Why the Grand Relativity Theory?

Our universe, as a system, has multidimensional surroundings. We could imagine it as concentric worlds consisting of 3D [ephemeral] material world at the innermost embedded successively by the infinite number of surrounding [energetic] realms having higher and higher dimensions. The grand relativity theory prevails in all of those worlds except absolute (unlimited dimensional "world").

The grand relativity theory holds that the energy conservation law prevails throughout all those relative worlds. As our 3D-world contains energy, any higher world embedding ours should also contain energy. The concept of nothingness in the sense of "something" devoid of energy is a mere human imagination ^a). The biggest blunder that scientists had ever made was their speculation about something created out of nothing (creatio ex nihilo). The Big Bang is one of such misleading popular products.

What most people mean by the creation is, in fact, the split of something preexisting—an example from the empirical reality of the rubbing of a glass rod with a piece of silk. The two kinds of electrification i.e., the positive charge found on the glass rod and an equal negative charge found on the silk, are not created by friction but are only separated.

This kind of split mechanism is what happened in the grand formations of those relative multidimensional worlds. As the energy of a particular world, say nD-world, splits into its positive and negative parts ^b), an (n-1)D-hypersurface ^c) is formed between the two. This kind of splits (spontaneous symmetry breaking) happened successively from the highest dimensional world to the lowest.

At the lowest level, where the split of 4D-world creates a 3D-hypersurface (our 3D-space), at this particular place, the 4D-energy transformed into 3D-matter ^d). Without such separation, the 4D-world would still have undistinguishable dimensions. In such a world, there could be neither present, past nor the future. It is only after the split that space and time are taking place ^e).

Mainstream physicists have wrongly taken such a world (unsplit spacetime), as representing the real world. No wonder Einstein was uncomfortable as the experience of the Now was beyond the reach of the realm of science. Had he known the cause of the problem, he would reconcile his relativity theory with that of quantum.

Without split, there would be neither space nor matter ^f). Matter can only be created and presents in the 3D-hypersurface, not throughout the whole spacetime. The gravity constant (G), one of the fundamental constants in nature, is a sort of hypersurface‘s "interfacial tension." Therefore, the gravity is acting only across the hypersurface, not out of it as what the brane theory postulates.

Physicists were perplexed when the superstring theory demands the multidimensionality of spacetime. They postulated that the extra-dimensions are curly as they refuted the existence of vast and extended multidimensional worlds beyond our conventional 4D-world. They don't want to believe that such extra-dimensions could be temporal as it would lead them to an extremely complicated situation. Nature, alas, has nothing to do with what physicists presume.

The grand relativity theory, however, is coming to secure the problem. It holds that the relativity of the space and time prevails in all of those worlds. The law of physics is invariant under the transformation of space and time no matter how many dimensions a particular world possesses ^g).

Notes:

a)    The multidimensionality of those worlds is nothing but the geometrical manifestation of a spectrum of energies having a different number of dimensions. This gigantic spectrum of cosmic energies is like a spectrum of lights having different frequencies, forming a colorless white light when in a mixture.

b) The symmetry is not a mere aesthetic aspect of nature but a derivative of the conservation law.  The opposite pairing of every existence in nature is one of its logical consequences. The energy is no exception; it inherently consists of positive and negative energy as the relative energy equation E² = m²c⁴ + p²c² indicates. Surprisingly, most physicists are against such a premise.

c)     In the superstring theory, such a hypersurface is called brane, which could have many dimensions.  Biblical Genesis calls it firmament (raqia in Hebrew) embedded between water above and water below. The term of water in this biblical account, undoubtedly referred to as energy. We should notice, however, that in the real world, no surface (including higher-dimensional hypersurface) configuration has a zero thickness (mathematical surface), which most physicists use in their theory. This oversight leads physicists to many annoyance infinity problems. The minimum thickness that nature allows is 10^-33 cm, the Planck distance, below which space and time have no meaning. It is where the quantum phenomenon mingles with the relativity world.

d) Following the energy equation, E=mc². The interactions between the positive and negative energy across through the hypersurface make such transformation appears as reversible. Matters and the hypersurface they abode are created and annihilated back and forth into energy at the rate equal to the speed of light. This weird phenomenon perpetually occurs at such a short time, and distance makes people perplex when they stumble upon the quantum realm.

e)   Space is the [4D]-time smallest unit, just like a point as the smallest part of a line or a surface as a small part of the space.

f)     There was yet no space where matter could exist, and no time where the dynamic action might occur. It was only after the split of such a chaotic world that the order established. Such as the basic principle of most of the ancient creation of mythology around the globe.

g)   For example, a system consisting of 3D-space embedded in 10D-world has the same physical law as that of 9D-space embedded in the same 10D-world. The latter world model represents better than the former as it is more uncomplicated and more comfortable to be resolved.

