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 
PROPER TIMES READS 1 SECOND INTERVALS which in itself ensures the 1:1 
correlation of proper times.

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.

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. 


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 <<javascript:>
> > 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 impossible to demonstrate experimentally, 
> and of course it's conceivable that relativity will turn out to be 
> incorrect as a physical theory).
> Also note that the ticks of the symmetric twins' own comoving clocks serve 
> as event markers. So if the proper ages of the twins are invariant to all 
> observers, then all observers can simply observe their clock tick markers 
> reading exactly the same for the same proper ages of both twins.
> Sure, they can observe that for each twin, the event of their clock 
> reading X coincides with their actually being X years old biologically, if 
> that's what you mean by "their clock tick markers reading exactly the same 
> for the same proper ages".
> That PROVES the 1:1 correlation that the real actual ages of the symmetric 
> twins always occur at the same clock tick markers and thus they are the 
> same proper ages at the same times.
> Total non sequitur, you are just confusing two different meanings of the 
> word "same" here. It's true that for any individual twin, their biological 
> age being X always occurs at a reading on their OWN clock that has the 
> "same" value of X. But this in no way leads to the conclusion that the 
> age/clock reading of one must be the "same" as the age/clock reading of the 
> other when they apart--that's an entirely different statement involving the 
> simultaneity of distant events, not just about ages coinciding with local 
> clock readings for each individual twin. After all, even if the twins 
> accelerated NON-symmetrically so you WOULDN'T claim that they must have the 
> same ages as one another, it would still be true that for each individual 
> twin, their biological age being X would occur when their age clock shows 
> the "same" reading X, so everyone would still see "their clock tick markers 
> reading exactly the same for the same proper ages".
> Thus all observers agree that the proper ages of both twins occur at the 
> same clock tick marker readings of the twins own proper clocks.
> This is one more proof the actual ages of the symmetric twins are equal 
> during the trip, and EVERY OBSERVER AGREES ON THIS. Thus it is a real 
> physical fact.
> Nope, your argument is just based on equivocating what you mean by "same 
> proper ages", whether you are comparing biological ages to age clock 
> readings for each individual twin, or making a judgment about simultaneity 
> in ages for two different twins.
> 2. What all these quotes mean in saying that all frames are equally valid 
> is that all observer VIEWS are real actual VIEWS of reality. That they are 
> what the observer actually observes. I certainly agree with that. However 
> as I've pointed out they don't all preserve the actual physical reality of 
> SPECIFIC facts.
> The quotes don't just say they are "real actual VIEWS of reality", they 
> use language like "equally valid" (a phrase used in two of the quotes, 
> along with "equally good frames for observing nature" and "equally suitable 
> for the description of nature" in the remaining two). If one person has a 
> view of a situation that is objectively incorrect, and another has a view 
> of the same situation that's objectively correct, then they are both "real 
> actual views" of different people, but they are certainly not equally VALID 
> (nor would they be equally "good" or "suitable" as descriptions of nature), 
> any educated English-speaking person should understand that to say two 
> perspectives are "equally valid" in a scientific context implies there is 
> no objective basis for favoring one over the other.
> I am sure we could easily find the email of any of the three living 
> authors of the quoted statements (they're all professionals who would have 
> contact info available online), and ask them if they think there are ANY 
> cases (like the case of symmetrically-accelerating twins) where they think 
> one frame's conclusions about simultaneity (or any other frame-dependent 
> quantity) represent "actual physical reality" while other frames' do not. 
> Do you really believe any of them would agree with you on this, or do you 
> understand on some level that what you are proposing is your own 
> "interpretation" of relativity which differs from the understanding of all 
> mainstream physicists? If the former, I would be happy to make a friendly
> ...

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