This chapter outlines the main framework of a model for TOE Called Universal Theory. It utilizes astrophysics, quantum mechanics and mind behavior to offer a model for theory of everything. You may find the whole paper on the website at www.universaltheory.org.

This is a work in progress. Your input to address the flaws is very much needed. We are currently writing the lagrange formula for the concepts presented. In that, we need a mathematician who is familiar with theoretical physics to assist us in establishing the mathematical base for them. Please send me an email or leave your input in message board.

Singularity

-- A Separate Entity --

"We must try to understand the beginning of the universe on the basis of science. It may be a task beyond our power, but we should at least make the attempt" Steven Hawking (6- p79)

So far, the efforts of the scientific community have been confined to reveal the secrets of our material world; we have progressed so far. At the dawn of the 21st century, every day a new and amazing discovery is brought forward. Each discovery though, presents to us even more puzzles and questions. In physics, the dilemma between General relativity and quantum mechanics has attracted much of the effort and research of physicists throughout the world. Through their endless efforts, the picture of our world, is becoming more and more understandable and interesting. In this spirit, I would like to submit the following concepts for scientists to review and examine. If it is proved to be, based on sound principles, it can shed light onto many unsolved dilemmas, which are facing us today. And if it does not, still we can take it as food for thought.

Revisiting Singularity

The idea of introducing a fabric for wholeness of the world is nothing new. The scientific findings provide numerous evidences, which support common sense, and every day experience that the world is an interconnected and closed system. Other attempts have been tried which was not completely successful and could not get popularity. Even David Bohem tried to present his Implicate Order as a model, but unfortunately, he could not finish his Unbroken Wholeness Theory before he died. 

This is another attempt to present a model for the wholeness of the world. This model is based on redefining the singularity and use it as the background for space-time universe. Singularity is the zero size ultra dense mass which according to Big bang theory our universe originated from it.

Singularity was brought to our attention after Albert Einstein presented his Einstein Field Equation on November 18th 1915. Einstein himself was trying to deny it, for the rest of his life. In 1939, he tried to show that "Schwarchild singularities do not exist in physical reality" (Reference 4-p 9). Then it was taken as the nucleous for big bang explosion in Big Bang theory.

Since then in physics, singularity has been labeled as a 'Catastrophe', 'problematic', 'non-real', and 'non -physical'. However singularity clearly present itself in every physical or astrophysical theory, as well as quantum mechanics, and all mathematical equations related to these theories.

As, mentioned above, several attempts where made to bypass singularities such as Super Symmetry, Super Gravity, Super String theories. They were primarily, developed to remove singularities and infinities from matter and fields.

Physicists have been trying to ignore it for almost a century;

"We knew that there were significant aspects that we would need to work out before we could establish that our second half of the story did not introduce any singularities- that is pernicious and physically unacceptable consequences." Brian Green (1- page 327)

But others such as John Earman see it otherwise:

"(This book is) written in the faith that, if adequately revealed, the problem of space-time singularities will not remain the orphan of the philosophy of science and that if adopted as a rightful child, it will enrich not only the philosophy of space and time, but other members of the family as well" (Reference 4-p.227)

To present an alternative view for singularity, I would like to refer to Einstein's remarks as the gateway for new definition:

"If we imagine the gravitational field... to be removed, there does not remain a space of type (1) {Minkowski space-time}, but absolutely nothing, and also no topological space. ... There is no such thing as space without field. Space- time does not claim an existence of its own, but only as a structural quality of the field." (Einstein 1961)

John Earman argues that "Einstein is surely right that, whatever the technical details of the definition of space- time singularities, it should follow that physical laws, in so far as they presuppose space and time, are violated or, perhaps more accurately, do not make sense at singularities. This is a good reason for holding that singularities are not part of space time." (Reference 4-p.19)

According to the above, we should forget about space-time as an adjective for singularity,rather we have to consider singularity as separate entity. From here on in, I also intend to refer to it, as a singular noun, not plural.

Space-time universe started and evolved from a zero size point called singularity

If we suppose that singularity is not part of space-time, we expose ourselves to a new definition for reality. Let us imagine a singularity as a separate entity out of our space-time universe.