Why the Grand Relativity Theory?

The Nature of Reality Revealed

One of the historical misfortunes that put the physics down in trouble was Minkowski's "sudden" death, one year after his important spacetime discovery. He did not have a chance to go after and fixed whichever idea diverged from his own or elaborate his idea that he might not yet express adequately ^a).

The crucial issue that Minkowski did not have a chance to touch was the nature difference of the space and time albeit their complete union. Einstein took charge on it but with an indecisive elucidation¹: "The non-divisibility of the four-dimensional continuum of events does not at all, however, involve the equivalence of the space coordinates with the time coordinate. On the contrary, we must remember that the time coordinate is defined physically wholly differently from the space coordinates".

Einstein certainly knew that any indivisible continuum [no matter how many numbers of its dimensions] should be completely symmetric, homogeneous and isotropic, in the sense that all of its dimensions are equivalent. However, he did not know why in the real world we experience with such different kinds of dimensions such as spatial and temporal. He had no better answer than taking for granted their difference as intrinsic. However, the cost we have to pay for it is too high.

At those days physicists knew nothing about the concept of symmetry breaking that would be developed later on in the quantum theory. The relativity theory has missed this kind of phenomenon which marked the beginning of the world we know today, a mechanism that broke the spacetime dimensions into spatial and temporal.

Ocean of Action, the Aeon

The discovery of quantum, if it were interpreted correctly would make the progress of physics much faster than it is now. Planck was unaware that he had revealed the fundamental nature of reality i.e., the union of energy and time (Et), the 4-dimensional quantum of action.

The spacetime, the union of space and time, that Minkowski had discovered, on the other hand, was merely a geometrical structure of 4-dimensional ocean of quanta. This ocean of temporal energy resembles eon_, a timeless undifferentiated epoch, the name which we propose to adopt ^b). As the current "broken" unit used for quantum does not reflect the inextricability of energy and time, we may use a more natural unit "eon," so that one eon = 6.63 10^-34 joule-second.

Nobody points to Planck discovery as the unification of time and energy as what Minkowski did on space and time. Energy and time are inherently inextricable just as space and time to be. Similarly, the dimensions of the spacetime in its undivided state are in a complete union; all are inherently equivalent, i.e. temporal.

A Series of Symmetry Breakings, the Aeon Split

One of the oft-abused expressions that physicists use is word creation. In the relativistic world there is no creation but separation ^c). Nature tends to break down unity into duality, and duality into plurality ^d). It is the underlying principle of what physicists call spontaneous symmetry breaking.

The beginning that marks any symmetry breaking is relative as such event happens successively in series. The beginning in physics always points to a relative one, even if it is about the beginning of the universe.  The absolute beginning is far away remote in time veiled by layers of worlds of various dimensions came into being in a series through symmetry breakings happened successively.

The symmetry breaking works on the premise that everything exists in pair, either in actuality or potentiality. The case also applies to the eon. Without its opposite partner, the eon will remain sterile. As such, there will be no reaction or interaction and no world "creation."

The eon is primordial, can neither be created nor destroyed.  All changes are just the manifestation of its transformations.  In its primordial state, the eon was extremely unstable as its opposite parts tended to segregate.  As it split apart a boundary (3-dimensional interface) appeared in between the embedding parts, which was much more tenser than the surrounding due to its [interfacial] tension ^e).

Due to its “rigidity” the dimensions along the interface ^f) are no longer equivalent with those of the surrounding. We perceive the former dimensions as spatial and the latter temporal, its original nature, and the interface as the space in which we live.

The Geometry and Reality of Space

The geometrical elements such as point, line, and plane are defined conceptually as having zero, one and two dimensions, respectively. These configurations are only in imagination and utterly different from those in the real world. However, physicists take those geometrical elements for granted for their world model both microscopically and macroscopically.

In real [3-dimensional] world what we call point is, in reality, a 3-dimensional small grainy object, a line is 3-dimensional small cross-section thread-like and plane is 3-dimensional thin surface-like. No wonder, as those elements in the model miss some "thicknesses," physicists are confronted with problems such as singularity or infinity in searching for solutions.

