Singularity of the Universe

Abstract
Cosmologists have developed many theories to explore the ultimate origin of the universe. There are three main branches including scientific cosmology, philosophical cosmology, and theology. Although all the existed theories get to the point very closely, every theory has its own weakness. Scientific cosmologies fail to explain singularity due to all the known laws of physics break down in it. Philosophical cosmologies stuck in the cause of the universe could not be the universe itself. Theologies meet with the same dilemma. God being the whole universe or a part of it if He/She exists in it cannot be the cause of it. Taking into account the advantages and disadvantages of all the existed theories, I neglect all the known laws of physics and make use of pure mathematical functions. The calculation result reveals there is a singularity. Interestingly, the singularity is negative universe that could be the answer to the first cause of the universe.
I. Introduction
Human beings have been trying to explore the beginning of our universe from time to time continuously. Cosmologists had developed a plenty of theories rapidly last century. From different points of view, cosmologies can be divided into three main branches such as scientific cosmology, philosophical cosmology, and theology.
As early as 1917, Alexander Friedman realized that expanding universe must have begun with a singularity1. In 1915, Albert Einstein developed his theory of general relativity2. He was interested in gravity3-8. The gravity will make the universe collapse into a singularity9-12. However, all the known laws of physics break down in singularity. To get around this difficulty, Einstein invented the “cosmological constant” -- a hypothetical repulsive force operating on large scales that prevented the collapse of the universe. According to this assumption, he could not find the first cause of the ultimate origin of the universe.
In 1983, James Hartle and Stephen Hawking developed quantum cosmology13. They proposed that a cosmic wave function could be applied to the entire universe similar to the wave function that quantum mechanics had applied to elementary particles. According to this approach, the usual distinction between future and past breaks down in the very early universe. In order to improve the theory of relativity, Stephen Hawking developed the black hole theory14-27. Nevertheless, after applied different laws to black holes, he could not get any breakthrough for the barrier of singularity. In 1988, he guessed that black holes are not so black in his book A Brief History of Time28. Penrose-Hawking theorems address that anybody undergoing gravitational collapse must eventually form a singularity. The singularity problem is still the barrier for the investigation of ultimate origin of the universe.
Edwin Hubble discovered the redshift of galaxy light in the 1920s. The redshift of the light from galaxies is proportional to their distance (as inferred from brightness). No cause of galaxy redshift other than a velocity away from the observer was considered plausible, so Hubble's result was taken to mean that, the farther away from us a galaxy is, the faster it moves away from us. Hence, the overall universe had to be expanding. And the ultimate origin of the universe should be a singularity for the time regress. This evidence supports the big bang theory. The big bang theory postulates that the entire universe originated in a cosmic explosion about 15-20 billion years ago. It is true that physicists hope to look behind the big bang, and possibly to explain the origin of our universe as, for example, the first cause of the universe. Unfortunately, the creation of universe could not be tested by experiments.
Edward Tryon first suggested that the universe might be a vacuum fluctuation29, “essentially from nothing at all”. Alexander Vilenkin also addressed that it would be better to start with “literally nothing”, which was not matter, space or time, but a total empty geometry of absolute nothingness from which the universe made the transition to a non-empty state by quantum tunneling30. Another originator of the idea of an inflationary early universe Alan Guth pointed out that the beginning of the universe there was nothing, a pure vacuum with no space or matter, a vacuum which is subject to quantum uncertainties so that things can come out of it and vanish back into it31. All of them are getting closer and closer to find the answer for the ultimate origin of the universe except singularity.
The cosmologist, P. James E. Peebles, said that there is strong evidence that most of the mass of the universe cannot be accounted for by the things we see, but there must be some sort of unknown dark matter32. Nevertheless, the dark matter as a part of the universe if it exists could not be the cause of the universe.
More recently, Vilenkin and Jaume Garriga developed a “many worlds in one” theory in which our universe contains an infinite number of other universes, or O-regions, where alternate histories play themselves out33. In 1957, Hugh Everett34-35 explained the possible states do not collapse, but the universe somehow divides, and accommodates each possibility in a new world. Bryce DeWitt36 and David Deutsch37 even claimed that each time we do something, or each time something, no matter how small, changes in the universe, a new universe is created, and therefore millions and billions of universes are being created at every moment. Considering the differences, one will wonder how to distinguish the edges of those different worlds. The question is back to singularity.
The philosophical cosmologists try to fathom two facts. Firstly, the universe exists. And secondly, it exists in a distinctive way. The philosophical challenge is whether something can come from nothing. Timothy Ferris38, for example, suggests that quantum cosmologists look at three fundamental problems: that of a first cause, that of something coming from nothing, and the issue of infinite regress. The philosophical cosmologies face with serious problem. Everything in the universe being a part of it cannot be the cause of it. It leads to a religion question.
The Bible starts with Genesis. God created the universe in six days. The physicist Frank Tipler pointed out in his book The Physics of Immortality: that “Either theology is pure nonsense, a subject with no content, or else theology must ultimately become a branch of physics. The reason is simple. The universe is defined to be the totality of all that exists, the totality of reality. Thus, by definition, if God exists, He/She is either the universe or part of it. The goal of physics is understanding the ultimate nature of reality. If God is real, physicists will eventually find Him/Her.”39 It seems God might be non-universe.
In the opinion of the physicist Charles Townes, the question of origin seems always left unanswered if we explore from a scientific view alone38. It is a common issue for science, philosophy and religion. Can we sum up all kinds of cosmologies to work out the solution? Nowadays, it is conceded that the universe is not perfectly isotropic or homogeneous. All cosmologies agree that the cause of the universe should not be the universe itself or a part of it. It is time to explore non-universe.

