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2.5.11 Beyond the Standard Model

2.5.11.1 Overview

The Standard Model was established, but faced some difficulties. Then the theory was improved one by one.
Firstly, Supersymmetric Theory was introduced.
The second step split into roughly 2 schools in reference to continuous homogeneity of Spacetime or minimum units of Spacetime. The 1st school based on the presumption that Spacetime is homogeneous continuum and absence of minimun units. In contrast, the 2nd school based on the presumption that Spacetime is inhomogeneous and consists of components with minimum units.
The 1st "absence of minimum units of Spacetime" school had difficulties in integrating Gravity with infinities arising in quantity calculation regardless of renormalization, and managed to propose Superstring Theory employing 10 or 11 dimensional Spacetime supported by Supersymmetric Theory. However, it seems mathematical fictional fantasy irrelevant to the General Theory of Relativity as a whole. Yet, the virtue of Superstring Theory might be seen in its multiverse theory.
The 2nd "presence of minimum units of Spacetime" school bore "Loop Quantum Gravity" (and "Causal Dynamical Triangulation") associated with the General Theory of Relativity.
Thus humans approached the final answer, the Whole Inclusive Theory of Everything.

2.5.11.2 Detals

2.5.11.2.1 Georgi and Dimopoulos's Minimal Supersymmetric Standard Model in 1981 CE

Background
The Standard Model was established, but it yet had some problems.
The 2 major problems claimed were 2 kinds of Hierarchy Problems, "Hierarchy Problem about Forces" and "Hierarchy Problem about the mass of Higgs particle."
"Hierarchy Problem about Forces" is the great difference between Gravity and other forces in strength. Gravity is extraordinary weaker even than the weakest force of the other 3 forces, 10-32 times weaker than the Weak Force. (The Electromagnetic Force is some 10-100 times weaker than the Strong Force. (The precise ratio depends on the distances of the forces.) The Weak Force is some 10 times weaker than Electromagnetic Force.)
"Hierarchy Problem about the mass of Higgs particle" is that the experimentally estimated mass of Higgs particle is rather smaller than theoretically estimated mass. Collecting and summarizing primary constants in physics such as Planck Constant and the speed of light, it results in Planck Mass, 1.22*1019 GeV. It implies the original mass or fundamental mass could be some 1019 GeV.
In contrast to that, bosons generally have light mass or no mass including Higgs Bosons. For example, photons have no mass. The mass of Higgs Boson was also experimentally estimated rather light, around 100-200 GeV, at that time from a viewpoint of mass of derived particles, employing particle accelerators, supposedly from likely Higgs Bosons. On the other hand, as mentioned before, the light mass or no mass of bosons could be accounted for by symmetry.
However, since the spin of Higgs Boson is 0, Higgs Bosons wouldn't have symmetry according to the Standard Model. Higgs Bosons had no reason accounting for the light mass. This Hierarchy Problem about Higgs Mass had to be resolved introducing a new theory.
* "Hierarchy Problem in Wikipedia" http://en.wikipedia.org/wiki/Hierarchy_problem

Minimal Supersymmetric Standard Model
Georgi and Dimopoulos presented Minimal Supersymmetric Standard Model introducing Supersymmetric Theory simply to the Standard Model assuming supersymmetric particles. (Supersymmetric particles are frequently called "sparticles," preceded by "s" representing "supersymmetry.")
The assumption of Supersymmetry with supersymmetric particles solves the Hierarchy Problem about Higgs Mass Since the Supersymmetry assumes supersymmetric particles of Higgs Boson, Symmetry of Higgs Bosons accounting for the light mass of Higgs Bosons is assumed.
* "Minimal Supersymmetric Standard Model in Wikipedia" http://en.wikipedia.org/wiki/Minimal_Supersymmetric_Standard_Model
* "Minimal Supersymmetric Standard Model Download" http://arxiv.org/abs/hep-ph/9709356
In addition, the Supersymmetric Theory implied seemingly favorable presumption in relation to the unification theory of the 3 forces. The reciprocals of the coupling constant of the 3 forces and temperature/energy level are illustrated as follows.
* "Coupling Constant in Wikipedia" http://en.wikipedia.org/wiki/Coupling_constant
According to the reciprocals based on the Standard Model, the reciprocals wouldn't match at any energy level. However, according to the reciprocals based on the Supersymmetric Theory, the 3 reciprocals of the coupling constant might match at a specific high energy level. It implies the 3 forces were originally unified based on the Supersymmetric Theory implying the legitimacy of the Supersymmetric Theory.