In dealing with the quantum realm where any things are small, one cannot neglect any thickness whatever small it is. The minimum thickness that nature allows is 10^-33cm or equivalent to 10^-44 second, below which everything would just disappear into thin air.  Such case also valid for the interface discussed so far in the sense that its thickness cannot be zero. Its small thickness reflects its brief lifetime, the universal now. The space as a whole and the universal now are two different aspects of the same thing.

At such interface exists only in a short time, the action (Et) is reduced to become [3-dimensional] energy E (Figure-1). It is the underlying quantization procedure in which a crazy looking differentiation to time replaces energy: E = iℏ  ∂/(∂ t).

On top of the interface's thickness other feature that most people overlook is its two-sided surface. As the interface is embedded in the opposite eons, one side that faces the positive eon has positive energy; the other side has negative energy. These opposing energies are the implicit solution of the relativistic energy equation E² = m²c⁴ + p²c². The Cashimir effect experiment demonstrates the existence of negative energy.

As Einstein equation E = mc² indicates, the side having positive energy will become the locus of matter while the opposite side the locus of antimatter. The transformation of energy into matter and vice versa takes place at the pace equal to the speed of light as implicitly indicated by Einstein equation. It is the reason why no matter can move faster than the pace of its perpetual creation.

Grand Cosmos, the Ensemble of Multidimensional Aeons

As mentioned previously there are many worlds of various dimensions as a result of symmetry breaking happened successively. Some recent theories, among other the string theory, support the existence of such multiple worlds indirectly, hence, the existence of eons of various dimensions.

The ensemble of those worlds, the grand cosmos, can be described in term of their respective positive and negative (frequency) eons. At the lowest level, we have 3-dimensional energy (E), at higher levels we have consecutively 4- aeon, Et₁, where t₁ is its corresponding time, 5- aeon (Et₁)t₂, 6- aeon (Et₁t₂)t₃ and so on and ultimately n- aeon (Et₁t₂t₃ …. t_n-1)t_n,  where t₂, t₃…t_n are their corresponding time, respectively.

The ensemble of positive (frequency) aeons:

       F⁺ = Et₁ + Et₁t₂ + Et₁t₂t₃ + ….. Et₁t₂t₃ ... t_n

As those multiverses have their own speed of [multidimensional] light c₁, c₂, c₃ …. c_n, then we may express t_1 = i µ₁ c₁t₁, t₂ = j µ₂ c₁t₁, t₃ = k, … µ₃ c₁t₁… t_n = w µ_nc₁t_1,

where µ_p = c_p / c₁ , the relative speed of the higher-dimensional light, in which

p = 1,2…….n, and  i,j,k…..w are imaginary numbers.

For the sake of simplicity we just write c₁ as c and t₁ as t:

F⁺ = iµ₁cEt + ij (µ₁µ₂) cEt² + ijk (µ₁µ₂µ₃) cEt³ + ….. ijk..w (µ₁µ₂µ ₃ … µ_n) cEtⁿ

F⁺ = a₁ Et + a₂ Et² + a₃ Et³ + ….. a_n Etⁿ

       where

a_{1 =} iµ₁c_, a₂ = ij (µ₁µ₂) c_, a₃ = ijk (µ₁µ₂µ₃) c_, a_n = ijk..w (µ₁µ₂µ ₃ … µ_n) c

Similarly the ensemble of negative (frequency) aeons:

F^- = a _-1 Et^-1 + a _-2Et^-2 + a _-3Et^-3 + ….. a_-n Et^-n

The totality of aeons within the grand cosmos ^g):

       F = F⁺ + E+ F⁺

which is nothing but the formulation of Laurent series.

This representation provides us with a deeper insight into nature.  We may recall that these Laurent series can be holomorphically mapped as Riemann sphere with its respective annulus of convergence (Figure-2). F is expressed as a sum of the positive frequency part (F⁺) which extends holomorphically into the southern hemisphere together with the negative frequency part (F^-) extending holomorphically into the northern hemisphere. The energy (E) as the constant term of F is located at the equator of the Riemann sphere.

This Riemann sphere represents reality faithfully. Its annulus of convergence indicates that nature abhors the singularity and infinity. The Big Bang and the black hole theories which heavily rely on the possible existence of such singularity may be unphysical. Likewise, the universe is forbidden to expand forever to infinity.  In the future, as the world becomes extremely unstable, it would be broken apart … the doomsday.