II. Analysis
Based on Hubble’s discovery, the big bang theory is the most acceptable cosmology. The big bang cosmology postulates that all matter in the universe was at one time located at a point in space, and then the universe would have a singularity. At the beginning of the universe, time is zero (t=0). What event had happened at t=0? Or what is the “first cause” of the universe? Let’s assume the unknown event is “x”.
The boundary conditions of the beginning of the universe are:
1. There was no universe before the big bang.
2. The universe existed after the big bang.
3. The x event happened at the big bang.
This model can be described as following:
Nil (t<0)  Big Bang (t=0)  Universe and “x” (t>0).
A pure mathematical equation is able to represent this model at t=0.
(1)
Where U is the universe and x is the unknown event.
One can easily to solve the eq.(1) and get the result.
(2)
The unknown event is negative universe. According to the postulation of the big bang cosmology, the negative universe should be the so-called singularity. There is a simple mathematical function for singularity.
(3)
This function has a singularity at x=0.
The first boundary condition above tells us
(4)
Where t is the time.
Thus,
(5)
The ultimate origin of the universe started at about 15-20 billion years ago. From then on, the universe is expanding for a long time continuously. Therefore, the singularity should be very far away from us. Our reference framework is the earth. It is reasonable to believe that the position of the singularity is very far away from the earth. Thus, p in the eq.(3) should be considered as the position function of the negative universe with respect to the earth.
After having the position function of the negative universe, one can compute its surface.
(6)
Where S is the surface of the negative universe and C is constant.
Furthermore, one can derive the volume of the negative universe, too.
(7)
Where V is the volume of the negative universe and C1 is constant.
One can obtain the value of S and V from the boundary conditions.
Substitution of eq.(4) into eq.(6), one can have
(8)
The minus sign represents the negative universe.
Substitution of eq.(4) into eq.(7), one will obtain
(9)
Again, the constant C1 can be solved by the boundary conditions. At the big bang, the volume of the universe is zero. By balancing the volume between the universe and the negative universe at the big bang (t=0), the volume of the negative universe should be zero as well. So that, the eq.(9) becomes
(10)

