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continuum”. Thus, conventional physics proceeds from this inductively, namely by inferring a continuum from the phenomenon.

      Deductive physics takes the opposite route, from the continuum to mass as the dynamic of it. The constituents of this continuum are pure bodies, defined as permanent, impenetrable volumes, the opposite of empty space and characterised by nothing else, which is why deductive physics adds “body” as a third a priori intuition in addition to those of “space” and “time”. Hence, all that is needed for the representation of the material world is the system of coordinates covering time and space, and the bodies within it, all material phenomena being derived from them.

      The three a priori intuitions have a correspondence in the three fundamental physical constants, which would confirm philosophy as well as science in their claim to be the basis for all knowledge—if a century ago the theory of relativity had not come up with ideas that declared a priori intuitions invalid: with time being stretched, space being stretched and curved, and with mass increasing as its own speed increases, tending to infinity at the speed of light.

      The triumphant proof by experimentation of Einstein’s predictions undermined philosophy, and in order to regain a firm footing it is necessary to get to grips with the theory of relativity. As children begin their development without consciousness of space and time as dimensions independent of their own existence, the first thing to be observed is how this emerges as a capacity for abstraction and objectification.

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      Deductive Physics

      What are the benefits to a person of knowing how matter can be thought about? Firstly, the natural reflex of wanting to have everyhing explained is satisfied. It can be built on, and an explanation for “life” found in a few steps. It is now possible to understand “intellect”, the essence of which, although it may go beyond matter, is nevertheless a structure of matter. Finally there comes freedom from all speculation, freedom to construct one’s idea of the world on the solid foundation of recognised laws.

      Acquiring space-time concepts

      With freedom of movement comes the need to explore the space where it occurs. Here it is only a matter of distinguishing between “space” and “impenetrability”, not of what the impenetrable barrier is.

      Infants’ first experiences of touch establish impenetrability: is there a body in the way of the hands or not? Playing with wooden bricks teaches them that two objects cannot occupy the same space at once, and conversely one cannot be in two places at the same time. By the age of eight months they have internalised the concept of permanence; if an object is covered they look for it, whereas previously they would simply have turned their attention to something else.

      At first, space manifests itself only as the distance from the child to an object; later the perspective widens with the awareness of differences in length. Time is initially understood in terms of earlier and later, faster and slower, longer and shorter. If one of two trains running on parallel tracks in a model railway is faster than the other, a toddler will see it as going further, without the ability to express the idea that it will arrive at its destination sooner.

      Children cannot conceive of objective time and objective space, both existing independently of the child’s own presence, until the age of seven or eight—and from then on they can never again imagine them not existing. They are inescapable, and yet philosophy was stalled in 1919, when an experiment during the solar eclipse in England confirmed Einstein’s mathematics, which he construed as a sequence of the stretching and bending of space and time, something which from the perspective of deductive physics is unnecessary.

      Fundamental constants

      Inductive physics represents the material world in space and time, but instead of the “body” dimension it relies on “mass”. It defines mass in terms of a specific volume of a specific substance: a litre of water is a kilogram, and all substances that are similarly inert and heavy are the same.

      All statements made in physics are stated using the three dimensions of length (for space) in metres, m, time in seconds, s, and mass in kilograms, kg. Electricity is linked to mass by means of the dimensionless fine-structure constant α, and does not represent an additional dimension. Also, as physics uses three dimensions to express itself, there are three fundamental constants1:

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      Metres, seconds and kilograms are arbitrary measures: a 40,000,000th part of the equatorial circumference, an 86,400th part of a day, the inertia and weight of a litre of water—while in contrast the fundamental constants c, G, ħ are facts, and are what they are independently of the measurement units of physics. If they had different values, the world would look different: elementary masses would be larger or smaller, or there would be none at all. Gravitation would be so strong that all celestial objects would be drawn together into a single lump, or would be so weak that nothing would hold together. Quantum mechanical interferences would be so weak that electrons would fall into their atomic nuclei, so that no molecules and no life could arise, etc.

      As in deductive physics the fundamental constants are the properties that determine the continuum in space and time, and as all materials are derived from the dynamics of this continuum, all phenomena are based on a priori intuitions and therefore assumed “according to the mind”.Thomas Aquinas

      Space and time coordinates run to infinity, revealing their nature as concepts. On the other hand, the universe as portrayed within these coordinates is seen to be finite. In retrospect the two giants can be reconciled: Newton’s “absolute space” and “absolute time” relate to the coordinate system of all representation, while Einstein’s “absolute speed of light” relates to the continuum represented within it.

      Irritation from the theory of relativity

      Kant’s a priori intuitions are the most fundamental examinations of thought that philosophy has produced, but at the same time they are the most persistently refuted: thinkers are constantly putting forward new speculations, in particular about the nature of time.

      In 1905, Einstein introduced the terms “expansion of time”, “time dilation” and “space-time continuum”, adding “curved space” ten years later, thus causing bewilderment and relief in equal measure: bewilderment for those who believed they understood the concept of a priori intuitions; relief for others as there was now something much more inconceivable, so it must be the truth.

      The special theory of relativity goes beyond any intuition right from the start of the derivation: a “four-vector” is first introduced for spaces, then rotated around an imaginary angle, and later it is concluded formulaically that impulse is also a four-vector (with time in the fourth dimension)—and after a chain of abstract operations, E = mc2 is obtained. A professor* at the Swiss Federal Institute of Technology (ETH) once said to his students, “You go through it step by step, accept what emerges, and understand nothing. No-one understands it.”

      In his lectures at Princeton in May 1921, Einstein made fun of the fact that physicists had been obliged to “bring down ... the concepts of time and space ... from the Olympus of the a priori ...” He was apparently confusing “a priori” with “absolute” and failed to appreciate that Kant’s a priori intuitions identified a more radical relativity than his theory of relativity, i.e. that between thought and reality—not merely that between two bodies moving relative to one another (special theory of relativity) or interacting with one another (general theory of relativity).2

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      Albert Michelson, 1852–1932 ; Edward Morley,

       1838–1923

      Knowledge grows from the resolution of contradictions, and the contradiction first resolved by Einstein was this: if a source of light moves towards an observer at speedv, and the light is moving away from the source at the speed of light

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