Reflections on relativity?....Rejections of relativity!

Welcome. This is a reasoned response to the relativity section at, a site promoted as the on-line and authoritative reference for all seeking explanations of mainstream relativity and its math support.

Mathpages is in fact our favorite comedy site on the Web, a truly modern fantasy, full of contradictions. Presented as mathematical support for relativity, it actually brings the errors into focus, a comedia errata. It is puzzling why it is cited to support any type of science, as the site is saturated with logical and mathematical errors, an unintended satire of modern thought. If grounded firmly in logic and mathematics, no one need be troubled by the intimidation of special relativity flak launched therein.

Does lack of response to the mathpages outrages signal descent into agnosticism and to nihilism beyond? God help us all.

All comments will be posted that are civil, relevant and coherent.


t/h to Peter and Amy for tech support.

Tuesday, October 26, 2010


.....He [Ptolemy] also argued that the surface of a rotating Earth would necessarily be moving faster than the clouds floating in the air above it, so we should never see clouds moving to the east.
 The logic is correct, but overlooks the surface cyclones that have flows faster that the rotational speed, so the statement is only true in the large. Ptolemy’s argument is still valid on average; the prevailing east-bound temperate zone winds and the eastbound jet streams refute the rotation of the earth eastbound.
 19 centuries later his logical statement about the conflict between atmospheric circulation and the West-to-East rotation of the Earth still stands as a refutation of a spinning Earth, a contradiction which establishment physicists choose to ignore.

Likewise the absence of any discernable parallax in the observed positions of the stars apparently rules out the possibility that the Earth revolves around the Sun – unless the distance to the stars is literally thousands of times the distance to the Sun, which seemed implausible. 
 Parallax is the apparent shift in position of 2 objects relative to a third fixed reference line/point. Parallax is observed today, but it has no bearing on what is actually moving, only on distances and directions derived from geometry.
 The heliocentric model assumes both the Sun and stars are fixed, which creates 2 absolute references, not one.  The Earth is constrained to move by this choice (which violates the parallax definition). If the  Earth were also fixed, then NOTHING WOULD MOVE!
 If we assume that the Earth and stars are fixed, then the same illogic proves that the Sun moves – and the Earth is fixed.   Classical circular reasoning.

...yet within a century of Copernicus' death the heliocentric model had been fully accepted by the scientific community - despite the fact that stellar parallax still had never been detected.
 Defiance and denial of empirical methods had started – the age of enlightenment plunges into darkness.
 Btw: The HC model is NOT fully accepted by the scientific community. It is rejected by relativists and mainstream physics today, yet it was the model for rejecting geocentrism.
 Acceptance by the scientific community is not the measure of truth; truth is found via the scientific method and valid reasoning.   Scientists once all believed in the caloric, a fluid that flowed from hot to cold objects.  How many so believe today?

The new theory of relativity was based not on purely kinematic relations, but on the dynamical concept of inertia, according to which there exists an infinite class of relatively moving coordinate systems that are all equivalent from the standpoint of mechanical dynamics.
 How long would it take to validate an infinite class of relatively moving coordinate systems? No infinities of any sort are testable within the scientific method.

...the principle of inertial relativity, i.e., every system of inertial coordinates is equivalent for the description of physical laws - at least insofar as those laws pertain to the motions of material entities. Indeed the complete operational equivalence of uniformly moving inertial reference frames remained an unchallenged principle of physics for centuries.
 IRFs have many problems, including actual existence.  There are 2 types: kinematic and dynamic…
 What natural objects in the cosmos move at constant velocity? None.
 IFRs are abstractions with no (usable) reality. There are many approximate IFRs, but no fixed rules for when approximation is acceptable. This provides wiggle room for relativists to accept or reject approximate IFRs, depending on their desired result. The experiments of Sagnac and Ruyong Wang demonstrate inertial frame inequivalence – the Earth is a preferred frame.
 For an English translation of Sagnac’s experiment:
 For the extended Sagnac tests done by Dufour and Prunier:
 For the Sagnac result applied to electrons and neutrons,
 not photons, see
 For the linear version of Sagnac, see the Wang FOC exp.