Mathematical discontinuity represents holes in the fields. Dividing a real number by zero creates discontinuity in math domain. This same problem renders itself in General theory of relativity. This gives the astronomers the sense that there should be holes in space-time.

I certainly do not intend to offer you a series of assumptions with no objectivity and practical proof. Underneath, I will introduce logical basis for above definition for singularity.

At first glance, one can ask, if our physical knowledge is derived from laws of space-time, how can we define and explain an entity which is out of this physical universe? With this belief, singularity looks abstract. Steven Weinberg questions "How can we get the ideas we need to formulate a truly fundamental theory, when this theory is meant to describe a realm where all intuitions derived from life in space-time become inapplicable?" 49

But we are also facing quantum behavior, which is far from understanding by our conventional logic and knowledge. At this time nature and origin of Mind are also obscure and may be can never be explained by our conventional understanding.

On the other hand, one may also denote, anything out of boundaries of our universe is so remote that it cannot have anything to do with our lives or our universe. Why should we bother spending time on it at all?

At least in one theory (Loop Quantum Theory) the boundaries of universe is believed to exists in every miniscule of space. The theory states that space is not a continuum; rather it has a fabric-like texture.

According to above we are exposed to out of space in every miniscule of space-time. Also in this paper, I hope, I can show that the singularity is involved in every basic activity in space-time.

Another reason that physics avoid the concept of a being out of the space-time universe is because it is considered incomprehensible and out of reach. I believe if we look closer, we come to realize that some characteristics of singularity are within our grasp. To further define singularity, let us discuss the different properties, which we can or cannot relate to it. Specifically I am going to mention six characteristics that we can attribute to singularity.

Matter

The confusion began when we refer to singularity as an ultra dense mass. Mass is a property of space-time universe. According to John Earman, mass cannot exist in singularity. If we define singularity as the origin of our universe but out of our space-time structure, we have to take it as a no-mass entity. We may hypothesize this because space and time originated at the time of big bang.

The Einstein formula (Larantz transformation) for a mass in motion is;

m = m0 / sqrt (1 - v²/c²)

The formula for time is

t = t0 / sqrt (1 - v²/c² )

If we take m as mass inside space-time after big bang (the time that space started and motion could be possible) and m0 as mass which was present at the beginning of time(t0) we come to following conclusion;

m/m0 = t/t0

m0 = mt0/t

m0 = 0/t = 0

So we can conclude that the mass at time equal zero (time of the big bang) had to be zero. Or we may say that singularity had to be mass less.

Alternatively, Nahid S. Gozin Is showing how singularity can not contain mass by following equations.

t = t0 / sqrt (1-v²/c² )

Or, sqrt (1-v²/c² ) = to /t , Where to is beginning of time and t is the time of appearance of mass in universe.

If to = 0, then sqr(1-v² / c²) = 0/t = 0, or sqr(1-v²/c² ) = 0, therefore (1-v²/c² ) = 0

So, v²/c² = 1, or v² = c² therefore v = c is speed of mass at the time when it appeared in space-time.

The mass at time 0 comparing to the mass after appearance inside space-time can be calculated from ;

m = m o / sqr(1-v²/c² ), and

m o = m* sqr(1-v²/c² )

If the speed of particle at time 0 was equal to speed of light then,

m o = m* sqr(1-1) = 0

According to above singularity could not contain mass. If we believe that singularity was a compressed mass then gravity would stop the infaltion and creation of the universe. Paul Davies argues that in state of maximum compression of matter, we need "some sort of outward force to overcome the enormous gravity, otherwise gravity would win, and the material would be still more compressed." 7-p48-49. He then conclude that under condition of extreme compression such as occurred during the big bang, there is no force in the universe capable of beating off the crushing power of the gravity. 

