Symmetry and Symmetry Breaking

The asymmetry and its associated diversity that we observe today was the result of symmetry breakings which occurred in the early stage of the cosmos. In the beginning, ^a), the conditions were very different from those prevailing today, they were symmetric. The spatial dimensions as we know today did not yet exist; all dimensions were inherently temporal. However, as those temporal dimensions were yet undivided, there was no past, present ^b) and future.

At those conditions, the energy ^c) was unstable and tended to break into its positive and negative components. When it happened, the associated 4-spacetime (cosmos) ^d) was split into two parts creating an interface (3-hypersurface) in between the two. The dimensions across the interface transformed into spatial; leaving the dimensions outside it remained intact ^e).  Space, therefore, was born.

The two opposing energies ^f) perpetually generated sort of 4-lights (quantum fields) piercing through the interface (space) inducing secondary 3-(classical) fields which permeated and propagated across the interface (Figure-1A). As the quantum fields hit the interface, the strongest of them (Higgs fields) generated bright sparks which immediately disappeared as the opposite fields annihilated them (Figure-1B).

 The fundamental particles as we know are in reality nothing but these quantum-sparks which perpetually appear and disappear at the interface. As those quantum fields hit the entire surface of the interface and penetrate it only a short distance (across through the thickness of the space), they seem to us (who live in such interface/3-space) as eternal, omnipresent and invisible objects that can create and annihilate quantum particles.

Minkowski ^{1, g)} brilliantly fused the space and time into its undifferentiated state and brought back the spacetime into its original condition. However, then, something wrong happened. Instead of bringing the spacetime back into its symmetrical condition, Einstein²assumed that such unification did not make the temporal and spatial dimensions equivalent. Einstein failed to recognize that the asymmetry as we see today was the result of the spacetime symmetry breaking. This blunder has hampered the progress of physics for more than one hundred years now.

On the discovery of the four-dimensional spacetime, Einstein³ commented: “The non-mathematician is seized by a mysterious shuddering when he hears of four-dimensional things, by a feeling not unlike that awakened by thoughts of the occult.” No wonder, even after one hundred years of experience dealing with such spacetime, physicists are still bewildered and fail to recognize that their chaotic spacetime model does not represent the post symmetry breaking we observe today.

Supersymmetry Breaking and Multidimensional Worlds

The symmetry breaking of the 4-spacetime as we previously described was only one of the long series of successive symmetry breakings. It was the last of the long chain of a successive splitting of a higher-dimensional spacetime into its lower-dimensional parts.

To make it clear, let’s take the ambient 10-spacetime as a start. As this 10-spacetime broke its supersymmetry, a 9-hypersurface came into being along with its associated temporal dimension, t₇.  The latter, in turn, was split creating a smaller 8-hypersurface and its associated time, t₆ and so forth. This series of splits continued resulting in successive creations of the spacetimes in descending order of their dimensions and ended when the 3-space came into being along with its associated time t₁. A total of seven worlds ^h) have successively come into being with their own individual time, t_i, light and its respective speed, c_i, Planck constant, h_i, and “gravitational” constant, G_i.  

We can depict those seven worlds in term of their relative dimensionality (Figure-2.) or pictorially described as concentric spheres whose dimensions are larger outwards, in which the innermost layer is the 3-space with all of its solar system, stars, galaxies and super-galaxies (Figure-3A).

It is worthy to note that this picture may clarify the exact physical meaning of the ancient cosmology. For hundreds of years, people had wrongly considered this configuration as the geocentric cosmology in which the earth was at the center of the universe (Figure-3B). Even now, modern physicists fail to properly grasp the multidimensionality of the seven heavens described in the ancient cosmology ⁴.