....but all efforts to detect the putative aether or its state of motion failed.
 All efforts?   All the following experiments allow inference of an aether presence…
 Foucault pendulum  1851
 Sagnac rotor 1913
 Stellar aberration  Bradley 1727
 Fresnel drag 1818-30
 Airy failure 1871
 Depalma-spinning ball drop  1977
 Depalma-Gyro Drop 1977 
 Quantum red shifts-Tifft  1984 
 Mirabel and Rodriguez superluminality 1994 
 Aspden Effect 1995
 Marinov Plasma Tube 1996   
 Casimir Effect 1997
 Roth Magnetic Memory 1997
 Lijun Wang superluminality 2000     
 Gravitomagnetic London Moment 2006
 Dayton Miller aether drift 1921
 Joos c anistropy 1930
 Pound-Rebka c anistropy 1959
 Jaseja & Champeny Spinning Mossbauer disc 1963 
 Silvertooth  c anisotropy 1986
 DeWitte coax cable anistoropy 1991
 Galaev aether properties 2002 
 Pioneer 10,11 anomaly as dual aether 1972 - 2004
 Faraday Rotor Generator  1831  
 Michelson&Morley c anistropy  1887
 Shapiro Venus radar anistropy  1969
 CMB dipole beam 996
 Global Positioning System vortex 1993
 Atmospheric circulation aether pattern

This [failure] created a puzzle for physicists, because their theories were based on the idea that light propagates at a characteristic speed relative to the medium, but they were unable to detect the presence of that medium, let alone to determine its state of motion.
 M&MX did measure a daily flow of aether, but not the magnitude expected for the Earth’s alleged orbital speed. Ideological exclusion of the M&MX – refusal to accept the option of both Earth and a dynamic aether at rest - led to the wrong left turn into the land of relativity. We have wandered in this barren desert of SR and GR for over a century.

…..Lorentz and Poincare, .., by about 1905, had arrived at the conditions that must be satisfied by all elementary entities and forces (including inertial forces) if the principle of relativity is to be satisfied.
 Lorentz and Poincare were forced to fit the worldview into the MMX false null result. But their attempts couldn’t succeed without a correct understanding of the M&MX.

...The coordinate systems given by the Lorentz transformation for reference frames in motion relative to the aether were regarded by Lorentz and Poincare as merely apparent (or “effective”) measures of space and time, rather than “true” measures, which they continued to believe were related to the aether’s rest frame coordinates by Galilean transformations …..
 They believed their models were only temporary resolutions to an underlying problem, for which the aether was the real solution.

……neither Lorentz nor Poincare explicitly identified the auxiliary coordinate systems as inertial coordinate systems.
 They probably realized that the concept of IRFs was useless and often circular when applied.

Einstein presented a simplified derivation – and a much broader interpretation – of the Lorentz transformation, based on the principle of relativity combined with the principle that the speed of light is c in terms of every system of inertial coordinates.
 Einstein’s premises of all motion being relative and yet light being absolute in motion is a contradiction. In logical conflict with itself starting from its very premises, relativity fails Popper’s rule of consistency and must be corrected or abandoned, since one can prove anything with an inconsistent theory.

[Einstein] showed that these two principles – which were just a small subset of the assumptions made by Lorentz and Poincare – were sufficient to derive all the known phenomena of electrodynamics, as well as new relativistic formulas for aberration, Doppler shift, and time dilation.
 A very broad statement, and certainly challenged by experiments whose interpretation is restricted to a single version of relativity. Einstein changed his mind on several practical applications of relativity; his followers can selectively quote whatever fits the situation. However, dissidents can also validly quote the contradictions in his writings – and others – to assert, along with Karl Popper, that inconsistent theories can prove anything.

……inertial coordinate systems (i.e., coordinate systems in terms of which “the laws of mechanics hold good”), which are by definition the "true" coordinate systems of Newtonian physics.
 The dynamic definition of an IRF. Does this agree with the kinematic definition of constant linear motion?  Doies anyone care that the two definitions may be in conflict?

He [Einstein] highlighted the reciprocity of those transformations, emphasizing the symmetry between relatively moving systems of inertial coordinates, and pointed out the crucial relativity of simultaneity exhibited by these systems.
 But didn’t point out the absence of IRFs in realistic experiments and natural events.

...he [Einstein] also derived the consequence that all energy must possess inertia, and that the inertial mass of an object is reduced by E/c2 when the object emits energy E.
 A classic historical fallacy – to enhance the Einstein urban legend.   E=mc<sup>2 was derived prior to Einstein.

...Thus relativity was restored by reinterpreting the measures of time and space on a more profound level.
 Re-interpretation of measures of time and space?? This destroys experimental proof, the validity and reality of testing, if the testimony of our eyes must be ‘re-interpreted! Are we to believe the relativistic distortion of measurements that replaces raw data – or our own eyes?

