Who Ages More in the Inverse Twin Paradox?

In summary: Therefore, in summary, according to the spacetime geometric approach, both rockets B and C age the same amount of time and the result is the same regardless of the reference frame. This is known as the twins paradox and is a consequence of the theory of relativity.
  • #1
granpa
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suppose we have a stationary observer 'A' at the origin. at t=0 rockets 'B' and 'C' pass the origin moving at gamma=10 but rocket B stops. when rocket 'C' reaches some point along the x-axis rocket 'B' accelerates to gamma=10 as measured by rocket 'C'. when rockets 'B' and 'C' meet its over. who ages more, rocket 'B' or 'C'? let us also assume that there exists a long line of evenly spaced clocks, perfectly synchronized to observer 'A', along the x axis.

obviously if rocket 'C' is considered to be stationary then we just have the twins paradox. but what is the result if we look at it from a different point of view? obviously the result should be the same.
 
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  • #2
granpa said:
suppose we have a stationary observer 'A' at the origin. at t=0 rockets 'B' and 'C' pass the origin moving at gamma=10 but rocket B stops. when rocket 'C' reaches some point along the x-axis rocket 'B' accelerates to gamma=10 as measured by rocket 'C'. when rockets 'B' and 'C' meet its over. who ages more, rocket 'B' or 'C'? let us also assume that there exists a long line of evenly spaced clocks, perfectly synchronized to observer 'A', along the x axis.

obviously if rocket 'C' is considered to be stationary then we just have the twins paradox. but what is the result if we look at it from a different point of view? obviously the result should be the same.
As always I would recommend the spacetime geometric approach. Here is an example, I used v = .6 c (gamma = 1.25) so that plotting it is easier and picked the inertial reference frame where A is at rest. Units of time are years and units of distance are lightyears so that c = 1.

Recall that the four-vector is (ct,x) and that the spacetime interval along a four-vector dr = (c dt,dx) is ds² = c²dt²-dx² = dr.dr and that ds/c is the proper time experienced by a clock moving along dr.

a0 = b0 = c0 = (0,0)
a1 = b1 = (5,0)
c1 = (5,3)
a2 = (15.625,0)
b2 = c2 = (15.625,9.375)

Let da1=a1-a0 and da2 = a2-a1 then total accumulated time on clock A is:
sqrt(da1.da1)/c + sqrt(da2.da2)/c = sqrt(5²-0²) + sqrt(10.625²-0²) = 15.625

Let db1=b1-b0 and db2 = b2-b1 then total accumulated time on clock B is:
sqrt(db1.db1)/c + sqrt(db2.db2)/c = sqrt(5²-0²) + sqrt(10.625²-9.375²) = 10

Let dc1=c1-c0 and dc2 = c2-c1 then total accumulated time on clock C is:
sqrt(dc1.dc1)/c + sqrt(dc2.dc2)/c = sqrt(5²-3²) + sqrt(10.625²-6.375²) = 12.5

I will leave it as an exercise for you to show that the intervals are the same in the inertial frame where C is at rest.
 

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  • #3


From the perspective of observer 'A', both rockets 'B' and 'C' start at the same point and end at the same point, so the time dilation effects should cancel out and they should age the same amount. However, from the perspective of rocket 'C', rocket 'B' is moving away and then coming back, while rocket 'C' stays stationary. This means that rocket 'B' experiences more acceleration and deceleration, which can affect the aging process. In this case, rocket 'B' may age slightly less than rocket 'C' due to the effects of acceleration. However, the difference would be very small and could potentially be negligible. Overall, the result should still be the same, with both rockets aging roughly the same amount.
 

1. What is the Inverse Twin Paradox?

The Inverse Twin Paradox is a thought experiment in Einstein's Theory of Relativity that explores the idea of time dilation, where time moves slower for objects moving at high speeds.

2. Who ages more in the Inverse Twin Paradox?

In the Inverse Twin Paradox, the twin who travels at high speeds will age less compared to the twin who stays on Earth.

3. What causes the difference in aging?

The difference in aging is caused by the time dilation effect, where the twin traveling at high speeds experiences time moving slower due to their velocity.

4. Is the Inverse Twin Paradox a real phenomenon?

Yes, the Inverse Twin Paradox is a real phenomenon that has been confirmed through experiments and is a fundamental aspect of Einstein's Theory of Relativity.

5. Can the Inverse Twin Paradox be observed in real life?

Yes, the Inverse Twin Paradox can be observed in real life, but it requires objects to travel at extremely high speeds, close to the speed of light, which is currently not possible with our current technology.

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