III. Discussion
The eq.(2) is the significant breakthrough. There is non-universe or negative universe. The eq.(10) reveals that the negative universe is a singularity. It is the theoretical proof for the postulation of the big bang cosmology. The redshift of galaxy light which was discovered by Edwin Hubble in the 1920s is the observation evidence for the expanding universe. Both theoretical and experimental results are able to prove that the negative universe singularity is the solution for the ultimate origin of the universe.
The eq.(5) tells us that the negative universe singularity is at infinitive position away from the earth. Although human beings could not observe the negative universe singularity, the theoretical calculation results have proven there is an edge and outside of the universe. It is common sense that the edge and the outside of the universe must not be the universe itself. The negative universe is non-universe. Hence, the negative universe should be the edge and the outside of the universe.
The eq.(8) shows that the negative universe has minus infinitive surface. The edge can cover the whole universe no matter how huge it is. The minus sign represents the negative universe. It is easy to understand that the edge of everything can cover the whole lot of itself.
The eq.(10) indicates that the volume of the negative universe is zero. This is contrary with traditional idea. The universe is immensely huge that the outside of it might be bigger than it. The fact is negative universe is a singularity so that our universe does not have any outside of the edge. From eq.(10), one can conclude that our universe is unique.
In a word, the negative universe model overcomes the barriers for all existed cosmologies. Scientific cosmologies will accept a singularity without the laws of physics. Philosophical cosmologies will satisfy with the universe comes from nothing with a cause but not itself. And theologies will proudly announce God is not a part of the universe.
When Einstein was writing his theory of general relativity in 1916 the prevailing feeling that the universe was static was so strong that when his equations indicated that the universe should be expanding, or contracting. The important issue is whether the gravity can reduce the expanding rate or not. By balancing the expanding rate, he introduced a cosmological constant to produce a universe at rest. However, he could not explain the problem that something is making the universe accelerate. The negative universe model offers the opportunity to improve the theory of general relativity. The acceleration comes from negative universe.
P. James E. Peebles suggested there must be some sort of unknown dark matter32. The dark matter would increase the gravity of the universe if it exists and reduce the expanding rate. It is contrary with accelerate expanding universe. The negative universe model opens another chance for further investigation to unknown dark matter. The dark matter could be the negative universe singularity.
Edward Tryon et al realized that the universe might be created from nothing29-31. They had tried to discover the cause of the creation but failed. The negative universe model gives a theoretical support for their postulations. The negative universe singularity created the universe.
Stephen Hawking et al described a black hole picture applying a series of laws of physics13-28. All the known laws of physics are able to explain the evolution of the universe but not for the creation of it. Any black hole being a part of the universe if it exits cannot be the cause of it. This is why the laws of physics break down in singularity. On the other hand, the gravity of the early universe should be greater than a black hole if it exits. The Hubble telescope has observed the light from the early universe. The early universe could not prevent the propagation of light why a black hole can. It is clear that the gravity is not the reason. The negative universe model provides the reason to overcome this problem. The negative universe singularity can eliminate anything in the universe including light.
Vilenkin et al imagined the many worlds or multiverse situation33-37. However, they could not distinguish the edges between the many worlds. The negative universe model is able to give them the hints. The edge of the world should be non-universe or negative universe.
The negative universe model is also a reason to believe God. Although human beings cannot see negative universe, it exists. Human beings ought to imagine that God is non-universe and powerful to create and eliminate the universe.
Let’s sum up the theories above. All existed cosmologies have their own advantages. Human beings develop many theories from different viewpoints to describe the beginning of the universe. The correct answer for the fact should be only one. A theory should obtain the only one correct answer for the fact if it is correct. The negative universe singularity has consensus with all the existed cosmologies perfectly. The negative universe singularity is the theoretical proof for Hubble’s discovery. Vice versa, Hubble’s observation is the experimental evidence to prove the negative universe model. The negative universe singularity is the conclusive solution for the ultimate origin of the universe.

IV. Conclusion
There is a negative universe singularity without any law of physics. It is non-universe. It is the edge of the universe. It is at the infinitive position away from the earth with minus infinitive surface and zero volume. And it is also the first cause of the universe. Our universe is unique without any outside of the edge.


