Tuesday, July 24, 2012

The Crumple of the Spacetime


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