Other than that, according to the Supersymmetric Theory, Dark Matter could be identified with some supersymmetric particles.
*As mentioned above, according to common physicists, "Hierarchy Problem about Forces" is claimed as well. However, it should be noted that the 3 forces (Strong Force, Electromagnetic Force, and Weak Force) and Gravity are different things based on different mechanisms. The 3 forces are mediated by particles (Gluons, Virtual Quarks, Photons, and Weak Bosons). However, as the General Theory of Relativity tells, Gravity is derived from curvatures of spacetime. (Gravitons might curve spacetime.) Gravitons wouldn't directly mediate Gravity.
Since the mechanisms are totally different, there would be no problem involving "Hierarchy Problem about Forces."

2.5.11.2.2 Aspect's Experiment in 1982 CE

Background
As mentioned before, based on the assumption of Quantum Entanglement's reality, Bell presented Bell's Inequality in 1964 CE to examine Einstein's assumption that based on the Principle of Locality observed properties of waves have been fixed prior to observation.

Aspect's Bell Test Experiments
Alain Aspect performed Bell Test Experiments on photons and proved Bell's Inequality's failure. It means that if Quantum Entanglement is real, Nonlocality is valid and 2 distant waves (particles) can relate instantly or simultaneously regardless of the Special Theory of Relativity. Nonlocality means that incidents, phenomena, or state, for example particles' change in a small area (local area) affects distant area's state. In other words, if Quantum Entanglement is real, an area's state is generally affected by distant waves' (particles') behaviors.
* "Bell Test Experiments in Wikipedia" http://en.wikipedia.org/wiki/Bell_test_experiments
* "Nonlocality in Wikipedia" http://en.wikipedia.org/wiki/Nonlocality

2.5.11.2.3 Exotic Differentiable Structure of 4-Dimensional Space in 1983 CE

2.5.11.2.3.1 Outline

It seems that this universe consists of 3-Dimensional space and 1-Dimensional time, while the context is unclear.
In topological mathematics, Donaldson presented a clue about the context through Donaldson's Theorem in 1982 CE. Integrated with Freedman's Theorem, it presented a special property of 4-Dimensional Euclidean space (mathematically common 4-Dimensional space) that is exclusively seen in 4-Dimensional Euclidean space, unlike Other-Dimensional Euclidean spaces. The special property is called "Exotic Differentiable Structure," in a sense, oddly non-smooth structure.
* "Exotic R4 in Wikipedia" https://en.wikipedia.org/wiki/Exotic_R4
* "4-Manifold in Wikipedia" https://en.wikipedia.org/wiki/4-manifold
* "Donaldson's Theorem in Wikipedia" https://en.wikipedia.org/wiki/Donaldson%27s_theorem

Three ideas (manifolds, homeomorphism, diffeomorphism) should be learned to figure out "Exotic Differentiable Structure" in 4-Dimensional Euclidean space, while it should be noted that topology (including manifolds, homeomorphism, diffeomorphism) is basically a conceptual thing (idea) rather than a real (existential) entity.

2.5.11.2.3.2 Manifold

The manifold is, in short, a smooth thing without any pointy corner, while it is a conceptual thing (idea).
For example, the edge of a circle is 1-Dimensional manifold. The edge of a square is not 1-Dimensional manifold, since it has corners then it is not smooth.

The edge of a sphere (the surface of a sphere) is 2-Dimensional manifold. The edge of a cube (the surface of a cube) is not 2-Dimensional manifold.
Specifically, the manifold would be defined as the conceptual thing with both 2 properties. One property is that local coordinates can be presumed around any points on the thing. Then 2 local coordinates can be presumed near a point on the conceptual thing. One local coordinate can be expressed (converted) on the other local coordinate. The other property is that the expressed (converted) local coordinate (on the other coordinate) should be differentiable infinitely many times. It means that the expressed (converted) local coordinate should be smooth or infinitely plane. (When the thing is infinitely plane, it has no corner and is differentiable infinitely many times.)


