What’s Wrong with Dirac Sea’s Existence?

The attempts to incorporate the special relativity principle into quantum mechanics always leads to the solution of negative energy states pairing with positive energy states. Klein-Gordon's and Dirac equations are among those having such property.  However, physicists cannot afford to take on such energy's negativity as physical reality since they believe that it may lead to a catastrophic instability of the entire universe.

The root of the problem comes from the solution ambiguity of the relativistic expression for energy, E = ± (m²c⁴ + p²c²) ^½. In classical physics, one can straightforwardly keep the solution bearing positive values separated from that taking the negative ones.  In quantum mechanics, however, things become complicated. One should then deal with operators acting on complex functions, giving way two square roots of complex-number terms that do not tend to separate neatly into positive and negative in a globally consistent way ¹.

But this is what happens in reality. In the real world, those two opposite energies split only momentarily before they once again mingle together. This phenomenon repeats itself, making the 3-interface between those two energy oceans appear and disappear perpetually.

This interface, the 3-dimensional space we live in, seems to be something that evaporates completely as one moment passes and reappears as a completely different space as the next moment arrives ^two, which makes our universe incredibly dynamic.

Such as the beautiful translation of the mathematics formulation to the deeper workings of the physical universe may go beyond most people's wildest imaginations. Alas, even a prominent mathematical physicist such as Roger Penrose, has missed such insight. This continuous "catastrophic" instability that he was worrying so much is, in fact, the underlying reality of dynamic time. The energy's duality and polarity are the most fundamental of the relativity principles, the cosmos' prime mover, without which the world would remain sterile, timeless, and standstill.

When Dirac formulated his equation, being unable to get rid of the unwanted negative energy. He posited the presence of the sea of negative energy states, later known as the Dirac Sea. However, physicists are not comfortable with such a bold idea and reinterpret it as corresponding to antiparticles with positive energy. 

Dirac, alas, didn't elaborate further about his energy sea, such as its location, how it came to be, etc. The answer is, in fact, relatively simple. The Dirac Sea must be present side by side with the sea of positive energy we refer to as anti-Dirac Sea (Figure-1). Both of them should be 4-dimensional conforming to the dimensionality of the spacetime they "occupy." The 3-dimensional interface naturally occurs between the two energy seas is nothing but the physical space we inhabit.

This kind of depiction greatly facilitates us in describing quantum fields, which so far seem to appear from nowhere, omnipresent, capable of creating and annihilating quantum particles. The interaction between the opposing energy potencies in Dirac and anti-Dirac seas giving rise to quantum fields, piercing through the 3-interface igniting quantum sparks ("quarks"), which appear and disappear perpetually on its surface (Figure-2).

Having elaborated that, we can now explain Fred Hoyle's C-field in a similar way. Hoyle hypothesized the existence of something similar to the Dirac Sea that continuously generates the fields. He further posited that the C-field had negative pressure and drove the expansion of the universe.

Subsequently, within the context of the standard model, Peter Higgs introduced fields, which later bore his name, capable of stimulating particles to acquire mass. Alas, he was silent about the nature and origin of Higgs fields or the existence sort of negative energy sea.

Another fundamental relativity principle underlying any process of creation is the spontaneous symmetry breaking. A preexisting energy sea, later on, splits into positive and negative energy (Dirac anti-Dirac seas) as what they are now. However, that symmetry breaking doesn't take place all at once but gradually (Figure-3), giving us a perception that the universe is expanding. This hypothesis is evidence against that of the "quantum" primordial explosion of Big Bang theory.

References:

1.     Penrose, R.: ”The Road to Reality," Vintage Books, London, 2005, p. 615

2.     ibid, p. 387

Space Thickness

 The relativity theory covers the macroscopic aspect of the world conceptualized as a flat or curved hypersurface.  However, hardly anybody is aware that we may incorporate the quantum phenomena into the theory by merely taking into account the hypersurface's thickness, its microscopic scale. We call such a unified theory the Grand Relativity Theory (GrRT).

Any physical object should have a thickness ^a) regardless of its dimensions; otherwise, it would disappear into thin air. Our physical space is no exception. The effect of space thickness, yielding a higher degree of freedom for particles to maneuver, intensifies as we probe to smaller distances approaching the thickness' magnitude (Figure-1).  

