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Local in the "snow globe theory" means on location. Local with respect to an object means that this object has neither momentum nor velocity.
In the system that is local to me, the sun orbits the Earth every day.
Suppose two massive objects moving toward me from opposite directions at more than half the speed of light.
After passing me, they move away from me. I see them moving apart at (seemingly) superluminal speed.
However, if one assumes the system of one of these objects to be local, the addition theorem of STR applies.
The other object in this system is moving away only at a speed slower than that of light.
The expansion of length is relative:
Imagine you are a meson created by cosmic radiation and have only a short time left to live.
If you observed the world passing by, you would only see a short section that is actually much longer.
The world therefore appears compressed like a pancake.
If the "snow globe law" is written as length scale times time scale is constant,
then the potentials cancel out in the product dtˇdr.
Locally, one obtains the Minkowski metric* instead of the Schwarzschild metric.
In a small neighborhood of a local point, pseudo-Euclidean space approximately prevails.
In "snow globe theory," the Schwarzschild metric is thus a non-local metric.
In the solar system, the "snow globe potential" differs only slightly from the Schwarzschild potential.
Measurement-wise, no difference could be detected. It results from the "snow globe theory" for the maximum length scale.
Therefore, the scale changes can be approximated differentially-geometrically, for example, with Einstein spaces in gravity.
They then only apply to an observer's rest frame. The deformation of the viewing cone would have to be factored out.
Since local points show no curvature, such a space always begins with a flat point in the rest frame.
*In a one-body system, the Minkowski metric is only valid on a spherical shell. Otherwise, nonlocal scale changes occur.
Ludwig Resch
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