As the traveler reaches the star he reads his clock at eight years as mentioned, but he sees the homebody?s clock as it was six years ago (the amount of time it takes for the light from the earth to reach him), or at four years (10-6). So the traveler also views the homebody?s clock as running half the speed of his clock (4/8).
On the trip back, the homebody views the traveler?s clock going from eight years to 16 years in only four years' time, since his clock was at 16 years when he saw the traveler leave the star and will be at 20 years when the traveler arrives back home (event 3). So the homebody now sees the traveler's clock advance eight years in four years of his time; it is now twice as fast as his clock. On the trip back, the traveler sees the homebody?s clock advance from four to 20 years in eight years of his time. Therefore, he also sees his brother?s clock advancing at twice the speed of his. They both agree, however, that at the end of the trip the traveler?s clock reads 16 years and the homebody?s 20 years. So the traveler is four years younger. The asymmetry in the paradox is that the traveler leaves the earth?s reference frame and comes back, whereas the homebody never leaves the earth. It is also an asymmetry that the traveler and the homebody agree with the reading on the traveler?s clock at each event, but not vice versa. The traveler?s actions define the events.
The Doppler effect and relativity together explain this effect mathematically at any instant. The interested reader will find the combination of these effects discussed in The Fundamentals of Physics, by David Halliday et al. (John Wiley and Sons, 1996). Paul Davies also does a nice job explaining the Twin Paradox in his book About Time (Touchstone 1995, ppf 59.) My explanation follows Davies?s closely; I hope my graph adds further clarity. The reader should also note that the speed that an observed clock appears to run depends on whether it is traveling away from or toward the observer. The sophomore physics problem, mentioned earlier, is a special case as it applies only when the motion of the traveler passes the observer?s reference frame with no separating distance in the direction of motion.
For those with a little more formal physics background, a spacetime diagram also explains the paradox nicely. It is shown with the supporting calculations for the Doppler effect on the observed time. Proper time is time in the frame of the observer.?
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12 Comments
Add CommentFor a alternate explanation of some of the ideas in this aritlcle see my blog http://science-community.sciam.com/thread.jspa?threadID=300005761&#msg300016893
Reply | Report Abuse | Link to thisHere is the link to my blog.
Reply | Report Abuse | Link to thishttp://science-community.sciam.com/thread.jspa?threadID=300005761
ttp://spacetime2007physics.blogspot.com/2007/12/another-look-at-twin-paradox.html
Reply | Report Abuse | Link to thisIn 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.
Reply | Report Abuse | Link to thisexactly all this means is that there is delay in how we get information from light as we get farther away
Reply | Report Abuse | Link to thisInteresting 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.
Reply | Report Abuse | Link to thisI 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?
Reply | Report Abuse | Link to thisAny 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.
Reply | Report Abuse | Link to thisI 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
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.
Reply | Report Abuse | Link to thisI 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?
Reply | Report Abuse | Link to thisFor 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.
Reply | Report Abuse | Link to thisI 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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