TrueHeart

You've heard of the Twin Paradox perhaps?? An astronaut speeds through the cosmos and then returns to Earth to find that he has aged less than his twin brother. When the two twins first started separating from one another, each twin asserts that the other one's clock is running slowly, as compared to his own clock. That is an apparent discrepancy, but it actually has no illogical implications. When the astronaut twin makes his turnaround, the acceleration causes him to now perceive his Earthbound brother's clock to be running *fast*, as compared to his own; yet this effect is not mutual, ie. the Earthbound twin continues to reckon his astronaut brother's clock to be running slower than his own. The math works out perfectly, and when the space cadet returns to Earth, BOTH twins agree on who has aged the greater, the stay-at-home twin, and they both agree on the precise amount of that aging difference.

No meaningful comparison of their respective clocks is possible until they unite in the same place. If they keep on their inertial courses then that will never happen, and the discrepancies will only grow. In order to affect a coming together, one observer will have to be accelerated, and that will have additional ramifications as to how the two reckon each other's time. Such updated reckoning will mathematically converge upon a noncontradictory truism, by the time they do meet up.

Each observer rightfully considers his own observatory to be stock still; no distortions whatsoever occur there. Forget about distortions of mass -- that's a veritable quagmire of confusion and outmoded terminology. Concentrate on the three clock-and-ruler distortions, of which only the time dissynchronicity element is dependent on direction, ie. the earlier clockface readings are forward. Time dissynchronicity might easily get overlooked because it only pertains to spans stretching along the perceived moving entity... if the moving entity is small, considered a virtual point, then time dissynchronicity needn't even be addressed.

Yes, light will always reach the other entity regardless of its speed. I think you might've meant to ask about the case where each spacecraft is moving away from a mutual landmark (like Earth) at .9c, in opposite directions. Because then it would seem that the two craft's velocity with respect to one another would be 1.8c... too fast for light to catch up. But relativity has an answer for that: the addition of any two speeds never results in a number greater than c; so no two entities can ever move apart with speed greater than light... it is not possible to outrun being seen. I have a web site on the subject. Find it under my name/profile.

Oh I'm sure there are alternate ways to look at it. "Nonsequitor" is kinda too harsh. For example, at Usenet Relativity FAQ it gives one possible alternate view: And that site has a little more to say about it too. You could say, the pseudo G-field, the "fictitious force" facilitates the simplicity of using the accelerating entity's "stock-still-in-space" frame for all physical computations -- which may be expedient; or even poignant.

I get a chuckle from your phrase, "and though it may not be c". Why should it be c? why should it even be close to c?? Relativity proclaims that it could never be c. If you're talking about landing on another planet in our own galaxy, then its velocity with respect to Earth would definitely be very small compared to c, and so the clock discrepancy effect would be miniscule, virtually negligible. Yes, there would be some tiny discrepancy, but realize that it's not Earth's velocity "through the universe" (as you say) that matters, because relativity permits no such absolute measurement to be defined. All that pertains in such relativistic computations is the velocity of those travelers with respect to Earth. With relativity, you can only compare one observatory to another... there's no "looking at the bigger picture".

