strangerep said:
That wasn't my question -- I already knew all that. I was asking whether you knew of a references that doesn't restrict early to linear transformations, but rather works through the LFTs.
The references I mentioned
do "work through the LFTs" in order to examine the behavior of such transformations and determine that they are not suitable to represent the relationship between standard inertial coordinate systems. Torretti, for example, is especially detailed and explicit in his treatment. But obviously when people like Einstein and Pauli say succinctly that LFTs don't map finite coordinates to finite coordinates, and don't map continuous worldlines to continuous loci of coordinates, and don't maintain homogeneity and isotropy, etc., they have "worked through the LFTs". So it's hard to see what more you could want. Are you asking for references that conclude LFTs actually ARE useful representations of the relationship between standard inertial coordinate systems? Or are you just looking for more slow-witted references that take longer to figure out that LFTs are not suitable? Or are you seeking references that hypothesize a universe in which space and time are not homogeneous, such that spacetime LFTs are physically meaningful?
strangerep said:
Part of the miscommunication in this thread may be due to the unfortunate coincidence that "LP" may stand for "Light Postulate", (meaning something we assume at the beginning of a derivation), or it may stand for "Light Principle" which can be interpreted more flexibly.
It's more than just a miscommunication, it's a fundamental misunderstanding about the inductive-deductive method in physics. Read Newton on this subject: "In this philosophy [physics] particular propositions are inferred from the phenomena, and afterwards rendered general by induction... from thence to deduce other phenomena..." This is absolutely basic to how physics is done. From observations of phenomena, such as that momentum always seems to be conserved, we apply induction (necessarily incomplete) to generalize this into a principle (momentum conservation), and THEN we ASSUME this, i.e., we take this principle as a formal postulate in the deductive construction of a theory "from thence to deduce other phenomena". That's how the inductive-deductive process of physics works. In this way, both the relativity principle and the light principle are inferred from observation, and then applied as postulates in the formal development of a theory.
Unfortunately, newbies often misunderstand this process, thinking that "postulates are something we assume at the beginning of a derivation", overlooking the fact that, in science, the beginning of the deductive derivation is not the beginning of the inductive-deductive process. Unlike pure mathematics, which is wholly deductive (as usually conceived) from arbitrary postulates, the postulates that represent physical principles underlying physical theories represent the distillation of our most secure empirical knowledge.
The misconception that the physical principles (and hence the postulates) on which special relativity is founded are simply baseless hypotheses is what leads newbies to get excited when they discover that those principles are actually well-founded in observation. They think "Hey! We can replace a baseless hypothesis with experimental results!" That's a complete misunderstanding, because both the relativity principle and the light principle are already distillations of experimental results. That's where those propositions came from. They are not arbitrary hypotheses that are merely assumed without foundation. Indeed they are the aspects of our empirical knowledge that are the most secure. (See Poincare and Einstein on the advantages of "principle theories".) They merely play the role of formal postulates in the deductive phase of theory building.