tfoster

2006-Nov-06, 03:08 PM

OK, here's a question I've been pondering.

Your friend is on a spaceship 50 lightyears away and takes off towards you at the speed of light. That speed is attained instantly, i.e., no gradual acceleration (I know that that is not possible but this is just a thought experiment).

In 50 years time our friend will reach Earth. You, armed with your unimaginably large telescope, can see the image of your friend 50 lightyears away (the light from that event just now reaching Earth). So you can see your friend standing next to you and simultaneously 50 lightyears away.

Halfway though his journey, his ship occupied a point 25 lightyears away from earth. The light from that event took 25 years to reach Earth, as does your friend's ship. Both will reach Earth 50 years from when he first took off (25 years for the first half of the journey and 25 years for the remainder). Similarly, the light from every "event" along the path of the journey will also arrive on Earth 50 years from the start of the journey.

So the instant your friend arrives on earth would you see a brief "light trail" that stretches for 50 lightyears, in effect a solid (but extremely brief) rod connecting you and the original position of the ship? Is this "accumulation of light" been observed in objects that are extremely far away of us (and moving extremely fast?).

To take the thought experiment one step further, imagine your friend is traveling in a faster-than-light ship. He would arrive before the light source of him leaving his original position, so that a few years down the road you could conceivably see your friend standing next to you and blasting off in his ship 50 lightyears away. As you continue to observe the ship it comes closer and closer until it lands, what happens then? Does his "image" land, walk over and merge into one with your "real" friend? Is this perhaps a paradoxical argument for the impossibility of faster-than-light travel? (kind of like "if time travel were possible then where is everybody"?).

I know time passes differently for observers moving at different speeds, but these are all observations made by one observer. A bit confusing I know, but the answer to the thought experiment can surely help one to have a better understanding of relativity.

Thanks all!

Your friend is on a spaceship 50 lightyears away and takes off towards you at the speed of light. That speed is attained instantly, i.e., no gradual acceleration (I know that that is not possible but this is just a thought experiment).

In 50 years time our friend will reach Earth. You, armed with your unimaginably large telescope, can see the image of your friend 50 lightyears away (the light from that event just now reaching Earth). So you can see your friend standing next to you and simultaneously 50 lightyears away.

Halfway though his journey, his ship occupied a point 25 lightyears away from earth. The light from that event took 25 years to reach Earth, as does your friend's ship. Both will reach Earth 50 years from when he first took off (25 years for the first half of the journey and 25 years for the remainder). Similarly, the light from every "event" along the path of the journey will also arrive on Earth 50 years from the start of the journey.

So the instant your friend arrives on earth would you see a brief "light trail" that stretches for 50 lightyears, in effect a solid (but extremely brief) rod connecting you and the original position of the ship? Is this "accumulation of light" been observed in objects that are extremely far away of us (and moving extremely fast?).

To take the thought experiment one step further, imagine your friend is traveling in a faster-than-light ship. He would arrive before the light source of him leaving his original position, so that a few years down the road you could conceivably see your friend standing next to you and blasting off in his ship 50 lightyears away. As you continue to observe the ship it comes closer and closer until it lands, what happens then? Does his "image" land, walk over and merge into one with your "real" friend? Is this perhaps a paradoxical argument for the impossibility of faster-than-light travel? (kind of like "if time travel were possible then where is everybody"?).

I know time passes differently for observers moving at different speeds, but these are all observations made by one observer. A bit confusing I know, but the answer to the thought experiment can surely help one to have a better understanding of relativity.

Thanks all!