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Old Jan 1st 2016, 05:17 AM   #1
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Special Relativity effects; real or imaginary?

Clock A is at rest in space.

Clock B is traveling at a uniform velocity 0.5C relative to A and is heading directly towards A.

As B passes A the clocks are synchronised.

A notes the distance B has travelled after one year is 0.5 light years.

Question: From B's perspective...
1. how long does it take to reach that same point in space?
2. and how far was it.

Allowing for time dilation and length contraction I make it...
1. 0.866 years
2. 0.433 light years

However this makes no sense to me if you can switch the reference frames around???
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Old Jan 2nd 2016, 07:39 AM   #2
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I don't like the way this worded. "Clock A is at rest in spaces" makes no sense - things can only be at rest relative to something else. I think we can assume that this means that clock A is in an inertial frame - neither accelerating nor being affected by a gravitational field. And the question "how long does it take for B t reach that same point in space" I would also argue is better worded as "how long does it take for B to be 0.5 LY from A?" - this allows for the valid point of view that B is actually at rest and A is moving past at 0.5c.

Imagine that A has a long pole attached to it that is 0.5 LY in length. What A is measuring is the time it takes for B to go from being immediately adjacent to A to B being adjacent to the end of that pole. We are told that A measures the time as 1 year, which is consistent with the relative velocities of A and B being 0.5c.

Now consider B's perspective. As far as he's concerned he is at rest and A is coming towards him at 0.5c, which means that the long pole attached to A's ship appears to be contracted to something less than 0.5 LY in length - I'll leave the math to you. As A and the pole rush past at 0.5c it takes somewhat less time for the the tip of A's pole to be adjacent to B, so he records a shorter elapsed time than does A. Hence note that while both A and B are in inertial frames, they disagree as to the length of the pole and the time it takes to go from A and B being adjacent to each other to B being adjacent to the tip of that pole. So each has a different perspective as to what has happened.

Last edited by ChipB; Jan 2nd 2016 at 07:42 AM.
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Old Jan 2nd 2016, 11:38 AM   #3
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Thank you so much for your answer, I think the penny has finally dropped.

I was having a problem with one observer experiencing a shorter time than the other as it seemed to me that there was symmetry in the scenario where two observers are moving away from each other at a constant relative velocity.

It was your introduction of the pole that caused the penny to drop!
The symmetry is broken because the pole is fixed to only one of the observers and so only the other will perceive it to be length contracted.

So if I have this right we could attach a similar pole to the tail end of B and then A would measure the same shorter time for the tail end to arrive while still measuring the longer time for B to reach the tip of his pole.

So, have I got it or is all the above wrong ;o)
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Old Jan 4th 2016, 03:10 AM   #4
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This was my first dip into a physics forum and I must confess to being more than a little disappointed by the low level of traffic here.

I have another question but I think I will try another forum with higher traffic in the hope of generating a more lively discussion than found here.

Normally I wouldn't bother to leave a message of this kind as it seems churlish to say the least, but I'm thinking many like myself would be put off by the lack of traffic, so it might just help to let you know.
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Old Jan 4th 2016, 07:09 AM   #5
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Originally Posted by fxfocus View Post
This was my first dip into a physics forum and I must confess to being more than a little disappointed by the low level of traffic here.
Or perhaps school is out and students don't have homework to do. I think that's the main set of users here, i.e. students. I think that college students are in between semesters right now and as such and therefore don't have any questions to ask. When they come back from vacation they'll have many questions to ask.

Be careful what to ask for. It may come true!
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Old Jan 4th 2016, 10:14 AM   #6
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Hi fxfocus. Your point is understandable. However, I would ask that you please don't bail out on us. There is nothing to keep you from being active in more than one physics site!
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Old Jan 5th 2016, 12:09 PM   #7
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Originally Posted by ChipB View Post
Hi fxfocus. Your point is understandable. However, I would ask that you please don't bail out on us. There is nothing to keep you from being active in more than one physics site!
Hi ChipB, I'm still around but don't have another question yet. I've been reading more threads and am impressed by the quality of the answers here, both from yourself and some others so it seems traffic isn't the only consideration. )
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Old Mar 8th 2016, 09:53 PM   #8
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Originally Posted by ChipB View Post
I don't like the way this worded. "Clock A is at rest in spaces" makes no sense - things can only be at rest relative to something else.
I've seen people do this a great deal of the time. In call cases they mean that the rest frame being spoken of is the rest frame of the clock. All ideal clocks determine a frame of reference. I agree that one should avoid speaking of it in that way though.
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