Thread: Time Differences from Far Distances

1. In Brian Greene's fabric of the cosmos on nova and probably also his book, he said that we have different "now slices", or perceptions of now. If I understood correctly, I think he said that if an alien in a very distant galaxy rode a bike towards earth, he would be riding into the future, and if he rode away from the earth, it would be riding into the past. The farther the alien is, the farther in the future or past the alien will go. Why is this? I didn't think that the direction or distance you are away from something mattered in relativity.

2. What he is referring to is an aspect of Relativity called the Relativity of Simultaneity. It means that frames in relative motion with respect to each other will not agree on what is simultaneous.

Let's say you have three clocks in a line. According to the frame in which the clocks are at rest all three clocks are synchronized with each other. However, for someone moving along the line joining the clocks, this is not true, for him, the clocks in front of him read ahead of the clocks behind him. Thus if as he passes the middle clock it reads 12:00, then the clock behind him reads something before that and the one ahead of him something ahead of that (even though according to rest frame of the clocks they all read 12:00.) The greater the distance between the clocks, the greater the difference in their times.

All three clocks still run forward in time and at the same rate, they are just out of step with each other. Time dilation, the rate at which the clocks run as measured in the different frames does not change with direction.

So if we take our alien on the bicycle and he he is riding towards us, it means this: If according to us, when his wristwatch reads a certain date and time, the date on Earth is Aug 23, 2014, then according him, when his watch reads that same time, the date on Earth will be sometime after Aug 23, 2014. If he is riding away from us, the date on Earth will be sometime before Aug 23, 2014. But in both cases the time on Earth will advance as he rides. So, when he rides away from us he isn't really riding into the past, it is just that according to him, it is earlier on Earth at any given moment than it is for us.

3. Originally Posted by Janus
What he is referring to is an aspect of Relativity called the Relativity of Simultaneity. It means that frames in relative motion with respect to each other will not agree on what is simultaneous.

Let's say you have three clocks in a line. According to the frame in which the clocks are at rest all three clocks are synchronized with each other. However, for someone moving along the line joining the clocks, this is not true, for him, the clocks in front of him read ahead of the clocks behind him. Thus if as he passes the middle clock it reads 12:00, then the clock behind him reads something before that and the one ahead of him something ahead of that (even though according to rest frame of the clocks they all read 12:00.) The greater the distance between the clocks, the greater the difference in their times.
Nice explanation, Janus

In mathematical terms , the moving observer reads the time difference to be (in his frame):

Since the clocks are synchronized in the "two-clock frame", so

So if we take our alien on the bicycle and he he is riding towards us, it means this: If according to us, when his wristwatch reads a certain date and time, the date on Earth is Aug 23, 2014, then according him, when his watch reads that same time, the date on Earth will be sometime after Aug 23, 2014. If he is riding away from us, the date on Earth will be sometime before Aug 23, 2014. But in both cases the time on Earth will advance as he rides. So, when he rides away from us he isn't really riding into the past, it is just that according to him, it is earlier on Earth at any given moment than it is for us.

In mathematical terms , the moving observer reads the time difference to be (in his frame):

(+v has been replaced with -v)

Since the clocks are synchronized in the "two-clock frame", so

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