Other than that, for example, the surface of a donut is 2-Dimensional manifold similarly. 2-Dimensional Euclidean space (Plane space) is 2-Dimensional manifold when the space is infinitely spread. (Since smoothness is required on manifolds, 2-Dimensional Euclidean space is illustrated with round corners here.)


2.5.11.2.3.3 Homeomorphism

Homeomorphism is that continuity is preserved between deformed 2 things. (As far as homeomorphism, smoothness is not necessary. Then, the illustrations below hold pointy corners.)
  
Various locations of the things are named "a, b, c, ..." When the conceptual thing (1) is deformed, the conceptual thing (2) is created, and various locations on (1) correspond to various locations on (2) as above, the continuity in (1) such as "a, b, c, d, e" and "f, g, h, i, j" is preserved similarly in (2).

When (1) below is a manifold and (1) is deformed like (2) below, the continuity represented by the lines of (1) is preserved in (2). As the blue thing's form of (2) below is smooth, (2) below is a manifold through this deformation.


In the thing (3), since the continuity of the lines is preserved, homeomorphism is held between (1) and (3). However, since the blue conceptual thing (3) has pointy corners, the blue conceptual thing (3) is not a manifold.


The deformation of (2) and (3) with homeomorphism is like deformation of a rubber sheet. In contrast, the blue conceptual thing (4) is split, the continuity of the lines in (4) is not preserved. Then homeomorphism is not seen between (1) and (4).


2.5.11.2.3.4 Diffeomorphism

Diffeomorphism is the property that when the original lines in the original conceptual thing are smooth, the corresponding lines in the deformed conceptual thing are smooth. For example, diffeomophism is seen between the blue conceptual thing (1) and the blue conceptual thing (2), since the both lines are smooth. However, for example, diffeomorphism is not seen between the blue conceptual thing (1) and the blue conceptual thing (3), since the lines of (3) are not smooth. (Since the blue conceptual thing (3) has pointy corners and (3) is not a manifold, it is natural that the blue conceptual thing (3) is not diffeomorphic.)

2.5.11.2.3.5 Exotic Differentiable Structure

In contrast, "Exotic Differentiable Structure" of 4-Dimensional Euclidean space is the special property that the conceptual thing itself is a manifold (with smoothness (differentiable) without any pointy corner) yet the lines corresponding to the other manifold's (original manifold's) smooth lines are not always smooth (with (a) pointy corner(s) and indifferentiable).
An image of this oddly non-smooth structure might be like the blue conceptual thing (5). If the hollow of (2) is deeply indented and twisted, then it might become to be the thing (5). The blue thing (5) is smooth without any pointy corner, while it seems to be partly twisted. Then, a line has a pointy corner.


Since 4-Dimensional Euclidean conceptual space (infinite space) widely spreads, a spread image like the blue conceptual thing (6) could be presumed. In (6), the oddly non-smooth structure is seen everywhere, while the blue thing is smooth without any pointy corner. It could be an image of "Exotic Differentiable Structure" of 4-Dimensional Euclidean conceptual space.


Contrary to naive assumptions that the properties of dimensional space would regularly vary depending on number increase of dimension, 4-Dimensional space and 3-Dimensional space particularly show odd properties in topology.

2.5.11.2.4 Green and Schwarz's Superstring Theory in 1984 CE

Background
Various theories were presented to account for Gravity.
String Theory was presented, but faced various problems. String Theory at that time failed except for assuming presence of 26-dimensional Spacetime.
The Standard Model solved some problems predicting Gravitons with zero mass and 2 of spin quantum number. However, when the distance of 2 fermions came to zero, the theory fell in serious contradiction.
On the other hand, Georgi and Dimopoulos presented Supersymmetric Theory.
For another thing, a considerable number of elementary particles couldn't be fundamental elements.

