Relativity & time dilation - more help please

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antandcharmi
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Relativity & time dilation - more help please

Post by antandcharmi »

I also have one other question which arose long ago when someone tried to explain relativity to me, but would love some help to understand.

i) If two spacemen travel directly toward one another, and their speeds are identical and over half c (let's say, 0.75 c) as it would apear to a third independent observer, is their speed relative to one another over c (1.5 c)?

ii) Whatever their relative speed, if they were twins and began moving at the same time, would they be the same age as one another when they met? As measured from either one of the twins inertial frames, would the other twin's clock appear to tick slower than the observer twin's clock? If so, how would either twin account for their respective ages when they met, whether the same or different?

Thanks again,
Anthony
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joe
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Re: Relativity & time dilation - more help please

Post by joe »

i) If two spacemen travel directly toward one another, and their speeds are identical and over half c (let's say, 0.75 c) as it would apear to a third independent observer, is their speed relative to one another over c (1.5 c)?
No, it is less than c. The relativity of velocities is explained here:
http://www.phys.unsw.edu.au/einsteinlig ... sforms.htm
as are the equations for calculating them
Joe
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joe
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Re: Relativity & time dilation - more help please

Post by joe »

ii) Whatever their relative speed, if they were twins and began moving at the same time, would they be the same age as one another when they met?
Yes, same age. This situation is much like part of the twin paradox. See
http://www.phys.unsw.edu.au/einsteinlig ... aradox.htm
Let's break the trips into three phases:
- During the accelerating phase, each sees the other to be ageing very rapidly (a general relativistic (GR) effect).
- Once acceleration is finished, each sees the other as ageing more slowly (special relativity SR).
- During deceleration, each sees the other as ageing slightly less rapidly than him/herself (GR again).

The magnitude of the two acceleration effects depend on separation and the second is much smaller. So, to an approximation that is probably fine for the situation you imagine, the first GR effect cancels the second SR effect and the last GR effect is negligible.

Joe
antandcharmi
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Re: Relativity & time dilation - more help please

Post by antandcharmi »

Wow! THANK YOU! At last, I understand it!

This was an old question I had, and it was dumb of me not to think of looking into the details of the Time Dilation section, so thanks for being so kind.

It seems that what I had always thought of as a universe whose fabric was spacetime, in which there are various expressions of electromagnetism, is actually a universe whose fabric is electromagnetism, in which there are various expressions of spacetime! As we get very close to the woof, space and time look very much more warped from those angles. It is like a projector being turned to play a movie at changing angles. The movie is constant but how we experience it changes with the angle. I feel like at last I have an intuitive grasp on it - and the equations don't seem so clinical anymore, but intimate.

Thank you very much for posting Einsteinlight, without which I would probably never have got here.

I cannot begin to tell you how grateful I am for your making it so easy to understand!
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joe
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Re: Relativity & time dilation - more help please

Post by joe »

Thanks for the kind words.

Yes, there is much to be gained from a geometrical representation of space-time. This is not explored in EinsteinLight, which aims just to give an introduction.

Joe
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