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Section 2 showed that the velocity vector of a falling particle begins to
rotate in 5D under the influence of a gravity field or curved space. When an
object is in rest,
this vector has magnitude c in the proper time dimension. When
falling begins, it initially rotates towards space (hence it's acceleration in
space), and finally, with increasing strength of the gravity field, it gains and
additional rotation towards the 5th dimension.
When a falling object hits the surface of a planet that it falls to, the rotation of
its velocity vector in 5D stops and it resumes its velocity c in
the proper time dimension in a
straight path in 5D. At least that is what is observed in a flat coordinate
system by an observer at infinity. In
Riemannian geometry however the geodesic path of the
freely falling object is a straight path. That means that from the perspective of a geodesic rest frame of a
continuously co-falling observer it is the 5D path of the object in rest on the surface of the planet
that is curved and, as a consequence of this, that object must sense a
(gravitational) acceleration according to the observer. During it's free fall
the object feels
no acceleration, since it is following a straight path in 5D with constant speed
c.
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Observed 4D path of a falling
object: from geodesic rest frame
and from flat coordinate space |
The difference in the shape of the observed paths is visualized in the picture
on the right. Here an approximation in 4D space-time is chosen
(sufficiently accurate in the neighborhood of ordinary planets) and the
curvatures are exaggerated. The object's speed is always c in 4D
space-time and only its direction rotates (take note of the labels of the
space-time axes!).
The example shows that, in a flat 3D coordinate system, an observer at infinity is indirectly able to
perceive the curvature of
space-time in the neighborhood of the planet because he observes the acceleration
of a falling object. If our universe is closed, its 4D space-time must be
curved on cosmological scale as well (and closed in the 5th dimension). Common
sense then says that the observer should see the same effect of that
curvature as he did near the planet, i.e., objects in the far distance of the
universe should show velocity and acceleration in his flat 3D
coordinate space. The observer will interpret this as an expanding universe in flat 3D coordinates while the
rate of this expansion is accelerating.
This is indeed what is observed empirically today, but it is traditionally
explained as a physically expanding universe.
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A mass particle cycling the universe
via a black hole |
Extending the considerations from section 1, where we closed 3D and 4D worlds,
we could now speculate that the "edge" of the universe is in fact the "inside"
of all black holes together, thus closing the circle in 5D. The universe then
resembles a 5D, multi-hole torus, or n-torus. It means that whatever falls into a black hole will
appear again instantly at the edge of the universe in a similar way as photons
that are absorbed by charges appear instantly as spontaneously emitted photons
by opposite charges (as explained in section 1). It defines the edge of
the universe as a gigantic "white hole" which should therefore radiate
energy (cosmic background radiation?). The "black-hole /
edge-of-universe" combinations on its turn form the conserved charges
(fermions) of gravity while mass particles (=energy) represent gravity's bosons
(see Section 4 in [2] ).
In the next section, this principle will be generalized across multiple
dimensions and types of particles.
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