Einstein introduces this idea of a rigid measurement, and that his theory is about the kinematics of rigid bodies. What, though, does "rigid" really mean? In what sense is bouncing light off a mirror and measuring the roundtrip time, a rigid measurement? Light isn't substantially rigid, like a measuring rod made of, say metal, but its velocity is fixed everywhere measurements can be made.
The path of light over the riemann manifold, the null geodesic, could be considered 'rigid' in the Einstein context since it's an invariant. I think. LOL. Evaluating spacetime events in terms of actual measurement is the best way to understand the physics. When you highlight the term measurements it gives me an intellectual woody.
OK, I want to make sure I understand you. Are you claiming the x-axis for the primed frame is not the same line as the x-axis for the unprimed frame? Please answer.
The light under consideration is in the direction of the positive x-axis for both frames. The "rotated hyperbolically" is the origin shift and is not a shift in direction of the positive x-axis for each frame. Is this what you meant?
Let's get some things straight here about the mathematics. On the common x-axis, there is no disagreement about the direction that light moves along the x-axis. It is only at places with y>0 where the frames can disagree on the direction that light moves and that is only along some lines y=k, k > 0.
Einstein is saying within a frame, the rules of Newtonian mechanics hold good. Further, he says the light motion follows the rules of the light postulate. Finally, he adds the relativity postulate which roughly says, these rules I stated hold true in any rest frame. Then, from this he derived LT. But, I showed if C' and M are co-located, the M' frame light postulate places the light flash at some M' frame space-time coordinate. But, then the M frame used LT and put that same light flash with C' and M co-located at some completely different M' frame space-time coordinate, which is a contradiction of nature. Light is not at 2 different places in the M' frame coordinate system given C' and M are co-located.
You also seem to imply that I am frame mixing. First I used the light postulate for the primed frame with C' and M co-located and produced an M' frame space-time coordinate. Then, I used the light postulate in the M frame with C' and M co-located and came up with an unprimed frame space-time coordinate. If I stopped here, you would be right. But, since I did not, you are wrong. I then translated that unprimed frame space-time coordinate using LT to come up with a primed frame space-time coordinate of the light flash. Now, if you are going to accuse me of frame mixing, prove it. You already agreed all the math in the Op is correct and now you are claiming frame mixing occurred. Prove your assertions. Guess what, given C' and M are co-located, SR claims one light flash is located at 2 different places in the primed frame, which is a contradiction with nature.
chinglu, Your argument claims it is a contradiction with nature for light to be located in two different places, at two different times. If you deny this, then you simply do not understand ROS.
Hardly surprising for someone who does not even recognise the observationally shown and supported concept of time dilation and length contraction, nor FoR's obviously.
No, that is not what I said. I said, given one unique configuration of the coordinate systems, i.e. C' and M are co-located, SR claims the light flash is located at 2 different space-time coordinates. See, this is a contradiction of nature.
Okay, here is your mistake: According to SR, frame Σ measures the x' axis as length-contracted compared to its own, and frame Σ' measures the x axis as length-contracted compared to its own. That is not a "unique configuration of the coordinate systems" now is it? The LT describes how that can work without contradiction. A true contradiction of nature would be if it predicted the light to be at two different places at the same time, but it doesn't.
I proved C' and M are co-located for the primed frame iff they are co-located for the unprimed frame. Check the OP. Therefore, you are claiming if C' and M are co-located for one frame they are not for the other. Since I proved this is false and you are claiming it is true, then you prove C' and M are co-located for the primed frame but are not co-located for the unprimed frame. Otherwise, your statement above is baseless. Also, based on the OP, given one unique configuration of the coordinate systems, i.e. C' and M are co-located, SR claims the light flash is at 2 different primed frame locations. This is a contradiction of nature. Note, I do not need "the same time" as you claim. I can use coordinate system configuration as the trigger. So, you are wrong.
Of course both frames agree that C' and M are co-located at some time. WTF? It's a single event. Do you even know relativity? No, that is totally wrong. I'm claiming that when C' and M are co-located in frame Σ, that frame measures the x' axis to be length-contracted compared to its own x axis. And the reciprocal is also true. When C' and M are co-located in frame Σ', that frame measures the x axis to be length-contracted compared to its own x' axis. You said your argument relies on "One unique configuration of the coordinate systems". You failed to account for the fact that SR is not dealing with "One unique configuration of the coordinate systems." Better luck next time.
