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#289
Jan3113, 03:15 PM

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explaining the twin problem by the light signals that are sent between the twins is an interesting way to do it. Once we define electromagnetism as a 'law' of physics, then say that the laws of physics are the same in all reference frames, then we have effectively only used the principle of relativity. (after all, this is how Einstein first came up with his relativity). I don't really understand what ghwellsjr meant by saying that the principle of relativity and the theory of special relativity are different things... I had always thought of them as synonymous.
Edit: well, maybe special relativity is a subset of the principle of relativity, because I would think that the theory general relativity is also a part of the principle of relativity. Another edit: "principle of relativity" could be used in a different context, too. For example, there is also Galileo's relativity, so you could also use Galileo's relativity to explain the twin problem. You could get the correct answers, but the laws of electromagnetism would be horribly complicated, compared to the laws of electromagnetism in Einstein's relativity. 


#290
Feb113, 01:19 AM

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First to clarify:
I am not interested in determining simultaneity only in coordinate synchronization. Nor am I advocating the MCIF implmentation as a preferrable convention. As stated, my sole ain is to gain a picrure of a chart generated with that convention to compare with the anomalous behavior in the area under discussion. Quote by Austin0 View Post But I suspect you are viewing what I am describing through an a priori assumption that the limited domain i am describing must fall inside the problematic area where intersection and divergence occurs in the standard diagram. not really analyzing the implications of what I am outlining. in the case under discussion per bobc2's diagrams the bad patch occurs in the positive x sector. In the chart i am outlining the limit to valid coordinate assignment , the point where coordinates overlap and have redundant assignments occurs in the negative x sector. In the positive x direction they can be extended indefinitely until reaching the actual limit of the Rindler Horizon , which I think we agree lies outside the range of the intersection and divergence we are talking about. So ,yes i am proposing that such a chart would cover the problem sector without internal problem whatsoever. With no anomalous events or temporal ambiguities. It appears to me that a complete chart constructed in the manner I outlined before T_{0} x=100,t_{0} and x=100, t_{0} T_{1}=T_{0}+20.. x=100,t_{1}=t_{0}+10,,,x=100,t_{1}=t_{0}+30 T_{2}=T_{0}+40 x=100,t_{2}=t_{0}+20 ,,,x=100,t_{2}=t_{0}+60 could not possibly contain any such artifacts. From this I infer that such artifacts could only come from the Minkowski graphing of such a frame and is not inherent in the use of the convention as the basis of an accelerated chart.. So if you see flaws in my thinking please let me know. 


#291
Feb113, 03:17 AM

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#292
Feb113, 03:33 AM

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#293
Feb113, 05:51 AM

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Something I absolutely cannot understand is this fascination with the twins paradox. It's been analysed in such detail so often, one would think there was some magic new physics in there just waiting to be discovered. There is no gold mine. The twins paradox happens because clocks show a time that is dependent on their worldlines, not universal Newtonian time. And SR gives us the means to calculate this for a given worldline.
Can anyone tell me what this detailed burrowing is hoping to achieve. I don't mean to be critical, but I don't remember going through this phase when I first encountered relativity ( not for long, in any case) so what am I missing ? 


#294
Feb113, 09:53 AM

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#295
Feb113, 10:05 AM

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#296
Feb113, 10:47 AM

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#297
Feb113, 12:06 PM

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By 'same predictions', I mean for electromagnetic phenomena. Using Galilean relativity will give incorrect results for mechanics when velocities are near the speed of light. They never noticed this before Einstein came up with his relativity, because such velocities are rare on human scale. 


#298
Feb113, 01:45 PM

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But I can see how saying that PoR is a subset of SR might be confusing, but I was just bouncing off your terminology. The important thing is that they are different and it's Einstein's arbitrary second principle that is added to PoR to make SR. That sounds to me like PoR is a subset of SR, but if it's still confusing, don't use the term "subset". 


#299
Feb113, 05:15 PM

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However, if you do not get overlap in the region where the graphing shows the overlap then I guarantee that you are not using the momentarily comoving reference frame notion of simultaneity. There is nothing wrong with that, but it is a different simultaneity convention and doesn't have any bearing on the Minkowski diagrams that bobc2 has presented. In other words, bobc2's drawings are correct and accurately reflect the inherent problem in the "MCIRF convention". His problem is that he refuses to recognize that as a problem and exclude that region from coverage (as you seem correctly willing to do). 


#300
Feb113, 06:12 PM

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#301
Feb113, 11:59 PM

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#302
Feb213, 12:08 AM

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Besides it doesn't make sense to say that PoR is based on observable raw data because it doesn't speak about raw data but about laws of physics instead. Laws of physics is certainly different thing than raw data. 


#303
Feb213, 02:00 AM

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Or to put it another wayif there were any data that was not symmetrical between two inertial observers with a relative motion between them, then it would be possible to write another law that would violate the PoR. But in this case, we are talking about the observed Doppler shifts between two inertial observers with relative motion. Do you doubt that they will see the same shift in each other? 


#304
Feb213, 02:21 AM

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I invite you to read the wikipedia article on the OneWay Speed of Light concerning Lorentz ether theory and Edwards' theory. Both of these use a clock synchronization convention that is different from Einstein's and yet they get the same physical laws. These examples should be enough to show you that clock synchronization conventions are arbitrary, meaning that we are not compelled by any raw data to select one over the other. We have a different kind of good reason to select Einstein's; as he stated, it's simple. 


#305
Feb213, 03:31 AM

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Let me see if I can summarize Bondi's argument. He says that if you have two inertial observers, A & B, in relative rest but separated by a great distance, and one of them, A, sends repetitive signals to the other, B, there will be no Doppler shifts. Then a third inertial observer, C, traveling from A to B will observe some Doppler shift ratio from A which will be less than one and which we can call DSR1. Then if that traveler creates his own repetitive signal(s) at the same rate he receives them from A and sends them to B, we know they will travel side by side on their way to B. When they get there, B will observe them both arriving at the same rate but the ones that were sent by C were sent with Doppler shift ratio that is the reciprocal of DSR1. We know that the speed that C is traveling away from A is the same as the speed that C is traveling toward B and so the Doppler shift ratios for the same speed coming and going are reciprocals of each other. Therefore, in the twin scenario, since the traveling twin spends the same amount of time going and coming at the same speed, we can simply average the two Doppler shift ratios and we will get a number greater than one, meaning the traveler sees the other twin's clock running faster than his own. If you want a better explanation, read Bondi's in the link in post #7. 


#306
Feb213, 04:22 AM

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We have two Doppler shifts and each Doppler involves two observers. One observer for each Doppler is the same. So it's three observers. 


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