References:
1. Friedman, A. Über der Krümmung des Raumes. Zeitschrift für Physik 377–386 (1922).
2. Einstein, A. Relativity The Special and the General Theory, (1916).
3. Einstein, A. & Rosen, N. On gravitational waves. Journal of the Franklin Institute 223, 0043-0054 (1937).
4. Einstein, A., Infeld, L. & Hoffmann, B. The gravitational equations and the problem of motion. Annals of Mathematics 39, 65-100 (1938).
5. Einstein, A. & Infeld, L. The gravitational equations and the problem of motion. II. Annals of Mathematics 41, 455-464 (1940).
6. Einstein, A. A Generalization of the Relativistic Theory of Gravitation. Annals of Mathematics 46, 578-584 (1945).
7. Einstein, A. & Straus, E.G. A Generalization of the Relativistic Theory of Gravitation .2. Annals of Mathematics 47, 731-741 (1946).
8. Einstein, A. A Generalized Theory of Gravitation. Reviews of Modern Physics 20, 35-39 (1948).
9. Einstein, A. & Straus, E.G. The Influence of the Expansion of Space on the Gravitation Fields Surrounding the Individual Stars. Reviews of Modern Physics 17, 120-124 (1945).
10. Einstein, A. Correction. Reviews of Modern Physics 18, 148-149 (1946).
11. Einstein, A. & Infeld, L. On the Motion of Particles in General Relativity Theory. Canadian Journal of Mathematics-Journal Canadien De Mathematiques 1, 209-241 (1949).
12. Einstein, A. The Advent of the Quantum Theory. Science 113, 82-84 (1951).
13. Hartle, J.B. & Hawking, S.W. Wavefunction of the Universe. Physical Review D 28, 2960-2975 (1983).
14. Hawking, S.W. Wormholes in Spacetime. Physical Review D 37, 904-910 (1988).
15. Hawking, S.W. & Laflamme, R. Baby Universes and the Non-Renormalizability of Gravity. Physics Letters B 209, 39-41 (1988).
16. Hawking, S.W. & Page, D.N. How Probable Is Inflation. Nuclear Physics B 298, 789-809 (1988).
17. Hawking, S.W. Inflation Reputation Reparation. Physics Today 42, 15-& (1989).
18. Hawking, S.W. Black-Holes from Cosmic Strings. Physics Letters B 231, 237-239 (1989).
19. Hawking, S.W. Gravitational-Radiation from Collapsing Cosmic String Loops. Physics Letters B 246, 36-38 (1990).
20. Hawking, S.W. Events in Time. Parabola-Myth Tradition and the Search for Meaning 15, 73-76 (1990).
21. Hawking, S.W. Baby Universes. Modern Physics Letters A 5, 145-155 (1990).
22. Hawking, S.W. & Page, D.N. Spectrum of Wormholes. Physical Review D 42, 2655-2663 (1990).
23. Hawking, S.W. The Beginning of the Universe. Primordial Nucleosynthesis and Evolution of Early Universe 169, 129-139 (1991).
24. Hawking, S.W. The No-Boundary Proposal and the Arrow of Time. Vistas in Astronomy, Vol 37, Pts 1-4 37, 559-568 (1993).
25. Hawking, S.W., Laflamme, R. & Lyons, G.W. Origin of Time Asymmetry. Physical Review D 47, 5342-5356 (1993).
26. Hawking, S.W., Horowitz, G.T. & Ross, S.F. Entropy, Area, and Black-Hole Pairs. Physical Review D 51, 4302-4314 (1995).
27. Hawking, S.W. & Ross, S.F. Duality between Electric and Magnetic Black-Holes. Physical Review D 52, 5865-5876 (1995).
28. Hawking, S. A Brief History of Time, (1988).
29. Tryon, E.P. Is the Universe a Vacuum Fluctuation. Nature 246, 396–397 (1973).
30. Vilenkin, A. & Shellard, E.P.S. Cosmic strings and other topological defects (2000).
31. Guth, A.H. Inflationary universe: A possible solution to the horizon and flatness problems. Physical Review D 23, 347 (1981).
32. Peebles, P.J.E. Principles of physical cosmology. (1993).
33. Garriga, J. & Vilenkin, A. Black holes from nucleating strings. Physical Review D 47, 3265 (1993).
34. Crease, R.P. The father of parallel universes. Nature 465, 1010–1011 (2010).
35. Byrne, P. The Many Worlds of Hugh Everett III: Multiple Universes, Mutual Assured Destruction, and the Meltdown of a Nuclear Family (1982).
36. DeWitt, B. & Graham, R.N. The Many-Worlds Interpretation of Quantum Mechanics. (1973).
37. Deutsch, D. The Structure of the Multiverse. (2001).
38. Ferris, T. The Whole Shebang. (1997).
39. Tipler, F. The Physics of Immortality (1994).

