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Showing posts with label superstring. Show all posts
Showing posts with label superstring. Show all posts

Monday, April 30, 2012

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=mc2The 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.

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Wednesday, April 20, 2011

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, ci is the speed of light of the respective temporal dimensions ti .
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 + x7x8x9oc7t7

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 +lc4t

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).


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Friday, January 7, 2011

Multidimensional Time and Hypercomplex Numbers

Long before physicists embarked on the study of higher-dimensional spacetimes, 19th-century mathematicians had firmly established the geometry concept of multidimensional metric manifolds. Many of these concepts were straightforward generalizations of ideas on the properties of surfaces embedded in the three-dimensional Euclidean manifold.
To simplify things, the mathematicians have introduced a multidimensional surface-like concept called hypersurface for modeling multidimensional space embedded in a higher multidimensional ambient manifold. A flat m-hypersurface can be appropriately embedded in an (m+1) space, but matters become more complicated when one comes to consider curved hypersurfaces. A curved m-dimensional hypersurface requires an ambient space whose dimensions are at least equal to or greater than ½m (m+1) 1.
Accordingly, a 4-dimensional curved spacetime requires at least a 10-dimensional ambient space. The spacetime's point position and, hence, the curvature of the spacetime is completely defined through a collection of numbers associated with the coordinate system set up in such 10-ambient space which we are more familiar with as the metric tensor's independent components of such 4-spacetime.
So what is so startling about it is when we explore the micro realm we would be confronting with the same 10-dimensional ambient space. Alas, in the later development, such as in that of the superstring theory, physicists made a blunder as they wrongly assumed the curly nature of the extra dimensions of such ambient space,  which made them going nowhere.

The same fate happened to Big-Bang theory as physicists firmly exclude the existence of the universe's surrounding spaces. In doing so, physicists throw away the more significant part of the system, and this might be the reason why the theory incorporates only five percent of the total mass and energy that it actually should be.
Now the only option to cope with this impasse is jumping off the ship and abandon not only about the curly nature of the extra dimensions but also the one-dimensionality of time.
As the last article has deliberated,  those multiple temporal dimensions are the results of a series of successive symmetry breakings occur which had created different worlds, each of which had its respective temporal dimension (Figure-1).
Quaternion and Octonion
Now, how do we describe the structure and the geometry of such multiple temporal dimensions? To do this, we need to build a coordinate patch within such ambient space framework. To start with, let us deal with our 3-dimensional physical space embedded, as it should be, in a 6-ambient space. In such a case, we assign a coordinate patch consisting of three real space coordinates x1, x2, and x3 and three imaginary time coordinates whose basis ij and k.
If we denote x= x(x1, x2, x3), then we can define any world point in such 3-physical space as:
q = x + ui + vj + wk,
where x, u, v and w are real numbers. This expression is found to be nothing but the quaternion; a generalized complex number discovered a long time ago by Hamilton who established the geometry and the algebraic structure of this quaternion in 1843.
If we express the time variables u, v and w proportionally to the speed of light ci of the respective temporal dimensions ti then we can write:
q = x+ ic1t1 jc2t2 kc3t3,
This quaternion describes a general vector within a 6-dimensional space expressed as a function of space and time coordinates. Quaternions, therefore, describe a 6-dimensional vector space over the real numbers, depicting the dynamical geometry of 3-space embedded in 6-ambient space.
Similarly, we can define the 4-spacetime whose ambient space is ten dimensional through a coordinate patch consisting of three real space coordinates and seven imaginary time coordinates.
Again if we assign a space coordinates as x= x(x1, x2, x3) and i, j, k, l,m, n, and o denote independent imaginary numbers as the coordinate basis representing seven different time coordinates, then we can define any point located at the 3-space in such coordinate patch as:
q = x + ai + bj + ck + dl + em + fn + go
where x, a, b, c, d, e, f  and g are real numbers. Graves and Cayley had already discovered this expression, known as double quaternion or octonion, long time ago in 1845, although they did not know about the physical implication of it.
If we express the time variables a,b,c ... g proportionally to the speed of light ci of the respective temporal dimensions ti then we can write:
q=x+ ic1t1 jc2t2 kc3t3 +lc4t4 mc5t5 nc6t6 oc7t7
Octonions form a 10-dimensional vector space over the real numbers, depicting a 3-physical space embedded in 10-dimensional ambient space.
In a later development, the original notions of quaternion and octonion are further modified and generalized through what so-called Clifford and Grassmann algebras applied to any higher dimensions framework which is found to have powerful implications in modern physics.
Many mathematicians and physicists wrongly perceived the quaternions and octonions as respectively describing 4-dimensional and 8-dimensional spacetime (having both one-dimensional time), which is inappropriate.
Penrose2 regarded Hamilton's 22 year-devotion in his life in attempting to develop the quaternion calculus resulted in relative failure. On the contrary, we regard the Brougham Bridge's stone carved with the Hamilton fundamental equation would become a momentous milestone of the application of the hypercomplex calculus on the geometry of multidimensional time in both macroscopic and microscopic realms.
References:
1.  Sokolnikoff, L.S: "Tensor Analysis," Wiley Toppan, Second Edition, New York, 1964, p. 205.
2.   Penrose, R.: "The Road to Reality," Vintage Books, London, 2005, p. 201


