- #1
Albertgauss
Gold Member
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Hi all, this is a follow-up variant to an earlier post
https://www.physicsforums.com/showthread.php?p=3804580#post3804580
In that post, I wanted to know what an Earth observer would see for a ship some distance off accelerating towards Earth and then reaching constant velocity. For the below, I have two ships that start on Earth and accelerate away from each other in opposite directions, one ship traveling to the right, the other ship traveling to the left. The rightward ship emits images itself. Both ships will ultimately achieve the same speed, close to the speed of light, but will remain traveling in opposite directions. I tried a spacetime diagram but did not include it here.
Ignore Doppler, Distortion, etc. I just want to make sure the following is correct.
Part 1: In the right-ship’s frame, images are continuously released one after the other by the same, microscopically small time interval. The first images from the right-ship to the left-ship arrive at the left-ship fairly quickly. But, as the accelerations continue, and the ships separate more, the right-ship’s images take longer and longer to get to the left-ship according to the left-ship’s frame. The left-ship will perceive everything happening on the right-ship to proceed in slow motion. Instant by instant, as things happen on the right-ship, the light pulses corresponding to each moment of whatever happens on the right-ship spread out more and more, so that two events that happen quickly on the right-ship will seem to take a lot longer when the left-ships receives images from right-ship events. And, because the ships accelerate, the time intervals between flashes on right-ship get longer and longer as perceived by left-ship. The slow motion gets worse and more drawn out as the ships continue to accelerate, almost like if a person on right-ship talks, left-ship will hear the voice really drawn out.
Part 2: The right and left-ships reach their target, constant velocities (which happens at the same time for the frame of the planet they launched at some time ago). Now the left-ship perceives everything to happen on the right-ship at regular time intervals; these intervals--via time dilation--are perceived to be longer time intervals for left-ship compared to right-ship, but they are constant time intervals nonetheless. Of course, since the right-ship and left-ships are well separated in distance at this point, left-ship knows everything going in the right-ship—time_dilated/length_contracted/etc---to have happened a long time ago. Left-ship knows that, as the ships continue to separate, what left-ship sees is happening on right-ship happened longer and longer ago, but the interval between snapshots remains the same.
Is this all correct?
https://www.physicsforums.com/showthread.php?p=3804580#post3804580
In that post, I wanted to know what an Earth observer would see for a ship some distance off accelerating towards Earth and then reaching constant velocity. For the below, I have two ships that start on Earth and accelerate away from each other in opposite directions, one ship traveling to the right, the other ship traveling to the left. The rightward ship emits images itself. Both ships will ultimately achieve the same speed, close to the speed of light, but will remain traveling in opposite directions. I tried a spacetime diagram but did not include it here.
Ignore Doppler, Distortion, etc. I just want to make sure the following is correct.
Part 1: In the right-ship’s frame, images are continuously released one after the other by the same, microscopically small time interval. The first images from the right-ship to the left-ship arrive at the left-ship fairly quickly. But, as the accelerations continue, and the ships separate more, the right-ship’s images take longer and longer to get to the left-ship according to the left-ship’s frame. The left-ship will perceive everything happening on the right-ship to proceed in slow motion. Instant by instant, as things happen on the right-ship, the light pulses corresponding to each moment of whatever happens on the right-ship spread out more and more, so that two events that happen quickly on the right-ship will seem to take a lot longer when the left-ships receives images from right-ship events. And, because the ships accelerate, the time intervals between flashes on right-ship get longer and longer as perceived by left-ship. The slow motion gets worse and more drawn out as the ships continue to accelerate, almost like if a person on right-ship talks, left-ship will hear the voice really drawn out.
Part 2: The right and left-ships reach their target, constant velocities (which happens at the same time for the frame of the planet they launched at some time ago). Now the left-ship perceives everything to happen on the right-ship at regular time intervals; these intervals--via time dilation--are perceived to be longer time intervals for left-ship compared to right-ship, but they are constant time intervals nonetheless. Of course, since the right-ship and left-ships are well separated in distance at this point, left-ship knows everything going in the right-ship—time_dilated/length_contracted/etc---to have happened a long time ago. Left-ship knows that, as the ships continue to separate, what left-ship sees is happening on right-ship happened longer and longer ago, but the interval between snapshots remains the same.
Is this all correct?