Superstring Theory
Green and Schwarz claimed Superstring Theory based on the Supersymmetric Theory (and homogeneous Spacetime) avoiding various problems of String Theory assuming presence of 10-dimensional Spacetime. If 10-dimensional homogeneous Spacetime is real, Superstring Theory wouldn't show clear contradiction.
Superstring Theory compares various particles to tiny strings with vibration. It tried to account for various particles, forces, and other things through tiny strings. Various vibration modes represent various quantum properties. The length of strings would be like the Planck length (1.616*10-35 meters).
There are various kinds of Superstring Theories.
The early version of the Superstring Theory (Type I) by Green and Schwarz assumed both "closed strings (loops)" and "open strings (ordinary strings not looped)." According to the Superstring Theory Type I, "closed strings (loops)" correspond to Gravitons and "open strings" correspond to other elementary particles.

Subsequently, some versions of Superstring Theories were presented.
*By the way it should be noted that "Strings" or "Superstrings" would be a parable to explain the properties of particles (or waves).
*In addition, it should be noted that "Strings" or "Superstrings" is presumed vibrating, and moreover, dominated by the Uncertainty Principle.
*Other than that, it should be noted that Superstring Theory wouldn't be associated with the General Theory of Relativity. Superstring Theory yet has no proper theory on Gravity.
*In short, Superstring Theory is incorrect. Yet, its multiverse theory (mentioned below) is instructive and attempt to unify a considerable number of elementary particles is agreeable.
* "Superstring Theory in Wikipedia" http://en.wikipedia.org/wiki/Superstring_theory
* "SUPERSTRING!" http://www.sukidog.com/jpierre/strings/index.html
* "String Theory Website Basics" http://www.superstringtheory.com/basics/index.html
* "First Superstring Revolution in Wikipedia" http://en.wikipedia.org/wiki/First_superstring_revolution#1984-1989:_first_superstring_revolution

2.5.11.2.5 Candelas, Horowitz, Strominger and Witten's Calabi-Yau Manifold in 1985 CE

Background
Improvement of Superstring Theories resulted in requirement of additional 6-dimensional space to existing 4-dimensional Spacetime (spatial 3-dimensions and temporary 1-dimension). Consequently, 10-dimensional Spacetime was required to justify Superstring Theory or homogeneous Spacetime.

Calabi-Yau Manifold
Candelas, Horowitz, Strominger and Witten employed Calabi-Yau Manifold (Calabi-Yau Space) anyway to deal with accounting for (excusing) the additional 6-dimensional space. According to the vague excuse, the extra dimensions were assumed folded (curled) as tiny Calabi-Yau Manifolds.
(On the other hand, the number of different configurations of Calabi-Yau Manifolds would be like 2^500=10^150 through 10^500, since Calabi-Yau Manifold has at least 500 donut holes.)
* "Calabi-Yau Manifold in Wikipedia" http://en.wikipedia.org/wiki/Calabi%E2%80%93Yau_manifold
* "Universe-Review Calabi-Yau" http://universe-review.ca/R15-26-CalabiYau.htm

2.5.11.2.6 Linde's Eternal Inflation in 1986 CE

Background
Guth attempted to account for the Cosmic Inflation through Quantum Tunneling assuming False Vacuum. However, such one-shot theory was rather poor in perspective.

Linde's Eternal Inflation
Linde claimed Mother Universe inflating eternally and baby universes randomly (chaotically) created in the Mother Universe like cracks or bubbles in carbonated water respectively starting with inflationary expansion, named "Chaotic Inflation."
* "Eternal Inflation in Wikipedia" http://en.wikipedia.org/wiki/Eternal_inflation
*The random creation of the baby universes in the eternal inflating Mother Universe would be depicted as follows.


2.5.11.2.7 Weinberg's Multiverse and Anthropic Principle in 1987 CE

Background
The presumption of homogeneous Spacetime resulted in Superstring Theory with extra dimensions folded as tiny Calabi-Yau Manifolds. The number of different configurations of Calabi-Yau Manifolds would be some 2^500=10^150 through 10^500 kinds.
On the other hand, Physical fundamental constants were studied.