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Wednesday, September 22, 2010

Energy Reality and the Creation of the Universe

Everybody knows about energy but rarely is aware of its true nature. People used to regard energy as something abstract, the same way as they do for the power, force or its kinds. What they concern most about energy is its function, not its reality. We learn from the school that energy is a mathematical abstraction that has no existence apart from its functional relationship to other variables or coordinates that do have a physical interpretation and which can be measured1.

The kinetic energy of a given mass has no other reality than as a function of its velocity. We know the potential energy from its position and the rest energy from its mass. What people know about energy is only superficial. They only see ripples moving across the surface of the ocean, not the water beneath. As we will see the energy is not at all an abstract thing. On the contrary, it is the only real substance from which everything is derived. Energy is omnipresence; eternal (in relativity term), neither can be created nor destroyed.

Energy and Its Bodily Form

From the relativity theory, if it is adequately understood, we can know the true nature of energy. Einstein's equation E = mc[and the energy conservation] pointed out that matter was nothing but a different aspect of energy. The relativity also unified other fundamentals, i.e. the space and time into a single entity called spacetime. The relativity, therefore, reduces the fundamentals in two namely the spacetime and energy.

Einstein ingeniously connected the two through the influence of energy on the spacetime resulting in the curvature of the latter. From this idea, he revealed the nature of gravity. It was a success story, but that was not enough. What Einstein supposed to do was taking a little step further unifying the spacetime and energy.

What Einstein failed to grasp was a fundamental [metaphysical] principle: a substance does not come into existence without its bodily form. Nature abhors nudity.  Just like the three-dimensional spherical structure is the bodily form of water in a drop of water, the [four-dimensional] spacetime is the bodily form for the energy.

There is no energy without spacetime and no spacetime devoid of energy. Science fails to recognize this very nature of  energy because physicists are more familiar with the energy's manifestation on the surface, not the underlying energy. Energy in its actual reality is more like an [four-dimensional] ocean of energy. As a three-dimensional being, we can only perceive the manifestation of energy on a three-dimensional hypersurface (space) a) in the form of fields and forces.

The spacetime is nothing but the structural quality of energy. The dimensionality of the spacetime is not its intrinsic property but the manifestation of the energy's degree of freedom. The higher the energy's potency is, the higher its spacetime's dimensions are. There should be a broad spectrum of energies of different potencies exist out there in nature, as indicated by the discovery of theoretical higher dimensional spacetimes in some more recent theories.

Another energy's feature, which physicists seem to be reluctant to deal with, is its opposing components which are revealed by the relativistic energy equation E= m2c4 + p2c2. As we will see, these two opposite energies, the positive and negative, play an essential role in the creation of material things and space.

Multidimensional Time

The physicists seem to have been forced to deal more and more with higher dimensional spaces. Kaluza and Klein were the first who believed that the gravity and the electromagnetic waves put together could be adequately described if the spacetime had five dimensions instead of the standard four. Under the superstring theory, physicists even proposed higher dimensions: ten and more recently eleven.

As did Kaluza and Klein, physicists presumed that all the extra-dimensions beyond the fourth curled into tiny, undetectable loops. This idea has brought us into many bizarre things such as doughnut-like and Calabi-Yau spaces2 which give us a hundred thousand possible solutions. One should have used Oscam razor to cut off those ugly curly dimensions long time ago and put back more elegant extended extra-dimensions in their places.

We cannot perceive the extra-dimensions because they are time dimensions. The term spacetime given to the unification of the space and time is misleading. The term gives us the impression that such a union has already different space and time dimensions since the beginning. On the contrary, in its originality the dimensions of the spacetime were equivalent. The union of the space and time at that stage is more like four-dimensional time (its dimensions were time-like).  The time dimensions were not yet divided. Neither space nor "Now" was there, nor was a material thing and even light. It was in total darkness and chaos.

At this condition, we better name the union of space and time 'eon,' the "eternity" (Figure-1a). It was only when the opposing energies had segregated from each other (the spacetime split in two) that we can call it spacetime (Figure-1b). As the energies separated, an interface (space) naturally appeared. As such, the [time] dimensions along the interface were transformed to become spatial.

