Twin Travelling: Age Difference between Twins When Reunited?

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Homework Help Overview

The problem involves a pair of twins, one of whom travels around the Earth in a fast car while the other remains in their city. The main question posed is about the age difference between the twins upon their reunion, with an additional query regarding the perceived color change of the car due to relativistic effects.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants discuss the implications of constant velocity versus constant angular speed for the traveling twin. There is also exploration of the time dilation equation and considerations of how to calculate velocity and time for the journey.

Discussion Status

Some participants have offered insights into the nature of the problem, questioning the clarity of the original question and suggesting alternative interpretations. There is an acknowledgment of the complexities involved in the scenario, particularly regarding the assumptions of motion and the effects of relativity.

Contextual Notes

Participants note that the problem may not be well-structured, with concerns about the feasibility of traveling around the world at constant velocity. The discussion also touches on the potential for Doppler shift affecting the perceived color of the car during the journey.

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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

Homework Equations



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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
 
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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.
 

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