Elsewhere John Earman suggests "Perhaps. In entailing singular behavior General Theory of Relativity is committed to empirically false predictions" Ref. 4-p224

According to Big Bang Theory quarks first appeared after cosmic inflation. The vacuum energy transforms itself to particles and anti-particles of matter in equal number. So at the beginning of time there was no mass present. Unless we assume that the ultra dense matter turned to pure energy before reformation to matter particles. We can as well assume that universe started with a burst of energy. With this assumption singularity does not have to contain mass.

In this case we will not have positive gravity force and/or event horizon for singularity. Even we may assume a kind of negative gravity force (Repulsive) to initiate space-time.

If we remove mass from singularity, it turns benign.

Dimension

Einstein mentions that singularity cannot contain topological space. So Singularity does not have space. It means there is no spatial dimension in it. In other words, singularity is a mathematical point. Space is a property of space-time. According to Big Bang theory space started at time0 and expanding since. Heizenberg uncertainty principle suggests that, in small-scale location gets blurred. We will discuss this in further detail later.

If we denied mass as origin of universe we have to consider its energy equivalent as the initiator. The formula for the venomous energy which built our space-time universe is as follows;

ψ (E) = E max e ^{i ( κr^n -ωt )} = E max e ^{i ( κnr -ωt )}

Where ψ (E) is energy function, i is imaginary number , κ is wave number, nr is number of dimensions, ω is angular velocity and t is time.

ψ(E) = E max e ^iκnr e ^{-i ωt}

in singularity t = 0, then e ^{-i^ω t} = e 0 =1

ψ(E) =E max e^iκnr

We told that energy is maximum in singularity then ψ(E) =E max therefore e ^{i κnr} = 1

If iκrn = 0 we may conclude that n = 0 which means there are no dimension in singularity. or we can claim singularity does not contain space.

The physical reality of imaginary numbers are not defined in space-time. For the time being let us attribute it to virtual functions in singularity. Remember dimensions of superspace in supersymmetry model have zero size.

Time

"As Einstein said, physical laws break down at space- time singularities, and for the big bang and big crunch they break down so strongly that it is physically meaningless to talk about before and after" (Reference 4-p20)

According to theory of big bang, notion of time does not exists in singularity. Time is a property of space-time universe. If we extend the uncertainty principle to energy and time in small-scale time gets blurry.

Energy

If we deny the ultra dense matter, of being the origin of our universe, we have to find another source to substitute it. Big bang model states that our universe started with burst of tremendous amount of energy. This initiated the primary inflation.

Not comfortable with it? this is another evidence; The Heisenberg Uncertainty principle can be extended to time and energy. The second Feynman Diagram for Compton Scattering leads us to such an uncertainty. its formula can be written as;

ΔE * ΔT = or greater than h/2π

Where h is (Planck Constant), ΔE is the uncertainty in energy and ΔT is the uncertainty in time.

ΔE = or greater than h/2πΔT. If the product of ΔTΔE is minimum, then we can write ΔE = h/2πΔT

While in larger intervals of time the change of energy of particles are related and proportional, in ultra short intervals the amount of energy increases exponentially. In zero time zone, the changes of time will be zero. Therefore the changes of energy amounts infinity. -later on we conclude that we are exposed to singularity in each Planck distance.

If the changes of energy in singularity is infinity we may conclude that the amount of energy itself is also infinity.

But what kind of benign singularity this can be if it contains infinite amount of energy?

On the above formula when time intervals are 10^-43 The amount of energy is huge but as time intervals get bigger energy reduces very fast to harmless levels. Later on we see that if the blast of energy last for ultra short time and disappears, it will not have any effect in our material world.

Energy, through the creation of matter and anti-matter, can initiate our space-time universe, as it is today.

"A black hole singularity can be appreciated both as the ultimate garbage dump, able to take care of any waste disposal problem without the need to recycle, and as a source of extractable energy" (Wald 1984a, pp. 324-330)

The energy inside singularity has to be vibrational and field like. This can offer an explanation for quantum fluctuation which will be dealt with it later in quantum mechanics chapter.

On the other hand, in the Hawking's formula for black hole's temperature is;

T = hc3/8πkGM

where h stands for Planck constant,c for speed of light, K for Boltzmann's constant,G for Newton's gravitational constant and M stands for mass.

