# How does relativity theory resolve the Twin Paradox?

Ronald C. Lasky, a lecturer at Dartmouth College's Thayer School of Engineering, explains.

Time must never be thought of as pre-existing in any sense; it is a manufactured quantity. --Hermann Bondi

Paul Davies's recent article "How to Build a Time Machine" has rekindled interest in the Twin Paradox, arguably the most famous thought experiment in relativity theory. In this supposed paradox, one of two twins travels at near the speed of light to a distant star and returns to the earth. Relativity dictates that when he comes back, he is younger than his identical twin brother.

The paradox lies in the question "Why is the traveling brother younger?" Special relativity tells us that an observed clock, traveling at a high speed past an observer, appears to run more slowly. (Many of us solved this problem in sophomore physics, to demonstrate one effect of the absolute nature of the speed of light.) Since relativity says that there is no absolute motion, wouldn?t the brother traveling to the star also see his brother?s clock on the earth move more slowly? If this were the case, wouldn?t they both be the same age? This paradox is discussed in many books but solved in very few. When the paradox is addressed, it is usually done so only briefly, by saying that the one who feels the acceleration is the one who is younger at the end of the trip. Hence, the brother who travels to the star is younger. While the result is correct, the explanation is misleading. Because of these types of incomplete explanations, to many partially informed people, the accelerations appear to be the issue. Therefore, it is believed that the general theory of relativity is required to explain the paradox. Of course, this conclusion is based on yet another mistake, since we don't need general relativity to handle accelerations. The paradox can be unraveled by special relativity alone, and the accelerations incurred by the traveler are incidental. An explanation follows.

Let us assume that the two brothers, nicknamed the traveler and the homebody, live in Hanover, N.H. They differ in their wanderlust but share a common desire to build a spacecraft that can achieve 0.6 times the speed of light (0.6c). After working on the spacecraft for years, they are ready to launch it, manned by the traveler, toward a star six light-years away. His craft will quickly accelerate to 0.6c. For those who are interested, it would take a little more than 100 days to reach 0.6c at an acceleration of 2g's. Two g's is two times the acceleration of gravity, about what one experiences on a sharp loop on roller coaster. However, if the traveler were an electron, he could be accelerated to 0.6c in a tiny fraction of a second. Hence, the time to reach 0.6c is not central to the argument. The traveler uses the length-contraction equation of special relativity to measure distance. So the star six light-years away to the homebody appears to be only 4.8 light-years away to the traveler at a speed of 0.6c. Therefore, to the traveler, the trip to the star takes only eight years (4.8/0.6), whereas the homebody calculates it taking 10 years (6.0/0.6). It is instructive to discuss how each would view his and the other?s clocks during the trip. Let?s assume that each has a very powerful telescope that enables such observation. Surprisingly, with careful use of the time it takes light to travel between the two we can explain the paradox.

Both the traveler and homebody set their clocks at zero when the traveler leaves the earth for the star (event 1). When the traveler reaches the star (event 2) his clock reads eight years. (Click here for graph.) However, when the homebody sees the traveler reach the star, the homebody?s clock reads 16 years. Why 16 years? Because, to the homebody, the craft takes 10 years to make it to the star and the light six additional years to come back to the earth showing the traveler at the star. So to the homebody, the traveler?s clock appears to be running at half the speed of his clock (8/16.)?

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1. 1. Polymath2007 09:01 AM 12/30/07

For a alternate explanation of some of the ideas in this aritlcle see my blog http://science-community.sciam.com/thread.jspa?threadID=300005761&#msg300016893

2. 2. Polymath2007 12:30 AM 1/22/08

Here is the link to my blog.

3. 3. Polymath2007 06:36 AM 1/29/08

4. 4. thereaintnojustice 11:20 AM 1/29/08

In my understanding, the Twin Paradox is not really a paradox at all. It doesn't actually require resolving. It's just an effect of relativity that seems a bit illogical to human insticnt. You accelerate the first twin to relatiivistic speed and the bring him back and he's aged less than the second. It actually would happen and wouldn't actually create any unresoved problems. At least that's how it appears to me.