The physicists totally missed this scenario and jumped instead using the undivided whole spacetime for representing the real worlds. The following statement reflects Einstein's standpoint3:” 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". This kind of vicious-circle thinking has brought us to the troubles that we have now in physics.

Grand Relativity Theory

In order to preserve causality and order, physicists have been forced to assign "artificial" light cones, as the fundamental structure, at every point within the spacetime. Within such a world, the simultaneity of Nows, even for two neighboring events, is totally beyond the grasp of the system.  Einstein was worried so much about this, as his friend Rudolph Carnap recounted 4:” Einstein said the problem of the Now worried him seriously …  That the science  cannot grasp the experience of Now seemed to him a matter of painful. So he concluded that there is something essential about the Now which is just outside the realm of science”.

The reason why physicists denied the existence of [universal] "now" is because it was against the principle of the relativity of simultaneity. We can avoid this dilemma if we are considering it under a multidimensional time framework. Events which happen non-simultaneously in a particular time dimension could be simultaneous in another higher dimensional time. We can always find a higher time dimension in which events happen simultaneously (flat hypersurface) whereas they were not so in a lower time dimension (Figure-2).

For example, a ten-dimensional spacetime can be equally described as a three-dimensional space having seven-time dimensions or as nine-dimensional spacetime having one-time dimension. The former has its physical law broken into many while the latter has less. We can always try to explore a higher and higher dimensional spacetime until we get one unified law.

The spatial and time dimensions are transformable to each other depending on how we regard the spacetime as a system. Whether we consider the system as a lower dimensional hypersurface having many time dimensions or as a higher dimensional hypersurface having one temporal dimension, the physical laws remain the same. We can only unify of physical laws can only be done at such a higher dimensional [flat] hypersurface (spacetime) where all events are taking place simultaneously. We may call this postulate the grand relativity principle.

Ghostly Rotating Universe

Under the general relativity theory, the arrangement of light cones can be quite irregular rather than uniform. In an extreme situation, they may form closed time-like curves. Penrose5 ruled this situation out as simply unphysical as it violates causality. However, his worry was unfounded. The two opposing energies do not create matters [and space] permanently but perpetually create and annihilate those  particles. Particles are created and annihilated perpetually at the pace equal to the speed of light as expressed by E = mc2 or dynamically by E= m2c4 + p2c2  b).  The interactions between the two energies are manifested as a flux of [four-dimensional] electrical currents (Higgs fields?) across through the surface generating quantum sparks (“quarks”) at the surface, analogous to the flashing pixels appear and disappear on a giant TV screen.



As the two energies are repulsive, they are "flowing" in the opposite directions to each other, forcing the surface rotates around an axis lying on its plane (Figure 3a). The electric currents which flow across through the surface induce [three-dimensional] magnetic fields which propagate traversing the surface.  It makes the surface rotate following the right-hand rule, around an axis perpendicular to the surface (Figure 3b). This rotation causes circular movements of heavenly bodies i.e., the solar system, galaxies, super-galaxies and spin of both macroscopic bodies and quantum particles.

The interface, the boundary which separates the two energies, is volatile c) like a mirage having virtual existence. The constant interactions of the two energies make the existence of the interface seem persistent. Penrose was very close to this idea when he discussed the Galilean relativity. However, he considered this idea as unphysical 6):” It may seem alarming that our very notion of physical 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."



What he stated was, in fact, correct except that space does not appear and disappear in time but, on the contrary, it is the appearance and disappearance of the space which creates time passage.  Had he done otherwise, he would lead us on the right track to reality.

The separation of the spacetime does not take place instantaneously but gradually. The "area" of the separation is stretching out across the spacetime just like a big crack propagates in a solid body. The former represents a static universe while the latter represents the expanding universe (Figure-4). It is the underlying reality of the expanding universe as against the Big Bang theory.

Notes:
a) We use the notations of space, hypersurface, and hyper-interface, or surface and interface interchangeably.
b)     At the quantum level these equations are completely reversible
c)   The relativistic expression (m2c4 + p2c2) involves complex numbers so that there is no clear cut separation (interface) between those two separated energies, in the sense that the interface appears only instantly and disappears immediately after.

References:
1.   Abbott and Ness, V.: Thermodynamics”, Schaum’s Outline Series, Mc Graw-Hill, New York, 1967, p. 1
2.     Greene, B.: "The Elegant Universe," Vintage Books, New York, 2003, p. 207-208.
3.   Einstein, A.: "The Meaning of Relativity," Fifth Edition, Princeton Science Library, New Jersey, 1988, p. 31
4.     Barbour, J.:" The End of Time," Phoenix, Second Impression, London, 2001, p. 14
5.     Penrose, R.:" The Road to Reality," Vintage Books, London, 2004, p. 408-409.
6.     Ibid, p. 387


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