I have written another summary about the apparentness and real ness of effects in Relativity among other attributes of the theory, when I get them I will put them here.
let me define something called a self proper frame: a frame where the variables are measured wrt certain conveniently chosen frame of ref., eg an arbitrarily chosen primed frame. a primed frame is a proper frame for all variables measured in that frame, but for another frame such as our lab or earth denoted as an unprimed frame which we choose to be proper for our purposes (local inertialness) the prime frame is moving at certain velocity wrt the unprimed frame that defines a boost factor or Lorentz transformation parameter (beta and gamma) SO in summary 1. primed frame is a proper frame only for a partial list of variables in the total physical problem. 2. unprimed frame or local inertial frame such as a lab or earth is a proper frame but again for a partial list of variables or quantities. A set of transformation laws is valid for converting one list of these quantities to have their correct values in another frame. This is called a Lorentz transformation and we say these are physical laws. Lorentz transformations are apparent changes occuring to these variables from the kind of Lorentz frame that is associated but a fact of nature that we do not have the ability to transform our selves into any chosen frame of reference disables us from testing the apparentness of these changes. In effect some of these apparent changes such as a shift in time or frequency are for our purposes real. If we were to have a frame which makes us capable to revert such shifts in physical effects we would not be seeing these effects in teh first place, in other words they would be apparent. But a fact of nature is we can’t, hence they are real.
SO there are two points here I am making.
i. the self frame is convenient. eg if you have one self-frame, you can define another self-frame till you obtain your parameters consistently in your original self-frame. For that you might need some Lorentz transformation into higher levels of self-frames. eg one particle decays into a bunch of others. You can go into one particular particle’s self-frame and see how the physical variables/parameters are actually transforming from it’s daughterage or parentage. This may not be readily appreciated as something of use, but if you are devising a good algorithm in particle physics theory or experiment you may need such forward and backward logic in terms of laws of Relativistic nature. For a good check you can devise consistent self-frames.
ii. the physical effects are apparent if you can revert them but real if you do not have the ability to revert them, eg through a thought experiment (Gedanken). SO in a consistent Gedanken if you can prove the apparentness of that process as long as it is occuring in nature, it will only be real if physical objects sustaining the effects of such do not have an ability to reverse the effect by attaining a reverse transformation.