You seem to be confused. The OP used LT which takes into account length contraction. Now do you understand? Further, you claimed Now, if C' and M are co-located for one frame they are co-located for the other. You have already agreed to this. Therefore, prove C' and M being co-located is not a unique configuration since that is your claim. Don't forget to show you math!!! Now, if C' and M are co-located, the OP proved SR claims the light flash is in 2 different places. You have failed to refute this therefore, the logic holds true.
The LT also takes into account ROS. That is why your transformed events have two different time coordinates. Because they happen at two different times. Please answer, yes or no, do you think it is a contradiction of nature for light to be located in two different places at two different times? And under exactly what conditions do you think that could ever possibly be is a contradiction of nature? I could understand if it violated x=ct or x'=ct' but it doesn't! SR says that the x and x' axes have different scales, reciprocally, according to the two different frames. So when you say there is one unique configuration of the coordinate systems, you are introducing an absolute scale that is not part of SR. Also, the clock synchronisation schemes are scaled differently, reciprocally, according to the two different frames. You are neglecting all of that.
Simultaneity in one inertial reference (M) does not confer simultaneity in any other reference (M'). This is just a remake of the "pole and barn" paradox. The more distant event, from the point of view of the moving frame, must occur first. This makes perfect sense. Nothing travels faster than light, including the information that an event has occurred. I keep trying to get certain people here to cut out the whole "Galilean Relativity" coordinate system mess and get to the meat of Einsteinian relativity (which does not even require such tortured coordinate system math), but does anyone listen? Neither did my nitwit freshman relativity professor. It's just a good method to make big physical and math mistakes in relativity. I think some people only do it so that they can forget about Einstein (whom they hate, for whatever reason) and do it Lorentz's way. Also, photons are bosons and the force carrier for electromagnetism. As such, they are perfectly capable of occupying the same space at the same time. As for occupying different places at different times: Don't photons actually do that all the time? Even ordinary matter can do such things. It's kinda what motion is all about, if you aren't all locked in focusing on "coordinate systems", that is.
Sounds about right, except "the more distant event must occur first." What relativity of simultaneity (ROS) really says is that, for events which are simultaneous in one frame, the other frame measures the 'rearward' event to occur before the 'forward' event. For example, if two events occur simultaneously on a train, the embankment frame would say that the event which is closer to the rear of the train occurred first. (Assuming the train is moving forward.) Not sure what you are talking about. Are you saying you know of a way to do relativity without using two coordinate systems in relative motion? I have no problem with the idea that a photon can be in two different places at two different times. It is chinglu who thinks that is a contradiction of nature, for some unknown reason. I'm trying to convince him that it is perfectly natural, and even required by x=ct and x'=ct'.
Light can be located at 2 different places given 2 different times. But, this make no difference in the OP. The OP notices that given C' and M are co-located, the primed frame light postulate places the light at \((d',0,0,d'/c)\). This is the only correct answer. However, given C' and M are co-located, the unprimed frame applies LP and LT and puts the light at primed frame \((d'(1-v/c),0,0,d'(1-v/c)/c)\). Therefore, LT gets the answer wrong. Now, you are applying scales and all that, except LT takes all that into account and LT was used by the OP. So, that is a non-argument on your part. Further, the OP proved the co-located event was unique since it was proven both frames agreed on the clock times at C' and M for the co-location event. So, LT simply gets the answer wrong. Remember, the job of LT is to translate into the other frame in terms of what it deems to be true. LT failed to do that. You are also getting the direction wrong in the logic. You are claiming the OP starts with two different primed frame times and claims light should be at the same place. That is not at all what is going on. The OP shows given the unique configuration of the coordinate systems where C' and M are co-located, SR claims light is at 2 different space-time coordinates in the primed frame and that is wrong. Given C' and M are co-located the light pulse is at one space-time coordinate.
He wont answer. I've asked many questions to reveal where he is coming from, but he refuses to answer. He does not recognise time dilation. He does not recognise length contraction. And he does not recognise the validity of all FoR's. He'll continue to contort, misinterprete, and ignore no matter how much you prove he is in error. That has been his operational style in many threads and many forums, some of which have been closed and himself banned. Best of luck anyway!
Uhhh, check the preceding post. I would appreciate a retraction from you since your statement is false.