Weinberg's Multiverse and Anthropic Principle
Weinberg noted that various fundamental constants are rather favorable for living things.
On the other hand, the critical density of this universe associated with the Flatness Problem was some 10^-26 kg/m^3.
In contrast, the Planck density (of this universe) is 5.1*10^96 kg/m^3. The critical density is some 120 orders of magnitude smaller than the Planck density derived from a natural inference.
On the other hand, the number of different configuration of Calabi-Yau Manifold would be some 10^150 through 10^500 kinds.
Then, Weinberg claimed there should be other enormous number of universes with inappropriate physical constants resulting in no living things. Weinberg claimed this harmonized universe with proper fundamental constants is merely one of a myriad of universes. There would be other some 10^150 through 10^500 kinds of universes. This universe has proper physical constants by chance.
* "Flatness Problem in Wikipedia" http://en.wikipedia.org/wiki/Flatness_problem
* Planck Density in Wikipedia" http://en.wikipedia.org/wiki/Planck_density
* "Anthropic Principle in Wikipedia" http://en.wikipedia.org/wiki/Anthropic_principle
*Consequently, based on the presumption that Spacetime is homogeneous, the sole solution was Superstring Theory with 10-dimensional Spacetime. Then the additional 6-dimensional space had to be accounted for (excused).
The account was Calabi-Yau Manifold. The extra dimensional space (like 6-dimensional space) is folded as tiny Calabi-Yau Manifolds. On the other hand, Calabi-Yau Manifold has some 10^150 through 10^500 kinds in configuration. However, homogeneous Spacetime should consist of one kind of Calabi-Yau Manifold in configuration. (Since the Spacetime was presumed homogeneous.) Then, presence of myriad of universes like 10^150 through 10^500 kinds of universes (with different configurations of Calabi-Yau Manifolds) were assumed.

2.5.11.2.8 COBE's Lambda-CDM Model in 1992 CE

Background
Einstein ignorant of the Big Bang at that time assumed repulsion (represented by Λ) opposing gravity in the universe to balance the size of the universe.
COBE (Cosmic Background Explorer), a satellite to investigate the cosmic microwave background radiation, was launched by NASA in 1989 CE.

Lambda-CDM Model
The observation by COBE implied presence of an enormous amount of Cold Dark Matter (CDM) and an enormous amount of unknown entities in the universe represented by Lambda (Λ) derived from or commemorating Einstein's assumption of the Cosmological Constant Λ.
* "Cosmic Background Explorer in Wikipedia" http://en.wikipedia.org/wiki/Cosmic_Background_Explorer
* "Lambda-CDM Model in Wikipedia" http://en.wikipedia.org/wiki/Lambda-CDM_model

2.5.11.2.9 Smolin's Loop Quantum Gravity in 1994 CE

Background
Superstring Theory to a certain extent succeeded in accounting for the Standard Model, the 3 forces, and mass. However, Superstring Theory wouldn't refer to "space (distance)" and "time." It also means less association with the General Theory of Relativity involving Gravity. As mentioned before, Einstein claimed close relationship between Gravity, space, time, and curvatures of spacetime in the General Theory of Relativity. Einstein rather claimed Gravity is not a force, but a property of curved spacetime. Curvatures of spacetime should be considered to unify the General Theory of Relativity (including Gravity) and the particle physics.

Loop Quantum Gravity
The Standard Model mostly accounts for Gravity through particles, Gauge Bosons (Graviton). In contrast to that, Loop Quantum Gravity Theory mostly attempts to account for Gravity through space (distance), time, and curvature of spacetime based on the General Theory of Relativity.
Loop Quantum Gravity Theory assumes that space consists of minute simple 3-dimensional shapes such as cubes and quadrangular pyramids with the Planck length (1.616*10-35 meters) and so forth in size. This theory presumes "presence of minimun units of Spacetime."
An example is a cube of 2 Planck length (2*1.616*10-35 meters) on a side. (2 Planck length assumed here is just for explanation) Then the center point of the 3-dimensional shape (cube) is defined as "node" commonly expressed by a dot. The center point (node) corresponds to the center of a particle with (assumed) angular momentum (spin). (Particles except Higgs Bosons have spin.) Then the center point (node) corresponds to the center of spin of a particle. Lines are extended from the node to (through) the centers of squares of the surface of the cube. (In addition, if additional information of the cube and the squares on the surface are required, the volume of the cube (for example, 8) and the area of the square (for example, 4) are added.) Consequently, the cube is simplified to be the node and the lines.

If a quadranglar pyramid is added, they would be depicted as follows.