Phase diagrams, dielectric response, and piezoelectric properties of epitaxial ultrathin (001) lead zirconate titanate films under anisotropic misfit strains

JOURNAL OF APPLIED PHYSICS 107, 114105 2010
Q. Y. Qiu and V. Nagarajan
School of Materials Science and Engineering, University of New South Wales, Sydney,
New South Wales 2052, Australia
S. P. Alpay
Materials Science and Engineering Program, Department of Chemical, Materials, and Biomolecular
Engineering and Institute of Materials Science, University of Connecticut, Storrs, Connecticut 06269, USA
Received 16 December 2009; accepted 13 March 2010; published online 3 June 2010
We develop a nonlinear thermodynamic model to predict the phase stability of ultrathin epitaxial
001 -oriented ferroelectric PbZr1−xTixO3 PZT films with x=1.0, 0.9, 0.8, and 0.7 on substrates
which induce anisotropic in-plane strains. The theoretical formalism incorporates the relaxation by
misfit dislocations at the film deposition temperature, the possibility of formation of ferroelectric
polydomain structures, and the effect of the internal electric field that is generated due to incomplete
charge screening at the film-electrode interfaces and the termination of the ferroelectric layer. This
analysis allows the development of misfit strain phase diagrams that provide the regions of stability
of monodomain and polydomain structures at a given temperature, film thickness, and composition.
It is shown that the range of stability for rotational monodomain phase is markedly increased in
comparison to the same ferroelectric films on isotropic substrates. Furthermore, the model finds a
strong similarity between ultrathin PbTiO3 and relatively thicker PZT films in terms of phase
stability. The combinations of the in-plane misfit strains that yield a phase transition sequence that
results in a polarization rotation from the c-phase polarization parallel to the 001 direction in the
film to the r-phase, and eventually to an in-plane polarization parallel to the 110 direction the
aa-phase is determined to be the path with the most attractive dielectric and piezoelectric
coefficients resulting in enhancements of 10 to 100 times in the dielectric permittivity and
piezoresponse compared to bulk tetragonal ferroelectrics of the same PZT composition. © 2010
American Institute of Physics. doi:10.1063/1.3386465

Misfit strain–film thickness phase diagrams and related electromechanical properties of epitaxial ultra-thin lead zirconate titanate films

Acta Materialia 58 (2010) 823–835
Q.Y. Qiu , R. Mahjoub, V. Nagarajan
School of Materials Science and Engineering, University of New South Wales, Sydney, NSW 2052, Australia
S.P. Alpay
Materials Science and Engineering Program and Institute of Materials Science, University of Connecticut, Storrs, CT 06269, USA
Received 19 March 2009; received in revised form 7 August 2009; accepted 29 September 2009
Available online 24 October 2009
Abstract
The phase stability of ultra-thin (0 0 1) oriented ferroelectric PbZr1–xTixO3 (PZT) epitaxial thin films as a function of the film composition, film thickness, and the misfit strain is analyzed using a non-linear Landau–Ginzburg–Devonshire thermodynamic model taking into account the electrical and mechanical boundary conditions. The theoretical formalism incorporates the role of the depolarization
field as well as the possibility of the relaxation of in-plane strains via the formation of microstructural features such as misfit dislocations at the growth temperature and ferroelastic polydomain patterns below the paraelectric ferroelectric phase transformation temperature. Film thickness–misfit strain phase diagrams are developed for PZT films with four different compositions (x = 1, 0.9, 0.8 and 0.7) as a function of the film thickness. The results show that the so-called rotational r-phase appears in a very narrow range of misfit strain and thickness of the film. Furthermore, the in-plane and out-of-plane dielectric permittivities e11 and e33, as well as the out-of-plane piezoelectric coefficients d33 for the PZT thin films, are computed as a function of misfit strain, taking into account substrate-induced clamping. The model reveals that previously predicted ultrahigh piezoelectric coefficients due to misfit-strain-induced phase transitions are practically achievable only in an extremely narrow range of film thickness, composition and misfit strain parameter space. We also show that the dielectric and piezoelectric properties of epitaxial ferroelectric films can be tailored through strain engineering and microstructural optimization.
2009 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
Keywords: Ferroelectricity; Thin films; Phase transformations; Electroceramics; Dielectrics

Film thickness versus misfit strain phase diagrams for epitaxial PbTiO3 ultrathin ferroelectric films

