Superstring Theory and the Seven Heavens

The superstring theory indicates for the first time the existence of multidimensional universes. It is supposed to be able to provide a comprehensive explanation of all known physical phenomena and answers the questions that the Big Bang theory cannot do: What happened before the creation (Big Bang)? Why did the universe explode?

 According to the superstring theory the universe initially existed in ten dimensions. However, because the ten-dimensional universe was unstable ^a), it creaked into two pieces, i.e. a four- and a six-dimensional universe ¹. The ordinary four dimensions well extended while the other six extra dimensions shrunk and curled to an incredibly small size (10^-33 cm), the reason why humans can not reach it.

Most physicists have deeply penetrated the mathematical aspect of the theory, but when come to translate it into physical reality it happened that they did it very lightly and carelessly. How come that a ten-dimensional body can be split in two to get a four- and a six-dimensional body? Surprisingly, nobody challenges and fixes such a bizarre idea. The perturbation theory, or whatever theory it is, would certainly fail to break a ten-dimensional body down to a four- and a six-dimensional body.

Let take an example of a three-dimensional body, say a cube of cheese. If we split it in two, indeed we did not get a thin piece of cheese and a fiber-like cheese (Figure-1A). In order to get a fiber-like form, we should make a series of slices; the first slices produce thin pieces of cheese, and the subsequent slices produce fibers of cheese (Figure-1B).

Now, how do we get a four-dimensional universe from the original ten-dimensional one? As the string theory postulated, the original ten-dimensional universe was so unstable that it broke in two parts. However, instead of creating one four- and one six-dimensional universe, a nine-dimensional universe was created in between the two separated parts of the original universe ^b). A series of subsequent splits took place successively in a similar way from higher down to the lower-dimensional universe.

In the end, we have a total of seven universes ^c), the one embedding the other in a successive lowering order of their dimensions.  As such, there is a ten-dimensional universe at the outermost embedding nine-dimensional one, the later embedding eight-dimensional one and so forth. At the end of the series we get the four-dimensional universe embedding a rotating ephemeral three-dimensional space, where we live in, perpetually appearing and disappearing across it (Figure-2) ^d).

Each universe contains the qualities and interactions of the one above, so that each descending level of the universe is in turn under more laws, more complex, and having much more varieties of kinds of stuff. It is the underlying purpose of the grand unification which hardly any physicist is aware. Regressing such cosmic creation process to the original condition of the ten-dimensional universe would give us a much simple physical law with fewer quantum kinds of stuff in it ^e).

Why, then, we cannot directly experience these extra higher-dimensional worlds? Just because the extra dimensions are temporal, not curly spatial dimensions as what the superstring theory hypothesizes. Each universe has its owned light ^f) with its corresponding speed (c_i), Planck constant (h_i) and gravity constant (G_i), depending on the degree of its dimensions.

The brane theory, as the extension of the superstring theory, should be adjusted accordingly. We better regard a brane as an interface lies between two [liquid-like] bodies, instead of a piece of paper floating in thin air. The brane’s dimensions which extend along its surface are spatial and off of it temporal.

The gravity fields propagate along the surface of the brane and not in the direction off of it as the brane theorists hypothesize ². We should, therefore, regard parallel branes as two sides of the same brane; otherwise, they coexist in different time which is absurd.

Notes:

a)    The superstring theory cannot elaborate on the reason why such a universe is inherently unstable. The bold answer to that is that the energy intrinsically consists of the opposites, the positive and negative energy. These two parts tend to segregate arousing [rotational] opposite motions within and eventually the universe creaks into two pieces.

b)  We may easily imagine this phenomenon as a separation of oil and water creating an interface in between. However, instead of three-dimensional, we have here ten-dimensional oil-water system.

c)    The ancient term of such worlds was the seven heavens

d)    The knowledge of such cosmic structure has been known since the antiquity but degraded as time evolves to become just that of the planetary orbits of our solar system. The conflicting misinterpretation of such gigantic macro-cosmic concept, which was beyond both the church and Galileo's imagination, had tragically taken Galileo's life.

e)   Peter Freund, one of the pioneers, worked in multidimensional space, even though he did not know about the geometrical structure of such worlds, accurately stated that the laws of nature become simpler and elegant when formulated in higher dimensions.

f)    In the ancient relative term: light upon lights.

References:

1. Kaku, M.:" Hyperspace," Anchor Books, Doubleday, New York, 1994, p. 195, 207.

2. Randall, L.:" Warped Passage," Harp

Superstring Theory and the Seven Heavens

Energeticist vs Materialist

The idea that the world consists of continuous substance against that of tiny material parts occurred since the dawn of human history. By the end of the 19^th century, the proponents of the substance theory which then became energeticists confronted openly and fiercely with those of atomic theory which also known as materialists.

The ancients believed that the world consisted of the transformation of a single continuous substance which they called water with its various phase transformations such as fire, air and solid (earth). The energeticists held a similar idea that the real underlying component of the universe was energy in its various forms ^a).

Energeticists led by Ostwald turned to [chemical] thermodynamics which successfully described the physical and chemical reactions without recourse to the atomic hypothesis ¹⁾. Ostwald and his colleagues claimed that the molecules and atoms were just illusions.