Minkowski followed in 1907 with a geometrical interpretation, emphasizing the fact that the invariant [interval] is simply a generalization of the Pythagorean theorem…….
 Not a simple generalization, but a significant distortion of the Pythagorean theorem. First the additional dimension must be space, not time. Second, all dimensions must be positive.
  dx2 + dy2 + dz2 becomes  dw2 + dx2 + dy2 +  dz2

 Minkowski also made extensive use of four-vectors, which had been introduced by Poincare. Important contributions and clarifications to the new relativity theory were also made by Planck, Lewis and Tolman, and others.
 The math abstraction of space-time has no clear meaning in the real physical world. Is it measured in meters times secs? What instrument measures spacetime?  A ruler-clock?
 Why isn’t the invariant interval measured as t2 –(x/c)2 -(y/c)2-(z/c)2, converting distance measurements to time by dividing by c ?(See the STEMU apps.)

The general theory of relativity established equivalence between the members of an even larger class of reference systems, and in so doing achieved a conceptual unification of inertia and gravity, while retaining the structure of special relativity locally at every point of spacetime.
 So locally GR reduces to SR.  Important to note for future discussion, when we see GR and SR conflict, or it’s claimed one does not apply. 

…….. Einstein was reluctant to concede the issue, having rescued relativity twice from seemingly intractable problems, both times showing that in fact relativity was the key to a deeper understanding of the very phenomena that were thought to be incompatible with it.
 Was this a rescue mission, or an effort to impose an ideology on physics, by a continuous patchwork of corrections and ‘refinements’, a path followed by his acolytes? 

………To this day the beauty and elegance of general relativity challenges the imaginations of scientists seeking to reconcile it with the latest theories of physics.
 What is beauty and elegance, without truth? And what beauty and elegance is there, when mired in the computational nightmare of the simplest GR calculation?
 Why reconciliation, instead of a return to the wrong turn a century ago to address the errors of the M&MX discernment?

This book examines the evolution of the principle of relativity in its classical, special, and general incarnations, both from a technical and a historical perspective, with the aim of showing how it has repeatedly inspired advances in our understanding of the physical world.
 We would say more wrong turns were followed since M&MX, instead of returning to the source of the error… Are mainstream physicists like obstinate (male) drivers, who refuse to admit they’re lost, or to stop for directions(examine modern experiments). The longer they persist, the deeper they wander into the wilderness, bewildered by all the wild false claims surrounding them and distancing their world view furtjher from reality.   

STEMU apps - Minkowski's madness

The STEMU Axiom – the Axiom of Unity - creates problems for modern scientists who ignore its existence. It is simple, clear and incontestably reveals errors based on mathematics models with incomplete relation to reality.
The main reason of crisis in theoretical physics is ignorance or rejection of the STEMU axiom. Its essence is that it is impossible to:
·         separate existence of space, energy/matter and time
·         separate energy/matter from space
·         contemplate their separate existence.
·         separate time from space or from energy/matter.

In reality space, energy/matter and time are primary and inseparable from each other as elements of the universe. Almost all modern physical theories contradict this axiom. STEMU must be reflected in all mathematical models describing a changing reality, to assure a foundation of the model in the real world. Motion of any objects in space are inseparable from time.
The Axiom of Unity has been broken by the modern transition to description of microcosm behavior. The result is an impassable jungle and many scientific fables that will need a lot of time to return to a classical and logical way of development. All experiments must proceed within the framework of the Axiom of Unity.
STEMU Axiom applied – Lorentz transformations.
The beginning of relativity was described by Galileo with the transformation from a rest frame F to frame F’, moving at speed V in Euclidean space.
                 x’ = x -Vt                         (1)
     t’ = t                                (2)
 Space and time represent absolute properties of the universe.
The corresponding Lorentz transformations for relative space and time that satisfy the special relativity premises are
               x’ = (x-Vt)/(1-V2/C2).5             (3) 
                t’ = (t-Vx/C2)/(1-V2/C2).5    (4)
 From (3) it follows that as V=>C the size of a spatial interval x’ decreases, corresponding to  relativity of space. From (4) when V=>C the size of t’ also decreases, corresponds to relativity of time. But experimental results contradicting the transformations of Lorentz and the special theory of relativity appeared…. The authoritative Sagnac experiment, largely overlooked by the   world scientific community.  
Fig. 1. Analysis of Lorentz transformations

Conclusions based on the same mathematical model of SR vary widely, changing the physical sense it represents.  In the Lorentz transformations (3) and (4) x’ and t’ are separate, contrary to reality. A changing spatial interval is always a function of time. Therefore the Lorentz transformations describe a false reality.
From STEMU it follows that space, time and matter cannot exist in an isolated condition, but only together.

