History of Relativity Dialectics

What is happening in physics is that the subject matter of recent experiments - sub-atomic particles and deepest space and time - is so difficult to directly observe and measure that mathematics combined with speculation have replaced measurement and observation.
The forbidden process of extrapolation beyond testability - unfalsifiability - has been adopted as the modern method of research. 
This change in analytic framework happened gradually, beginning around 1870 or so. Pure mathematics - where imagination was king - migrated into applied mathematics and then into physics. 
The psychology of this transformation in mindset is worth discussing. Faced with the empirical limits set by the scientific method, to continue research (and funding!), physicists needed to keep wide open the door of discovery. The limitation of experiments in space and time  drives exploration to extrapolate into areas beyond testing - speculations become established mainstream tenets. Physical reality became a product of the mind; testing was accepted if it allowed a version supporting the mathematical hypothesis. 
Relativity isn't science - it's treated as a marvelous puzzle that only the high priests of physics can comprehend. Psychologists call this phenomena group think. The persistence of special relativity in the mainstream of physics is a matter for the department of psychology. Its supporters constitute a kind of priesthood, full of their own mystification and magical insights, aimed at stupifying the masses. They rant and rail against the intrusion of other knowledge domains into science, like religion, yet religion is where their faith-based dogma belongs.
The history of science reveals that at least half of the prominent physicists of the early 20th century could not accept special
relativity. The consensus was that Einstein's relativity was ambiguous, vague and unintelligible. But unintelligible could mean too complex for most to understand..... or that it was pure nonsense. Sadly the media propaganda machine went for 'clever', not 'contradictory' - a victory of speech control and bias over objective logic.

Modern applied mathematicians - aka physicists - prefer abstractions and thought experiments to reality and testing. They claim abstractions allow more general laws, a wider scope of applicability. But abstractions ignore details that can only be discovered by testing, which mainstream physics eschews. When conflicts with nature surface, then more abstractions and assumptions are added, complicating the model and discouraging careful logical analysis. The scientific method has been deserted and replaced with mathematical speculation.  
Relativists were taught to compute answers to simple but abstract physical tests. The focus is on careful calculation rather than on meditation why the answers seem preposterous. Calculation is the only tool they have because common sense is useless.
The mindless crunching of the equations is the fun and easy part - the transforming back and forth between reality and abstractions of reality is the hard part. We are now in an era where the confusion between mathematics and physics is total because over a century of physicists have been trained to consider the reality checks of logic and tests are no longer necessary.
 
