The General Relativity theory was
developed based on the premise that the gravity force is the manifestation of
the 4D-spacetime curvature a). This physical concept was derived
from Riemann’s idea1 that the force was nothing but a consequence of
geometry, thus, banished Newton’s unnatural concept of “action-at-a-distance”.
However, Einstein mindset was to
stick with intrinsic geometry in the sense that the spacetime as a system was
regarded as having no surroundings or being embedded in nothingness b).
In fact, when physicists talk about the wrinkle of the [4D-] spacetime they
never care about which directions (dimensions) it wrinkles goes.
The strict concept of the geometry
dictates otherwise 2. The geometry concept of m-metric manifolds
(hyperspaces) c) is a straightforward generalization of ideas of the
study of surfaces embedded in 3D-space. However, it has been proven that in the
circumstances in which an m-dimensional curved hypersurface can be embedded in
the n-dimensional [Euclidean] d) manifold if at least n = ½ m(m +
1).
The crumple of the ordinary
2D-surface, a piece of paper, for example, requires a third dimension
(3D-ambient space) for it to occur. But hardly anybody is aware that the
crumple of 3D-space requires not only a fourth dimension but at least 3
additional dimensions (6D-ambient spacetime) e). Similarly, the
crumple of 4D-spacetime would require at least 10D-ambient spacetime for it to
occur without constraint in any direction (Figure-1). Does the nothingness have
such properties for being able to embed something? What is nothingness anyway?
Nobody should blame Einstein on this
negligence. People were just horrified about the idea of 4D-spacetime which had
been introduced by Minkowski beforehand, not mention the 10D-spacetime. Had
Einstein been aware of this higher dimensional surrounding requirement he would
probably still prefer to take the surrounding as nothingness rather than 10D-ambient
spacetime.
A more recent theory such as that of
superstring requires 10D-ambient spacetime f) for its equations to
be solvable. Alas, being uncomfortable with such bizarre vast extension g)
of the ambient spacetime, physicists blow down h) the majestic
surroundings assuming the extra dimensions being curled leaving the ordinary 4
dimensions to remain intact.
Even after the superstring theory
was established, Big Bang theory as the cosmological application of the General
Relativity theory maintains its premise on the nothingness instead of
10D-ambient spacetime taken as the surrounding of the expanding 4D-spacetime.
As such, Big Bang theory misses a bigger part of the “stage” that in no way it
can explain the substantial missing dark matter and dark energy.
Having many defects in its premise
Big Bang theory would eventually fall short except it takes among other the
10D-ambient spacetime as the surrounding of the universe (4D-spacetime) instead
of nothingness.
Notes:
a) Arthur Eddington expedition carried out to South Africa during the solar
eclipse in 1919 verified the shifting of the position of a star within the
field near the sun, thus, proving Einstein's general relativity prediction of
the bending of light around a massive object.
b) There is a vague definition of
absolute nothingness or emptiness but we may guess that what most physicists
mean by it is a sort of extension (spacetime) with an indefinite number of
dimensions [zero or infinite dimensions?] having neither matter nor energy.
c)
The notation of n-spacetime is
equivalent to n-hyperspace or n-hypersurface.
d)
This is the reason why the laws of
nature look simpler in higher dimensions. If the dimensions of the surrounding
spacetime are high enough then we might have a flat (Euclidean) surrounding
where the physical laws become simpler.
e) We may speculate that the existence
of three generations of particles is the manifestation of 4D, 5D and
6D-particles abiding in the respective 4D, 5D and 6D-spacetime. The
manifestation of the last two generations into our world could be only the
cross-section of their whole body.
f) The string theory accidentally
derived the 10 dimensions mathematical requirement from Beta function
originally dedicated to solving the strong force quest. The coincidence with
the 10 dimensions geometrical requirement of the ambient spacetime embedding
the 4D-spacetime is stupendous.
g)
Since they are not visible, the
string theorists regard the extra-dimensions as spatial and being curled into
tiny loops.
h) Physicists assume that the
10D-ambient spacetime splits into a 4D-spacetime and a tiny curly 6D-metric
manifold. This premise doesn't absolutely make sense just like the
impossibility of splitting a 3D-cube into one 2D-plane and one 1D-line. The
proper way to do it is successively splitting the 10D in two creating 9D as
their interface and so forth down to 4D which we get as the interface of the
two halves of the 5D split. We would, then, have a total of 7 spacetimes
embedding each other in descending order of their dimensions.