Notes:

a.    Minkowski concluded²:” We should then have in the world no longer space, but an infinite number of spaces, analogously as there are in three-dimensional space an infinite number of planes. Three-dimensional geometry becomes a chapter in four-dimensional physics…” Physicists seemed at lost as he did not elaborate explicitly whether those spaces may exist simultaneously or potentially. They refute the existence of even a single [universal] space.

To avoid further confusion, I wish to make it clear that all those spaces exist in successive order, in the sense that the individual space appears and disappears one after another successively [at the pace equal to the speed of light]. It is the underlying mechanism of what we perceive as the succession of time.

Now, from a time perspective, we see all things upside down. We say that we have a different space for each moment in time. Penrose defined this "alarming" situation as Galilean spacetime³: “space seems to be of something that evaporates completely as one moment passes, and reappears as a completely different space as the next moment arrives." Nobody knows that this is precisely the reason why the [quantum] world looks so bizarre. It underlies quantum jump and quantum entanglement phenomenon. The former is a kind of inherent micro-teleportation across time while the latter is the mechanism required to avoid chaotic teleportation from one fading space to the next arising space as a whole.

b.    We better use the term 'eon' instead of action to underline the tangibility of this ocean of temporal-energy continuum. What we perceive as fields are nothing but the "surface" manifestations of the 4-dimensional ocean of this immaterial substance. Nature only allows the use of this action modestly and economically.

c.    In a simple ordinary case, when one rubs the glass rod with a piece of silk, the glass rod becomes charged with positive electricity and the silk with a precisely equal negative charge. The friction does not generate but only separate the two kinds of electrification.

d.  The dynamics undergo from simplicity to complexity and from the state of higher order into disorder. The measure of such changes is the entropy of the system.

e.   From an earthly perspective, this tension is equivalent to what we know as the gravitational constant.

f.    It is more convenient to use the concept of a hypersurface, which is an extrinsic concept of the world as a system together with the surrounding rather than hyperspace which is an intrinsic view covering only the system.

The brane theory also adopts the concept of the hypersurface but in the wrong design. The dimensions along the brane should be a strictly spatial while off the brane temporal. Another hint to fix the theory is that the graviton should not allow floating off the brane; otherwise, the brane will be broken apart.

g.  This expression clearly shows that time is intrinsically multidimensional. The extra dimensions are invisible because they are temporal. We used to see the world upside down. Time dimensions are more fundamental than space dimensions. Space, no matter their dimensions, is incidental and ephemeral.

Physicists, like anybody else, used to consider that time is unique. They believe that there can be only the same time dimension prevails in the universe and anywhere beyond. Moreover, physicists hold that all spatial dimensions other than the ordinary three should be curled-up into tiny loops; hence, their invisibility. It leads us to exceedingly complex formulations with its many possible solutions.

References:

1.  Einstein, A.:" The Meaning of Relativity," Princeton University Press, New Jersey, 1954, p. 31.

2.  Einstein, A. et al.:” The Principle of Relativity,” Dover Publication, Inc., New York, 1952, p. 79-80.

3.    Penrose, R.:" The Road to Reality,"  Vintage Books, London, 2005, p. 387.Bottom of Form

The Nature of Reality Revealed

Multiple Time Dimensions, why not?

One of the biggest misconceptions deep-rooted in the human mind is the one-dimensionality of time. When physicists discover a theory that calls for multiple extra dimensions, such as the string theory, their first reaction is to assign those extra as spatial dimensions. They do so because they abhor the plurality of time ^a).

In order to give the reason for their invisibility, the physicists hypothesize that the extra dimensions are curled up into tiny loops ^b). However, as there are so many possibilities on how those extra-dimensions may be curled up, the outcomes of such string theory can reach billions.  It gives us a good reason to allow the Occam razor getting rid of this dire hypothesis without delay.

Internal symmetry

The second reason for the invisibility of the extra-dimensions is that they are time dimensions. A world with multiple space and time dimensions certainly complies with the principle of the relativity. We would have in our worlds no more bizarre things such as donut-like or Calabi-Yau tiny manifolds. As such, the world may preserve its internal symmetry in which changing [reversibly] the time dimension with the space dimension leaves the physical laws identical. 

It is evident that the physical laws' formulation in the world with many time dimensions would be exceedingly complicated. However, we may have a more natural way to solve the formulation by transforming all but one time dimensions into space dimensions. Having done that,  we get a simple system of higher-dimensional space with only one temporal dimension without altering the outcome of the result. 