PHYSICAL REVIEW B 78, 064117 2008
Q. Y. Qiu and V. Nagarajan
School of Materials Science and Engineering, University of New South Wales, Sydney, New South Wales 2052, Australia
S. P. Alpay
Materials Science and Engineering Program and Institute of Materials Science, University of Connecticut, Storrs, Connecticut 06269, USA
Received 1 June 2008; revised manuscript received 14 July 2008; published 27 August 2008
We present a full scale nonlinear thermodynamic model based on a Landau-Ginzburg-Devonshire formalism and the theory of dense polydomain structures in a multiparameter space to predict the phase stability of 001 oriented PbTiO3 epitaxial thin films as a function of film thickness and epitaxial strain. The developed methodology, which accounts for electrostatic boundary conditions as well as the formation of misfit dislocations and polydomain structures, produces a thickness-strain phase stability diagram where it finds that the rotational phases the so-called r and ac phases in epitaxial PbTiO3 are possible only in a very small window. We find that for experimentally used thickness or strains or both that often fall outside this window, the film is in either single phase tetragonal c phase or in a c/a/c/a polydomain state; this explains why rotational polar domains are rarely observed in epitaxial ferroelectric thin films.
DOI: 10.1103/PhysRevB.78.064117
PACS number s : 77.80.Bh, 77.84.Dy

Band structure of surface states and resonances for clean Cu(110) surface

Surface Science 601 (2007) 5779–5782
M.N. Read *, Q.Y. Qiu
School of Physics, University of New South Wales, Sydney, NSW 2052, Australia
Available online 30 June 2007
Abstract
We have used the layer KKR method to calculate the Shockley and Rydberg surface states and resonances for Cu(110) for a given model of the surface potentials. This method has not been used before to predict all of the surface band structure for the energy range from the bottom of the conduction band to 7 eV above the vacuum level. The previous methods that used only local electron interactions in ab initio calculations could not produce the Rydberg surface barrier bands while those relying on nearly-free-electron parameterisation of bands could not deal with d-bands.
2007 Elsevier B.V. All rights reserved.
Keywords: Cu(110) surface electronic states; Surface electronic structure calculations; Shockley and Rydberg surface bands; Layer-by-layer KKR
scattering method

Theoretical investigation of polarization scaling in ultrathin epitaxial PbZrxTi1−xO3 films

JOURNAL OF APPLIED PHYSICS 102, 104113 2007
Q. Y. Qiu and V. Nagarajana
School of Materials Science and Engineering, University of New South Wales, Sydney,
New South Wales 2052, Australia
Received 21 August 2007; accepted 27 September 2007; published online 29 November 2007

We present a theoretical analysis of the scaling of the polarization and the static dielectric susceptibility through a mean-polarization approach for ultrathin epitaxial PbZrxTi1−xO3 thin films. We use the traditional Euler-Lagrangian framework applied to a Landau-Ginzburg-Devonshire LGD nonlinear thermodynamic treatment. The novelty of our approach is that the model hinges on using experimentally measured correlation lengths and temperature scaling relationships to give the size-dependent expansion parameters of the nonlinear thermodynamic potential. These are then used in a Taylor series expansion of the polarization at the center of the film. We show that this method is able to correctly predict experimentally observed scaling without the need for the so-called extrapolation length which is impossible to measure experimentally . Furthermore, as no implicit correlation between the correlation length and the coefficient of the gradient term in the LGD potential g11 is assumed, the model thus involves fully experimentally measurable parameters and their systematic temperature dependence rather than implicit assumptions. The model finds that the Curie temperature in ultrathin films is more sensitive to epitaxial strain as compared to the polarization and that the critical thickness is strongly dependent on the “temperature-epitaxial strain” parameter space. Interestingly, while it finds that at lower temperatures the depolarization field does play a strong role in the thickness dependence as well as spatial profile of the polarization, with increasing temperature, a significant weakening of the role of depolarization fields occurs. Consequently the interface-induced suppression is lower and, as a result, the polarization profile is more homogenous at higher temperatures. This indicates that systematic temperature dependent studies are fundamental to further understanding of size effects i ferroelectrics.
© 2007 American Institute of Physics. DOI: 10.1063/1.2809334

丘乔羽: Scientific Research

丘乔羽: Scientific Research: "The Time Dilation Factor Could Not Obtain a Negative Time Qiao Yu Qiu** School of Materials Science and Engineering, University of New South..."