This scenery is spectacularly demonstrated by the string theory which, albeit of its imperfectness, can [mathematically] discover the ten-dimensionality of the ambient space. Whether the string theorists can properly portray such higher-dimensional space or not is a different story.

GrRT posits, on the contrary to the classical theory's premise, that the 4-dimensional spacetime doesn't at all represent the real but the primitive world. Inherently, the spacetime is symmetric, static and eternal. As such, all of its dimensions are entirely equivalent.

It is only when the spacetime splits in two ^b) that the dimensions are differentiating themselves into spatial and temporal. Following this spontaneously symmetry breaking, a thin 3-dimensional interface (hypersurface) ^c) is taking place in between the two halves of the split spacetime.

Now, the interfacial tension that holds the interface intact makes the dimensions extending along the hypersurface tenser and more "tangible" than that normal to it. We call the above dimensions spatial while the latter we call temporal. The hyper-interfacial tension which is responsible for this differentiation we recognize as the Gravity Constant.

The fourth [temporal] dimension extending normal to the hypersurface manifests the dynamical aspect of the world. The space thickness measured along this dimension is extremely thin, around 10 ^-33 cm or equivalent to 10 ^-44 second, the minimum thickness that nature allows, below which space and time have no meaning.

Because of its small thickness, the hypersurface is inherently unstable. Such a space barely exists, perpetually appears and disappears which makes the world extremely dynamic.

The size of the space thickness which determines the duration of space's presence we call now. Space and the now are the different aspects of the same thing. We perceive the sequence of space's appearance, presence, and disappearance as the successive transformations of the future into now and the past.

Matters exclusively present at now. They exist only along the thin hypersurface (space), not outside of it, which is nothing but pure energy ^d). The parts of the spacetime on either side of this thin space, we call the future and the past (Figure-2).

The extension of this concept for higher dimensional spacetime is straightforward, except that there come about successive spontaneous symmetry breakings. A hypersurface of one dimension lower than its embedding space, together with its corresponding temporal dimension, is created every time the split occurs.

Within the ten-dimensional ambient spacetime which the string theory reveals, a total of seven successive splits have taken place before our dynamical world comes to the existence. We thus have seven worlds embedded one within another, each with its corresponding temporal dimension.

Multidimensional time is still an alien concept for physicists. Physicists thought that the only vast and extended world existing in nature is that of four-dimensional. They believe that time is unique, the only dimension of its kind. The extra-dimensions, if they exist, should be spatial and curled up into extremely tiny loops.

This premise makes the task of string theorists extremely untenable as there are around 10⁵⁰⁰ possible ways on how the extra-dimensions may curl up. Nobody is crazy enough for not using the Occam’s razor to get rid of such problem and for good.

Notes:

a.    A physical object may have some thicknesses depending on the ambient space dimensions we take into account. Within our 3-dimensional ambient space, a 2-dimensional plane has one thickness, while the 1-dimensional thread has two thicknesses.

b.     The energy which is inherently composed of the opposing components tends to break up into its component, i.e. the positive and negative energies.  When this happens, the spacetime which is nothing but the geometrical manifestation of the [vacuum] energy, splits into two halves creating a hypersurface in between the two.

c.    We use the notation of space, hypersurface, and interface interchangeably. The hypersurface is a straightforward generalization of the concept from the geometry of surfaces embedded in the three-dimensional Euclidean manifolds.

d.    The mainstream physicists portray the 4-dimensional spacetime, dubbed the world, as being filled with matters throughout the full extensions. There are no [microscopic] universal now, matters existing in the past, now and future "have" an equal reality, as such that time travel becomes possible leading to paradoxes and chaos.

The Crumple of the Spacetime

The General Relativity theory was developed based on the premise that the gravity force is the manifestation of the 4D-spacetime curvature ^a). This physical concept was derived from Riemann’s idea¹ that the force was nothing but a consequence of geometry, thus, banished Newton’s unnatural concept of “action-at-a-distance”.

However, Einstein mindset was to stick with intrinsic geometry in the sense that the spacetime as a system was regarded as having no surroundings or being embedded in nothingness ^b). In fact, when physicists talk about the wrinkle of the [4D-] spacetime they never care about which directions (dimensions) it wrinkles goes.

