
#1
Aug1510, 04:24 AM

P: 11

I have been considering this thought experiment for some time, and the principle seems "broken". I'm wondering if by playing devil's advocate you can show me what is going wrong.
In SR, the light clock was used to predict time dilation in a "moving" object. According to the Twin Paradox, two distinct frames of reference in different inertial motion would see time dilating in the other one, because all motion is relative. The counter argument to this is that the frames of reference are not identical, because in the Twin Paradox, the Twin flying away from earth accelerates and is not in constant inertial motion. We therefore can't use SR to answer the Twin Paradox, we have to use GR. Using a GR thought experiment, the Light Clock would no longer function if acceleration is great enough. The acceleration would cause the beam of light to bend outside the light clock, even from the light clock's frame of reference. 



#2
Aug1510, 05:31 AM

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You can use SR even when acceleration is involved by doing a different "SR" calculation for each instant, treating the speed at that instant as constant.




#3
Aug1510, 06:58 AM

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Special relativity is the theory of Minkowski spacetime, which includes accelerating observers, see Rindler chart,en.wikipedia.org/wiki/Rindler_coordinates and also this is very interesting http://gregegan.customer.netspace.ne...erHorizon.html




#4
Aug1510, 09:03 AM

P: 665

Why "light clock" is flawed.Acceleration plays no part in the resolution of the paradox. In fact, the whole point of the paradox from a tuition point of view is to get student's to realise that there is no paradox. The point is to illustrate the absurdity of our ordinary concept of simultaneity  which is what the 'paradox' relies on for it's puzzle effect. 



#5
Aug1510, 09:11 AM

P: 3,967





#6
Aug1510, 04:36 PM

P: 11





#7
Aug1510, 07:48 PM

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#8
Aug1510, 09:02 PM

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#9
Aug1510, 10:57 PM

P: 47

I got some good replies when I asked a question about this myself. It might be helpful to you. http://www.physicsforums.com/showthread.php?p=2549150 



#10
Aug1510, 11:33 PM

P: 3,967

Let us say for the sake of argument that acceleration does affect time dilation and see how that affects the twins paradox resolution.
Consider one twin accelerating from 0 to 0.8c in one second and then traveling at a constant velocity for 10 years as measured in the Earth frame) before turning around in the space of 2 seconds and returning at 0.8c and finally coming to a stop by decelerating to zero in 1 second and reuniting with his twin. The total journey time is 20 years (+4 seconds) and the SR time dilation factor at 0.8c is 0.6 so the travelling twin has aged roughly 12 years in the time the stay at home twin has aged 20 years. Now the acceleration takes place in a total of 4 seconds. If time stops still during the acceleration (worst case) then the largest error that is introduced by ignoring the time dilation during the acceleration phase in this example is 4 seconds and that fails to account for why the travelling twin has lost a total of 8 years compared to his stay at home twin. DrGreg also produced a very nice diagram that makes it very intuitively clear why acceleration is not the explanation in the twins paradox here: http://www.physicsforums.com/showpos...55&postcount=4 Lastly, as I mentioned before, analysis of a light clock parallel to the axis of motion would give us an informative insight into how an ideal clock performs during acceleration. This should not be too difficult to calculate for constant acceleration. Are you interested in that aspect or just acceleration as it applies to the twins paradox? 



#11
Aug1610, 05:59 AM

P: 11

You are stating that time dilation over the course of the 10 years is caused by this inertial motion, but the formula from this is derived from the light clock thought experiment which we have resolved on the basis of the twin paradox yet. 



#12
Aug1610, 07:01 AM

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#13
Aug1710, 07:40 AM

P: 3,967

It can also be shown that if an object is accelerating away from us, its instantaneous clock rate relative to our clock, is a function of its instantaneous velocity relative to us (i.e t' = t*sqrt{1v^2/c^2) where v is its instantaneous velocity, and is independent of its acceleration. 



#14
Aug1710, 07:59 AM

P: 3,967

We can do the twins paradox in anther way that removes all acceleration from the problem. Consider one observer A that remains at location A (EDIT: A remains at rest in frame A). Another observer B is passing A and moving at constant velocity v relative to A. A and B synchronise clocks so that they read the same time. B travels for some distance away from A, until he passes another observer C moving with velocity v towards A. C adjusts here clock so that it reads the same as B's clock at the instant they pass each other. All observers agree that at the passing event, when C synchronises her clock with B, that C's clock reading is a good representation of the elapsed time on B's clock. When C passes A, C and A compare elapsed times at the passing event and agree that the elapsed time on C's clock is less than the elapsed time on A's clock. No one has accelerated at all during this thought experiment, so the acceleration aspect has been completely removed. 



#15
Aug1710, 08:30 AM

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There's no way to understand this generally by looking at bits of journeys and talking about 'changing frame'. The fact is that what is shown on a clock is the proper time of the worldline. The proper time takes into account the details of the trip in 4 dimensions and always gives the correct answer. It's got nothing to do with whether one traveller is inertial or not, although it's perhaps a little simpler. Talking about acceleration doesn't help much eaither. The proper time takes into account all changes of velocity on the worldline. 



#16
Aug1710, 09:10 AM

P: 3,967

First lets take the equation for the instantaneous velocity on a accelerating rocket with constant proper acceleration (a) at time (t) in the non accelerating frame: v = at / sqrt[1 + (at/c)2] as given by Baez http://www.xs4all.nl/~johanw/PhysFAQ...SR/rocket.html We can solve this equation for (at) to obtain: at = v/sqrt[1(v/c)^2] Baez also gives the instantaneous gamma factor of the accelerating rocket at time t as: γ = sqrt[1 + (at/c)^2] and if we substitute the symbolic value for (at) obtained earlier into the equation for gamma immediately above we get: γ = sqrt[1+((v/c)/sqrt[1(v/c)^2]] = 1/sqrt[1(v/c)^2] demonstrating that the instantaneous time dilation of an accelerating particle can be formulated in such a way that it is only a function of the instantaneous velocity at any given instant and independent of the acceleration. 



#17
Aug1710, 09:19 AM

P: 1,555

I do not see any problem with what you write Kev it is as you say: it all depends on the relative speed. But what causes a relative speed to change? Right, inertial and proper acceleration. So what drives a change in clock rates?




#18
Aug1710, 09:57 AM

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Kev, you said it in post #14, so my #15 is redundant.



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