# Twin Travelling: Age Difference between Twins When Reunited?

• kel
In summary, the problem involves a pair of twins, one of whom drives around the world in a fast blue car at a constant velocity v while the other stays in the city. The question is what is the age difference between the twins when they meet again. There is also an optional question about whether the color of the car changes during the journey. The solution involves using the time dilation equation and taking into account the circular path of the car. The color change is due to the doppler shift.

## Homework Statement

A pair of twins live in (city). one drives around the world in his fast blue car, leaving the city in a fixed direction with a constant velocity v. The proper circumference of the Earth is 2PiR - ignore the rotation of the earth.

1 -What is the age difference between the two twins when they meet again??

Also, have an optional question - no marks for this, but would be interested in hearing any ideas:

2 -The twin who stayed in the city looks at the car of his brother - does the colour of the car change during the journey? how?

I would say yes, but not sure if it's due to length contraction i.e of wavelengths of the light that hit the car at different points around the world (i.e differing frames of reference), hence fading the paint - may be wrong, but like I said, no marks for it anyway

None given

## The Attempt at a Solution

At the moment I have the time dilation equation

dt= t2-t1 = Tau/ sqrt(1-(v^2/C^2)

My main problem is that I can find values for the length of the journey (ie circumference of Earth and speed of light is easy enough) but how do I calculate the velocity travelled?

I know that v=s/t (but I'm trying to work out t anyway)

Starting to think it may be a question that doesn't require a numerical answer

Thanks

The twin doesn't travel with constant velocity v. He travels on a circular path with constant angular speed.

I've just written the question as it is on my sheet. Eitherway, I still need help.

Thanks

The color of the car changes as per doppler shift ?
BTW, $\ 2\pi r$ is so small compared to relativistic speeds...will there be much of a difference?

It's not a very well written problem- as matt grime said, you can't go "around the world' at constant velocity.

I suspect it was an attempt to get around the resolution of the "twin" problem- that you can't have one moving away at a constant velocity and still have them meet up again.

Treat it as a straight line problem. How long will it take the moving twin to travel a distance (in a straight line) equal to the circumference of the earth?

How much will the Lorentz time change be?

As for the second question, yes, it is the "doppler" shift.