Relativity is all about how light behaves, and from that some truth is differentiated from some myth. Light's behavior is particularly at issue because the cosmos is ever expanding... some of the very distant galaxies are receding from us at near light speed -- we find that true while looking in any direction. Getting right into it, if a fleet ("The Fleet") of spacecraft left Earth and headed out into space, moving at a significant fraction of lightspeed, then how would light (and/or radio, EM) signals behave between us and them? And how would such signals behave amongst The Fleet members themselves? Would a radio signal sent from Earth take extra time to reach The Fleet, because it is receding away? Yet the reverse is not true?? ie. signals from The Fleet will transit only the predetermined distance through Earth's fixed coordinate system? Who is actually receding from whom?? Does it depend on how Earth is moving with respect to a higher coordinate system -- some master cosmic coordinate system?? In a word, no, none of that is true. Ok, it's all true, relatively true. What's absolutely true is the denial of any fixed master framework serving as a medium for EM signal transmissions: EM signals find their own way, somehow transcendent of mortal ciphering. It's uncanny: we don't know the how but we know the how much. We realize now that light behaves relativistically, which means that every clock and every ruler in the world must cede something to accomodate the feat -- sorta. In the scenario cited, The Fleet astronauts experience one thing while us Earthbound folk experience something altogether different, something that seems contradictory. By all reckoning, the astronauts witness their Fleet's signals to Earth move at fixed lightspeed with respect to The Fleet's native 3D coordinate system -- and by "native" I mean, "that x-y-z frame with respect to which The Fleet is stock still in space." Those astronauts... they witness their outgoing signals as requiring extra time to "catch up" to the receding Earth, while incoming Earth signals need only travel the predetermined distance from their release point. And all the calculations work out... no, there is no incompetence. And wouldn't y'know? Earthlings can make the very same claim. By all reckoning, they witness EM signals behaving as if Earth's native 3D coordinate system is boss. Their outgoing signals require extra time to catch up to the receding space Fleet, yet incoming Fleet signals need only travel the predetermined distance from their release point. This relativity carries over to within The Fleet itself (assuming it moves in a fixed formation): individual member craft can send and receive messages with one another as if their distance of separation were the sole influencing factor. Light and radio signals don't take longer to transit in one particular direction because of The Fleet's supposed motion "through space" -- that element is negated entirely. And now the final concluding point. Isn't it great that light behaves this way? especially considering that many millions of distant galaxies are flying away from us at tremendous speeds. If light simply moved relative to Earth, or relative to some master cosmic coordinate system (with respect to which Earth is fairly still), then how could those (hypothetical) zillions of aliens who populate those myriad distant galaxies ever live, eh?? they couldn't!! They would live in a giant ever-distorted world, where a simple twisting of the neck means drastic changes in their view of the surroundings -- red-shifted in one direction and blue-shifted in the other. They would be burned alive by a single candle flame if its radiations were coming from the wrong side. See also my modest treatise on the web.

Maybe I understand Companiero's original question perfectly. Companiero: perhaps you make the most common mistake of them all... perhaps you forget that the distortions of SR are THREEfold, entailing length contraction, time dilation plus time dissynchronicity. You can't compute anything at all under relativity without working in that third element. I offer my web site for plain elucidation of it all, with diagrams. The appended diagrams illustrate how the three distortions conspire to make all seem relativistic.

Yes but here's the problem: the Earth is gradually encircling the Sun, as is that observer (A) who is 'hovering' over the N.Pole. Since Earth's is a very gradual movement, we'll call it an inertial frame for purposes of a suitably brief snapshot. The Sun's motion WRT our galaxy can likewise be designated as inertial for a suitably small window; and there's an observer (B) hovering over our galaxy. The Milky Way is headed one way, yet the Sun is headed some way perpendicular to that, we'll surmise... AND, the Earth's motion is along yet a third oblique axis when viewed by this new observer B. The narrow laser beam does eventually land on a precise point on some celestial body... let's say on the Moon, just a brief second or two later. And of course, the Moon is seen to be moving along yet another oblique course WRT to all of the foregoing landmarks, per B's observatory. So if the path from the beam's origin to its eventual landing is a straight line per observer A, then wouldn't it be a curved line according to observer B?? Assume that there are only straight-line inertial motions of each entity during the brief 1.3-second window, but they occur in every crazy-which relative direction. Maybe: what one inertial observer perceives as a straight line will transform to be a straight course in the metric of all other inertial frames. I can see a logic to that. But I mean, maybe according to observer B, the carefully-aimed laser beam doesn't appear to be destined to land right at those particular coordinates on the Moon's surface.

You have to tell me where the laser beam will go after it goes beyond the target station, what planet will the beam land on so-to-speak and why. According to what metric of what frame will the beam advance?

Let's say you have two stations a short few miles apart, straddling the actual (not magnetic) North Pole. You shine a strong laser pointer from one station to a target positioned at the other station, employing a precalculated bearing/aim that would hit perfectly true if it weren't for Earth's rotation. Where does it hit? ..and if you're answer is "just west of true" then I question how all of a sudden there's a preferred 'aether' frame with respect to which light moves. Do you think it kind of "defaults" to the next higher 'realm', and behaves as if it's in Earth's center's inertial frame?? Duh.