What happen time dilation is videotaped?

[Ruari1967]

I am sure this question is a lot more elementary than a lot of other posts on here - I am definitely a layman rather than a specialist, so I hope this isn't a problem. My hypothetical question is this:

Person A is standing directly on earth, looking at his watch (so moving at the same speed relative to each other); Person B is moving close to the speed of light away from earth, again, looking at his watch. My layman's knowledge would tell me that time for Person B would slow down and take longer than Person A due to time dilation. However, if Person A was to watch a live video stream of Person B, what would he see? If 5 minutes for Person A takes 15 minutes for person B, there is a 10-minute gap, which I can't explain.

Thanks in advance.

 

[russ_watters]

Welcome to PF!

There are no gaps. Time is perceived to run slower, making everything appear to happen in slow motion.

...unless the video tape is recorded by a local observer and then mailed, then the video tape looks normal but short.

 

[Ruari1967]

Thanks for the reply! How fast would an object have to be going to make this noticeable? Would a 2-hour video on a satellite traveling at 250,000mph would be a few seconds slower for the observer on earth?

 

[Doc Al]

However, if Person A was to watch a live video stream of Person B, what would he see?

Not sure what you have in mind for a 'live' feed, since it takes time for the signal to reach person A. And as time goes on B gets further away, so the signal takes longer to reach A.

 

[Ruari1967]

I suppose Person B doesn't actually have to be traveling away from the Earth - if they were in orbit, the same principal would still apply, wouldn't it?

 

[PAllen]

The simplest scenario getting at what I think is your question is to imagine an un-accelerating space lab far from any massive body, and a rocket accelerating in a circular path (constant speed but constant acceleration to maintain circular path) around the space lab at high speed. Let's say each broadcasts video of people dancing to the same recording of the same music. Then, the lab will see the rocket video as in slow motion, and the rocket will see the lab video as in rapid motion.

This assumes the rocket people are able to 'ignore' extreme acceleration. Alternatively, the rocket could be moving at high speed on the circle, but at extremely large radius. Then the acceleration could be made small - e.g. 1 g. The larger radius would have no effect on the observed video once each was receiving the others video.

If you pose this on earth, you would have to take into account gravity as well, but this would be a much smaller effect as long as the rocket is going very fast (if the you were talking about a satellite orbiting, the orbital motion and gravitational effect would be of similar order of magnitude; that's why GPS systems have to account for both).

 

[ghwellsjr]

I am sure this question is a lot more elementary than a lot of other posts on here - I am definitely a layman rather than a specialist, so I hope this isn't a problem. My hypothetical question is this:

Person A is standing directly on earth, looking at his watch (so moving at the same speed relative to each other); Person B is moving close to the speed of light away from earth, again, looking at his watch. My layman's knowledge would tell me that time for Person B would slow down and take longer than Person A due to time dilation. However, if Person A was to watch a live video stream of Person B, what would he see? If 5 minutes for Person A takes 15 minutes for person B, there is a 10-minute gap, which I can't explain.

Thanks in advance.

If Person B is traveling at 80% of the speed of light away from the Earth and transmits a live video stream of his watch back to earth, Person A would see B's watch running at 1/3 the rate of his own watch. That means that after 15 minutes according to A's watch, he will see B's watch advance by only 5 minutes.

Now according to Special Relativity, in the frame of the earth, Person B's watch is time dilated so that it runs slow at 60% of normal and will have advanced by 9 minutes after 15 minutes goes by on Earth but since it takes time for the "live video stream" to get from B to A traveling at the speed of light an additional 4 minutes is tied up in the transmission. This combined effect of time dilation and increasing transmission time is called Relativistic Doppler in case you want to investigate it further.

 

[ghwellsjr]

Thanks for the reply! How fast would an object have to be going to make this noticeable? Would a 2-hour video on a satellite traveling at 250,000mph would be a few seconds slower for the observer on earth?

Yes, at that speed if a "satellite" were traveling directly away from earth, a 2 hour video transmitted back to Earth would take 2.7 seconds longer but this is essentially all caused by the increasing transmission time since the time dilation at this speed is miniscule. 250,000 mph is only 0.037% of light speed.

I suppose Person B doesn't actually have to be traveling away from the Earth - if they were in orbit, the same principal would still apply, wouldn't it?

No, if Person B or the satellite is in orbit, then the transmission time is not always increasing and so it's just the time dilation that is a factor. The satellite would have to be going much faster than 250,000 mph in order for more than a 1 second slow down in a 2 hour video. At 1% light speed (6,706,152 mph), there is about a third of a second increase. At 2% light speed (13,412,304 mph), the increase is a little less than one and a half seconds.

If Person B were traveling around the Earth at 80% light speed, the time dilation would result in Person A seeing 9 minutes go by on B's watch while 15 minutes goes by on A's watch. Person B would have to be orbiting at 95.3% light speed in order for Person A to see only 5 minutes go by on B's watch while 15 minutes goes by on A's watch.