Notes:

a.    It is the relative beginning, not the beginning of time.

b.   The notation of spacetime given for the cosmos at its original state is misleading as it gives the impression as it was asymmetrical from the beginning. It would be more appropriate if we use the notation world, cosmos or more technically [metric] manifold.

c. Energy in its entirety (4-energy); to avoid misunderstanding it would be more appropriate if we use the ancient notation: eon or simply eon.  The energy as we know is merely its superficial property (3-energy).

d.   There was no space, as space and the present time are different aspects of the same thing.

e.  This symmetry breaking is analogous to the phenomenon which occurs in the separation of two immiscible liquids, such as oil and water. In the body of the liquids, the cohesive forces are symmetric exerting equally in all directions. At the interface, however, such symmetry is broken because of unbalanced force exerting at the interface. As the system is in equilibrium,  the potential energy known as interfacial tension counter the net unbalance force. In terms of coordinate geometry, we may say that the interfacial tension differentiates the dimensions across the interface ("superficial" dimensions) from those of the original.

f.     The relativistic energy is composed of two opposite components as expressed in E² = m²c⁴ + p²c²

g.    Minkowski died one year only after the discovery, leaving confusion on his discovered object (spacetime)’s structure.

h.   The ancients called such worlds seven heavens.

References:

1.    Einstein, A. et al.: " The Principle of Relativity," Dover Publications, Inc., New York, 1952, p. 75.

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

3.    Einstein, A.: "Relativity," Crown Publishers Inc., Fifteenth Edition, New York, 1952, p.55

4.    Hawking, S.: "A Brief History of Time," Bantam Books, London, 1989, p. 3.

Space Thickness, Supermanifold and Multidimensional Time

We used to conceptualize the geometry elements such as point, line, surface and space as having, respectively, zeroed, one, two and three dimensions. There is nothing wrong with that as far as we are dealing with abstract objects such as a corner point between a floor and two walls, meeting line between ceiling and wall, table's surface or hall's spaciousness.

However, we cannot apply such a concept for real bodies, whatever the size is. A grain of sand is not a zeroed-dimensional object, but a three-dimensional cubic-like body, which has small length, width, and thickness. A string is a three-dimensional long cylindrical object having a small section. Similarly, a piece of paper is a three-dimensional surface object whose thickness is very thin (Figure-1). Had their thickness been reduced to zero, those objects would all have gone into thin air.

Nature does not seem to give any exception to natural bodies such as space or any other higher-dimensional spacetimes. For their existence to have physical meaning, all those bodies should have thickness.

It implies that space or spacetime, whatever its dimensions, are always be embedded in an ambient spacetime of at least one dimension higher. At the same token, the later is also embedded in turn in another much higher manifold (Figure-2).  This kind of infinite regress makes us believe that nature is vast and infinite, not only its areas but also its dimensions. 

System and Surroundings

Now, the formulation of the laws of nature depends naturally on which system we choose. Suppose we want to formulate physical laws within a system of an m-dimensional spacetime embedded in  N-dimensional ambient manifold, we get, then, physical laws of a system having (N-m) extra dimensions. The directions of these dimensions determine those of the spacetime’s thicknesses pointing outwards away from it.

We can also describe the same physical laws in a much simpler system where the same N-ambient space embedding (N-1)-hypersurface, instead of an m-spacetime. The thickness of such a hypersurface has the same direction as at the N^th dimension pointing outward away from it.

The laws of nature in the first system have very complex formulations and are difficult to resolve, as the system has too many extra-dimensions and, hence, fewer symmetries.  The laws of nature in the second system are relatively more straightforward as the system has only one extra-dimension and is highly symmetric.

We can best describe the laws of nature when the number of the dimensions of the ambient space embedding the system is large enough which "stretches" out the hypersurface to become completely flat and perfectly symmetric.

How do we determine the dimensions of the ambient space (N) vis-a-vis that of the embedded spacetime (m)? There is a minimum requirement for the number of the ambient space's dimensions in order that the spacetime can be “properly" embedded in the ambient space. The [non-flat] m-spacetime can be embedded in N-manifold only if at least N = ½ m(m+1) ¹⁾. The metric tensor of the m-spacetime dictates that the ambient space should have that amount of dimensions for all of its components can be properly defined.