To give an illustration, let us take the example of our space (or 3-brane as you wish ^c)) which we interpret as embedded in a 10-ambient spacetime. Under multiple time dimensions framework, such a system consists of three space dimensions and seven temporal dimensions. By transforming all temporal dimensions  (except the highest dimensional one) into space dimensions, we get a system having nine space dimensions and one temporal dimension  (a 9-brane embedded in the same 10-ambient spacetime). The physical laws' formulation in the latter system is much simpler than that in the first one ^d).

Under such a system we can also transform only some of the time dimensions into space dimensions and keep the remaining intact. As such, we would have various dimensional branes ranging from 3-brane to 9-brane embedding in the same 10-ambient spacetime without even changing the outcome of the result. 

These are the various dimensional branes which we encounter in the superstring theory. However, in most of the cases, each of those branes is assumed to have only one temporal dimension. As such, the physicists who deal with those branes have not any simple way to solve the respective formulation ^e). 

Even in dealing with the 9-brane, we may have no good solution. We may, in this case, extend the dimensions of the ambient spacetime higher and higher until we get the solution ^f). 

We may say that the higher the brane's dimensions are, the flatter it is.  This situation makes the mathematical formulation of the physical laws simpler.

Figure-1 diagrammatically shows how events which are not simultaneous at a particular time dimension t₁ become simultaneous at a higher time dimension t₂. It is as though space flatten out as the number of temporal dimensions becomes higher that makes the physical laws formulation more straightforward ^g).

Notes:

a)   Physicists wrongly regard the 4-spacetime as having three space dimensions and one temporal dimension which should be inherently multidimensional. The underlying of what we know as 4-spacetime is 4-dimensional time having a 3-dimensional cross-section (3-brane) in it.

b)   Kaluza and Klein first introduced Kaluzathe idea to unify the electromagnetic field with that of gravity by adding the curly fifth dimension to the classical four. Later on, the idea is extended for much higher dimensions in which the loop size of the extra dimensions is at the order of Planck size (10^-33 cm).

c)  We use the notations of space, hypersurface, hyper-interface or brane interchangeably.

d)   A system consisting of 3-space embedded in 10-dimensional ambient spacetime can be formulated as Hypercomplex function:

q = x₁ +x₂ + x₃ + ic₁t₁ + jc₂t₂ + kc₃t₃ +lc₄t₄ + mc₅t₅ + nc₆t₆ + oc₇t₇ 

under a coordinate patch consisting of three real x₁, x₂, x₃ and i, j, k, l, m, n, and o as independent imaginary numbers as the basis coordinate representing seven different time dimensions, c_i is the speed of light of the respective temporal dimensions t_i .

It is identical to Octonion :  

q = x + ic₁t₁ + jc₂t₂ + kc₃t₃ +lc₄t₄ + mc₅t₅ + nc₆t₆ + oc₇t₇ 

where x = x(x₁ , x₂ , x₃)

The physical laws prevailing in such a system would be extremely complicated. Under the internal symmetry, we can make it much simpler by changing the extra time dimensions into spatial ones transforming the system to get a system consisting of 9-space embedded in 10-dimensional ambient spacetime.

Its mathematical formulation then becomes a simple ordinary complex number:

q = x₁ +x₂ + x₃ + x₄ +x₅ + x₆ + x₇ + x₈ + x₉+ oc₇t₇

Denoting x = x (x₁, … x₉), we get a simple form:

q = x + oc₇t₇

e)   For example, if we have a system consisting of 6-brane embedded in 10-ambient spacetime (a system with 6 space dimensions and 4 time dimensions): 

q = x₁ +x₂ + x₃ + x₄ +x₅ + x₆ +lc₄t₄ + mc₅t₅ + nc₆t₆ + oc₇t₇ 

Usually we consider such a system having only one time dimension and disregard the other three: 

q = x₁ +x₂ + x₃ + x₄ +x₅ + x₆ +lc₄t₄ 

the solution of this formulation would be the only approximation of the former.

f)   The dimensions of macro-cosmos are assumed to be [quasi] infinite. It happened that we need only an ambient spacetime having 11 dimensions embedding a 10-brane  as in the case of supergravity theory.

g)   In such a diagram, simultaneous events would flatten their loci, an n-surface (hyperinterface, brane) embedded in (n+1) ambient spacetime; otherwise, the surface would not be flat. Figure-1B shows events which happen simultaneously at a certain time dimension t₂ while they do not happen simultaneously at a lower time dimension t₁ (Figure-1A).

Multiple Time Dimensions, why not?

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.

The Brane Theory as It should be