The Twin Paradox: Reconciling Time Dilation and Relative Velocity

[Thrice]

Just an easy question.. What does each observer see? The Earth one obviously sees time running slower on the spaceship. When the spaceship observer heads out, I assume he sees time running slower on the Earth frame? As he heads back, what does he see?

I'm finding it hard to reconcile the fact that the spaceship observer sees time running slower on the Earth with the fact that he should be able to see the (say) 2 years pass on Earth during his 1 day in space. Time dilation depends on the direction of relative velocity?

 

[topsquark]

Just an easy question.. What does each observer see? The Earth one obviously sees time running slower on the spaceship. When the spaceship observer heads out, I assume he sees time running slower on the Earth frame? As he heads back, what does he see?

I'm finding it hard to reconcile the fact that the spaceship observer sees time running slower on the Earth with the fact that he should be able to see the (say) 2 years pass on Earth during his 1 day in space. Time dilation depends on the direction of relative velocity?

The spaceship observer will see time running slower on the Earth while moving at a constant velocity, so on the way out and on the way back, time on Earth appears slower.

BUT the spaceship has to turn around at some point and this means the spaceship accelerates. This seriously messes with the rate of time flow on the spaceship, and is the direct reason that the spaceship observer is much younger than the Earth observer upon the spaceship's return.

-Dan

 

[loom91]

Hi,

It is possible to find quantitative solution to this problem by using the Minowski Space metric tensor and invariance of space-time interval. Just equate the two space-time intervals between Earth and the spaceship as observed from the respective reference frames of the spaceship and the Earth and plug in a high (+0.5c) relative velocity. That should give you the time-dilation. You will find that the clock aboard spaceship records one second when the Earh clock has recorded several seconds, thus the personal time of the spaceship twin is slower and less yaers has elapsed inside the spaceship than the Earth.

I don't think this has anything to do with the accelaration of the spaceship or turning back. It's easy to encounter difficulties like this when using ambiguous terms like goes slower and goes faster, so it's always better to quantify the phenomena using Minowski geometry. If you can't do the maths, tell me and I'll derive the paradox from the two assumptions (choice of metric tensor and invariance of length). You may also consider visiting http://en.wikipedia.org/wiki/Introduction to Special relativity .