Relativity/Speed of Light question #2....Question about Time Dilation and Relative speed.?

Question

Ok, I kind of have a pretty good handle on the whole time dilation thing....as I understand it, objects moving very fast, in a frame of reference from something standing still will experience time dilation. In other words if you take 2 synchronized clocks and give one to guyA, and one to guyB...and guy B takes a trip in his spaceship around the solar system, moving at really high speeds...then from his frame of reference less time will have passed, than from the frame of reference of guy A. When guy A and Guy B meet up again and look at there clocks, they will say different things. Ok, then...I got all that...but my question (and I am assuming that I have some misconception of how the whole space-time thing works, here...cause this makes no sense) involves a situation with 3 frames of reference. Guy A Guy B and Guy C. Now...same situation...they all synchronize their watches. Guy A stays behind again (apparently he really doesn't like to travel much) and Guy B AND guy C both get into their own separate spaceships. Now here is the thing....Guy B takes off South...or Left...or whatever makes sense when you are speaking of traveling through outer space. And Guy C takes off in the exact OPPOSITE Direction (North...or Right...or however you'd say it) Guy C and Guy B are both accelerating at the exact same speed away from Guy A, but in different Directions. So Lets say that (for simplicities sake) that this level of acceleration will have caused a Time Dilation of 5 minutes in comparison to Guy A's frame of reference no matter the direction they both traveled in, so that when they both get back....thinking of it in this way at least, when they all look at their clocks Guy C, and Guy B's clock will show 5 minutes difference with Guy A's. Now here is where my apparent misunderstanding must be coming into play.....because if you look at it from Guy C's Frame of Reference (and vice verca)....Won't Guy B (who is traveling at the same speed, but in the exact opposite direction) actually be moving Twice as fast, since he is moving away at the same speed?!?! Wouldn't this cause More time Dilation between Guy B's clock, and Guy C's Clock than it would with Guy A's Clock?!?! And if from Guy A's Frame of Reference, the two of them were moving as to cause 5 minutes of Time Dilation....When they get back and compare clocks, how can this be true, if from Guy C's Frame of reference Guy B has more Time Dilation than he does?!?! According to His Frame, Guy B's clock should say 5 minutes of difference but (lets say, just for simplicities sake that twice as much speed equals twice as much time dilation...not sure if the math is that simple, but just for the argument Ill say it is) , according to Guy A's Frame it should say 10 minutes of difference!!! How Guy A's clock show five minutes of difference with BOTH Guy C and Guy B....yet Guy C, and Guy B's clocks show TEN minutes of difference between the two of them!?!?! Of course an easy answer would be that Guy C's clock went five minutes ahead, and Guy A's Clock went five minutes behind.....but that's not how Time Dilation works (at least not as far as I have ever heard)....that would suggest that you could travel backwards in time by moving North, and you could travel Forwards by moving South!!! LOL! Or alternatively That perhaps it is not true normally but, the only thing you would have to do, to set up such a thing would be to perform the experiment as I suggested with three people. OR perhaps it means that Time Dilation ONLY works for a Frame of Reference that is standing still, but not for two Frames of Reference Moving away from each other......but if this was the case where would you draw the line? "Standing Still" is sort of a misconception, considering that the planet itself is moving, in a moving solar system, in a moving galaxy...etc, etc. So surely Relativistic Speeds are only measured by Frames of Reference, in their relation one to another.....But that Idea is where this whole paradox comes from!!!!! LOL!!!!
So anyway......the way I am seeing this MUST be wrong somewhere......So is there anyone who could please explain, in a fairly simple way, where my misunderstanding if Relativistic Time Dilation is.......OR if I am Not wrong, and this paradox does exist....then what exactly does that suggest?!?!

Answer 1

Information propagates at the speed of light (Light from a galaxy 1000 light years away from earth tells us what the galaxy looked like 1000 years ago. To know what it looks like today we will have to wait 1000 years for today's photons to get to us.) ===>and the speed of light is constant for all observers. The rate of time passage in time dilation is as seen from OUTSIDE the FoR the clock is in.









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Answer 2

The difference between A and either B or C, is that A's frame is inertial, while B and C are accelerated. It's not just a speed difference. B and C can't leave to travel to high relative speeds, turn around, return to A and stop to compare notes without accelerating. Physics, including timekeeping is only simple in an inertial frame.



This is why (leaving C out of the picture for the moment) when B returns and both A and B see that B's clock has run slower, it's no surprise to either of them. B can build his own accelerometer to detect how much his clock time (also called B's "proper time") is different from A's. Observing A, B can see A's apparent motion and compare that with B's own accelerometer readings to deduce that A's frame is inertial. A can build an accelerometer, too, and detect the same things: That A is not accelerated and, by observing B's apparent motion, that B is accelerated.



The principle of relativity (to both Galileo/Newton relativity and Einstein's special relativity) is that no experiment can distinguish between two different *inertial* reference frames.



Bring C back into the picture, and everybody knows that B and C are accelerated and have no reason to expect simple timekeeping rules between B and C. They can both, however, use accelerometers to determine their accelerations and use that, plus observations of the others, to work out what everybody's proper time should be.

Answer 3

http://en.wikipedia.org/wiki/Relativity_of_simultaneity



I think you are asking about "simultaneity." Yes, whether or not events are VIEWED as simultaneous depends on the Frame(s) of Reference of the observer(s) of the event. (From inside there is no difference.) Information propagates at the speed of light (Light from a galaxy 1000 light years away from earth tells us what the galaxy looked like 1000 years ago. To know what it looks like today we will have to wait 1000 years for today's photons to get to us.) ===>and the speed of light is constant for all observers. The rate of time passage in time dilation is as seen from OUTSIDE the FoR the clock is in.



Google "Relativity simultaneity" and read several links beyond the one above.



The time dilation for your question is AS measured by guy A. He will observe guy B and guy C clocks being equally dilated AND B & C will see A equally dilated. We could bring in the Twin Paradox at this point, but that is NOT a true paradox because acceleration of FoRs B & C allow us to consider A a Perfered FoR



http://en.wikipedia.org/wiki/Twin_paradox



Now:



Imagine that every tick (1 second) of the clock in FoR A sends one photon each toward B & C. Both are moving away from A, simultanity requires that those photons arrive at B & C at the same instant as viewed by A. So, in space between A and B&C there is a stream of photons for every tick. Time is dilated so every photon appears more than a second apart to B &C ===> A's clock is running slower as seen by B & C. B & C turn around and head back toward A traveling through the stream of photons, Spacetime dilation conspires to allow A's clock to catch up while B & C remain dilated relative to A.

Answer 4

Guy B will not be seen by Guy C as moving "twice as fast". There are ways of adding velocities in relativity, given the information you have provided.



When the Guys get back, given the identical acceleration and speed profiles, Guy B and Guy C are the same age. No one saw anyone else get younger. So there is no way to "go back in time". Everyone saw everyone else age, just not at the local rate.



No paradox.