Based on the above rule, the 2-surface requires  3-ambient space for which we do not doubt it. The non-flat 3-space, in our surprise,  requires 6-ambient spacetime, not to mention the 4-spacetime which requires 10-ambient manifold. It may indirectly explain why we have three generations of elementary particles and the 10-ambient manifold as revealed in the current theoretical physics. 

Multidimensional Time

Now, what are these dimensions all about? As we have discussed previously, the spacetime is the physical manifestation of energy. In its original state, the spacetime was perfectly symmetric. All of its dimensions are indistinguishable, and they are all "temporal." When the respective energy segregates into the positive and negative energies, the [temporal] spacetime's dimensions along the interface [separating those opposing energies] are transformed into spatial dimensions.  

For the classical 4-spacetime, the energy segregation transforms three of the spacetime's temporal dimensions along the interface into spatial (Figure-3). In a 6-spacetime, the energy’s segregation transforms the spacetime's five temporal dimensions along the interface into spatial dimensions. The same case also prevails for the 10-spacetime., where nine temporal dimensions along the interface become spatial.

The temporal dimensions  t1, t3 and t7 related to the 4-, 6- and 10-spacetimes, respectively, are different from each other. It is against the mainstream premise which tacitly asserts that there is only one temporal dimension in nature.

Based on the rule we have, a 4-spacetime requires a 10-ambient space for the physical laws to have solutions. However, as we have in this case 3 spatial dimensions and seven [imaginary] extra-temporal dimensions, the physical laws we get would be very complicated. It is imperative, therefore, to have the same laws applied to a system consisting of a 10-ambient space embedding 9-hypersurface, which are simpler as we have only one imaginary temporal dimension on top of the nine real ones.

 It is more or less what physicists have done in developing the string theory, except that the extra-dimensions were assumed to curl into tiny loops. Also, the temporal dimension of the system was assumed to be the same as that of ordinary time. Such wrong assumptions have been put forward because mainstream physics holds the premise that time is one-dimensional as previously mentioned. 

The relativity theory should rigorously hold the equivalence of space and time dimensions. The spatial and temporal dimensions should be transferable to each other depending on the system they become part. The extra dimensions are undetectable not because they curl into tiny loops but because they are temporal.

Supermanifold and Supersymmetry Generators

Physicists have many problems with their mathematical propositions as they used to conceptualize the spacetime as a standalone basis. Under such a concept they have taken the part of the reality out of the system. Such as is the case of the Big Bang theory, which is entirely Platonic, a system without any geometrical thicknesses, surrounding, nor even 3-space.

A reader of the Scientific American²⁾ once asked: "Where is the universe expanding to?"  The authoritative answer from the expert was: "... the universe's expansion does not push it into new territory - rather the spacetime grid itself is expanding".  The issue has arisen again and again since the Big Bang theory was put forward, as only a few people were satisfied with such an explanation. The excellent answer should be that the universe is expanding to at least the 10-dimensional ambient space, and not into nothing.

To make their model closer to the reality, some physicists artificially introduced what they called supersymmetry generators, replacing the thicknesses which they have “forgotten” to incorporate in their mathematical model. They call this manifold having thicknesses “Supermanifold”³⁾. The physicists should put forward the problems of embedding at the forefront of physical researches and develop a more holistic model instead of a piecemeal one.

References:

1.      Sokolnikoff, L.S.: ”Tensor Analysis," Wiley Toppan, Second Edition, New York, 1964, p. 205

2.      Kashlinsky, A.: "Where is the Universe Expanding to?", Scientific American, (Ask the Experts Forum), May 2007, p. 104

3.      Penrose R.: "The Road to Reality," Vintage Books, London, 2005, p. 879

Expanding Space, Convergence and Hyperfunction

So far we have shown that the process of the spacetime splitting can be described purely from mathematical analysis. We transformed the complex plane into a Riemann sphere to get a more pictorial representation of the entire spacetime, including the infinities. The real space axis (X) on the complex plane is now represented by the real equatorial circle while the imaginary time axis (it) of the complex plane by the imaginary longitude circle of the sphere (Figure-1).

