The brane theory is the
derivative of the string theory, a mathematical model which was built to
simulate the empirical particle interactions. The theory holds on the premise
that the most basic indivisible objects underlying all matter are tiny
vibrating segments or loops of the one-dimensional string-like entity.
In its later development,
string theorists discovered that the strings do not freely move throughout the
whole spacetime continuum but are constrained along the surface of
membrane-like objects, coined as "branes," whose dimensions may
extend over some, but not all of their embedding space's dimensions.
The branes are not just
loci of matters and forces interactions, but also real objects which can be
slack, wiggling and moving, or stretched tight. Branes are distinguished not
only by the number of their dimensions in which they extend but also by their
charges, their shape and tension1.
Despite the development
intensity of the theory, the brane theorists are not yet to know whether their
branes exist in the real world. They are like a blind man wondering about the
big picture of the elephant after having felt the ear and the trunk of such
animal.
1.
The spontaneously symmetry breaking
of the spacetime
The brane theory proves
that the spacetime world model as currently conceptualized is wrong. It is the
existence of a 3-brane embedded in such spacetime that makes the latter's
dimensions differentiated. Otherwise, the spacetime's dimensions are equal, in
the sense that the spacetime is perfectly symmetric, homogeneous and isotropic a).
Paradoxically, as Lisa
Randall remarked, many physicists think otherwise2:" They did
not want to include branes in a physical realization of string theory because
brane violated their intuition that all dimensions are created equal. Brane
distinguishes certain dimensions – those along the brane are different from
those that extend off it – whereas the known laws of physics treat all
directions the same. Why should string theory be different?”
In fact, following the
Minkowski’s discovery [1908] on the inextricability of the space and time,
physicists have confusedly taken for granted the inequality of the dimensions
of the spacetime, the union of the space and time3. They thought
that the light cone system set up in every point within such spacetime could
establish order and preserve the causality.
The special relativity, as
currently conceptualized, is inconclusive. In order to explain the inequality of such
continuum's dimensions, the physicists should include in their world creation
scenario the spacetime's spontaneous broken symmetry. As it happens, the
3-brane comes into being in between the two spacetime's distinct halves, in
which the dimensions along the brane become spatial and those off it temporal
dimensions.
It is just like the
separation of oil and water which we can observe in our daily [3-dimensional
ambient] life b). The dimensions along the
interface, because of the effect of the interfacial tension, would be different
from those off it.
The gravity constant (G)
that we are familiar with is nothing but the interfacial tension of the 3-brane
embedded in 4-spacetime. Consequently, the gravity field like the other
classical fields is trapped along the brane, not propagate off it as what the
brane theory currently assumes c). The fields
that may propagate off the brane are quantum fields including those of Higgs.
2.
Why a brane traps matter
and classical fields?
Randall took for the
analogy of trapping matter on a brane among other things water droplets on a
shower curtain which travel only along the curtain's surface.
We wish here to provide a
better and physically more appropriate analogy for describing the braneworld
model. Matters are analogous to tiny flashes appearing and disappearing on the
surface of a giant TV-screen. The impact
of streams of electrons fired onto and hit the screen resulting in the generation
of these tiny flashes.
The seemingly trapped
matters on the brane are tiny sparks appear and disappear on the TV screen-like
brane. These tiny sparks, which are quantum in sized),
are generated as the effect of the quantum fields (Higgs fields) hitting in the
normal direction through the brane.
The quantum fields are themselves generated as the result of the constant interplay between the positive and negative energies located at the opposite sides of the brane (Figure-1A). As the quantum fields piercing through the brane, the classical fields including those of light are generated, under the right-hand rule, propagating along the surface of the brane (Figure-1B).
3.
Why there exist various
dimensional branes?
So far we have shown that
the special relativity theory ultimately leads us to the union of the spacetime
and energy. The spacetime has faded away into a mere shadow to become
just the geometry of the energy, the only independent reality in nature.
Some
physical theories identify the existence of higher dimensional manifolds
(spacetimes). It leads us to the conclusion that energies of higher dimensions
corresponding to such spacetimes should exist as well.
The splits of those
spacetimes are taking place starting from the highest dimensional spacetime
down to the lowest one, which is nothing but our universe, the 3-brane
(Figures-2 and 3).
We may imagine an interface of oil and water as a
2-dimensional slice of a 3-dimensional liquid, similarly, a 3-brane as 3-slice
of 4-dimensional spacetime, 4-brane as a 4- slice of 5-spacetime and so on. We
should underline that the dimensions along the brane are always spatial and off
the brane temporal, and never mix them up e).
4.
Why the branes exist in a
pair?
The brane theory includes
the existence of two parallel branes bind higher-dimensional worlds such as
Horava-Witten and Randall-Sundrum brane-worlds. In such world models, the
standard model particles are constrained on one brane, and non-standard
particles are sequestered on the other branes.
Why does such a pair of
parallel branes exist?
A brane, like a piece of
paper, has a very thin thickness and two opposite sides. The two parallel
branes that the physicists refer to are not independent of each other but just
two different sides of a single brane.
This kind of brane world-model can be extended merely to the higher dimensional world. Within the 4-spacetime framework, the distance between these two sides of brane might be equal to Planck distance of 10-33 cm (10-44 second), and it would be much more significant in a higher dimensional spacetime.
5.
Why 10- or
higher-dimensional branes exist in nature?
The brane theory consists
of two theories of10- and 11-manifold. To explain why such duality may arise,
we have to refer to the mathematical concept of hypersurface whose geometry is
equivalent to that of the brane. We define a hypersurface as a
multi-dimensional surface having one or more dimensions lower than those of the
embedding space.
A rule dictates that an n-dimensional
curved hypersurface does have a solution if and only if it is embedded in an
ambient space having at least ½ n(n+1)-dimensions4. Accordingly, a
4-brane (spacetime) requires an ambient space containing at least ten
dimensions. It seems that the 11-ambient
space provides enough room for such a world model has a solution than the
10-ambient space does.
Notes:
a. In the ancient cosmology,
the condition where the spacetime's dimensions are still equivalent, in the
sense that the time is not yet divided (there is no present, past and future),
is termed as chaos and the spacetime 'eon.'
b.
Surprisingly, this kind of
analogy had been proposed a long time ago, since the dawn of the history, by
Enmeduranki, the king of Sippar, Babylon, who lived and reigned before the
Flood5
c. As the graviton is a
close-loop string having no ends, the whole parts of its length are pinned down
on the brane, on the contrary of what happened in the brane theory.
d. We guess it is more
appropriate to use the term of quark as the acronym of quantum spark, the
underlying nature of the fundamental particles, not limited to those which
compose the nucleons.
e. It may lead to the
establishment of multidimensional times theory which is naturally more
appropriate than one-dimensional time.
References:
1. Randall, L.: "Warped Passages," Harper, New
York, 2006, p. 305-306.
2. Idem, p. 307
3. Einstein, Albert: The Meaning of Relativity, Princeton
University Press, New Jersey, Fifth Edition, 1954, p. 31
4. Sokolnikoff, L.S: "Tensor Analysis," Wiley
Toppan, Second Edition, New York, 1964, p.205
5. Wright, J.E.: The Early History of Heaven, Oxford
University Press, Oxford, 2000, p. 43.
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