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Again on twin paradox 
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#1
Jan3111, 12:04 PM

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Hi!
I'm trying to definitely solve the twin paradox (after 5 years of efforts :) ) In every physics textbook, it is studied the motion of the twin in an inertial frame (so the proper time is that measured in the twin frame), so we can express time delta t in the earth frame using: delta tau = int[ sqrt(1/gamma(v(t)) dt ] or something like the more general formula http://arxiv.org/pdf/physics/0411233v1 now I want to, and that's my question, study the earth motion in the astronaut's frame... so in this case the proper time is that of earth.... in particular, what happens if the astronaut simply accelerate himself, makes a constant speed trip, turns himself and returns home? 


#2
Jan3111, 12:17 PM

P: 32

for special relativity, when he returns home nothing changes.
for general relativity, when he returns home he will be younger than the people who were as old as him before. 


#3
Jan3111, 12:25 PM

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#4
Jan3111, 12:32 PM

P: 39

Again on twin paradox
well,
in special relativity he cannot return home.... but if you want to use special relativity when the twin is travelling at constant speed, you can use lorentz transformations and say that delta tau = 1/gamma (v) * delta t. <= delta t where tau is the (proper) time in the earth's frame, which can be a problem(?) cause at the end earth's proper time should be > then astronaut's time... btw, I need some math explanation in general relativity... I cannot find anything interesting... 


#5
Jan3111, 12:35 PM

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The twin "paradox" is fully resolved by a calculation of the proper times of the two world lines. (That's how you find out what SR says their final ages will be).
To understand why the reasoning that leads to the apparent contradiction is flawed, you need to study the flawed argument. That doesn't seem to be what you want to do. You're talking about "the astronaut's frame", and by that you seem to be referring to a specific coordinate system that's associated with the astronaut's motion. It can be a somewhat interesting exercise to work out the details (of what events on Earth this coordinate system says is simultaneous with different events on the astronaut's world line), but I don't think it will add much to your understanding of this problem. It will certainly not help you "solve" it. It might however be good for you to make an effort to understand why that particular coordinate system is chosen (yes, chosen) to represent the "accelerating point of view". Since there must be hundreds of twin paradox threads already, I think you should try to ask very specific questions. All the general stuff has been covered again and again in the other threads. Are you Swedish by any chance? (Just curious, because of your name). Edit: I wrote this post before I saw post #4 above. That's exactly the kind of stuff that has been explained over and over and over and over... Could you please have a look at a few of the other threads? 


#6
Jan3111, 12:50 PM

P: 39

OT: well, althought I can understand swedish a bit, I'm not swedish... I chose this nick before I knew what it means in swedish/danish/norwegian :) kknull is a musician btw, my specific question is how can I express analitically the earth motion in the astronaut's frame.. I imagine that it can involve a gravitational field (the inertial force of the acceleration can be erased assuming that there's gravitational field in the opposite direction...) what is always done is to express astronaut's motion in earth frame.... and yes, it will solve all my problems... in particular, I have this doubt: the effect of the accelaration is finite, whereas the effect of the special relativity's time dilation can be undefinitely big ( the astronaut's can accelarate for few seconds and then travel for 100000000 years.... so what is the math explanation of what the earth space and time looks like from the astronaut's point of view?) edit: for post #5, ok, I'll take a look... do you have some specific link? 


#7
Jan3111, 01:13 PM

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Edit: That post also contains a link to an article that gives you the explanation that's appropriate when we have chosen to represent the accelerating point of view by "radar time coordinates". I will address one of your mistakes in #4 right away. Special relativity is defined by the choice to use Minkowski spacetime as a mathematical representation of space and time, and by a few axioms that tell us how the mathematics correspond to results of experiments. The most important one can be stated like this: "A clock measures the proper time of the curve in spacetime that represents its motion". (This axiom tells us that the final ages can be calculated by doing the proper time integral). Since there's nothing in that definition that requires the curves that represent motion to be straight lines, SR can definitely handle accelerated motion. GR is defined by a different choice of spacetime, a spacetime with properties that are influenced by the properties of the matter in it. The twin "paradox" is just a SR problem. GR doesn't really have anything to do with it. 


#8
Jan3111, 01:28 PM

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#9
Jan3111, 03:05 PM

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#10
Jan3111, 03:14 PM

P: 39

I don't think I have understand..
so the problem is that I cannot use a constant inertial frame in which the astronaut is at rest? can I use a frame in every time interval dt which is inertial and comoving with the astronaut and then study the proper time in earth frame? 


#11
Jan3111, 03:39 PM

P: 39

but I want to calculate earth proper time in function of astronaut's time... 


#12
Jan3111, 03:42 PM

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The relativity of simultaneity is a very important concept in SR, and people's failure to understand it is the source of nearly all confusions about basic conceptual matters in SR, so make sure you review this notion and understand it before trying to tackle the twin paradox! 


#13
Jan3111, 05:20 PM

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#14
Jan3111, 06:02 PM

P: 250

Mike Fontenot 


#15
Feb111, 01:26 AM

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There are other ways to define the traveler's point of view. The "radar" coordinates used by Dolby and Gull are at least as natural a choice as the comoving inertial frames. 


#16
Feb111, 01:47 PM

P: 250

For me, there are two "showstoppers" with Dolby & Gull's simultaneity: 1) D&G is noncausal. If the traveler has never accelerated, before or during his outbound leg, D&G says he CANNOT calculate the current age of the home twin at any instant during his outbound leg, because there is no way for him (or anyone else) to know at that instant if he will actually choose to accelerate in the future. 2) Like ANY of the alternative reference frames (other than mine) for the traveler (frames in which the traveler is perpetually stationary), D&G contradicts the traveler's own firstprinciple conclusions about the current age of the home twin ... conclusions that he arrives at from his own elementary measurements and elementary calculations. I've described the nature of those measurements and calculations in a previous post: http://www.physicsforums.com/showpos...7&postcount=38 , and the calculations are shown in detail in my paper: "Accelerated Observers in Special Relativity", PHYSICS ESSAYS, December 1999, p629. Mike Fontenot 


#17
Feb111, 02:03 PM

P: 3,187

 http://www.fourmilab.ch/etexts/einstein/specrel/www/ (section 4 near the end)  http://en.wikisource.org/wiki/The_Ev...Space_and_Time (from p.48, in particular from p.50) PS: I had not seen the other posts. You may still see this to realise how old the answers are! And if you really want to see an answer with a gravitational field approach (messy and truly paradoxical if you ask me!), then you may adventure into Einstein's GRT solution here:  http://en.wikisource.org/wiki/Dialog..._of_Relativity 


#18
Feb111, 03:01 PM

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