Since the energy in its purest nature can be described as a wave, mathematically it can be best formulated in the form of Laurent series f(z) expressed as a sum of its positive frequency part and the negative frequency part:

                      f(z) = F⁺(z) + c₀ + F^–(z)

When it is mapped on the Riemann sphere ^a), the positive frequency F⁺(z) extends holomorphically into the southern hemisphere, and the negative frequency F^–(z) extends holomorphically into the northern hemisphere.

The constant c₀ is represented by the real equatorial circle which is the shared boundaries of those opposing frequencies.

This is how the energy split is described mathematically into its positive and negative energies. Physically, we can explain such energy split through the division of the spacetime into two halves. One half, the southern part of the spacetime, represents the positive energy zone and the other half, which is the northern part, the negative energy zone.  The interface between those two opposing zones is the space where all material things, the super-galaxies, a cluster of galaxies, galaxies, stars, solar system, and the earth are located.

So far we have assumed that the size of the real equatorial circle on the Riemann sphere or the space in the spacetime is not changing in time.  The whole spacetime is completely split instantly which makes the universe static. In term of the Riemann sphere the real circle, which physically represents the space, immediately gains the infinite equatorial size. 

In reality, there is no such a static universe as supported by the astronomical observations (among other the Hubble's redshift)^b). In line with that, space should be gradually expanding in time ^c), depicted by an expanding interface in the spacetime (Figure-2B). In term of the Riemann sphere, this is represented by an expanding real circle (Figure-2A).

Now we come to an essential question as to whether the expanding real circle is starting from the beginning as a point (singularity) or from certain definite size? As we remember, the Riemann sphere has a kind of annulus of convergence which excludes a particular area surrounding the zero point and that of the infinity (Figure-3).

The real circle starts to appear only after gaining a certain size. This means that space begins to materialize just after achieving a certain minimum size, below which nature abhors the existence of such space and all materials within. Also, the annulus of convergence also indicates that space will disappear entirely after gaining a certain maximum size for the space to exist.

Does nature allow a partial spacetime split? According to excision theory, the hyperfunction of the shared boundaries (the real circle of the Riemann sphere) is independent of the particular choice of the region of the f(z) as shown in Figure-4.

 

This means that the real circle (space) ^d) can take any size as far as it is within the annulus of convergence. Space appears only after it gains a sufficiently large size and expands afterward up to a maximum allowable size for the space to exist. After that space dissolves completely into pure energy. Nature keeps the physical world to take place outside the vicinity of the singularity and infinity.

Notes:

a)     As the spacetime is the structural quality of energy, the Riemann sphere becomes the domain of the energy wave function.

b)     The interpretation of which gave rise to the Big Bang theory

c)     According to the Big Bang [and the general relativity] theory, it is the spacetime instead of space which is expanding.

d)     The real circle on the Riemann sphere or the physical space within the spacetime framework is not necessarily flat and may be curved more or less significant.

References: 

1. Penrose, R.: "The Road to Reality," Vintage Books, London, 2005, pp. 159, 172-175.

Energy, Spacetime and Riemann Sphere

The ultimate goal of the special relativity theory, if we are aware of, is the unification of the spacetime and energy. The union of these two would reveal the reality of energy which differs entirely from what we used to think about. Energy is a substance whose geometrical structure is reflected by the dimensionality of its spacetime.

Our ordinary [four-dimensional] spacetime is the physical manifestation of the energy whose vibrations are four-dimensional. As a [three-dimensional] human being we can only perceive this pure energy through its superficial three-dimensional aspect. Many underlying higher-dimensional ambient spaces which physicists have discovered, as they are adventuring deeper and deeper into the micro-world realms, are nothing but the reflections of various hyper-vibrations energies.

The relativity theory demonstrates that energy as a whole is inherently composed of positive and negative energies, as implicitly expressed in the relativistic energy equation E² = m²c⁴ + p²c². The segregation of its opposite parts that resulted in the split of energy created a 3-hypersurface (space) between the two halves of its separated respective spacetime. The world was not created through the "big" tiny bang bursting out of nothing.