The strict concept of the geometry dictates otherwise ². The geometry concept of m-metric manifolds (hyperspaces) ^c) is a straightforward generalization of ideas of the study of surfaces embedded in 3D-space. However, it has been proven that in the circumstances in which an m-dimensional curved hypersurface can be embedded in the n-dimensional [Euclidean] ^d) manifold if at least n = ½ m(m + 1).

The crumple of the ordinary 2D-surface, a piece of paper, for example, requires a third dimension (3D-ambient space) for it to occur. But hardly anybody is aware that the crumple of 3D-space requires not only a fourth dimension but at least 3 additional dimensions (6D-ambient spacetime) ^e). Similarly, the crumple of 4D-spacetime would require at least 10D-ambient spacetime for it to occur without constraint in any direction (Figure-1). Does the nothingness have such properties for being able to embed something? What is nothingness anyway?

Nobody should blame Einstein on this negligence. People were just horrified about the idea of 4D-spacetime which had been introduced by Minkowski beforehand, not mention the 10D-spacetime. Had Einstein been aware of this higher dimensional surrounding requirement he would probably still prefer to take the surrounding as nothingness rather than 10D-ambient spacetime.

A more recent theory such as that of superstring requires 10D-ambient spacetime ^f) for its equations to be solvable.  Alas, being uncomfortable with such bizarre vast extension ^g) of the ambient spacetime, physicists blow down ^h) the majestic surroundings assuming the extra dimensions being curled leaving the ordinary 4 dimensions to remain intact.

Even after the superstring theory was established, Big Bang theory as the cosmological application of the General Relativity theory maintains its premise on the nothingness instead of 10D-ambient spacetime taken as the surrounding of the expanding 4D-spacetime. As such, Big Bang theory misses a bigger part of the “stage” that in no way it can explain the substantial missing dark matter and dark energy.

Having many defects in its premise Big Bang theory would eventually fall short except it takes among other the 10D-ambient spacetime as the surrounding of the universe (4D-spacetime) instead of nothingness.

Notes:

a)    Arthur Eddington expedition carried out to South Africa during the solar eclipse in 1919 verified the shifting of the position of a star within the field near the sun, thus, proving Einstein's general relativity prediction of the bending of light around a massive object.

b)   There is a vague definition of absolute nothingness or emptiness but we may guess that what most physicists mean by it is a sort of extension (spacetime) with an indefinite number of dimensions [zero or infinite dimensions?] having neither matter nor energy.

c)      The notation of n-spacetime is equivalent to n-hyperspace or n-hypersurface.

d)    This is the reason why the laws of nature look simpler in higher dimensions. If the dimensions of the surrounding spacetime are high enough then we might have a flat (Euclidean) surrounding where the physical laws become simpler.

e)      We may speculate that the existence of three generations of particles is the manifestation of 4D, 5D and 6D-particles abiding in the respective 4D, 5D and 6D-spacetime. The manifestation of the last two generations into our world could be only the cross-section of their whole body.

f)     The string theory accidentally derived the 10 dimensions mathematical requirement from Beta function originally dedicated to solving the strong force quest. The coincidence with the 10 dimensions geometrical requirement of the ambient spacetime embedding the 4D-spacetime is stupendous.

g)   Since they are not visible, the string theorists regard the extra-dimensions as spatial and being curled into tiny loops.

h)    Physicists assume that the 10D-ambient spacetime splits into a 4D-spacetime and a tiny curly 6D-metric manifold. This premise doesn't absolutely make sense just like the impossibility of splitting a 3D-cube into one 2D-plane and one 1D-line. The proper way to do it is successively splitting the 10D in two creating 9D as their interface and so forth down to 4D which we get as the interface of the two halves of the 5D split. We would, then, have a total of 7 spacetimes embedding each other in descending order of their dimensions.

References:

1.      Kaku, M.:” Hyperspace”.Anchor Books," Doubleday, New York, 1994, p. 36 – 42.

2.      Sokolnikoff, L.S.: "Tensor Analysis,"John Willey & Sons, Inc., New York, 1964, p. 202 – 205

Why the Grand Relativity Theory? (Part III)

One of the significant physicists' misconceptions about nature is the uniqueness of time. When physicists encounter higher-multidimensional surroundings in their theory, they instinctively assign the extra-dimensions (beyond the ordinary four) as spatial. This premise, regarding the inequality of space and time footing, is evidence against the relativity principle.

