Drawing  System

The system employed in The Tracing of Relative Motion Using Rotating Frames is based on the Principle of Equivalence and is represented by trimetric projection onto a  picture plane.  Since lines depict the loci of moving points it is possible to include a time co-ordinate.  The Principle of Equivalence states that gravitation and inertia are inextricably linked and that the effects of gravitation and acceleration are equivalent and cannot be distinguished.  As Max Born put it in 'Einstein's Theory of Relativity' (Dover Publications Inc. N.Y. 1962, page 316):

"We may say that by choosing the accelerated system appropriately we can produce a constant gravitational field, reduce one that is given, or annul, intensify or reverse it."

Dealing only with the acceleration of a mathematical point and not with gravitational fields, the system is of a very much simplified nature in comparison with the Principle itself, but that notwithstanding, it will have similar effects on the acceleration of the point, to those described above on gravitational fields.

The unit of the system is a three-dimensional Cartesian co-ordinate frame with its origin the centre of a 40cm diameter sphere.  The rotation of the sphere is used to represent the time co-ordinate.  To use a simple illustration, take two pieces of card, a pencil, a ruler and a drawing pin.  Push the pin upwards through the centre of both pieces of card, the bottom one of which should be larger than the top one, which is roughly circular in shape.  Place the ruler over the smaller piece of card with its ends protruding and tape these to the larger piece. The smaller card is now free to rotate between the larger one and the ruler.  Draw a line with the ruler on the smaller card while rotating it.  The line is curved.  Remove the small card and draw the same line on the large card.  The line is straight.  It is both straight and curved depending on which piece of card one chooses as a base.

In our experiment, the bottom piece of card is one accelerated system, and the top piece , another.  Only from the point of view of the ruler the bottom piece is inert, it has zero acceleration, so it shows a straight line, while the top piece is positively accelerated so it shows a curved line.  It does not matter if the card is turned at a constant speed, the fact that it is not moving uniformly in a straight line means, mechanically speaking, that it is accelerating.  Turn the top piece of card the other way, and it becomes negatively accelerated.  (Which direction we call positive and which negative is quite arbitrary).  A curved line is now drawn freehand on the smaller piece, and it is placed in its former position between the large piece and the ruler.  If the small card is Rotating slowly the line may be traced along the edge of the ruler with the pencil point (the ruler should be as near to the drawing pin as the nearest point on the line).  The system enables us to do this in three-dimensional space and to measure the rotations necessary to produce a given curved line from a given straight line and vice versa.

A detailed description of method is given in a book entitled "Rigid Eels and Wriggling Steel Rods - The Perception of Relative Motion Through Rotating Frames" available from David White.  The titles of prints, also available for purchase, refer to chapter headings, and like the book's title, are derived from a quotation from "The ABC of Relativity" by Bertrand Russell (George Allen & Unwin, London, 1958):

"The point is not that eels are really rigid, but that steel rods really wriggle.  To an observer in just one possible state of motion the eel would appear rigid, while the steel rod would seem to wriggle, just as the eel does to us.  For everybody moving differently both from the observer and ourselves, both the eel and the rod would seem to wriggle.  And there is no saying that one observer is right and another wrong."