In (3) and (4) changing the size of x’ in F’ is independent of time t’ in the same frame.  To correct this erroneous interpretation equations (3) and (4) must be analyzed together. So we divide the first into the second,
          x’/t’ = (x-Vt)/t-Vx/C2        (5)
This now reflects the dependence of coordinate x’ on time t’, consistent with the STEMU axiom. Energy/matter is present in (5) implicitly via the speeds V and C, since only material objects can have speed.
In fig. 1 x is a position coordinate for a light signal in F, equal to the product of C for a time t.  
Substituting x = Ct in (5) yields x’ = Ct’, the position of a light signal in F’. This signal is located on the co-terminus axes OX and OX’, at a point K - the crossing point of light spheres with two axes OX and OX’ (fig. 1). The geometrical sense of the Lorentz transformation is simply to fix x’ of a point K in F’ and x in F(fig. 1).
Lorentz transformations must give all mathematical symbols x,x’,t,t’,V,C included in these transformations a precise geometrical and physical sense. But there is no information in these transformations that reflects any physical effects.

Lorentz transformations can carry out the role of a theoretical virus. At the origin of time, if a light source flashes at point O (fig. 1) then x=Ct. Substituting in (1),
 Ct = Vt + x’            (6)
Squaring both sides and simplifying,
  0 = C2t2 –(Vt+x’)2 = C2t2 –v2t2 – 2Vtx’-x’2   (7)
0 = C2{t(1-V2/C2).5 –Vx’/C2(1-V2/C2).5}2 – x’2/(1-V2/C2)  (8)
  T’ = t(1-V2/C2).5 –Vx’/C2(1-V2/C2).5   (9)
       X’ =   x’/(1-V2/C2).5                  (10)
Replace  from (1)
       X’ = x - Vt                                  (11)
The result is
     T’ = (t-Vx/C2)/(1-V2/C2).5           (12)
     X’ = (x-Vt)/(1-V2/C2).5                (13)
Expressions (12) and (13), derived from the Galilean transformations, completely coincide with the Lorentz transformations (3) and (4). Once it was thought that Galilean transformations are a special case of Lorentz transformations, but careful analysis shows the reverse - Lorentz transformations are a special case of Galilean transformations, which are also contrary to the Unity Axiom.
In (8) x’ and t are interdependent variables. We have taken x’ and t from (8), and made them independent of each other, violating the Axiom of Unity and distorting reality.

STEMU Axiom applied – Minkowski space
Uncontrolled intrusion into physics by mathematicians – such as Minkowski’s four-dimensional geometry - has made mathematical knowledge primary and physical secondary. Advances in physical knowledge have been held back by interminable complex mathematical models and their transformations, many of which are erroneous.
To show this we call the mathematical models containing only geometrical parameters, mathematical, and the temporal we call physical and mathematical.
The equation of a sphere containing only geometrical parameters, 
         x2 + y2 + z2 = R2           (14)
let's call mathematical. The same equation, but with a variable radius of sphere R=Ct, automatically becomes physical and mathematical by including time and a physical parameter, C.
         x2 + y2 + z2 = C2t2        (15)
By analyzing transformations we have made obvious the inept manipulation of the physical parameter time. The lesson is that maximal care must be taken in analyzing the consequences of mathematical models containing time.
Lorentz's transformations are said to follow from Minkowski geometry. (see Modern physics in applied sciences, B.Robertson).
In F the light sphere equation is
            x2 + y2 + z2 = C2t2      (16)
In F’
x’2 + y’2 + z’2 = C2t’2     (17)
x2 + y2 + z2 - C2t2 =  x’2 + y’2 + z’2 - C2t’2  (18)
x’ and t’ are defined as in (3) and (4) and physical and mathematical equality is claimed from
          x2 + y2 + z2 - C2t2 = 0       (19)
          x’2 + y’2 + z’2 - C2t’2 = 0.    (20)
 Equating two zeroes is equating nothing. To bypass this difficulty, Minkowski uses
   x2 + y2 + z2 - C2t2 = S2         (21)
   x’2 + y’2 + z’2 - C2t’2 = S’2   S,S’ <> 0  (22)
This is not Euclidean geometry because the 4-D Pythagorean theorem is invalid.  The interval S has an invented physical sense of mixed dimensions – space-time. Physicists have surprisingly simply agreed with the absurdity of this interval.
We shall check on its conformity to the Axiom of Unity.
Comparing (19) and (21), we see that in the geometry of Euclid  Ct = OM   - a rectilinear diagonal of a rectangle(fig. 2); in the geometry of Minkowski this diagonal cannot be rectilinear, as this equation does not correspond to the Pythagorean theorem. The presence of S in (21) forms a diagonal – the curvilinear ОЕМ (fig. 2). This implies that parallel straight lines may cross (at M).