5. 5. Unreeld in reply to thereaintnojustice 06:47 PM 12/1/08

exactly all this means is that there is delay in how we get information from light as we get farther away

6. 6. Archnawan 08:50 AM 5/12/09

Interesting that this implies that information is relayed faster than the speed of light. However I don't see why the travelers clock would read any different than the 10 years that actually passed. It seems the descrepancy to the traveler would be in his percieved velocity, not his percieved time. He percieves the shorter distance of 4.8 vs an actual 6, but in reality is at a constant velocity over a constant distance meaning a constant time. The net result would be a percieved lower relative velocity not a time change.

7. 7. abertsos 12:18 PM 9/4/09

I order to avoid all asymetries lets assume 2 twins each on a spacecraft in opposite directions travelling at 0,3*c each for 3 light years and back to the point they started. From A point of refference times passes slower for B and for B time passes slower for A. Lets also assume that they dont see eachothers clock but they only see when they meet. According to relativity A expect to see B clock writing 16 years and his clock 20 while B expect to see A's clock writing 16 years and his clock 20. They find out however that both clocks write the same. Please tell me what do the clocks write 16,20 or something else? Also how can you call the fact that relativity formulas predict different time for each A,B clock when they meet if not a paradox?

8. 8. xaterri 11:22 AM 2/21/11

Any transformation between two observers is a space-time dialogue between two entities A and B about a third entity C. In the 'Galileo Transformation', the third entity C is understood, does not appear in the notation. But the 'Lorentz Transformation' completely ignores the entity C, and this is why the twin paradox.
I would like to introduce some new transformations that preserve the local velocity of light. Also resolve the twin paradox.
Relational Transformation: http://vixra.org/abs/0909.0022

9. 9. Bollinger 10:06 AM 3/27/11

The above article does not in my view explain anything. Suppose 2 ships way out in space were at rest relative to each and side by side. If ship 1 containing twin 1 is to be seen as moving close to the speed of light then the ship containing twin 2 has been arbitarily chosen to be the frame of reference and then the lorentz equation can be used with regard to ship 1 including the length contraction equation( dervied from the Lorentz equation) But if we arbitrarily use the ship 1 as the frame of reference then ship 2 containing twin 2 should be seen as moving in the opposite direction as we thought ship 1 was and likewise then the length contraction equation should apply only to ship 2. The above article assumes that we should only use the length contraction equation with regard to the Travelers ship. Why? If we regard the traveler as the frame of reference then it is the Earth etc that is moving and the length contraction equation now applies to the person on the Earth.

10. 10. wagrodr 10:22 AM 4/25/12

I aggree that is lack of logic on the explanation. I am start learning Special Relativity but for me it may be key the fact that the traveller leaves but return to the the initial frame of reference. The experiment takes place on the Earth/Star reference frame, but could be otherwise. If we consider that twins are in the spaces and one jumpt to the Earth, decelaring up to 0.6c in relation to the spacecraft for later returning to the spacecraft at 0.6c versus the spacecraft will not occur exactly the inverse? Or it is impossilbe to make any physics experiment at 0,6c relative to the frame of reference of the spacecraft? I understood physics is the same for the spacecraft and Earth reference frames. I still do not know enough to satisfy my mind, but the explanation is not enough. Does somebody really knows if Special Relativity is sufficient to explain why the traveler is young and why it could not be exactly the opposity if the frame of reference was the spacecraft?

11. 11. bklinger 09:49 AM 7/4/12

For anyone with lingering doubts about whether the accelerations are key to the argument, I think you can consider a slightly different thought experiment. Suppose there is a spaceship that is already going at .6 c that passes very close to Earth at t=0 and then travels to another star where it passes very close to a planet orbiting the star. Suppose also that another spaceship going at .6 c happens to pass the other planet at the same time and continues on to make the trip back to Earth. The spaceships can send information about what their clocks read and any other relevant data as they pass by each other. I think the space-time diagrams are exactly the same as in this article but there is no acceleration at all.

12. 12. jamjam 04:49 AM 8/8/12

I know the theory and explanations given should be utterly correct as it's from Einstein and it's been reviewed by so many experts in the field. However, perhaps i'm slow, something about the explanation doesn't sit right for me. I can't grasp how traveling fast should affect the growth or aging of a biological system. Clocks... etc had been used to prove the theory but is it right to say (or make the leap) that a mechanical or quantum or other non-biological system should behave as a living, biological system? i can see how time may seem to move slower or quicker due to relative velacity, but I can't see how cells should divide or decay more quickly or how a set of twins should age differently because of differences in their velacity.

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