If we have three frames of reference A, B and C such that frames B and C are both moving with the same acceleration with respect to frame A. Now let us assume that we do not know whether frame A is inertial or non-inertial, then are we able to say anything about frames B and C in terms of being inertial or non-inertial?
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Are you allowed to conduct experiments in the non-inertial frames? – Emil Feb 20 '22 at 07:43
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1Thanks, Your question solved my question. If we were to conduct experiments in frame B and it turned to be inertial then frame C is also inertial but frame A will not be inertial. Is that correct? – Ahmad Eldesokey Feb 20 '22 at 07:50
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I was more thinking like if stuff moves on their own and you have to hold them down it's noninertial, like how balls move outwards in a rotating disk or how you get dragged down to earth by gravity, but then if you add them as fictitious forces your equations might work again. – Emil Feb 20 '22 at 07:59
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What if we assume that frame A is non-inertial and we cannot conduct experiments in frames B and C, then can we say anything about B and C in terms of being inertial and non-inertial? – Ahmad Eldesokey Feb 20 '22 at 08:35
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We really need oracles in our lives – Ahmad Eldesokey Feb 20 '22 at 08:46
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I misread your question. I think you need to state if the acceleration is constant or not to know for sure. I mean, if the thing wobbles and stays put for a while, is it you that wobbles or the thing, hard to know. – Emil Feb 20 '22 at 08:47
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I assume constant acceleration. – Ahmad Eldesokey Feb 20 '22 at 08:49
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Okay, then I think someone can work out the condition for the other objects to be inertial. Probably the nullspace of some map. – Emil Feb 20 '22 at 08:50
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Dale's answer in this post gives a simple definition of when a frame is inertial. This has nothing to do with other frames. – Kurt G. Feb 20 '22 at 09:06