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.
References:
1.
Kaku, M.:” Hyperspace”.Anchor
Books," Doubleday, New York, 1994, p. 36 – 42.
2.
Sokolnikoff, L.S.: "Tensor
Analysis,"John Willey & Sons, Inc., New York, 1964, p. 202 – 205
