A Twin Paradox Question, totally lost.

In summary, Anna and Bob, both 20 years old, are discussing the twin paradox and the effects of traveling at 0.6c. Anna travels to planet W, 12ly away, and back at 0.6c. According to the theory of relativity, time is dilated and length is contracted for Anna during her journey. When she returns, Bob will be 60 years old and Anna will be 52 years old, due to the effects of time dilation and length contraction.
  • #1
Engineergirl2
7
0

Homework Statement



Planet W is 12ly from earth. Anna and Bob are both 20 years old. Anna travels to planet W at 0.6c, quickly turns around, and returns to Earth at 0.6c. How old will Anna and Bob be when Anna gets back?



Homework Equations





The Attempt at a Solution



I've tried so many things and nothing is working. Apparently Bob is 60 years and Anna is 52 years. I'm completely lost on the idea of twin paradoxes, I could use some serious help. Thank you!
 
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  • #2
Can you see why it is 60 years for Bob?

For Anna, the distance to W and back is Lorentz-contracted.
 
  • #3
B/c 24cyrs/0.6c is equal to forty. Therefore you add them and get 60. Then, Anna is 52 years because the total distance that she appears to travel is 19.2? And 19.2cyrs/0.6c is equal to 32. add that to20 and you get 52. I ended up using length contraction. Sorry that was actually pretty easy!
 

1. What is the Twin Paradox?

The Twin Paradox is a thought experiment in the theory of relativity that explores the concept of time dilation. It involves one twin traveling at high speeds in space while the other twin remains on Earth. When the traveling twin returns, they will have experienced less time compared to the twin on Earth, resulting in a paradox.

2. Is the Twin Paradox a real phenomenon?

No, the Twin Paradox is not a real phenomenon. It is a thought experiment used to explain the effects of time dilation in the theory of relativity. However, time dilation has been observed in experiments with atomic clocks and is a real phenomenon.

3. How does time dilation affect the Twins in the paradox?

Time dilation causes time to pass slower for objects in motion compared to stationary objects. In the Twin Paradox, the traveling twin will experience time passing slower due to their high speed, resulting in a shorter amount of time passing for them compared to the twin on Earth.

4. Can the Twin Paradox be resolved?

Yes, the Twin Paradox can be resolved by taking into account the effects of acceleration on time dilation. In the thought experiment, the traveling twin experiences acceleration when turning around to return to Earth, which affects their experience of time. When this is taken into consideration, the twins' ages will be the same when they are reunited.

5. How does the Twin Paradox relate to the theory of relativity?

The Twin Paradox is a thought experiment used to explain the concept of time dilation in the theory of relativity. It demonstrates that time is relative and can be affected by factors such as speed and acceleration. This paradox helps to illustrate the principles of the theory of relativity and how they apply to our understanding of time and space.

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