Twin Travelling: Age Difference between Twins When Reunited?

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.
  • #1
kel
62
0

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



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
 
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  • #2
The twin doesn't travel with constant velocity v. He travels on a circular path with constant angular speed.
 
  • #3
I've just written the question as it is on my sheet. Eitherway, I still need help.

Thanks
 
  • #4
The color of the car changes as per doppler shift ?
BTW, [itex]\ 2\pi r [/itex] is so small compared to relativistic speeds...will there be much of a difference?
 
  • #5
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.
 

FAQ: Twin Travelling: Age Difference between Twins When Reunited?

What is the ideal age difference between twins for twin travelling?

There is no definitive answer to this question as it ultimately depends on the individual twins and their personal preferences. Some twins may prefer to travel together at a younger age, while others may feel more comfortable waiting until they are older. It is important for twins to discuss and come to a mutual decision about when they feel ready to travel together.

Is it safe for twins of different ages to travel together?

Safety is always a top priority when it comes to travel, and this is no different for twin travelling. As long as both twins are responsible and mature enough to handle the challenges of travel, there should be no issue with twins of different ages traveling together. It is important for twins to have a plan in place and to stay in communication with each other to ensure their safety.

Are there any benefits to twin travelling with an age difference?

Yes, there can be many benefits to twin travelling with an age difference. For example, the older twin may have more experience and knowledge about travel, making it easier for the younger twin to navigate new places. Additionally, twins with an age difference may have different interests and perspectives, leading to a more diverse and well-rounded travel experience.

Are there any challenges to twin travelling with an age difference?

As with any type of travel, there can be challenges when twin travelling with an age difference. One potential challenge is finding activities and experiences that are suitable and enjoyable for both twins, as their age difference may impact their interests and abilities. Communication and compromise are key to overcoming these challenges.

Is there any research on the effects of twin travelling on twins with an age difference?

While there is limited research specifically on the effects of twin travelling on twins with an age difference, there is research on the benefits of travel in general for personal growth and development. Additionally, there are many personal accounts and stories from twins who have traveled together with an age difference, highlighting the positive impact it can have on their relationship and individual growth.

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