Twin Paradox: Solving Confusing Explanations

In summary, the twin paradox can be explained by time dilation, length contraction and relativity of simultaneity.
  • #1
Snip3r
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This question about the twin paradox(twins A,B). I hope everyone knows the statement. I have read explanations for this but they differ. Some authors say twin(say B) who takes the trip accelerates so he can't be an inertial frame of reference. Some say it has nothing to do with acceleration and it can be solved by time dilation,length contraction and relativity of simultaneity. Okay this brings me a lot of doubts

a)Which explanation is correct?(it doesn't have to be practically possible)
b)those who say acceleration is the culprit, if you can blame the other guy as moving when in constant velocity why can't you do the same for acceleration?
c)are there any frames in universe which can be validated as inertial?for example if you say Earth is one it is certainly not because it revolves around itself,sun,galaxy etc. Like wise if you take a point in space(or any where else) how can you be sure its not accelerating or revolving etc?
 
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  • #2
a) It depends on what you need explained. If you only want to know what SR says about the final ages of the twins, the answer is an unambiguous "the astronaut twin is younger". If you want to know what's wrong with the incorrect argument for why they should have the same age, both of the explanations you mentioned are correct. The time dilation formula doesn't apply, since the astronaut's world line isn't the time axis of any inertial coordinate system. However, you can compensate for the error introduced when you apply it, by also taking relativity of simultaneity into account.

b) Experimentally, because an accelerometer will display something other than 0 when you're accelerating. Mathematically, because acceleration is defined as a measure of the deviation from geodesic motion. The Earth twin's motion is a geodesic (according to SR) and the astronaut twin's motion is not. ("Being a geodesic" is a a coordinate-independent property of a curve).

c) Here it looks like you want the answer given by GR rather than SR. (SR describes a universe without gravity). If your accelerometer displays 0 no matter which way you turn it (i.e. if you're in free fall), it's possible to define a local inertial coordinate system that has your world line as the time axis, but it gets less like an inertial coordinate system in SR the farther you go from the event that you took as the origin of the coordinate system.
 
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  • #3
The simplest way to look at is without acceleration as such. However the traveling twin has to change velocity during the round trip.

Ignoring practical problems, he can start out at almost light speed leaving the earth, getting to his destination in almost no time (in his reference frame). Then he stops and returns to Earth at almost light speed, again in almost no time (in his reference frame). The net result is that he hardly ages during a trip that in Earth years take a long time.

The reason it takes him almost no time is a result of the Lorentz contraction of the distance along his path.
 

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 two identical twins, one who stays on Earth and one who travels through space at high speeds. When the traveling twin returns to Earth, they have aged less than their twin who stayed on Earth, despite both twins experiencing time at the same rate.

2. How is the Twin Paradox resolved?

The Twin Paradox is resolved by understanding that the traveling twin experiences acceleration when they turn around to return to Earth. This acceleration causes a change in their frame of reference, which results in them experiencing time at a slower rate compared to the twin on Earth. This explains why the traveling twin has aged less when they return.

3. Why is the Twin Paradox confusing?

The Twin Paradox can be confusing because it challenges our intuition about time and space. It goes against our everyday experience and understanding of time as a constant and universal concept. Additionally, the concept of time dilation is a complex and abstract idea that can be difficult to wrap our minds around.

4. Can the Twin Paradox be observed in real life?

Yes, the Twin Paradox has been observed in real-life experiments. For example, atomic clocks on airplanes have been found to run slower than clocks on the ground due to the planes' high speeds. Similarly, astronauts who have spent extended periods of time in space have returned to Earth slightly younger than they would have been if they had stayed on Earth.

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

The Twin Paradox is a thought experiment that illustrates one of the key principles of the theory of relativity, which is that time is relative and can be affected by factors such as speed and gravity. It also demonstrates the concept of time dilation, which is a fundamental principle of the theory of relativity.

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