By Prof. Lefteris Kaliambos (Λευτέρης Καλιαμπός) Τ.Ε. Institute of Larissa Greece. ( May

2014)Historically, Poincare joined the debate by declaring in 1887 that the axioms of geometry are neither empirical nor true a priori but are, instead, conventions whose truth it is meaningless to question. In 1891 he argued that, if we measure the angles between the lines joining three stars and find their sum is not 180º (the Euclidean value), we could either give up Euclidean geometry or assume that light travels in curved instead of straight lines. He believed the latter possibility could neither be proved nor disproved but would be more convenient to adopt than giving up Euclidean geometry.

In fact, according to my discovery of photon mass m = hf/c^{2 }and in the absence of a gravitational force F_{g } a photon travels always along a straight line in accordance with Newton’s first law based on the fundamental straight line of the Euclidean geometry. However when the velocity c is perpendicular to the gravity F_{g } I discovered that it accelerates in accordance with Galileo’s curved trajectory of a projectile based on the concept of vectors which are the fundamental straight lines of the Euclidean geometry . Galileo discovered that the observed motion of a projectile may be thought of as the result of two separate motions, combined and followed simultaneously by the projectile, the one component of motion (here is c) being an unchanging, the other component being a vertical, accelerating motion obeying the laws of free fall. Furthermore, these two components do not impede or interfere with each other; on the contrary, the resultant at any moment is the simple effect of a superposition of the two individual components of the Euclidean geometry.

Unfortunately Einstein under his fallacious massless quanta of fields believed incorrectly that the bending of light near the sun is due not to the application of the well-established laws of Newton but to a strange *curvature of space* with three dimensions in which he involved the time as a fourth dimension.

In 1905 (published 1906) it was noted by Poincare that, by taking time to be the imaginary part of the fourth spacetime coordinate √−1 ct, a Lorentz transformation ( based on the fallacious Maxwellian ether) can be regarded as a rotation of coordinates in a four-dimensional Euclidean space with three real coordinates representing space, and one imaginary coordinate, representing time, as the fourth dimension. Since the space is then an Euclidean space, the rotation is a representation of a hyperbolic rotation, although Poincare did not give this interpretation, his purpose being only to explain the Lorentz transformation in terms of the familiar Euclidean rotation. Unfortunately this idea was elaborated by Minkowski (1907), who used it to restate the invalid Maxwell's fields in four dimensions, showing their invariance under the wrong Lorentz transformation. He further reformulated in four dimensions the then-recent invalid theory of special relativity of Einstein. ( See my INVALIDITY OF SPECIAL RELATIVITY in my FUNDAMENTAL PHYSICS CONCEPTS ).

From such a false theory he hypothesized that time and space should be treated equally, and so arose his concept of events taking place in a unified four-dimensional space-time continuum. In a further development, he gave an alternative formulation of this idea that did not use the imaginary time coordinate, but represented the four variables (x, y, z, t) of space and time in coordinate form in a four dimensional affine space. Points in this space correspond to events in space-time. In this space, there is a defined light-cone associated with each point, and events not on the light-cone are classified by their relation to the apex as space-like or time-like. It is principally this view of space-time that is current nowadays, although the older view involving imaginary time has also influenced special relativity. Minkowski, aware of the fundamental restatement of the theory which he had made, said:

The views of space and time which I wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength. They are radical. Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality. – Hermann Minkowski, 1908 .

Note that Einstein using his fallacious coordinate systems of his invalid relativity (relative motions with respect to a randomly moving observer) made popular the abstract notion space-time, a four-dimensional space with three spatial and one time-dimension of Minkowski.

In fact, the increase of the electron mass in the Compton scattering (1923) is due not to the velocity of the electron with respect to a randomly moving observer but to the absorption of the photon mass m = hf/c2 . ( See my CORRECT COMPTON EFFECT ). Under Einstein’s fallacious ideas if one inspects the four dimensions of Minkowski – x, y, z, −ct – then one can hypothesize that the fourth dimension isn’t the time, but a distance which the light is traveling with speed c during time t.

It is of interest to note that Schrodinger in 1926 formulated his independent-time equations in three dimensions. It was soon recognized to be a satisfactory generalization of Bohr’s model, because it solved all the atomic phenomena. However despite the enormous success of the independent-time Schrodinger equations in three dimensions, Einstein influenced by mathematical tricks of the mathematician Minkowski (introducing a strange spacetime of four dimensions) in his book the evolution of physics (1938) emphasizes that the system of the proton- electron is characterized by a six-dimensional space!