"Daryl McCullough" <email@example.com> wrote in message news:firstname.lastname@example.org... > harald says... >> >>On Jul 3, 4:10=A0pm, stevendaryl3...@yahoo.com (Daryl McCullough) wrote: > >>> I'm not sure what paradox you are referring to, then. >> >>I did some digging to understand the main cause of confusion. What I >>found, is the clock paradox started out as the one that Einstein was >>confronted with, as criticism of his GRT. At least, concerning SRT, >>before the development of GRT, I found no trace of such a paradox in >>the old literature. Did you? > > No, but I haven't really looked. But I guess it makes sense. > From the point of view of SR, it is clear that the traveling > twin is different from the stay-at-home twin, since he is in > a noninertial coordinate system. But if you generalize to allow > *any* coordinate system (inertial or not) then you have to explain > what's wrong with viewing the traveling twin at rest. > > But it's not really a paradox with GR, either, since GR doesn't > use the Lorentz transforms to relate noninertial coordinate systems. > > It's hard for me to see how the "twin paradox" is a paradox in any > sense other than being a surprising result. > >>> GR doesn't really *have* a notion of "rest". >> >>Einstein's GRT holds that reference systems in any form of motion may >>be used as physical reference system, relative to which objects are >>"in rest" - that's the basis of the "clock" or "twin" paradox, and how >>it started. > > >>> For a particular coordinate system, >>> you can use the term "at rest" to mean that the time derivative of the >>>spacial coordinates are all zero, but that doesn't have any particular >>> physical meaning, except in the cases where the metric is >>> time-independent. >>> >>> >> because GR is a generalization of SR. In the case of empty space far >>> >> from any large gravitating bodies, GR reduces to SR, so any GR >>> >> solution >>> >> to the twin paradox would have to have already been a solution in SR. >>> >>> >Irrelevant. >>> >>> It's not irrelevant to *MY* point. It is my point. And this is my >>> thread, so my point counts. >> >>Irrelevant for Einstein's clock paradox, which KW brought up in your >>thread. ;-) > > I thought KW was suggesting that Einstein used GR as a *solution* to the > paradox. I was responding to the idea that GR was a solution (whether or > not > Einstein viewed it as such). > > -- > Daryl McCullough > Ithaca, NY >
What of the observed traveler?, which is to say the trick of light, the virtual traveler, always observed by the observer to be somewhere between himself and the unobserved -- the unobservable -- real traveler in space but always observed by the observer to be behind the unobserved real traveler in time? Going away from the observer the unobservable real traveler always pulls farther and farther ahead of the observer's observed trick of light, the virtual traveler, in both space and time (the virtual traveler [apparently] slowing down in time in falling farther and ever farther behind the unobserved real traveler whose biology and clock and clock time is now far advanced in time over what is being observed by the stay at home observer.
The unobserved real-time traveler turning around to come home changes nothing regarding the location of the observed trick of light virtual traveler always located between him and the stay at home observer in space and now observably -- by the stay at home observer -- far behind him in time, thus appearing far younger in time, due to the original stretching out of distance and c's unchanging constancy never accomodating the stretching out (which is why the trick of light virtual traveler will always be between observer and the unobservable real traveler in space, yet always slowed down in time -- thus a history -- relative to both the real-time traveler and the stay at home observer). But the unobserved real-time is now closing, shortening or constricting in, in distance upon the stay at home observer rather than opening, lengthening or stretching out, in distance. The light he is putting out has a ever shortening distance to run, thus the trick of light virtual traveler is no longer more distant from either the unobserved real-time traveler or the stay at home observer. Though still between, with all involved distances now closing, now contracting, the trick of light virtual traveler is now closing in spatial distance, thus in appearance rushing up in time -- no matter the direction -- to both the observer and the unobserved real-time traveler propagating the light (light with an ever shorter, an ever more contracting, distance in space and time to run).
This of course means the trick of light virtual traveler, the only observed traveler, is getting ever closer in time and age to the real-time traveler emitting the light for his only existence as the stay at home observer's observed traveler. As the distance closes between the unobserved real-time traveler and the observer, so does the history close as the light-time-distance contracts. Light-time-distances and observable histories / times, in these cases, are one and the same thing.
Now only a fraction of a light second exists between the still unobservable real-time traveler emitting light (and thus projecting the time-line-historical image of himself as the trick of light virtual traveler) and the observer who stayed at home. But still, within that fraction of a light second expanse existing between reals -- within that fraction of history still existing between reals -- resides that virtual traveler in a space now only ever so slightly forward of the real traveler, and a time, a history, now just ever so slightly behind the times of both the unobserved real traveler and observer observing. At the observer the real-time traveler catches up to (CATCHES UP TO) and merges with the virtual in space. At the observer the trick of light virtual traveler catches up to (CATCHES UP TO) and merges with the real-time traveler in time (having closed up from a much more distant past in time than both the more recent pasts of both the previously unobservable real-time traveler and stay at home observer observing).
The virtual imaged traveler always positioned somewhere between the unobserved -- and unobservable -- real traveler in space, thus always observed to be somewhere, somewhat, closer in space to the observer than the real will actually be (as the entire "observable universe" versus the entire 'unobservable universe' proves) will also be observed, whether going away or coming on, to have a relative velocity slightly to greatly less than the unobserved real's actual [relative] velocity by virtue -- or curse -- of that observed closer [relative] positioning to the observer in space.
How much farther away, farther away in space, farther forward in time (+), from the observer (0) is the unobserved, the unobservable, real-time traveler (0) than the observed trick of lengthening, expanding, dimensions of distance; trick of shortening, contracting, dimensions of distance; trick of light and a light-time (thus histories') grid; trick of a UNIVERSAL constant of c, imaged virtual traveler (-)?
And why is it that so many physicists make the trick traveler and clock, the observed virtual traveler and clock, always one and the same with every real-time traveler and clock (never splitting them up to form an expandable / contractible three corner dimensioned picture rather than just a two point -single string- dimensioned picture)? Why is it that they always stop at the observed, the relatively superficial, point / horizon and, like implacable dark age priests, implacably demand that it be recognized to be all there is or can be? Having the observation of one I can see, but why is it that they also have the perceptiveness, too, of a strictly 1-dimensional being? To wit, no perceptibility, no deeper layers of observability, at all.
Of course few of them are first tier thinkers and seers, nor even second tier, nor even third tier, nor even fourth tier....