In above formula, if mass (M) is zero, the temperature would amount infinity. Of course here with lack of matter, temperature relates to internal energy of the system or energy of singularity in this view.

Stephen Hawking Says "the uncertainty principle of quantum theory means that fields are always fluctuating up and down even in apparently empty space, and have an energy density that is infinite." 6 p144

Not convinced yet? May be you can consider that the spooky infinities come up when we are dealing with mathematics of different kinds of energy and energy related force fields, whereas bizarre zeros appear while doing the mathematics of matter, space and time.

Here are more evidences of energy presence in zero field.

Zero point posses energy

Lamb shift and Casimir force is a proof for it. If you consider how many zero points exists in the universe, you will come to recognition of incredible source of energy which can be derived or is being derived from point zero. Robert Forward (4) at Hughes Research Laboratories in Malibu, California has shown in a paper that at least in principal we can extract that point zero energy to produce electricity.

Dr. Forward mentions in his derivation, when equations of quantum mechanics are used to determine the average energy (with a bracket on both sides of the E) of the vibrations of the atoms, the answer is

E = n(T) + hf/2.

In a harmonic oscillator the energy levels are quantized. The formula for energy state is ;

En = (n + 1/2) h/2π * w

En = n * h/2π * w + 1/2 * h/2π * w

if w = 2πf

En = n * h/2π * 2πf + 1/2 * h/2π * 2πf

En = nhf + 1/2hf

Where n is quantum number (photon number) and f is frequency of photon which emitted by exited atom. In above formula, if temperature equals to zero the particles (electrons,) have vibration at energy corresponding to the n=0 state. Then at T=0, n=0 because the atom is not excited (it can not emit any photon) therefore the value of energy in this case is;

En = 0 + hf/2 = hf/2

This is the lowest value of energy. Thus, even at zero temperature quantum mechanics predicts that each of the atoms will still have an average residual energy (as we can see if we let n go to zero) there remains the hf/2. Physicists have been grappling with this for years because there appears to be an infinite amount of energy available if f is allowed to increase without limit. Ever since Casimir predicted it and various other scientists have verified it, this simple equation is really all that is underlying the theory of the zero point field and zero point fluctuation.

Since it was first introduced, so many unexplained found explanation. Such as,

The New Scientist (July 1987, "Why Atoms Don't Collapse") gives an impressive endorsement of the importance of ZPE:

"There is a dynamic equilibrium in which the zero-point energy stabilizes the electron in a set ground-state orbit. It seems that the very stability of matter itself appears to depend on an underlying sea of electromagnetic zero-point energy." (21)

Both theory and experiment have shown that there is a non-thermal radiation in the vacuum and that it persists even if the temperature could be lowered to absolute zero. Therefore, it was simply called the "zero point" radiation. Further proof is evident, as Dr. Forward points out in his tutorial below, when physicists have cooled helium to within micro degrees of absolute zero and still it remains a liquid! Only ZPE can account for the source of energy is keeping helium from freezing. (21)

This issue has been re-addressed in a recent paper by the same author, this time taking into account what has been learned over the years about the effects of zero-point energy. There it is shown that the electron can be seen as continually radiating away its energy as predicted by classical theory, but simultaneously absorbing a compensating amount of energy from the ever-present sea of zero-point energy in which the atom is immersed, and an assumed equilibrium between these two processes leads to the correct values for the parameters known to define the ground-state orbit. Thus the ground-state orbit is set by a dynamic equilibrium in which collapse of the state is prevented by the presence of the zero-point energy. The significance of this observation is that the very stability of matter itself appears to depend on the presence of the underlying sea of electromagnetic zero-point energy.(22)

The common believe about the source of zero point energy is explained below,

"Historically there have been two schools of thought: Existence by fiat as part of the boundary conditions of the universe, or generation by the (quantum-fluctuation) motion of charged particles that constitute matter. A straightforward calculation of the latter possibility has recently been carried out by the author. It was assumed that zero-point fields drive particle motion, and that the sum of particle motions throughout the universe in turn generate the zero-point fields, in the form of a self-regenerating cosmological feedback cycle not unlike a cat chasing its own tail. This self-consistent approach yielded the known zero-point field distribution, thus indicating a dynamic-generation process for the zero-point fields." (22).