Dalton and the proponents of the atomic idea held that all matter was made up of an extremely small solid having no internal structure, indivisible, unchangeable and indestructible. This theory has taken more than two millennia to evolve, from the time of the Greek philosopher ^b) Democritus of Abdera in the 5th century BC but has only been proved experimentally in the early 20^th century.

Debates between the proponents of the energetics and the atomic hypothesis were so fierce and rude that was believed to become part of the tragic suicide's cause of Boltzmann, one of the strong proponents of atomic hypothesis. However, following the work of Einstein on Brownian motion which pointed out the existence of atoms, Ostwald and his followers finally accepted that the atomic theory was scientifically well-founded.

Today nobody doubts about the existence of atoms. We do not have any problem with that,  but our main concern is on the question of the degree of existence of atoms or subatomic particles we are talking. In our previous articles it was concluded that at the quantum level there is no such matter which exists persistently. At every brief instance of time matter is created and annihilated perpetually out of and into energy at the pace equal to the speed of light ^c) as implicitly expressed in the Einstein equation E = mc² (Fig.1).

The theory of relativity which holds the equivalence of energy and mass in some extend dethrones the concept of matter as the building block of reality, bringing in a new notion of rest mass as a residual concept. However, the quantum theory launches a coup de grace sinking the materialism and classical mechanism for good as we interpret it in Figure-1.

Matter exists only ephemerally. The persistence of matter is just human illusion. The only substance persisting in time is energy from which all matters are derived. The final score of the debates was 1 to 1/2; the energeticists were right, and the materialistic proponents were only half right. The materialism including Marxism which holds matter as the sole subject of change is wrong both physically and philosophically.

Notes:                                                   

a)   The ancient “water” is nothing but the immaterial substance which is called energy in modern time. The ancient water and energy are two different names of the same thing. The ancients acknowledged that energy existed in different phases which ancient called earth (solid), water, air, and fire. In our modern time, we may comprehend these different phases of energy as having higher dimensions in successive order.

b)   The word atom comes from Greek which means indivisible.

c) It is the underlying reality of the wave and particle duality and its related phenomenon observed in the double-slit experiment.

References:

1.   Herbert, N.: "Quantum Reality," Anchor Books, New York, 1985, p. 10.

Energeticist vs Materialist

Energy and Information

Thomas Alva Edison was an outstanding inventor, some of whose works were unintentionally making use of the deepest secret of nature. His invention on the motion picture, for example, miniaturized the dynamic mechanism on how nature works.

He devised the camera capable of taking snapshots of events at 24 pictures per second and concurrently invented a projector in which a series of pictures printed in a film was projected on a screen giving us the perception of seeing events running continuously through time.

Nature works similarly as motion picture does, but instead of having 24 snapshots of events per second, we have in nature 10⁴⁴ snapshots of the whole universe per second ^a).

While the pictures taken for the movie consisted of a series of two-dimensional images separated by gaps, those of universe is three-dimensional ^b) separated by a gap of nonexistence (Fig.1).

 

In reality, there is no such thing as a continuous [material] existence prevails in nature. Every (material) thing perpetually appears and disappears through time, except the energy which alone persists ^c). The persistence of matter is just an illusion ^d).

The law governing such mechanism should be nonlocal in order to avoid chaos during the quantum "teleportation" from the vanishing space to the new emerging space (as proved by Bell theorem). The fundamental particles that make up the universe should be teleported from the vanishing space to the new space as inseparably connected to some indivisible whole.

Such teleportation requires the preservation of [nonlocal] information to avoid chaos albeit the abrupt changes caused by perpetual creation and annihilation of the whole existence. As energy is the only substance persisting through time, this energy should carry such information. The energy and information are the two sides of the same coin.

In its development, the physics has heavily explored the energy related to the aspects of force, power or action and very little to those of information¹. There are various degrees of higher dimensional energies in nature and thus higher degrees of information.

The higher the dimensions of energy, the higher the dimensions of its corresponding aspect of information are; thus the higher the degree of consciousness they possess ^e). It may ultimately lead us to reveal the deepest secret of life itself.

Notes:

a.    It takes the snapshots at the pace equal to the speed of light.

b. We may relate this to Minkowski's statement that we have in the world no longer a single 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 ². We should remind, however, that those spaces do not exist simultaneously but in successive order, in the sense that the individual space appears and disappears one after another

successively giving us a perception the succession of time.

c.   This phenomenon is described by the Einstein equation E = mc² in the sense that m (mass) perpetually created and annihilated out of and into energy (E) at the pace equal to the speed of light (c).

d.    The Copenhagen interpretation holds that the unmeasured electron is not a real one in the sense that it never possesses definite but all possible attribute values. The electron becomes real only in the act of measurement. This interpretation was comically extended to the macroscopic thought experiment using a famous cat [named Schrodinger] ³ in place of an electron where the poor cat was both alive and dead at the same time when was not observed.

e.   The energy inherently capability to store and process information may in some extent be called consciousness. It is the underlying reality of why there are various degrees of consciousness and lives in nature.

References:

1.  Davies et al.: "Information and the Nature of Reality," Cambridge University Press, Cambridge UK, 2011.

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

Energy and Information

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?