Compared to other 'softer' sciences the contrast with the beliefs of physics is huge. Even economics and psychology, with all their empirical weaknesses, would cringe at the thought that twins are each older - or younger - than the other.  What could possibly be evidence that this contradiction is true? Who can even imagine a square circle?  Modern physicists, apparently. Only in physics can pure logical contradiction be embraced because they claim experimental evidence actually confirms it. But experiments also refute the predictions of relativity, as we expect from an inconsistent theory, according to Karl popper. In logic, when you make a false assumption anywhere, then anything can be proven true.... or false.
In medicine paper after paper discusses correlations that are always couched in statistical caveats, having always less than 100% likelihood of being truly cause and effect. In physics the same data would be interpreted as a unique cause. 
Geometry is appealing to physics, because it allows the right side of the brain to picture what the equations created by the brain's left side represent. This visual appeal provides a convenient way for a physicist to invoke a magical solution when he faces an impasse. Rather than say: "When I add more contradictory assumptions to my theory they work just fine," physicists say "My illogical reasoning can easily be remedied by changing the geometry of space". To a mathematical physicist, any mathematical concept, no matter how senseless, can be injected at any time to save a floundering theory.
The space Minkowski invented made possible the solution of relativity problems through invariants, which meant it became possible to get the
prescribed answer on a test while maintaining zero insight into the futility of the underlying math. Space-time diagrams give a marvelous illusion of resolving paradoxes without providing any new information. No paradox can be "solved" by using them, but they provide the user comfort in his own analytic abilities. This comfort is a delusion. Invariants and space-time diagrams make it possible for students to be mathematically consistent with the Lorentz transformations while still making latent reasoning errors.
Minkowski's relationship intended to demonstrate that time could be thought of as a "dimension" in relativity. In algebra, he is right, but in physics this is lunacy. How could space-time be measured... with a ruler-clock measuring meter-secs?
Unfortunately, this mathematical relationship provides a mindless calculation shortcut with great precision, without having the slightest intuition about what is happening.  After Minkowski, thinking was no longer necessary, so nobody did it anymore.
Curved space is a good example of concepts that are easy to create in mathematics, but unlikely to have any real-world counterpart. Even Einstein acknowledged its absurdity when he said around 1920 that "space without ether was unthinkable". Of course this same Einstein said in 1905 that the ether was irrelevant. Einstein eventually decided to attribute the properties of curved space to ether, rather than continue along a line of total absurdity.
Einstein understood fully that Ehrenfest's paradox (the rotating disk with shrinking circumference and fixed radius) refuted relativity. The only way to avoid the insurmountable obstacles that were presented by the paradox was to add a new mathematical assumption that would solve the problem - so he changed geometry. The rotation had to somehow maintain a consistency with the Lorentz transforms, but that wasn't completely possible unless some new assumption was introduced. Einstein was forced to make an absurd assumption in order to save the theory of relativity. He assumed that linear motion was relative, but rotation was absolute.Einstein was like the Dutch boy with his fingers in the dike. Each leak was a SR contradiction. Popper said one leak kills a theory, but Einstein kept plugging leaks until he ran out of fingers.
So special relativity does not include rotation. Objects can accelerate in special relativity, but they can't rotate. Rotation requires general relativity. General relativity wasn't created just to include gravity - it was intended to solve Ehrenfest's paradox. Einstein solved Ehrenfest's paradox by creating a new theory because the original theory would not permit the routine phenomena of rotation. Special relativity didn't need an experiment to contradict it - it had been contradicted just by Ehrenfest's thought experiment.
The conversion of SR into GR raises unsurmountable problems:
- They each contradict the other
- prior to Ehrenfest's gedanken contradiction Einstein said SR did apply to rotation. It applied to straight line motion, so a n-sided polygon would satisfy SR, even if the sides were unlimited.
- If GR completely replaced SR then only GR would be promoted today. But MS physics claims that SR still holds in cases of weak gravity, so GR is an extension of SR, not a replacement. In technical terms GR reduces to SR locally, when one constructs the tangent hyperplane to the object's world line. 
By 1910 the transformation from a science that tried to explain natural phenomena to a branch of mathematics was nearly complete. Most pysicists lack the skill to distinguish mathematics from physics because they have been trained to believe there are no important differences. Soon physics labs - if they do persist - will perform only simulations, which are artifacts of the programmer, not nature. Students will graduate, never having performed a physical experiment, and seeing no need to. Although the Lorentz contraction is not a visible effect, all the mainstream mavens believe that relativistic objects appear shrunken. They never considered this needed empirical testing.
The only way physics can now move forward is through accidental experimental discoveries or a reawakening that the explanation of natural phenomena is the goal of theory. This would require theoretical physicists to break out of the only specialty they know - mathematics - by learning the art of understanding when a pure mathematical assumption is too absurd to add reliable explanatory power. In short, they need to understand Popper's emphasis on axiomatic and empirical consistency.  Detection of the first non sequitur can have only one immediate result : discard the theory or restore consistency BEFORE PROCEEDING. To accept the numerous paradoxes in Einstein's relativity is, for some, a strength of the theory!  Yet Popper says to stop as soon as a contradiction arises.
Relativity sets a very high bar for what will be accepted as contradiction. There are no real contradictions, only 'seeming' or 'apparent' ones. It is absolutely not possible to develop a logical conflict that would convince the mainstream - they are allowed to ignore or mis-interpret experiments that contradict SR because they are also allowed to use any version of SR that will work. There is no modern theory of relativity, but only theories of relativities. They  ask: "If these are really contradictions, then why can I calculate them?" Why... because the connection with reality is ignored.... and inconsistency proves anything.... and thus nothing.
Relativities are saturated with inconsistencies, but the mainstream isn't searching for the errors because they were taught that no errors exist. Physicists have been educated to believe they already have the solution, so deeper thought isn't productive.
Physicists crank out page after page of mathematical analysis that is seldom experimentally cross-checked. This is dangerous. For all practical purposes we are flying blind, counting completely on thought experiments and pure math models to guide us through the fog.
Math alone can't really accomplish possession of the truth, because all mathematical deductions are just restatements of the axioms. Sorting out axioms can no more avoid disaster than could rearranging the deck chairs on the Titanic. All mathematical analyses can be simplified back to the axioms, which are assumed. It is crucial to recognize its limitations; math lacks the frequent experimental reality-checks that would flush out the errors in a different science.
Mathematics does not exist in nature. It is contained entirely in the human mind.  Relativists believe they can calculate the "right" answer without resorting to reasoning. Is this the goal of modern physics education - mental degradation of natural understanding, where abstractions and 'exciting new mathematics' lead to agnosticism - and beyond that to nihilism? We are well on the agnostic path - there have been no new fundamental discoveries in physics for over half a century. The Big Bang fantasm must now confront the 'Axis of Evil' - the local symmetries present in the CMB sky scans. Not a word is said about the consequences of this discovery for modern cosmology - only desperate attempts to save the Big Bang by claiming contamination - which was never mentioned before. The Big Bang Theory is a system of indocrination that people believe because they want to believe it, not because they have been convinced by the supporting data.
Relativities created an enduring dogma. It was a psychosocial imperative that characterized all widely defended dogma, including Evolution and the Big Bang Theory. Once the new dogma has become entrenched within the educational system, it is set in stone. Some universities become in effect propaganda machines and produce scientists who cannot practice or teach physics any other way.
If the promoters have seductive charisma (which Einstein, Gamow, and Sagan had in abundance) then the theory, though not the least bit understood, becomes the darling of the media. GR and Big Bang Theory are sacrosanct, and it's most certainly not because they make any sense. In fact, they have become the measure by which we sanctify nonsense and institutionalize scientific confusion.
The response of relativists to counter-proofs is stereo-typical:
• Ignore contrary proof  - AE’s strategy.
• Claim that the experiment was faulty - the protocol was invalid.
• Accept the result if c is measured
• Use Lorentz contraction and time dilation (SR consequences) to ‘correct’ the result .... if c is not measured.
• Claim SR does not apply to rotations.  (contrary to Albert the Great)
• Claim SR does not apply to accelerated systems. (contrary to Einstein and Misner-Thorne-Wheeler)
• Bury the explanation in pages of mathemagic.
• Avoid prediction of future experiments....  only post-diction of conforming interpretations.
• Deny that measurements can be defined in a moving frame – the agnostic approach.
• Dispute the measurement of speed as distance over time.

For these reasons physics is dying, being suffocated by meta-mathematics, and physics departments at major universities with grand histories in physical science are closing down for lack of interest.  Who can blame students - if they want science-fiction they can save money and buy a book or CD. Physics needs to return to the fundamentals of philosophy - rejection of untestability and inconsistency - and validation via empiricism.