The later concept tries to attribute the zero point energy to the familiar matter particles, which exist, inside space-time. This kind of reasoning seems logical and objective and offers comfort. On the other hand thinking that it can come from boundaries of universe, exposes us to scary unknown arena beyond it. Most physicists would prefer to accept the matter origin for source of zero point energy.

You may ask how zero point is related to singularity. We explore the relation In "Where is Singularity" chapter where we conclude that we are exposed to singularity in each miniscule of fabric of space(Planck Distance).

Craig Hogan says, "It is ironic that gluons, which are forces and not matter, make up most of the mass of familiar matter. How flexibly our thinking must adapt to unfamiliar realm of nature!" 13p 35

And Last but not the least, recent NASA observations reveals the presence of a non-zero cosmological Constant which is responsible for acceleration of expansion of the world. According to NASA scientists and other astrophysicists the reason for this non-zero amount is the dark energy, which permeates in from empty space and separates the galaxies and push them away from each other. which is responsible for acceleration of expansion of the world.

I finish this part by a conclusion derived by NASA after non-zero cosmological constant Proved to be true by WMAP findings;

"Many cosmologists advocate reviving the cosmological constant term on theoretical grounds. Modern field theory associates this term with the energy density of the vacuum. For this energy density to be comparable to other forms of matter in the universe, it would require new physics: the addition of a cosmological constant term has profound implications for particle physics and our understanding of the fundamental forces of nature."

Information

Burst of energy was not the only factor, which initiated our universe. They were also physical laws, which guided and shaped the universe as it did. This laws and information was also present at the beginning. Can I conclude that information is also a property of singularity, which was leaked inside our universe at the time of big bang?

The concept of zero point energy proposes that there is energy available at zero point. The amount of this energy is calculated as 1/2 h, where h is Planck Constant which is equal to equal to 6.64*10^-34 joule per second. Further on in this model we take Planck Constant (h) as minimum amount of energy debriefed from singularity.

If h=J.s -1 then its dimension is dimension of energy divided by dimension of time.

Δh = ΔE/ΔT = M c²/T = ML² T^-2/T = ML² 2 T^-1

Where M is mass, L stands for dimension and T is time. Here we want to conclude that the properties of mass, distance and time is included in (h), which means information about these basic elements is contained in minimum amount of energy (h) found in zero point.⁽⁴⁰⁾

Above we concluded that energy in singularity is maximum. Energy always accompanies with field. Field contains information. So singularity has to have maximum information.⁽⁴⁰⁾

Let us discuss it further. Our hypotheses assume singularity as media to connect different part of space-time. On the other hand in an empty infinite universe movement of one object does not have a meaning. Motion is relative to other objects. Even spatial position of each object is relativistic. How would an object aware of another remote object, which is moving compare to it? Where do the laws of physics obtain the spatial information from different objects in distant places to act upon them accordingly?

Time is also relativistic. There should be information about a universal clock in every miniscule of space so the laws of physics utilize it and acting according to it. 

How are different objects aware of each other's presence?

It seems that information is flowing and is accessible everywhere. And as such it has to be the property of the medium. We assumed singularity as our medium.

Just as a token, remember that space, time and matter are not the only elements, which are swallowed by black holes. Information pours into them as well. There is actually a debate about where this information ends up in black holes.

Although recently, Stephen Hawking claimed that information is brought back at the end of black hole dissolution. In any case it is an indication that information can travel back and forth to singularity. What lies inside and beyond singularity is the question.

Last but not the least, on the story of big bang we follow a road from zero organization to more and more organized world. In a sense we start from maximum entropy. Maximum entropy means no organization and maximum information. ⁽⁴⁰⁾

Fields: information Domain

May be we can interpret fields as information domain. Any mass entering it, will be affected by the background order. Remember we chose information as one of the irreducible principles of singularity.