Fig. 2. Analysis of Minkowski geometry
The straight line diagonal Ct = OM in (19) corresponds to a photon moving rectilinearly in space. The curvilinear diagonal Ct = OEM in (21) contradicts this property. So we have no justification for putting photon speed C in Minkowski space to represent reality.
We test this statement by trying to define coordinates for a light signal in space at the moment of time t, when x = y = z. From (21) we have
x = y = z = {(S2+C2t2)/3}.5       (23)
The unknown spatial interval leaves undefined x = y = z. Equation (21) does not permit defining the photon position on a trajectory OEM during time t, breaking the STEMU axiom.
The length of a diagonal Ct = OM is measured with the help of the photon moving rectilinearly with speed C so, using (19), we can define the photon location on a diagonal Ct = OM at any moment, corresponding to the Axiom of Unity. At each point on a diagonal Ct = OM the photon (energy/matter), space and time have indissoluble unity. For example, for the special case x=y=z , (19) gives the result
         x = y = z  = Ct/3.5   (24)

For any t we can find corresponding coordinates x ,y ,z.
Introduction of interval S in (21) automatically transforms a rectilinear trajectory Ct = OM into a curvilinear path Ct = OEM, forcing light to move on a curve. The curvature radius of this path is undetermined…
Imagine the chaos if light moved on a curved path.  In fact from a distant star to Earth it is possible to have only one direct line. Physicists did not care to analyze the conformity of these transformations to reality. Note that Riemanian geometry, as a non-Euclidean geometry, is automatically inapplicable in all cases involving C.
STEMU Axiom applied – quantum mechanics  
The Axiom of Unity will allow us to establish the reality of theories on which modern quantum physics is based.  We shall start with the equation of a monochromatic DeBroglie wave .
     Psi = A sin 2pi(ft – x/lambda)   (26)
              f = frequency, lambda = wavelength
In nature movement of any object in space is ultimately synchronized; the coordinate x always can be represented as a function of time t. In (26) x and t are considered independent variables. This does not happen in reality, since the coordinate x of varying position of any object in space is dependent on time t. Hence (26) contradicts the basic axiom of natural sciences – the STEMU Axiom. Therefore we exclude (26) from the arsenal of valid equations!  The same is true for the Schroedinger equation in three-dimensional space, although solutions are more complex, and also for the Dirac equation.
Nevertheless the De Broglie equation (26) and Schroedinger are widely used now in quantum physics and in some cases describe results of experiments, though they are fictional. The wave function psi can have the same amplitude for different values of x, so solutions of these equations have the nature of probabilities, not allowing an exact solution. The reason is the violation of the Axiom of Unity.
Newton’s laws of mechanics do operate within the framework of the Axiom of Unity; the equation of Schroedinger contradicts this axiom.
Schroedinger’s equation has caused enormous harm to physics and, especially, chemistry.  
Differential equations of partial derivatives violate the Axiom of Unity. Such equations usually include time, and the change of other parameters is considered independent of time, contradicting the Axiom of Unity.
The Maxwell equations also do not permit opening up the structure of electromagnetic radiation and, in particular, of a photon. The field theory developed by D. Landau and textbooks written by L.D. Landau and E.M. Lifshitz are ideal, lacking contradictions.

Sunday, October 24, 2010

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.


Space-Time-Energy/Mass Unity (STEMU) axiom:
proposed by Filip Kanarev.

