
Originally Posted by
somfooleishfool
if gary was to jump in a space ship and travel away from earth at say 90% the speed of light and for the sake of arguement (although untrue) this slows time by 50% for garys point of reference. *now given einsteins thingy where he says that a train going the speed of light still passes a train going say 50% the speed of light AT the speed of light instead of the expected just 50% the speed of light. i would assume that gary and earth could have a conversation through radio waves because radio waves travel at the speed of light and so the radio waves for the conversation would reach gary pretty instantaniously. so all this assumed true. my question is this: if gary traveled 5 years out into space then turned around and came home at the same speed taking obviously 5 years to come back. how long was the conversation assuming they talked for the full 10 years (or 5 years according to gary). simply put. did they have a 5 year conversation or a 10 year conversation. and how does that work out. who misses some of the conversation etc.
It would quickly become very difficult for them to have any type of normal conversation as the increasing distance between them would cause longer and longer delays between transmission and response.
For example:
One second after Gary leaves, you send him a message. By this time Gary is 0.9 light seconds from you. It will take 0.9 sec for your signal to travel that far at c. However, by then, Gary has moved another 0.81 light seconds, so the signal still hasn't reached him yet. Your signal will continue to chase after Gary until finally after 9 sec, your signal finally catches up with Gary. Gary will be 8.1 light sec from you when he sends back the reply, which will then take 9 secs to return to you. So even if your messages are just little "blips" to make contact, it will be 18 seconds before you get a reply.
If you then respond with a second "blip", It will take 3 min for your blip to reach Gary and another 3 min for his blip to get back to you.
A third blip sent by you won't get a reply for 2 hrs. As you can see, things get quickly out of hand just sending blips back and forth.
This increasing distance has another effect. Assume that Gary sends you a full sentence as a message. He will be closer to you when he starts the sentence then when he ends the sentence. This means that you will receive the end of the sentence later than you would than if he had sent the signal while not receding. To you, he will sound like he is talking in slow motion. (this is different from the time dilation that makes his clock run slow as far as you are concerned, and is an additional effect.)
If he is approaching, the opposite occurs, and he will seem to talk at high speed.
He will notice the same thing about your transmissions to him, stretched to a slow drawl while he is receding and compressed to a chipmunk squeal while he is approaching. This is known as Doppler shift. For objects traveling at high enough speeds, relativistic effect have to be added in, and the result is caused "Relativistic Doppler effect".
For your example, the Relativistic Doppler effect works out to be about 0.27 when Gary is going away and 3.73 when he is coming back.
So now we can start to answer your question. We'll assume that in order to avoid the time delays mentioned above, You and Gary just constantly transmit to each other. You continuously talk for 10 years by your clock and Gary talks continuously for 5 years by his clock.
So what does each hear.
For 2.5 years, Gary will hear you talk at 0.27 normal speed, meaning he will hear 0.675 years of your conversation during this time.
For the next 2.5 years as Gary is coming back he will hear you talk at 3.73 times normal speed and hear 9.325 years of your conversation. 0.675+9.325 = 10 yrs, so he hears all of your conversation.
You, on the other hand hear the following:
It take 5 years for Gary to reach the turnaround point (4.5 ly away), It will take another 4.5 years for you to find out about this. IOW, you will hear Gary talk at 0.27 times normal speed for 9.5 years hearing 2.5 years
* of his conversation. (this makes sense, since according to his clock, 2.5 years will have passed when he reaches the turn-around point)
You then will hear him talk at 3.73 times normal speed for 0.5 years
*, hearing 2.5 yrs of his conversation. 2.5+2.5 =5 yrs so you hear all of his conversation.
So both of you hear the entire conversation of the other.
You may wonder why Gary notices the change in Doppler shift immediately when he turns around, while you have to wait for an additional 4.5 years after he turns around to notice the change in shift. This is because Gary is the one that turns around and since he is "right there" so to speak, he doesn't have to wait to know that he turned around, while you, being 4.5 light years away, have to wait for 4.5 years for this information to reach you at c.
The math doesn't quite work out here because your assumption of 0.9c resulting in a time dilation factor of 2 is not quite right. It is actually a speed of 0.866 c that causes that factor. This difference skews the math a bit.