The string theory, which had its origins in experimentally observed features of the strong force, requires the existence of six compactified extra spatial dimensions (a) and the four known spacetime dimensions. This presumption leads the theory to grave difficulties as it should deal with myriad different kinds of Callabi-Yau tiny manifolds or other similar bizarre things.

On the other hand, the grand relativity theory holds that the extra dimensions are temporal; thus, circumventing such complexities. Therefore, we may regard a system such as our world consisting of a 3D-space (hypersurface) embedded in 10D-manifold in which all extra dimensions are temporal ^b). Under the grand relativity theory, we have every right to transform it into, for instance, 9D-hypersurface embedding in the same 10D-manifold, by turning some of the temporal dimensions into spatial (Figure-1). The latter is exceedingly simpler than the former in terms of mathematical formulations, and yet it gives us the same solutions.

Physicists are used to oversimplifying their physical model using geometrical objects, such as 0D-point, 1D-line, and 2D-plane. However, one should be extremely cautious of using such objects, having no thickness at all as he or she probes more in-depth into the quantum realm.  At the quantum level, the range of actions could be concise, which might be approaching the object [quantum] thickness (at the range of 10^-33 to 10^-17 cm) ^c) that one deliberately ignores. It is no wonder that with such zero depth for their physical objects or models, physicists are confronting many irritating infinity problems.

The grand relativity theory requires any physical objects or hypersurfaces having thicknesses, the number of which depends on the number of dimensions of the embedding manifold ^d) (Figure-2). However, physicists obliged to do a similar way by incorporating such forgotten thickness into their model called supersymmetry generators e).

In Brane theory, physicists assign some space and time's dimensions on and along its surface while off of it spatial. They certainly make a significant confusion as to the brane, like hypersurface embedding in a higher dimensional spacetime, should have solely spatial dimensions on and along its surface and temporal dimension[s] off of it.

The hypersurface or brane is the loci of things that co-occur if not at lower temporal dimensions it would certainly so at higher temporal dimension (Figure-3). 

The hypersurface tends to flatten out as it has higher dimensions. But how high should they be? Mathematically, a spacetime may embed an n-dimensional hypersurface properly only if the former has at least ½ n(n+1) dimensions. Our 4D-world, for example, requires a sufficient ample ambient space i.e., 10D-manifold, for having a complete degree of freedoms without being constrained at whatever directions.

It turns out that some theories, such as Supergravity, require an embedding spacetime of even higher dimensions. The Supergravity demands an eleven-dimensional ^f) embedding spacetime, but still, nobody can fully renormalize the Supergravity.

Notes:

a.  Physicists are assumed to be curled up into tiny loops as nobody ever directly experiences them.

b.   It can be expressed mathematically as Octonion, a Hypercomplex consisting of one real and seven imaginary variables. The real part is the spatial variables' function, while the seven imaginary parts represent seven different temporal dimensions.

c.  No real particle smaller than the hypersurface's thickness, except virtual particles perpetually emerge and submerge across the depth. This thickness size, which becomes the minimum size of the real particle is what physicists call hierarchy problem.

d.  Analogically under 3D-ambient space, a point has three thicknesses, string two thicknesses (cross-section), and plane one thickness. Otherwise, they would be evaporating into thin air.

e.  Mathematically physicists may express such a framework in terms of Superalgebra equation whose ordinary and super parts are sometimes called body and soul, respectively ¹. It is equivalent to Octonion Hypercomplex with its real and imaginary parts. Amazingly, this is a proper way to describe a subtle structure such as [higher dimensional] soul embedding a body, contrary to what most people think the soul is inside the body.

f.  It is a sort of pseudo dimension representing the tip of the 11+ "iceberg" dimensions. The ancients (among other Empedocles: 490-430 BC) described the realms consisting of earth, water, air, and fire analogous to a changing phase from ice, water, vapor, and steam.  We may interpret that earth representing energy/material stable things in 3D-space, water representing energy in 4D - 10D-spacetimes, the air in 11D - 55D-spacetimes and fire in 56D - 1540D-spacetimes, the dimension ranges of which are speculated under the ½ n(n+1) rule, if we may do so. This metaphor shows us that the energy associated with particular spacetime is hotter as the spacetime dimensions become higher. The reality beyond those dimensions is far from our wildest imagination and concern.

