Let's say a spacecraft is traveling away from earth @ close to the speed of light. There is computer on the spacecraft, that is streaming data from earth. How would this data feed look as the space craft travels further and further away from earth?<p>If this was a video stream(that did not buffer), how would the video play? Would the video start playing faster and faster?
I will take a stab at this, maybe a proper physicist will correct me.<p>If you are on the ship moving away from earth at nearly the speed of light but, we'll say, with a constant relative velocity, your time would slow down as observed by earth.<p>Also assuming that the streaming video signal is coming from earth at the speed of light, relative to earth, and as observed by someone on earth, it would take the stream quite a long time to get to the ship (though it would only take the normal amount of time to leave earth). This is because if you are moving at 99.9% c and the video is streaming at c then relative to the ship the video is streaming at .1% c. Thus, it takes a long time to get there.<p>However, since it's not buffering and just playing as it streams in, and because time has slowed for those on the ship, I will posit that the video would play at relatively the normal speed to the observers on the ship as both their time and the stream itself have slowed significantly.
Distance shouldn't matter. Assuming you can pick up the (extremely) redshifted signal. Also assuming it's headed directly away from Earth.<p>What'll happen is that it'll be slowed down by a constant factor dependent on speed. How? Depends on the video player.<p>The factor should be, if I remember my relativity right, sqrt((1 + v/c) / (1 - v/c)). The formula for relativistic doppler shift of wavelength.<p>Note that "what factor does the video slow down by" is equivalent to saying "if you have two points a certain time apart in the video, what factor is it stretched out by on reception". Which is equivalent to redshift in wavelength terms where the time is just wavelength / c.<p>There's also a gravitational effect, but it should be relatively negligible.