The Twin Paradox: Reconciling Time Dilation and Relative Velocity

In summary, the spaceship observer sees time running slower on the Earth while he is moving at a constant velocity, but when he turns around and returns to Earth, time appears to be running faster.
  • #1
Thrice
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Just an easy question.. What does each observer see? The Earth one obviously sees time running slower on the spaceship. When the spaceship observer heads out, I assume he sees time running slower on the Earth frame? As he heads back, what does he see?

I'm finding it hard to reconcile the fact that the spaceship observer sees time running slower on the Earth with the fact that he should be able to see the (say) 2 years pass on Earth during his 1 day in space. Time dilation depends on the direction of relative velocity?
 
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  • #2
Thrice said:
Just an easy question.. What does each observer see? The Earth one obviously sees time running slower on the spaceship. When the spaceship observer heads out, I assume he sees time running slower on the Earth frame? As he heads back, what does he see?

I'm finding it hard to reconcile the fact that the spaceship observer sees time running slower on the Earth with the fact that he should be able to see the (say) 2 years pass on Earth during his 1 day in space. Time dilation depends on the direction of relative velocity?

The spaceship observer will see time running slower on the Earth while moving at a constant velocity, so on the way out and on the way back, time on Earth appears slower.

BUT the spaceship has to turn around at some point and this means the spaceship accelerates. This seriously messes with the rate of time flow on the spaceship, and is the direct reason that the spaceship observer is much younger than the Earth observer upon the spaceship's return.

-Dan
 
  • #3
Hi,

It is possible to find quantitative solution to this problem by using the Minowski Space metric tensor and invariance of space-time interval. Just equate the two space-time intervals between Earth and the spaceship as observed from the respective reference frames of the spaceship and the Earth and plug in a high (+0.5c) relative velocity. That should give you the time-dilation. You will find that the clock aboard spaceship records one second when the Earh clock has recorded several seconds, thus the personal time of the spaceship twin is slower and less yaers has elapsed inside the spaceship than the Earth.

I don't think this has anything to do with the accelaration of the spaceship or turning back. It's easy to encounter difficulties like this when using ambiguous terms like goes slower and goes faster, so it's always better to quantify the phenomena using Minowski geometry. If you can't do the maths, tell me and I'll derive the paradox from the two assumptions (choice of metric tensor and invariance of length). You may also consider visiting http://en.wikipedia.org/wiki/Introduction to Special relativity [Broken] .
 
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1. What is the Twin Paradox?

The Twin Paradox, also known as the Twin Paradox Question, is a thought experiment in the theory of relativity that involves two identical twins, one of whom travels through space at high speeds while the other remains on Earth. This experiment highlights the concept of time dilation and the idea that time can pass differently for observers in different frames of reference.

2. How does the Twin Paradox work?

In the Twin Paradox, one twin stays on Earth while the other travels through space at high speeds and then returns to Earth. According to the theory of relativity, the traveling twin will experience time passing slower due to their high velocity, while the twin on Earth will experience time passing at a normal rate. This means that when the traveling twin returns to Earth, they will have aged less than their twin who stayed on Earth.

3. Is the Twin Paradox a real phenomenon?

The Twin Paradox is a thought experiment and has not been observed in real life. However, the concept of time dilation has been confirmed through experiments with atomic clocks and high-speed particles.

4. Can the Twin Paradox be resolved?

The Twin Paradox can be resolved by taking into account the fact that the traveling twin must undergo acceleration and deceleration in order to change directions and return to Earth. This acceleration causes the traveling twin's frame of reference to be different from the twin on Earth, leading to a difference in their experiences of time passing.

5. What implications does the Twin Paradox have?

The Twin Paradox highlights the fact that time is not absolute and can pass differently for observers in different frames of reference. It also supports the theory of relativity and has implications for space travel and our understanding of the universe.

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