Monday, June 28, 2010

Multidimensional Reality (Part I)

The mathematicians used to say that there is no branch of science in which the tyranny of authority has been felt more strongly than in geometry1. We would instead say that this statement is no longer valid but in physics. The relativity theory under the giant name as of Einstein together with its derivative, the Big Bang, dominated the thought and shaped the development of physics and cosmology for around one hundred years up to now.

However, its endless conflict with quantum mechanics has put the physics in crisis as we see today. There were a few brave physicists to whom the relativity theory did not seem convincing, but the hands of authority were so heavy that it is almost impossible to put forward their different ideas to fix up the theory. Notwithstanding, let us scrutinize the fundamental concepts of the relativity theory aimed at improving the theory in concordance with quantum mechanics.

Spacetime as the Geometrical Quality of Energy

The special relativity theory deals with an idealized four-dimensional spacetime whose energy hidden behind the scene. As such, everything is in rest or steady motion forever. There is no force or friction which might accelerate or decelerate the motion. Even gravity is abhorred to exist. Such a world should be completely flat. In this particular circumstance, because of the energy's passive role, the spacetime appears as though it is an independent reality.

The general relativity theory, on the other hand, deals with a more real-world whose energy is lively on the go. The spacetime can be no longer flat but somewhat curved here and there due to the effect of gravity and forces exerting in those particular parts. The spacetime is not independent of energy. 

The spacetime is not like a container and energy something that fills the container. The energy and spacetime are respectively more like water substance and the spherical form in a drop of water. Undeniably, the spacetime by itself does not have the existence on its own; it fades away into shadow to become merely the geometrical quality of the energy. Einstein2 has inaccurately interpreted that the spacetime was the geometrical quality of the fields instead of energy.

Geometrical Intrinsic View of the General Relativity Theory

The fault of the relativity theory is that it treats the spacetime's geometry properties intrinsically, without due reference to the surroundings in which the spacetime might be embedded. It ignores the majority part of the reality: the surrounding. Take, for example, Einstein's metric tensor, wh Intrinsically, this tensor is mathematically explained as a function of ten independent variables without further explanation about what these variables physically could be.

As we may recall, a curved m-dimensional spacetime (m-hypersurface) can only be embedded in the n-dimensional [Euclidean] manifold if the embedding manifold has at least n = ½ m (m+1) dimensions. We know that a curved two-dimensional surface can be easily embedded in three-dimensional space, but a curved three-dimensional space can only be freely (no constraint in any direction) embedded in a hyperspace if and only if the latter has six dimensions. Had the embedding hyperspace been four-dimensional, space would be completely flat.

A further generalization is straightforward. A curved four-dimensional spacetime requires at least 10-dimensional surrounding hyperspace, and so on up to infinity, the Absolute realm, whose surrounding has no meaning. Only then, we can talk about a system without surrounding, not the one which the general relativity assumes. Even when the general relativity assumes that the spacetime's surrounding is an absolute void, the following question naturally arises: how many dimensions the void has for it could embed the four-dimensional spacetime? Are they none, ten, infinite or else?

You know now that even long before physicists formulated the string theory, the general relativity theory has tacitly demonstrated that the reality was at least ten-dimensional, which the theory has, alas, overlooked it. However, the so-called "extra" dimensions are well extended, not curled into tiny loops such as prematurely hypothesized in the string theory. How come, then, we cannot see those extra dimensions? The bold answer is that those extra dimensions are temporal. To everybody's amazement, time is indeed multidimensional.


(to be continued)


References:

1.     Sokolnikoff, L.S.: "Tensor Analysis," John Wiley & Sons, Inc., Second Edition, New York, 1964
2.  Einstein, Albert: "The Meaning of Relativity," Princeton University Press, Fifth Edition, Princeton, N.J. 1954.

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