Kant was wrong to take time and space as the fundamental intuitions. Relative station and motion are more fundamental; causality is of course the most fundamental. Time a space are distinct and intuitive for inertial motions, and for certain generalisations of inertial motions; time and space are notions derived from the more primitive intuitions of station and motion. Looking for a start in studying relative station (with slow movements permitted, with respect to an inertial frame), Euclid told us about a geometry that is one of the main foundation stones of our civilisation. But Euclid’s geometry does not work for observers who travel near light speed with respect to the objects that they observe (keeping to constant velocity motions in inertial frames for the present exercise). They cannot practically put metre rods next to the objects, nor can they compare times without regard to their speed. They have to observe the moving objects by other methods. Radar and photography are the obvious methods to use. Effectively, light speed has become a new standard of motion. We find that moving straight edges look like arcs of hyperbolas. Minkowski geometry is a hyperbolic geometry. It describes the nature that we know, at least far from heavy objects, when we are looking at fast inertial motion.

Going to accelerated relative motions, we need a new standard: a standard that tells us about acceleration. Inertia is the obvious one. Mass tells us about the force needed to cause acceleration. But how does acceleration affect clocks and measuring rods? It seems that the size of a clock governs how it will be affected by acceleration.

Who can educate me about the effect of acceleration on clocks? Circular motion is about acceleration at right angles to the velocity. Do we have to rotate the accelerated clock to make it keep time? What happens if we don’t rotate the clock in time with the circular motion? What about acceleration that stays in the same direction as the unrotated clock, not at right angles to it? It seems that there is no need to rotate A.D. Fokker’s spherical light clock. Differential geometry tells us that we can’t deform a spherical material surface without making it buckle. Its size affects its performance. Does the size of an atomic clock affect its response to acceleration? To gravity?

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