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 We would instead say that this statement is no
longer valid but in physics.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.