In the quantum realm, energy as a wave can be described proportionally to its frequency as expressed by the Planck equation, E=hv.  We can express the energy, not only microscopically but also macroscopically, in term of the wavefunction whose character is completely holistic and non-local. However, the more natural way for us to grasp, is to express it in a periodic function such as a Fourier series ^a) or its complex form: the Laurent series ^b). 

In the relativistic framework, we map events in a complex plane where we express time in term of an imaginary variable. In such a plane, we have a Laurent series written as:

              f(z) = F⁺(z) + c₀ + F^–(z),

which is a wave function expressed as the sum of its positive frequency (F⁺(z)) and negative frequency (F^–(z)). Physically, the constant term c₀ represents the real space at t=0 (the present now). This c₀, wholly or partially, becomes either the part of F⁺(z) or F^–(z) or maybe both. However, as there is only positive energy, at least in this corner of the world where we live in, the space (c₀) should be part of the positive ocean of energy, F⁺(z), and on the other side of the world it should be part of negative ocean of energy, F^-(z).

Geometrically, we can figure out this more clearly in terms of the Riemann sphere, the stereographic projection of the complex plane. On this sphere, we can transform the real axis (X) of the complex plane into a circle located on the equator, while the imaginary time coordinate (it) by the longitudinal circles. The positive frequency F⁺(z) extends holomorphically into the southern hemisphere, and the negative frequency F^–(z) extends holomorphically into the northern hemisphere (Figure 1). 

From this description, we have a complete similarity between that of purely mathematical geometry with the relativistic (Minkowski) spacetime geometry (Figure 2 A and B). The real circle on the Riemann sphere represents the 3-hypersurface (space) in the Minkowski 4-spacetime which separates it into two 4-halves. The positive energy segregates to one half, and the negative energy segregates to the other half of the spacetime. We can These two halves are respectively represented by the southern and northern hemispheres on the Riemann sphere. The real circle on the Riemann sphere and the hypersurface in the Minkowski spacetime, each represents the loci of all matters which may exist in the whole universe.

With this simple mathematical representation, we can have a deeper insight into how nature may work. As we have figured out previously, the real circle in the Riemann sphere represents the space, and the imaginary circle represents the time path. As time passes by along the imaginary circle, space (real circle) is rotating accordingly along the time direction (imaginary circle). As time flows resemble electric current, space is also rotating on its plane following the right-hand rule. The rotation of this space as a whole rotates, in turn, all celestial bodies from the super-galaxies down to galaxies, solar systems, and the earth.

Notes:

References:

1. Penrose, R.: “The Road to Reality”, Vintage Books, London, 2005, pp. 157-162.

IT’S NOW OR NEVER

    For St. Augustine who knew about time until someone asked for him to explain ¹
    For Albert Einstein who was worried about the problem of Now
    For him who felt so sad that the experience of Now could not be grasped by science ²
    For Eckhart Tolle who claimed of getting power from the Now ³

    Also,… for Elvis Presley who used to sing the song

What is Time? What is Now?

The "now," the present time, is when everything is there
The past time is when everything was there but is not there anymore
The future time is when everything will be there but is not yet there

The present is when everything is present
The past is when everything was present but is not present anymore
The future is when everything will be present, but is not yet present

The present is when everything does exist
The past is when everything did exist but does not exist anymore
The future is when everything will exist but does not yet exist
 Everything does exist simultaneously in a very brief moment of now ^a)
Nothing does exist in the past and the future
Everything does exist just only now, right now, in this very brief moment of now

When now becomes the past, everything is annihilated
When the future becomes now, everything is created ^b)
Nothing persists; everything is created and annihilated perpetually and orderly
Space is nothing but the simultaneous presence of everythingSpace is the totality of now
Now and space are indistinguishable, the two different aspects of the same thing ^c)

Now separates the past from the futureSpace separates the past from the future Space is there to establish cosmos out of chaos ^d).

