>
>
>
> The problem is that in this limit, they also approach a state of simply 
> moving right alongside each other (since the spatial separation they can 
> achieve between crossings approaches zero), remaining at exactly the same 
> point in space at any given time, so their worldlines are identical. Of 
> course it is true in such a case that their ages will remain the same at 
> every moment in a frame-invariant sense, but this tell us anything about 
> simultaneity in a case where they have a finite spatial separation 
> throughout the trip.
>
>
>  
>
>
> Since a criss cross symmetric trip is no different in principle than our 
> previous symmetric trip (only a single meeting) it is clear that we have 
> proven there is a 1:1 proper age correlation for any symmetric trip during 
> EVERY MOMENT of the trip. 
>
> Edgar
>
>
>
> On Sunday, March 2, 2014 1:18:27 PM UTC-5, jessem wrote:
>
>
>
> On Sat, Mar 1, 2014 at 7:09 PM, Edgar L. Owen <edga...@att.net> wrote:
>
> Jesse,
>
> To address your points in order:
>
> 1. Yes, you said that proper ages are invariant. But note the important 
> point that the proper age of A to himself is a direct observation (he looks 
> at his age clock), but to anyone else is a computation and NOT an 
> observation.
>
>
> If he "looks at his age clock", that's a direct measurement that is not 
> specifically tied to ANY frame, including his own comoving frame. And 
> there's nothing stopping an observer who is moving relative to him from 
> stealing a glance at his age clock too as she passes him nearby (or looks 
> at him through her telescope), so she can make a direct measurement of his 
> age just as easily.
>
> A reference frame only needs to be used when you want to PREDICT some fact 
> you don't already know through direct measurement, given some other known 
> facts. For example, if you know that someone has a coordinate velocity v at 
> coordinate time t0 in some frame, and you know their proper age is T0 at 
> coordinate time t0, then as long as they move inertially, you can PREDICT 
> that at some later coordinate time t1, their proper age T1 will be equal to 
> T0 + (t1 - t0)*sqrt[1 - (v/c)^2]. Of course if you happen to be using the 
> person's inertial rest frame where v=0, this formula reduces to the simple 
> one T1 = T0 + (t1 - t0), but this still qualifies as a CALCULATION to 
> predict his proper age at a later coordinate time t1, not a direct 
> measurement.
>
>
>  
>
> In fact from their native comoving frames they will observe A at some 
> other age than their calculation. So the calculations trump the views.
>
>
>
> Huh? You're not making any sense--you just got through agreeing "proper 
> ages are invariant", how can you still maintain they'll "observe A at some 
> other age than their calculation" if you agree all frames will predict 
> exactly the same age for him at any event on his worldline, and this will 
> also be the age that he will be observed to have on his personal clock at 
> that event? 
>
> Do you just mean that the time coordinate they assign to that event may be 
> different than his proper age? That would be true, but no one familiar with 
> relativity would conflate a time coordinate with an "age", and anyway it's 
> quite possible to have an inertial coordinate system where he's at rest but 
> his age still doesn't match the coordinate time, because his birth is 
> assigned some time coordinate different from t=0.
>
>
>  
>
>
> Thus it is valid in relativity to CALCULATE things we CANNOT OBSERVE from 
> our frame.
>
>
> Actual physical measurements can be seen by any observer, like the example 
> of looking at the age clock of someone you're in motion relative to, so 
> there's nothing that one person can "observe" that someone else "cannot 
> observe" just because they're in a different rest frame, if by "observe" 
> you mean "measure using a physical instrument". Of course, actual physical 
> measurements may be interpreted differently depending on what frame we 
> use--for example, if I see an object pass the x=10 meters mark on some 
> ruler when the clock there reads t=5 seconds, and later pass the x=20 
> meters mark on the same ruler when the clock there reads t=6 seconds, then 
> if I am using a frame that defines the ruler and clocks to be at rest and 
> the clocks to be synchronized, I'll say these measurements imply the object 
> had a velocity of 10 meters per second, but if I'm using a frame where the 
> ruler itself is moving and the clocks are out of sync, I can say that the 
> velocity of the object itself was larger or smaller.
>
>
>  
>
> That's what I do to establish 1:1 correlations of actual ages. I use 
> calculations that trump Views, that trump observations. We don't always 
> have to use frame views to establish relativistic truth. Do you agree with 
> that? You must if you accept proper age invariance.
>
>
> Of course, you can determine relativistic truth by direct measurement, 
> like looking at someone's clock. But this only applies to quantities that 
> are frame-invariant, like proper time or proper acceleration. Other 
> quantities are DEFINED with respect to reference frames, there's absolutely 
> no way to determine them in a way that doesn't involve a frame. The 
> x-coordinate of an event would be an example of a quantity that's defined 
> in terms of a reference frame, you can't determine some object's 
> x-coordinate except in reference to a particular coordinate system that has 
> a particular spatial origin and its x-axis oriented in a particular 
> direction. Likewise, the t-coordinate of an event can only be defined 
> relative to a particular frame, and since simultaneity is DEFINED in 
> relativity to mean nothing more than "events that have the same 
> t-coordinate", simultaneity can only be defined relative to a particular 
> frame (talking specifically about physical definitions of simultaneity in 
> relativity--this doesn't preclude the possibility of some "metaphysical" 
> truth about simultaneity that's impossib
>
> ...

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