Schwarzschild Metric in Snow Globe Theory
Consider the change (Q) in the scales of space and time from a large radius, at a point closer to the central star.
For time, Qt = 1+T/R, T = M·G/c² (=rs/2), and for radius,
Qr = 1/(1+T/R). Along a spherical shell, the scales do not change.
If one now wants to describe the path of light at these changed scales, the light path is the integral of the inverse of the change. This would give the light in spacetime with its original scales. The Euclidean path is described by ds² = dx² + dy² + dz².
However, for a path of light in this spacetime, the four-metric, called the Minkowski metric, applies.
With dtLight = 1/Qt ·dt* and drLight = 1/Qr ·dr und Kugelkoordinaten, one obtains
the Schwarzschild metric with the "snow globe potential".
The Schwarzschild metric provides an approximation of the gravity, as seen from the large radius, of a central star. Within the solar system, this metric, using the "snow globe potential",
agrees with the solution found by Schwarzschild to such an extent (10-11),
that the measurement accuracy presumably does not yield any deviation. The Schwarzschild metric is not a constant metric,
but depends on the radius under consideration..
According to the "snow globe theory", it doesn't matter which starting point one uses.
However, it is computationally expedient to consider everything from the maximum longitude scale—that is, from the stellar coordinate system.
This way, every point receives a scale factor, even if it is in the local system. Otherwise, one would also have to consider longitude magnification and time compression.
* Understandable for the distance, but for the time?
Time is indeed lengthened in the shortened space. However, if the relative speed of light c/(1+T/R)²,
is taken into account, the lengthening is reduced, and the inverse remains: c·dtLicht = c/(1+T/R) ·dt.
The factor of the relative speed of light is also the "snow globe potential".
1/(1+T/R)² ("Snow globe potential": change in distance scale / change in time scale).
Ludwig Resch
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