Why the Grand Relativity Theory? (Part II)

As the dimensions of a drop of water to its water substance, the dimensions of spacetime are the geometrical manifestation of a particular cosmic energy.  Our world, together with its multidimensional surroundings (grand cosmos), comes into existence as the natural manifestation of a broad spectrum of different cosmic energies ^a). 

How these multidimensional worlds come into being? It begins with the separation of positive and negative energy in the highest-dimensional world. This separation creates a hypersurface (space) of one lower dimension between the two opposite energies. The newly created hypersurface, in turn, splits in two, and so forth. Thus, the separation happens successively, creating many hypersurfaces (spaces) embedding one after another in descending order of their dimensions. 

The energy segregation in each world, however, doesn't happen instantaneously. The area of the hypersurface formed in between the two opposite energies broadens up gradually from a specific minimum size to what the current magnitude is (Figure-1). It is the underlying reality that makes our universe expanding ^b). 

This kind of phenomenon also explains why our world is flat ^c).  As such, we don’t require buying the concept of inflationary phase happened in the early life of the universe (at around 10^-35 to 10^-30 second after Big Bang) whose inflation rate is far exceeding the speed of light. Besides, the existence of energies at the surroundings of our universe (hypersurface) may explain the possible source of dark energy we miss so dearly.

The advantage of using hypersurface over the hyperspace is clear. With the former, we can easily describe objects such as fields propagating on its surface (classical fields) as well as those off its surface traversing through its thickness ^d) (quantum fields)^, as depicted in Figure-2. 

The interaction of the opposite energies generates those quantum fields which propagate across through the hypersurface. As the quantum fields hit the hypersurface's surface, they ignite quantum sparks ("quarks"), which we recognize as fundamental particles. These sparks (particles) together with the hypersurface (space) which they abode ^e) perpetually appear and disappear at the rate equal to the speed of light ^f). 

The two interacting opposite energies move at the different directions forcing the normal axis of the hypersurface to rotate around the grand perimeter of the spacetime at the speed of light ^g). This dynamic grand rotation creates what we perceive as time (Figure-3). 

The combination of these two phenomena makes our physical space, together with all matters it contains, disappears completely as one moment passes, and reappear as a completely different space as the next moment arrives ^h). Most physicists overlook this underlying reality, which reflects both the relativity and quantum realms.

The interactions of the opposite energies also make the hypersurface rotate around its normal axis. It rotates, in turn, all objects it contains from super-galaxies, galaxies, solar systems, planets down to atomic and subatomic realms.

Notes:

a. The ensemble of such grand cosmos can be mathematically expressed in the form of the Laurent series or depicted as the Riemann sphere.

b.   As shown by Riemann's annulus of convergence, the world can evolve only from a specific minimum size. It starts to get its stable form and expands to its maximum magnitude, beyond which it becomes precarious and tears apart into pieces doomsday. As nature abhors the singularity, do we need the Big Bang cosmology and black hole postulate?

c.   It is flat but locally curved and undulates due to the gravitation effect exerted by local concentrations of energy and mass.

d.   In the order of Planck distance i.e., 10^-33 cm or equivalent 10^-44 second, below which the hypersurface would disappear into thin air. Assuming a zero thickness of such hypersurface would lead us to many annoyance problems of infinity.

e. The separation of energy never creates a stable hypersurface between the two halves. Mathematically, in quantum mechanics, the square roots of the relativistic energy formula, E² = m²c⁴ + p²c², do not give a neat separation of its positive and negative roots. It means that physically, the split of the positive and negative energy never creates a stable interface (hypersurface) between them. It is ephemeral in the sense that it appears and disappears perpetually.

f.   It is just like sparks appear and disappear on the surface of large TV or computer screen. Amazingly, the display also appears and goes together with the flashes.

g. The energies’ movement as the result of their mutual interaction also makes the hypersurface rotate around its lateral axis resulting in a hyper-helical type of rotation. In a higher-dimensional ambient space, we can depict this hypersurface movement as a 3D-front wave propagating across the 4D-surface of a grand 5D-ocean.

h.    Heraclitus (500 BC) said that the world is in flux. We can never step into the same river twice. He also stated that the world was like a gigantic flame. At any instant, the fire we see is entirely different from the flame we saw just a moment ago. Everything in the world is always changing and yet is still exclusively itself.

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.

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).