Pedestrian Physics 12

A Fairy Tale

Once upon a time, in a formless void, two immense globs of energy collided. When the dust had settled after their mutual destruction, a vorpal had been created. At the center was a ball of anti-mass, separated from a capsule of mass. Pressure, f₀, compacted the center and pushed the shell outward, preventing implosion. Mass and anti-mass, on the other hand, had a mutual attraction,f₁, that prevented explosion. The expansion stopped when this force and the pressure were in balance.

This is a fairy tale; I do not have to explain how this would work. The sole purpose is to demonstrate that some geometric model may explain gravitational attraction as a pseudo-force and thus permit Newton’s law to co-exist with Einstein’s axiom.

The distance between any two points on the surface is measured along the great circle between them:
s = Rß,
where ß is the central angle. If the separation is large, the chord will be the relevant definition of s:
s = 2R*sin(ß/2)

The “surface” tension, γ, is defined by the work needed to increase the volume of the surface:
γdV ≈ f₀dR
f₀ is treated as a constant:
γdV = γ(96π²(R²)/17)dR ≈f₀dR
The surface tension is:
γ=17f₀/(962(R²))=f₀*1.84*10^-3/R²

The γ- vector is tangential. In the vorpal model it is the equivalent of the universal gravitational constant in a flat universe.

Distance, x, is defined by the central angle, ß, and the diameter, 2R, either as the length of the chord, or as the length of the circle segment.

In the first case Newton’s law reads
F = γ*sqrt(1-(x/2R)²))/x² (x is a straight line)
In the second case
F = γ/x² (x is a curve)
For practical purposes, on the local level, the distinctions are irrelevant. By ‘local’, I mean our entire galaxy and surroundings, including local galaxies and maybe half he vorpal shell.

This graph illustrates the distinction between the two definitions.

The vorpal chord curve ends at the value of he vorpal diameter.
The Newton curve continues forever in a flat universe.
The vorpal surface curve ends with a small but finite value when ß = π.

For now, the exercise has served its purpose. Given the liberty to pick and choose premises at will, one can define models where gravitation does not depend on the existence of mutual force fields. In the present case, it is not a mutual attraction but the shared tendency to seek towards the center that gives the appearance of a gravitational force.

For a model to have merit, it must be consistent with other, unrelated observations on events in the universe. For the vorpal model to pass this test, it is necessary to revisit the fundamental premises of the current model.