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#1
Jan1013, 09:44 PM

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I'm studying special relativity and I can't understand the following.
Let's imagine me and my twin brother making the following experiment: I stay in Earth and my brother travels in a spaceship with velocity 0.5c. For moving referentials the time passes more slowly, but for the first principle of special relativity, the Physics laws are the same for any inertial referential. So for me, my brother are in slow motion (I became older). But for my brother, he became older. When he arrives here, who will be older? 


#2
Jan1013, 10:07 PM

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As you say, the first postulate of relativity is that the laws of physics are the same in all INERTIAL frames. Your brothers frame is not inertial. 


#3
Jan1013, 10:11 PM

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#4
Jan1013, 10:31 PM

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Time paradox



#6
Jan1113, 07:43 AM

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Given phinds' point, I surprised your variation of the twin paradox hasn't been asked / discussed. 


#7
Jan1113, 09:06 AM

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Hermann Bondi's book, Relativity and Common Sense, pages 77 to 80, describes the process to show that this is true. So whatever ratio your brother sees of your clock compared to his on the way out plus its reciprocal on the way back added together and divided by two gives us the final average ratio of your clock compared to his when you reunite, since the times for his two halves of the trip are the same because he is traveling at the same speed over the same distance (although we aren't specifying what that speed, distance or time are). That average ratio is always greater than one. Let's say that that ratio is R for the return trip and 1/R for the outbound trip. Adding these together and dividing by two gives us (R + 1/R)/2 or (R^{2}+R)/2R. For any value of R greater than 1 this evaluates to a number greater than 1. Try it and see. 


#8
Jan1113, 10:38 AM

P: 248

But isn't acceleration relative too? When I say my brother is accelerating at acceleration a, shouldn't he say the same of me? 


#9
Jan1113, 10:54 AM

P: 718

Personally, I find the clearest explanation is to not bother with any talk of when various age milestones are seen in each twins' frame and just focus on when they happen in each frame—i.e. the spacetime diagram approach. It's easy as pie to show that, while time dilation is indeed symmetric on each leg of the trip (separately!), relativity of simultaneity means that when the traveling twins makes her aboutface, her brother ages a large amount in her frame in a very small amount of time—instantaneously in the limit of an instantaneous turnaround—and this more than makes up the difference. Everyone has their pedagogical preference, but I really think not futzing around with super telescopes does a much better job of showing precisely how the asymmetric aspect of the twins' experience (one inertial reference frame vs. two) directly leads to the correct calculation in both frames. 


#10
Jan1113, 10:59 AM

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*The type of acceleration which is not relative is called "proper acceleration". There is also a type of acceleration called "coordinate acceleration" which is relative to some specified coordinate system. Coordinate acceleration cannot be measured by an accelerometer and doesn't have any physical effects, only proper acceleration does. So usually when people just say "acceleration" they mean "proper acceleration" which is not relative. 


#11
Jan1113, 11:02 AM

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#12
Jan1113, 11:05 AM

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We can build black boxes called accelerometers which display measure the acceleration they're being subjected to, and you can't do the same thing with speed (think about how an automobile speedometer "knows" that the car is moving relative to the roadway). 


#13
Jan1113, 12:05 PM

P: 248

I think I've got what you mean. Pretend I'm sending messages to my brother year by year, and he does the same . At the moment of the aboutface my brother will receive many messages of mine, and when he arrives in Earth, I will be older. But does't it mean that in the accelerated referential of the spaceship (at the moment of the aboutface) see the light would aprroximating with a velocity bigger than c? I know that c is constant for intertial referentials, I don't know how it works for accelerated referentials. Is it possible? 


#14
Jan1113, 12:24 PM

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(One unfortunate side effect of this tendency is that it's easy to get the impression that special relativity only works for inertial frames, and you need general relativity to handle acceleration . Although widely repeated, that is not true  you only need GR if the spacetime is not flat). 


#15
Jan1113, 12:59 PM

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There are also noninertial reference frames, such as a rotating referece frame. In noninertial frames the usual laws of physics take different forms unless you write them using tensors. Specifically, this means that unless you use tensors then you may get that the speed of light ≠ c in a noninertial frame. Again, consider a rotating reference frame, in such a frame even nearby planets or the moon may be moving faster than c. 


#16
Jan1113, 01:44 PM

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As L1S says, this is a matter of taste, and we all know that de gustibus non disputandum est... but there is much pleasure to be had in discussion, as opposed to dispute. My experience has been that there are two basic approaches to SR thought experiments: Start with the actual observable physical behavior of the light signal, as ghwellsjr does; and start with the spacetime picture and Lorentz transforms to construct consistent histories of events in each reference frame, as L1S does. I find that many people naturally gravitate towards one style or the other, and find the other one somehow sneakily unsatisfying and unconvincing. For example, I've never found the light behavior explanations to be gutlevel satisfying; I feel as as if I could do something just a bit more clever with my moving mirrors and light sources I could somehow subvert the experiment. (This suspicion may be what's motivating the posters who show up asking whether relative effects are just an "optical illusion"). I prefer t work through the spacetime diagram and Lorentz transforms to satisfy myself that no matter how I manipulate the experiment, it all has to come out just as relativistic doppler and similar phenomena say it will. On the other hand, I also know from endless friendly discussions that there are people who find the coordinatebased description to be completely nonfundamental; it's all full of coordinate artifacts and abstract mathematical relationships meaningful only if they connected to some real physical observers. My personal opinion on the subject: 1) You don't really understand until you're comfortable using either style of description. (It's worth noting that Einstein, and just about any serious stdent of relativity after him, are effortlessly fluent in both styles). 2) When solving problems for yourself, use whichever style you're most comfortable with. When reading someone else's analysis in the style that you don't prefer, consider transforming it to the one that you do prefer. It's good practice for you and may help someone else understand. 3) When explaining to someone else, start with the style that you're most comfortable with. But be alert for signs that it's not working, and be prepared to switch to the other style. This doubles your chances of getting the magical "Aha  now I get it!" moment that is the goal of all explanation. 


#17
Jan1113, 02:58 PM

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Also, the twins don't need to do any calculation, they just watch their siblings age (or their clocks) and when they return, they each agree on what actually happened. We need to do some calculation to determine what they will see, but that's a different matter and it's very easy because it doesn't involve any understanding of Special Relativity or any other theory. We don't have to learn about synchronizing clocks or defining an Inertial Reference Frame or what the Lorentz Transformation is all about. 


#18
Jan1113, 03:48 PM

P: 718

As I said in my original post, I was merely commenting on what I believe to be the educational value of one approach over the other. Frankly, I find it more than a bit insecure that you instantly decided my preference for a different teaching method reflects a "backwards" understanding of relativity. Do you assume that everyone who teaches things differently than you do does so because they don't understand it as well as you? 


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