Loop Quantum Gravity Theory assumes that space is filled with such nodes (representing the centers of spins of particles) and lines connecting them. They are called "Spin Network." Consequently, lines form loops. Curved spaces would be expressed through combinations of 3-dimensional shapes (or nodes and lines).
* "Universe Review Quantum Gravity" http://universe-review.ca/R01-07-quantumfoam.htm
* "Loop Quantum Gravity Einstein Online" http://www.einstein-online.info/elementary/quantum/loops
* "Loop Quantum Gravity in Wikipedia" http://en.wikipedia.org/wiki/Loop_quantum_gravity
In addition, considering time passage, Spin-Network is improved into Spin-Foam. If 3 nodes and the 3 lines connecting the 3 nodes form a triangle (as an example of a part of Spin-Network) and the triangle doesn't move depending on time, time passage of the triangle is depicted as a triangular pole.
*The upward direction of the following figure involving the stationary triangle (and stemmed lines) designates time passage like Minkowski spacetime, although Spin Foam is commonly illustrated designating the downward direction to be time passage.

If the 3 nodes leave each other (or space curves accordingly) depending on time, the time passage of the triangle is for example depicted as an upside-down triangular pyramid, an upside-down triangular tower, or an upside-down trapezoid. Such depiction representing time passage of Spin-Network is called Spin-Foam.

However, it should be noted that the transition of the triangles (as an example of a part of Spin-Network) is not depicted continuously depending on time. Triangles are depicted discretely digitally like sequential photographs (with sequential strobe light) at intervals of the Planck time (10-43 sec) and so forth. Pictures of television and movies seemingly change smoothly. However, the transitions of the pictures of television and movies are in reality aggregations of static images frequently replaced. Transitions of triangles and Spin-Networks (Spin-Foam) are just like that.

2.5.11.2.10 Witten's M-Theory in 1995 CE

Background
Various Superstring Theories were presented after Type I. The circumstances became confusing.

Witten's M-Theory
Witten claimed some Superstring Theories would be united employing 11-dimensional Spacetime, instead of 10 dimensional Spacetime, to be a theory named M-Theory.
* "M-Theory in Wikipedia" http://en.wikipedia.org/wiki/M-theory

2.5.11.2.11 Polchinski's D-Branes in 1995 CE

Background
Superstring Theory had to account for extra 6 dimensions.
As mentioned above, an account was Calabi-Yau Manifold.

D-Branes
Polchinski claimed another account of the extra 6 dimensions. Polchinski claimed high-dimensional objects, named D-Branes. Some endpoints of Superstrings are connected to D-Branes. D-Brane was assumed drifting in higher dimensional space.
*For example, a D-Brane would be 3-dimensional space drifting in 9-demensional space. The D-Brane of 3-dimensional space represents this universe. Since the whole space is 9-dimensional, it amounts to 10-dimensional Spacetime and Superstring Theory wouldn't fall. Since this universe is 3-dimensional, the extra 6 dimension wouldn't be recognized.
Most Superstrings adhere to Branes. However, Superstrings of Graviton (closed strings) wouldn't adhere to Branes and they would rather escape to the extra dimensions. Then Gravity is extraodinary weaker compared with other forces ("Hierarchy Problem about Forces").
*This is the excuse by D-Branes Theory.

* "SUPERSTRINGS! D-Branes" http://www.sukidog.com/jpierre/strings/dbranes.htm
* "D-Brane in Wikipedia" http://en.wikipedia.org/wiki/D-brane
*However, if Gravitons escape to the extra dimensions, it results in an error that Gravity wouldn't comply with the Inverse-Square Law.
* "Inverse-Square Law in Wikipedia" http://en.wikipedia.org/wiki/Inverse-square_law
*Since dozens of elementary particles couldn't be fundamental existence, particles should be summarized by appropriate theories such as Superstring Theories. However, despite such attempts involving Superstring Theories, Superstring Theories seem drifting and reaching a dead end without promising perspectives and without considering curvature of Spacetime, the General Theory of Relativity. Consequently, Superstring Theories would be incorrect. Yet, some claims of Superstring Theories could be still implicative.