To achieve simplicity in inital analysis mathematicians sometimes abstract reality to a bare manifold, a coordinate system resident in a modeling space unrelated to physical reality. Bare Minkowski diagrams somehow come to mind...
Consider a world in which there's no time, just space and matter. Nothing would change; this is not the real world as observed.
If there's no space, where would the matter go?
If there's no mass, then there is no observable event.
This subtle axiom points out that all three descriptors must be present and unified for an observable event to occur in the reality of a physical world.  Without observable events to record there can be no scientific method - no testing of theory.
Sailors on the open ocean need a navigation guide to locate their position.
In the cosmos the islands needed to locate events are visible objects - radiation sources.
That's why mass is needed to unify/connect space-time models with experiments - mass/objects give the location of events.
Real events require a description using a  Space,Time and Energy/Mass location Unified in the chosen reference frame, the STEMU completeness  condition. Space-time-energy/matter are inseparable and have meaning only when unified into triune relationship.
The point of this axiom is to validly and completely link mathematical models with physical reality.
A model that uses a time-ordered coordinate system alone, without locating the origin in the real universe, violates STEM unity.
Any theory violating the STEMU axiom is logically incomplete - the model lacks the capability of testing.
To Minkowski diagrams there must also be added a light cone and world lines of particles => mass/energy located in space and time.
Relativity violates STMU when treating space and time separately (for example, length contraction and time dilation).

Googol Axiom

From Popper's consistency criterion we find that as soon as a contradiction is found, we should
 a) abandon the theory
 b) eliminate the contradiction(s)
Why the quick reaction?  Accepting contradictions allows any theory to be proven true, which implies that
nothing can be proven true!

For example, to the consistent logical system of arithmetic, we introduce a super tiny conflict, unlikely to arise in any scientific calculation:
Googol axiom:   googol = googol + 1/googol  
where googol = 10^100
1 and (100 zeros) =  1 and (100 zeros) .  (99 zeroes) and 1
If we -
Subtract    a googol  :     0 = 1/googol    
Multiply by a googol  :     0 = 1
Add to itself n times :     0 = 1,2,3,4,5,6,7,....
The valid and consistent system of arithmetic is thus reduced to nonsense by insertion of a tiny contradiction, the googol axiom.
Moral: there is no tiny or ignorable contradiction.
The physics establishment claims - Relativity predicts the correct results of all its experiments.
This is true.  Relativity also predicts the wrong results for the same experiments, the hallmark of inconsistency.
Relativity exhibits many contradictions/inconsistencies.
Consider - from the SRT 1905 paper:
1. The laws by which the states of physical systems undergo change are not
affected, whether these changes of state be referred to the one or the other of
two systems of co-ordinates in uniform translatory motion.
So -   if a,b,c are 3 different  inertial frames and a is stationary,
Then take Va = 0 and take Vb,a= v1  and  Vc,a = v2, where v1 <> v2
Then   Vb,a <> Vc,a

2. Any ray of light moves in the “stationary” system of co-ordinates with
the determined velocity c, whether the ray be emitted by a stationary or by a
moving body.
So - Vb,a  = c    and Vc,a = c 
Then  Vb,a  = Vc,a

3.   SRT premise 1 contradicts SRT premise 2 ; SRT is inconsistent

The problem is that discussion continues with SRT already proven to be inconsistent, without demanding that the conflict be resolved immediately!

MS physics will claim that SR gives the ‘right’ answers to all its tests…… Of course it will…..

Another MS position is that the conflicts are small and outweighed by the empirical success of SRT.

This contradiction in consistency must be resolved before any further consideration of SR, as the googol axiom shows.
If not, anything will be believed, like:
 There is an aether and there is not.
 The traveling twins contradiction: 
A is younger than B and B is younger than A.


A slice of Bacon, please....
Epistemology is a mouthful that means the rules for discovering truth.  Science has used a scientific method to find natural truth since Aristotle; we will use the improvement due to Francis Bacon, a standard which has unfortunately been abandoned by modern science. 
Bacon's scientific method:
Testing - "Mere argument is never sufficient; it gives no satisfaction or certainty, which can only be evinced by immediate inspection or intuition, which is what experience gives by verifying hypotheses and conclusions by direct experiment."
Four common causes of error are : authority, custom, the opinion of the unskilled many, and the concealment of real ignorance by a pretense of knowledge.

..... seasoned with Popper.
Karl Popper established criteria for scientific logic, which we will follow.
Falsifiability:  exclusion of theories outside the scope or possibility of testing in space or time or technology 
Consistency: no logical conflict among premises, hypothesis, conclusions and predictions
Sound reasoning: logically valid argument form and true premises
Testing: empirical applications of the conclusions and predictions