Technical Notes:

a)      The relativity theory denies the existence of the absolute simultaneity of now. What we are talking about in this case is within the framework of multiple extra-temporal dimensions (as against the concept of curled extra-spatial dimensions), where the term of “now” here is similar but in a higher temporal dimension. We can always find a higher temporal dimensional where everything happens simultaneously (a completely flat higher-dimensional space).

b)     We view it from human perspectives and languages. It turns the reality entirely upside-down.  The perpetual creation and annihilation do not happen in time. On the contrary, the act of perpetual creation and annihilation which makes time appears to pass by. Enough for wishful time travel debates and no more chronology protection is required.

c)      The "now" and space is the smallest unit of [four-dimensional] time. Space, which can be regarded as a 3-hypersurface, having a thickness (in the direction of the fourth dimension) of 10^-33 cm. This thickness is also representing the duration of fundamental time unit (10^-44 second) which we call Now.

d)     The interplay between the positive and negative energies perpetually creates a dynamic ephemeral space. A spacetime without space (universal "now") is chaotic.  Under the current light-cones framework, we cannot single out the simultaneity of events from the chaos of coexistence and succession of things.

References:

1.   Russell, B.:” History of  Western Philosophy," Routledge, London, 1996, p. 352

2.   Barbour, J.:" The End of Time," Phoenix, London, 2001, p. 143

3.   Tolle, E.:" The Power of Now," New World Library, Novato, California, 1999

Energy and Quantum Information

So far we have paid our attention to the nature of energy on its potency, its capability to generate power and strength. There is another aspect of the energy which hardly any physicist is touching namely its capability to store and process the information. The power and information are two sides of the same coin.  

Let us revisit the phenomenon of the wave-particle duality as diagrammatically shown in Figure-1. A particle which we perceive subsisting through time is, in reality, a series of different but similar particles appear and disappear successively.

Particle "A" disappears as one moment passes, and new particle "B" appears as the next moment arrives. This process takes place perpetually so that another new particle "C," "D," "E" and so forth appears and disappears successively. We wrongly perceive as though all those different particles are the same particle ("A") like a bullet flying through the air.

So what bewilders us more is that those processes take place simultaneously upon all particles in the whole universe. Even though there is a gap of nothingness between the two consecutive moments of the appearance of the whole universe, the order in macroscopic level is rigorously maintained. We, our form and shape appear to be the same today and tomorrow. A chair will remain the same as of yesterday, today and tomorrow, and never randomly changes to become a table.

So what does this imply?  Energy, which survives throughout the whole process of creation and annihilation, should possess a sort of information that it carries and processes along with at the speed of light.  At the quantum level, energy performs like small processing units which are integrated at macroscopic level as a large supercomputer processing all those information at the speed of light.

The appearance and disappearance of matter to and fro energy might function as natural binary digits which are the basis of quantum computation. It opens to a new era of information technology. Some physicists¹ seriously consider the possibility to tap and wangle this quantum processing which will radically change, one way or another, the conventional methods of information processing.

What is life?

The natural capability to store and process the information, in psychic terms, is called awareness. At a higher degree, we may call it consciousness and intelligence. The higher the dimensions of energy are, the higher the degree of its consciousness and intelligence. The [four-dimensional] energy which is intimately related to matter possesses the lowest degree of awareness. Those related to the plant, animal, and human possess higher and higher dimensions, thus, higher capacity and capability in carrying and processing the information.

Plants and animals might evolve for the better, but this evolution cannot pass through the barrier of their owned energy dimensionality. There is no missing link between the plant and animal kingdoms and between the latter with that of human, just because there are no links between them. Darwin's evolution theory was correct but within the corridor of the respective kingdom.

Schrodinger² was one of the prominent physicists who tried to embark on the study of life. Physicists, who are interested in doing so more deeply, should be prepared to confront something having infinite-dimensionality.

REFERENCES:

1.      Jurgen, A., et al.:” Entangled World”, Wiley-VCH GmbH, Weinheim, 2006

2.      Schrodinger, E.:” What is life”, Cambridge University Press, Cambridge, UK, 1967