The Brane Theory as It should be

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 size^d), 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 energy in itself inherently consists of a pair of positive and negative components. As the opposing energy components tend to segregate, all of those spacetimes are highly unstable. The segregation of the positive and negative energies causes the spacetime to split in two, creating a brane in between.

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.

As one side of the brane faces positive energy, and the other side faces the negative energy, the two brane's sides have accordingly opposite charges (Figure-4). For example, under a 4-ambient space, the positive side of the 3-brane contains matters while the negative side sequesters antimatters. 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.