With the above definition we have hypothesized that singularity is in equilibrium. It has maximum amount of entropy (no material or even spatial structure). It also contains maximum amount of information.

In space-time universe what mass does for matter and gravity, motion does for space and time, fields do for energy and information.

The above Characteristics, describes a kind of entity, which I suppose can exist outside of space-time universe. Although, singularity may not be the best name for this entity, because it may get confused with condensed mass singularity. On the other hand I cannot resist choosing it because otherwise, it perfectly describe the proposed entity. This singularity is not as pernicious, because it does not contain ultra dense mass.

Shrinking World

Einstein's special relativity tells us that when an object is moving relative to a framework, its size shrinks for some one residing in that framework. the amount of shrinkage depends on speed of object. If we take this principle to extreme, for a framework which is not moving at all, the moving object downsizes to zero.

If notion of distance is not present in singularity, logically there is no movement for such entity, so we can take it fixed and motionless .therefore in such framework, the size of moving space-time will reduce to zero.

I adapted this concept from the universal theory of relativity by By Roland Michel Tremblay and Big Shrink by Richard Quist. It is interesting how the above authors reflected and expressed the non locality and shrunk world that they sense in their minds to a new model for universe.

So far we tried to follow physical laws to reach the proposed singularity. But the result is something, which may not occur in physics that we know. On the other hand, departing from classic physical laws, when evidence dictates it, is not a very extraordinary action. Please note that, quantum mechanics, which are dealing with particles that are the building blocks of our physical universe, are also accepting non-locality (not spatial) and wavelike (no-mass) characteristics, which are similar to characteristics, I proposed for singularity.

I would like to bring Kurt Godel's philosophy of mathematics on his works on undecideability as an indication for the possibility of presence of entities beyond our space-time universe.

"He reasoned that there would always be mathematical statements that are true but can never be proved to be true from existing axioms. He envisaged these true statements as therefore already existing- out there- in a platonic domain, beyond our ken." 7 p 142

Now, lets see if the above definition of singularity can help us to find solutions for the unexplained paradoxes which exists in theoretical physics and questions about nature of consciousness.

At this point, for the concept to get more familiar and tangible, let us explore the mind. We have to accept the mind as an inseparable part of our world. Abner Shimony agrees with Roger Penrose that mentality can be treated scientifically. 5- P144 

Paul Davies states "I have come to the point of view that mind is conscious awareness of the world. It is not a meaningless and incidental quirk of nature, but absolutely fundamental facet of reality." 7-p16

Mind is the tool that we use to interpret and recognize the world around us. Let us use this tool to clarify the above concept further.

Summary; in this view, we define singularity as a separate entity from space-time universe, which lacks space, time and matter and includes infinite amount of energy and information. We further speculated that energy fields are originated in singularity. In case of gravity, any object inside space-time would derive this force proportionate to its mass. We also assumed that space-time universe exists and expands inside the proposed singularity.

In following chapters I will offer explanations for many unexplained phenomena in physics in the basis of proposed model and explore the mystery of mind and its relation to other elements of reality.

References

1. The Elegant Universe, Brian R. Greene, March 2000, Vintage Books

4. Bangs, Crunches, Whimpers, and Shrieks, John Earman, Oxford University Press 1995

5. The Large, the Small and the Human Mind, Roger Penrose et al, Cambridge University Press, 1955

6. The Universe in a Nutshell, Stephen Hawking, 2001, Bantam Books

7. The Mind of God, Paul Davies, 1992, Touchstone Book, Simon & Schuster

11. The Quantum Challenge, George Greenstein, Arthur G. Zajong, Jones and Bartlett Publishers. 2001

13. The Little Book of Big Bang, Craig j. Hogan Springer Verlag New York Inc. 1998

21. http://users.erols.com/iri/ZPENERGY.html

40. Coutesy of N. Sahelgozin, Alzahra University, Tehran, Iran

41. http://www.crownedanarchist.com/relativity.htm

42. http://www.geocities.com/bigshrink2000/

49. A unified physics by 2050?, Steven Weinberg, Scientific American, Volume 13 Number 1

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