Relative Time Dilation and Aging in Space Travel

AI Thread Summary
In the discussion on relative time dilation and aging in space travel, a participant calculates the age difference between themselves and their twin after traveling at 0.85c for three years. They encounter a mathematical error when substituting values into the time dilation formula, mistakenly using the same variable for both speed and light. The correct formula involves using the speed of light (c) as a constant, which resolves the zero denominator issue. The key takeaway is that the age difference results from the comparison of proper time and dilated time. Understanding these concepts is essential for accurately calculating time dilation effects in space travel.
disneygirl828
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Homework Statement


I have a twin brother, and we're 30 years old. If i travel for three years at 2.55 X 10^8m/s (0.85c) while my brother is a rest on Earth, how much older than me will my brother be upon my return?

Homework Equations



t=To/√1-v^2/c^2

3. Try to work out
To=3
T=?
V= 2.55 X 10^8 m/s
C= (.85c) 2.55 X 10^8 m/s
T= 3/ (all of this under a square root sign -->)1-(2.55 x 10^8)^2/(2.55 x 10^8)^2
t=3/0
*i get stuck here because you can't have a zero in the denominator*
 
Last edited:
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disneygirl828 said:
T= 3/ (all of this under a square root sign -->)1-(2.55 x 10^8)^2/(2.55 x 10^8)^2
t=3/0
*i get stuck here because you can't have a zero in the denominator*

Hmm, you've done:
T= \frac{3}{\sqrt{1- \frac{v^2}{v^2}}}
I'm guessing you've accidentally done this?
 
BruceW said:
Hmm, you've done:
T= \frac{3}{\sqrt{1- \frac{v^2}{v^2}}}
I'm guessing you've accidentally done this?
Yes i used that equation, should I have used something different? If so what?
 
disneygirl828 said:
t=To/√1-v^2/c^2

This was the right one, i.e. :
\frac{3}{\sqrt{1- \frac{v^2}{c^2}}}
c is the speed of light, but you used v instead, which is why the denominator came out as zero.
 
Last edited:
C = 3 x 10^8 m/s.
Remember this: the difference in ages will be the difference in the proper time and dilated time.
 
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