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The first postulate of relativity 
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#1
Dec1412, 07:02 AM

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I just want to make sure that the following assumption is equivaent to the first postulate.
Consider two inertial frames S and S'. By inertial frame, is meant, a frame where all the laws of physics are valid in their simplest form. Now let an observer in S measure the velocity of S' to be 'v' towards his/her right. Now we automatically assume, that when an observer in S' measures the velocity of S, he/she will measure it to be 'v' to his/her left. How can we say that the two observers will agree on the magnitude of the velocities they measure, of the other frame, from their frame? Is this just an assumption equivalent to the first postulate of relativity which says that : Given an inertial frame S, a frame S' moving with constant velocity with respect to S, will also be inertial. According o the above postilate then, Given S is inertial, and an observer in S measures constant v as the velocity of S', this implies S' is inertial. Now we know S' is inertial and S is also inertial, so an observer in S' measuring the velocity of S would observe a constant velocity according to the first postulate. It doesn't however garauntee that this velocity's magnitude is going to be v itself. 


#2
Dec1412, 07:24 AM

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That seems to be like saying that if you put a minus sign in front of an integer, you have changed the absolute value of the integer. Just doesn't seem to make sense.



#3
Dec1412, 10:41 AM

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#4
Dec1412, 11:05 AM

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The first postulate of relativity
As an assumption, this is so totally unobjectionable (no observed violations, ever) that I doubt many people spend much time considering the question. But if you want to prove it, there are some pretty convincing reductio ad absurdum arguments. 


#5
Dec1412, 11:33 AM

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#6
Dec1412, 12:12 PM

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#7
Dec1512, 01:45 AM

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By muzzle velocity, i understand the velocity of the bullet with respect to the gun kept at rest in a particular frame, just at the moment the bullet leaves the gun. This velocity will be fixed for a particular make of the gun. Now an observer in S could fire the gun, and measure the muzzle velocity to be v_m, say. Now, an observer in S' , with an identical gun, may obsetve the same consequences. But this has no bearing on the velocities of the others' frame that each of them observes ... 


#8
Dec1512, 11:08 AM

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#9
Dec1512, 01:30 PM

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To say that the principle of relativity doesn't hold is the same as saying that the laws of physic are differnt in the two frames. That would lead to the gun behaving differently in the two frames. Which means the two observers will measure different muzzle velocities. But this still doesn't lead to the my initial problem of v≠u. 


#10
Dec1512, 01:57 PM

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Consider e.g. two identical objects A and B attached to a compressed spring that's prevented from expanding e.g. by a string. If you cut the string, the two objects will be shot away from each other. These objects are being subjected to essentially the same thing, so it would be pretty weird if the speed of A relative to B is not the same as the speed of B relative to A. If those speeds are different, then what would be the reason for that difference? Since the objects are identical, something else would have to differ. For example, there could be something fundamentally different about the two positions in space where the objects started, or the two objects could have started out with a nonzero velocity relative to some kind of invisible "stuff" that fills up all of space, and the speed of one of the objects relative to the "stuff" increased while the speed of the other relative to the "stuff" decreased. These are the sort of things that the principle of relativity is used to rule out. 


#11
Dec1512, 02:17 PM

P: 126

Now your argument definitely makes sense because theres a spring thats doing the same thing to both A and B, and so, unless theres some weird stuff going on related to initial positions and stuff, by symmetry, the relative velocities of A wrt B and vice versa should be the same. But this entire argument depends upon the common spring, doing the same thing to the two frames. What if there isn't a spring? Just frame S and S' , having constant relative velocities w.r.t. Each other? How do i now prove that the velocity of S w.r.t. S' is the same as the velocity of S' w.r.t. S ?? 


#12
Dec1512, 04:58 PM

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#13
Dec1512, 05:06 PM

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I have seen An inertial frame is one which is not accelerating. and An intertial frame is one that is either at rest or moving with constant velocity. 


#14
Dec1612, 01:18 AM

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#15
Dec1612, 01:20 AM

P: 126

The definition i used is a textbook definition. An inertial frame is one where all laws of physics are valid. Now, if some other frame i moving with respect to this inertial frame at constant velocity, then even that becomes an inertial frame. 


#16
Dec1612, 02:21 AM

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See below... With these definitions, we can formulate (still following Rindler): Postulate 1 (Principle of Relativity): The laws of physics are identical in all inertial frames, or, equivalently, the outcome of any physical experiment is the same when performed with identical initial conditions relative to any inertial frame. 


#17
Dec1612, 02:29 AM

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I.e., one does not need to assume that the inverse corresponds to the parameter ##v##, (as is done in some group theoretic derivations). Afaict, this establishes the frame reciprocity mentioned above. 


#18
Dec1612, 02:57 AM

P: 126

Any resources i could use at this point to understand the above ?? 


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