"Aide Memoire"
Einstein's Theory of Special Relativity has played a key role in Physics throughout the twentieth century. This has led many to treat it as a final and definitive description of how the world works. There is an alternative view which does not accept this, but considers that the quirks and oddities it shows are an indication of some unwise, ill-chosen, or unjustified assumptions along the way. Encouragement to pursue this possibility is given by recalling from Scientific History a series of developments in the theory of Celestial Movements.
Here, the starting-point is Ancient Greece round about 400 B.C. The Greeks observed that the stellar constellations were unchanging in configuration and in location one to another, and that they moved in unison across the sky. Using their experience on earth they concluded that there must be a framework holding the stars in their places, but being invisible would have the qualities of totally transparent crystal. After some misconceptions about the shape of the earth and the vault of the sky, they settled on a spherical earth surrounded by a spherical crystal sphere with stars imbedded in it. Further independent spheres for the Sun and Moon completed the scheme, giving a very acceptable and reasonable-sounding description of how the World was put together. Except for the wandering stars (the Planets) which defied all their efforts to give each Planet its own sphere and each sphere its proper motion. This last was abandoned as insoluble for many centuries.
Coming forward in time to the nineteenth century, physicists had made great progress on the firm foundation of Newtonian Dynamics. Towards the end of this century they came across their equivalent of the wandering Planets – the anomalous behaviour of Electromagnetic Waves in that these failed to conform to Newton's Law of the Composition of Velocities. These two situations, so far apart in time, each found its genius, both pragmatists, Ptolemy of Alexandria for the Planets, and Einstein for the Electromagnetic Radiation. They did not address the reasons for the anomalies, they accepted them as facts and devised the necessary mathematics to make the numbers come out correctly. This was so successfully done by both, that their solutions, although as bizarre as the original anomalies, were accepted as a true description of how the world works. From the time of Ptolemy it took more than a thousand years until Copernicus rediscovered an idea that the early Greeks had considered and rejected – that the Earth spins about its polar axis and travels in orbit round the Sun. The challenge today is to make a similar fundamental reappraisal of Special Relativity.
That the human display system -- "Consciousness" or perhaps "Mind's eye", is not some exact representation of an external world, but is pre-processed for human consumption. The degree of processing is not trivial. Colour, (not Wavelength/Frequency), is painted on somewhere inside the Nervous System. Space is a way of presenting small time-intervals, which are inaccessible to biological receptors.
If space intervals are replaced with time intervals, what dimensional system takes over? If conventional numbers, as set down in formulae, are the criterion, then the formula for the propagation of Electromagnetic Waves is perhaps relevant. x2 + y2 + z2 = c2t2 This becomes: tx2 + ty2 + tz2 = t2 This might indicate a three-dimensional time-world, but this would neglect an important type of number -- clock-numbers, or ticking numbers, now readily available courtesy of modern electronics. They are needed when we ask "How long ago did such and such event happen?" This calls for a steadily ticking number. When we ask for the interval between the Earth and the Moon, a combination of fixed and variable numbers is needed. Today this is easily done on a VDU. Finally consider the situation of a flashgun pointed out into space and fired. Two questions should be asked, "How long ago did it occur?" (in seconds), and "What interval of time separates us from the photons that are speeding into space?" The answer is a pair of identical ticking numbers staying absolutely in step, one for the event , and one for at least some of the photons. In today's terminology one is called "The Lapse of Time", and the other "The Velocity of Light", Some reappraisal of our fundamental imagery seems to be called for here.
If the switch from space to time seem unnatural, consider these two statements. "If you journey from A to B the distance travelled can vary widely, but cannot be less than say s, which is considered to characterise the gap between them, and is known as the shortest distance between two points". "If you send a message from A to B the time taken can vary widely but cannot be less than say t, which can equally be called the shortest time between two points".
A big obstacle to reform of our ways of thinking is the human need to visualise a model. There seems no alternative to the human display system for this purpose, and this is close to a contradiction. This may turn out to be insurmountable.