A video conference between earth and a space shuttle

I have just started looking into special relativity and I have come up with an intriguing gedanke, as Einstein himself called such theoretical thought experiments.

Imagine a space shuttle traveling through space at a constant velocity close to $c$. As the shuttle passes earth, a previously set-up camera starts broadcasting from earth to the shuttle. Since radio waves travel at the speed of light, the shuttle is receiving a constant transmission feed, assuming the camera is broadcasting 24/7.

Now, from what I have understood of special relativity so far, time will flow slower for the astronaut than for the earthlings. Hence, assuming $v=0.8c$, the astronaut will after 30 years have received a video transmission 50 years long!

Is my reasoning correct, that even though the transmission is live, the astronaut would actually be watching things that happened many years ago, while still receiving the "live" feed, which would be stored/buffered in the shuttles memory, thus making it possible for the astronaut to fast-forward the clip to see what happened more than 30 years after passing the earth?

My second question is, what happens when we consider the space shuttle to be at rest and the earth to be moving instead? If that would imply that it has been 50 years from the astronauts point of view, while only 30 years have passed on earth, then the astronaut would run out of video material after the first 30 years of watching the broadcast. Then what?

I hope it makes sense. Thank you!

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Gedanke is "thought", was Einstein loved to "do" was "Gedankenversuch", in english thought experiment. – Georg Apr 12 '11 at 20:41
"Now, from what I have understood of special relativity so far, is that time will flow slower for the astronaut than for the earthlings" No. Or, better, "yes and no". In the inertial frame of the earth, time appears to be slowed down for the astronaut. In the inertial frame of the spaceship, time appears to be slowed down for the earthlings. – Lagerbaer Apr 12 '11 at 21:07

The astronaut will not have received 50 years worth of transmissions at the time you specify.

Let's start by stating precisely what time dilation means in this instance. Consider two "events":

1. The people on Earth have a party to celebrate 50 years of radio broadcasting.
2. The astronaut on board the ship has a party to celebrate 30 years of travel.

In a reference frame in which the Earth is at rest, those two events are simultaneous. That's what we mean when we say that the astronaut's clocks run slow.

But the astronaut won't receive the 50th year of radio broadcasting until much later -- to be precise, 200 more years of Earth-time will elapse before he receives this signal. (Let's check this: in 200 years at $0.8c$, he will travel 160 light-years. Add that to the 40 light-years he's already gone, and you find that he's 200 light-years from Earth at the time. The radio signal will just be reaching that distance at that time.)

Of course, because of time dilation, that's only 120 additional years of astronaut time. Still, it means the astronaut can't see into the future.

To say it another way, at the moment in question (when the astronaut throws his 30-year party), the radio signal he is receiving is one that left Earth merely 10 years after he passed Earth. In Earth's reference frame, that radio signal traveled a distance of 40 light-years (since that's how far away the astronaut is at that moment), and took 40 years to do it (50 years minus 10 years).

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So if I understand it correctly, the astronaut will not receive a smooth continuous video stream, since each bit will take longer and longer to receive - hence, the astronaut will need to buffer the video for some time before playback? – 0sh Apr 12 '11 at 22:28
Yes. And he will also have to work around the doppler shift: The radio waves will be shifted in their frequency, and quite drastically so. The relevant formula is $f = f_0 \sqrt{(1+v/c)/(1-v/c)}$. – Lagerbaer Apr 12 '11 at 22:51
He'll receive a perfectly smooth stream; it'll just be slower than if he weren't moving. – Ted Bunn Apr 13 '11 at 13:21
@Lagerbaer: You guys seem to disagree. @Ted what do you mean that it'll be slower? – 0sh Apr 13 '11 at 16:29
I don't think we disagree. The astronaut will indeed receive a smooth stream. By "slower", we mean that if, on earth, the stream contains real time data (i.e. the data in 1 sec. of the stream corresponds to 1 sec of video), then one second of stream on the spaceship corresponds to $1s \cdot \sqrt{1-v/c} \sim 0.48s$ seconds of video. If the stream is encoded analogously, the astronaut will just see a slower video. If it's encoded digitally, he will have to buffer. – Lagerbaer Apr 13 '11 at 16:48