Vacuum Physics

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On the Kinematic Properties of the Vacuum in Two Dimensions

This paper demonstrates the fundamental mechanism that, in its absence, is responsible for the existence of the many none intuitive arguments extending back to the time of Poincare, Lorentz and Einstein.

Inertia and the Mechanism

Inertia as qualified for all classical functions in respect to all known classically derived actions and interactions. In as far as, the exchange principle is defined in the absence of a direct fundamental exchange process.

The Emergence of Gyroscopic Spherical Curves

The images on this page have been taken from a paper (1988) relating to research work carried out by the author some years prior to the above date.

Images

Commuting Pair View Large Image

The illustration shows one example of a pair of commuting radial points marked by (+/-), each (point) potential following an identical cycloid curve, demonstrating a 180 degree phase shift with a changing 'sign' through each half cycle. The accompanying two catacaustics (one shown) of both commuting cycloids represents the line the fulcrum of the Exchange Lever follows.

Trapezium Linkage View Large Image

This trapezium linkage with their two-fixed axis, demonstrates the cyclical nature where if each end continues around their respective circles the sign will change for the second half cycle (not shown) creating an alternating period. This is one example of an exchange from maximum value to a minimum. The minimum, in this case, always being a value greater than Zero.

Deltoid and Cusp View Large Image

The Exchange lever's dimensional mid-point for the Deltoid and Cusp configuration moves in a circular orbital curve while the null-point world-line traces out a deltoid. The Generation of the Epicycloids and the inner Epitrochoids forms two independent shells when particular energy levels are taken from the perimeter of a rolling wheel having equal diameters which are taken as fractional multiples of the exchange lever's length.

Atroid and Cusp View Large Image

The exchange between two oppositely situated cusps in the above configuration involves the superposition of two Astroid and Cusp configurations set at 45 degrees to each other where a single configuration with an Astroid and Cusp is none commutative, unlike an odd numbered geometry that commutes between its own Epicycloids. This even-numbered combination produces an eight-point star hypocycloid doubling as an Exchange Lever's null-point world line.

The Trammel of Archimedes View Large Image

The Trammel of Archimedes exhibits the fulcrum world line in the guise of an Astroid and the lever, giving the ratio of sides for Pythagoras for this special case of Commuting Simple Harmonic Motion connects the two orthogonal lines x, y.

Propogating Trammel View Large Image

For photon propagation the Trammel would have a third dimensional translational motion added to its function achieving yet again a combined commutative value of: 0.

Applets

Commuting Pairs View Applet

An animation demonstrating the commuting pair of quantum points.

The Trammel of Archimedes View Applet

An animation demonstrating the trammel as a commuting exchange.

Trapezium View Applet

An animation demonstrating the commuting trapezium.