First the answer to your question at the end of your post.

Yes, of course I agree. Again that's just standard relativity theory. 
However as you point out by CONVENTION it means "the observer's comoving 
inertial frame" which is the way I was using it.

Now to your replies to my post beginning with your first paragraph.

Certainly there are equations that do what you say they do, but I don't see 
why what I say isn't correct based on that. Why do you claim it is 
impossible to just take proper acceleration and calculate what my age would 
have been if there was not any proper acceleration? An observer knows what 
his proper acceleration is, and he knows how much various accelerations are 
slowing his proper time relative to what it would be if those accelerations 
didn't happen. He has a frame independent measure of acceleration. He knows 
that particular acceleration will slow his proper time by 1/2 so he can 
define and calculate an 'inertial time' whose rate is 2x his proper rate.

You seem to think it would be necessary to MEASURE THIS FROM SOME FRAME for 
the concept to be true. It's not an observable measure, it's the 
CALCULATION of a useful variable. Therefore there is NO requirement that 
it's measurable in any frame because it's a frame independent concept, a 
calculation rather than an observable.

Therefore I don't see any reason to accept your criticism in this 
paragraph. If you disagree, which I'm sure you will, then explain why this 
concept of inertial time is not frame independent and valid. Perhaps a 
clear example would help?

Another way to approach this is do you deny that if we drop a coordinate 
grid on an area of EMPTY space that the coordinate clocks at the grid 
intersections all run at the same rate? And if not, why? 

And don't start making up other frames on me here. Just compare the proper 
times of those coordinate clocks. Do they all run at the same rate or not?


On Thursday, February 27, 2014 11:56:08 AM UTC-5, jessem wrote:
> On Thu, Feb 27, 2014 at 9:25 AM, Edgar L. Owen <<javascript:>
> > wrote:
> Jesse,
> I haven't answered those questions out of any disrespect or rudeness but 
> because I was working on a new explanation which I think does specifically 
> address and answer all of them which I present in this post. I will be 
> happy to answer any of your questions if you think they are still relevant 
> after reading this post which I think solves the 1:1 age correlation to 
> your satisfaction.
> That's the problem, you continually come up with new arguments and 
> explanations that you think resolve the questions I asked and therefore 
> mean you don't need to address them, but inevitably I disagree. Please just 
> respect my judgment about what's relevant TO ME, and answer the questions 
> that I ask ALONGSIDE any new arguments or explanations you might want to 
> supply. You say above "I will be happy to answer any of your questions if 
> you think they are still relevant after reading this post", so I will hold 
> you to that by repeating a question I'd like you to answer at the end of 
> this post.
> If you find any of the terminology confusing please let me know what you 
> think it SHOULD be rather than just saying it's wrong.
> Twins A and B start at the same location in deep space. No acceleration, 
> no gravitation. Their ages are obviously the same, and their age clocks are 
> running at the same rate.
> They exchange flight plans and embark on their separate trips according to 
> those flight plans.
> Now the only effects that will alter the rates of their age clocks are 
> acceleration or gravitation. But each twin can continually measure the 
> amount of acceleration or gravitation he experiences with a scale.
> Let's consider just the issue of accelerations in flat SR spacetime for 
> now, since it's simpler. The problem with this statement is that although 
> it's true each twin can measure their proper acceleration, there is no 
> FRAME-INDEPENDENT equation in relativity for how a given acceleration 
> affects the "rates of their age clocks", the only equations dealing with 
> clock rates and acceleration in SR deal with how changes in coordinate 
> velocity (determined by acceleration) affect the rate a clock is ticking 
> relative to coordinate time in some specific coordinate system.
> So each twin can always calculate how much his age has slowed relative to 
> what his age WOULD HAVE BEEN had he NOT experienced any gravitation or 
> acceleration. Let's call that his 'inertial age', the age he WOULD have 
> been had he NOT experienced any acceleration or gravitation.
> I see no way to define this in any frame-independent way. The only version 
> of this that relativity would allow you to calculate is what your age would 
> have been at a PARTICULAR COORDINATE TIME if you had remained inertial, and 
> you can compare that to what your age is at that SAME COORDINATE TIME given 
> your acceleration history. But this comparison obviously gives different 
> results in different coordinate systems. So, I don't agree with your 
> subsequent conclusion that this allows two twins to define a 1:1 
> correlation in their ages in a frame-independent way.
> There are a number of questions I asked in the last few posts that none of 
> your answers have addressed, but I'll restrict myself to repeating one for 
> now:
> 'Also, do you understand that even for inertial observers, the idea that 
> an observer's own rest frame can be labeled "his view" or taken to describe 
> "his observations" is PURELY A MATTER OF CONVENTION, not something that is 
> forced on us by the laws of nature? Physicists just don't want to have to 
> write out "in the observer's comoving inertial frame" all the time, so they 
> just adopt a linguistic convention that lets them write simpler things like 
> "from this observer's perspective" or "in his frame" as a shorthand for the 
> observer's comoving inertial frame. Physically there is no reason an 
> observer can't assign coordinates to events using rulers and clocks that 
> are moving relative to himself though, lots of real-world experiments 
> involve measuring-instruments that move relative to the people carrying out 
> the experiment.'
> Do you agree with the above paragraph?
> Jesse
> </d
> ...

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