Twin Paradox Explanation Needed

[jam.muskopf]

So in the twin paradox, the traveling twin ages less in the end. According to time dilation, each twin sees time passing in the other twin's frame of reference slower than his own. However, if the twin on Earth is ultimately older, doesn't time have to appear to be moving faster for the twin on Earth at some point in the traveling twin's frame of reference?

 

[csmcmillion]

So in the twin paradox, the traveling twin ages less in the end. According to time dilation, each twin sees time passing in the other twin's frame of reference slower than his own. However, if the twin on Earth is ultimately older, doesn't time have to appear to be moving faster for the twin on Earth at some point in the traveling twin's frame of reference?

The difference in ages is due to the traveling twin jumping to non-inertial frames. You can find lots of threads on this by searching this forum for "twin paradox".

 

[jam.muskopf]

so when the twin is in a non-inertial frame, does he perceive the Earth time to be passing faster than his own time?

 

[csmcmillion]

so when the twin is in a non-inertial frame, does he perceive the Earth time to be passing faster than his own time?

Yes. See the section "viewpoint of the traveling twin"

http://en.wikipedia.org/wiki/Twin_paradox

 

[jam.muskopf]

WAHOOO! Feels good to finally understand the paradox! THANKS A TON MAN!

 

[PatrickPowers]

So in the twin paradox, the traveling twin ages less in the end. According to time dilation, each twin sees time passing in the other twin's frame of reference slower than his own. However, if the twin on Earth is ultimately older, doesn't time have to appear to be moving faster for the twin on Earth at some point in the traveling twin's frame of reference?

Yes. If looked at from the point of view of General Relativity then it is all explained. The answer is that all of the time dilation that is observed when the two clocks meet again is due to the acceleration they experience. The younger twin experienced more acceleration.

http://muj.optol.cz/richterek/data/media/ref_str/styer2007.pdf

"How do two moving clocks fall out of sync?" Daniel F. Styer, Pof. Physics, Oberlin University

 

[bobc2]

So in the twin paradox, the traveling twin ages less in the end. According to time dilation, each twin sees time passing in the other twin's frame of reference slower than his own. However, if the twin on Earth is ultimately older, doesn't time have to appear to be moving faster for the twin on Earth at some point in the traveling twin's frame of reference?

It's the difference in path lengths taken through the 4-dimensional space-time continuum. The traveling twin takes a shorter path. You can put clocks along the path of each observer to see how time is passing in the 4-D continuum. Of course acceleration is needed to put the traveling twin on a new path.

If you are racing with someone and you take a short cut to beat him to the finish line, you had to accelerate when you turned off of the main path, but it's the shorter path that won the race.

The sketch to the right shows a sequence of simultaneous 3-D spaces experienced by the traveling twin on the out-going and in-coming trips. But those are just his cross-section views associated with the usual time dilation phenomena. Each twin moves along his own world line at the speed of light, and this suggests the progress along the paths. You can mark equally spaced clock times along the world lines. The sudden jump in time of home-twin, observed from the point of view of traveling twin is just the time dilation phenomena.

Some physicists like to focus on the time dilation phenomena, while other physicists like to focus on the progress along the world lines using the sequence of proper times (with observers moving along their world lines at light speed). Take your pick. Both concepts give you the same results in the end.

 

[bobc2]

Notice in the right side sketch (previous post) that when the traveling twin makes his turn to return home, from his point of view the clock at home suddenly speeds up, i.e., jumps to a much later clock time. In effect the home twin appears to move to a new position on his world line at a speed far in excess of the speed of light.

But, that's just the effect of "turning his head" as it were. You can get a similar effect looking through a telescope in the night sky. You swing the telescope from one galaxy to another galaxy light years away, traversing the sky in just a few seconds. Your view moved at a speed far in excess of the speed of light. But, no object really moved. It was just a change in view.

That's the way it is with the traveling twin when he changes his 3-D cross-section view of the 4-dimensional space-time universe.

 

[jam.muskopf]

Alright, thanks guys that is very helpful. I'm a senior in high school, in my first year of calculus. Any suggestions of reading I can do on my own that would be mathematically understandable at my level? Thanks