Traditional science ended in 1905 when Einstein’s relativity theory (but not Einstein) discovered (a) that clocks do not measure time, (b) that rulers do not measure distance, and (c) that speed should be redefined as the sine of an angle and the speed of light as the sine of a right angle.

Those radical changes made time, distance and the speed of light, redundant and their elimination caused the rest of traditional science to collapse. Einstein’s theory had converted traditional science into the objective science proposed by George Berkeley in 1710, so objective science took over smoothly from traditional science and a new regime in science began. Einstein was unaware of all this though and succeeded in imposing his own illogical, traditional science-oriented, mis-interpretation of his theory on the logical interpretation of the theory itself.

Einstein cut himself off from his theory by refusing to obey its instruction to change his variables in equation (1).

γ^{-1}=(1-(v/c)^{2})^{1/2}(1)

This equation signaled to Einstein that he should change his variables from v/c and γ^{-1} to sin(p) and cos(p).

That told Einstein that his theory only had one independent variable because he had redefined speed to be the sine of an angle and the speed of light to be the sine of a right angle. Einstein was completely unaware of having done anything of the kind but instead of looking to see, he ignored the advice and kept his two variables. From then on, Einstein and his theory went their separate ways.

At the beginning of his theory Einstein had adopted a new rule for combining a trio of relative speeds.

v_{3}=(v_{1}+v_{2})/(1+(v_{1}v_{2}/c^{2})) (2)

He intended (2) to be a step towards explaining the constancy of the speed of light.

What he did not know is that equation (2) belongs to a family of simple geometrical diagrams consisting of a pair of lines with gradients D and D^{-1} diverging about an angle, p. With a little trigonoetry one finds that

sin(p)=(D-D^{-1})/D+D^{-1}) (3)

Then if one takes three such diagrams with

D_{3}=D_{2}D_{1}(4)

and substitutes (3) into (4), one obtains, after a few simple manipulations,

sin(p_{3})=((sin(p_{1})+sin(p_{2}))/(1+sin(p_{1})sin(p_{2})) (5)

which is the same as Einstein’s equation (2) with v/c replaced by sin(p). Einstein’s assumption that he could introduce (2) without changing his variables was therefore wrong but when that was pointed out to him through (1) he ignored the warning. From that point he and his theory diverged and it is the theory we follow, not Einstein.

He wanted an equation like

v/c= (D-D^{-1})/(D+D^{-1}) (6)

which he saw as a relation between speed and the Doppler parameter. What his theory got though was the purely geometrical equation, (7).

sin(p)=(D-D^{-1})/(D+D^{-1}) (7)

That is a geometrical relation between the sine of the angle of divergence of two lines and a combination of their gradients.

Einstein’s theory had discovered geometrised science and made traditional science redundant.

It is well known that everything we see is in the past. The present is unobservable. Since the beginning of science, scientists have imagined the unobservable present with their own named concepts, like time and distance and then compared their imagined present with what they could see. When, in 1667, they found out that they could only see the past, they assumed that the past is like an earlier present and corrected for what they interpreted as delays due to the finite speed of light. They had got themselves into the absurd position of changing the visible past to make it fit the invisible, and therefore, imagined, present.

In 1710, George Berkeley advised scientists to stop trying to describe the invisible present with their own named concepts and to describe instead the purely geometrical data of the visible past. He thus proposed a switch from science based on named concepts to a purely geometrical science. It was this science which Einstein’s theory (but not Einstein), discovered in 1905.

The discoveries were paradigm changing. Scientists have two options. They can go on ignoring the discoveries of Einstein’s theory of relativity by using Einstein’s contrived explanations as an excuse. Or they can face up to the consequences of the discoveries, abandon traditional science and start again with George Berkeley’s geometrical, objective, science

Goodbye for now and thank you for joining me

Stan Clough 1.7.18