2.5.11.2.12 Riess' Discovery of Accelerating Expansion of the Universe and Dark Energy in 1998 CE

Background
Rubin discovered Dark Matter in the universe amounting to some 10 times than the observable mass.
The observation by COBE implied presence of an enormous amount of Cold Dark Matter (CDM) and an enormous amount of unknown entities in the universe represented by Lambda (Λ).

Riess' Discovery of Accelerating Expansion of the Universe and Dark Energy
Riess et al discovered an Acceleration Expansion of the universe. It implied presence of a hypothetical form of energy amounting to 73-74% of the total mass-energy of the universe. Subsequently, other observations followed.
The energy was named "Dark Energy." The Dark Energy might be identified with "Vacuum Energy," while details are unknown.
On the other hand, Accelerating Expansion of the Observable Universe after the Inflation coud be illustrated as follows.
If the observation is correct, the Whole Universe would be larger than that (for example 5 times larger in length), but details are unknown.

* "Observational Evidence from Supernovae" http://arxiv.org/abs/astro-ph/9805201
* "Accelerating Universe in Wikipedia" http://en.m.wikipedia.org/wiki/Accelerating_universe
* "Dark Energy in Wikipedia" http://en.wikipedia.org/wiki/Dark_energy
* "Vacuum Energy in Wikipedia" http://en.wikipedia.org/wiki/Vacuum_energy

2.5.11.2.13 Zeilinger' Verification of Quantum Entanglement in 1999 CE

Zeilinger verified Quantum Entanglement on photons.
It means 2 waves (particles) are related regardless of distance and Nonlocality in this Universe.
* "Anton Zeilinger in Wikipedia" http://en.wikipedia.org/wiki/Anton_Zeilinger
* "Science News 75 Years of Entanglement" https://www.sciencenews.org/article/75-years-entanglement

2.5.11.2.14 Randall and Sundrum's Warped Extra Dimensions in 1999 CE

Background
As mentioned above, if D-Branes Theory claims that Gravitons escape to the extra dimensions, it results in an error that Gravity wouldn't comply with the Inverse-Square Law.

Randall and Sundrum's Warped Extra Dimensions
Randall and Sundrum claimed that the extra dimensions are warped (curved) and Gravitons rarely escape to the extra dimensions, then Gravity approximately comply with the Inverse-Square Law.
*It sounds like a mere excuse.
* "Randall-Sundrum Model in Wikipedia" http://en.wikipedia.org/wiki/Randall%E2%80%93Sundrum_model

2.5.11.2.15 WMAP's Observation in 2001 CE

Background
NASA's WMAP succeeded COBE.

WMAP's Observation
WMAP's Observation supported presence of an enormous amount of Dark Energy. Then the universe is presumed consisting of 74% unknown Dark Energy, 22% unknown Dark Matter, and some 4% of ordinary matter.
Other than that, WMAP estimated the radius of the observable universe to be more than 39 billion light years.
* "Universe Review" http://universe-review.ca/F02-cosmicbg.htm
* "Observable Universe" http://en.wikipedia.org/wiki/Observable_universe

2.5.11.2.16 Khoury, Ovrut, Steinhardt, and Turok's Ekpyrotic Universe in 2001 CE

Background
The origin of the Big Bang was controversial.
D-Branes Theory was claimed to account for the extra 6 dimension of Superstring Theory.

Ekpyrotic Universe
Khoury, Ovrut, Steinhardt, and Turok proposed the Ekpyrotic Universe Theory. According to the Ekpyrotic Universe Theory, this 3-dimensional universe and other similar 3-dimensional universes are drifting in a higher dimensional Mother Universe. two of the 3-dimensional universes (baby universes) would sometimes collide. Then this universe came from a collision of two 3-dimensional universes. The 3-dimensional universes are compared to branes (D-Branes).
* "Ekpyrotic Universe in Wikipedia" http://en.wikipedia.org/wiki/Ekpyrotic_universe
*3-dimensional spaces (Universes) in the higher dimensional Mother Universe are compared to 2-dimensional branes like in the following depiction.
*Since a D-Brane corresponds to a universe, the claim of Ekpyrotic Universe Theory means that a collision of two baby universes (through an extra dimension) resulted in the Big Bang.


2.5.11.2.17 Susskind's Landscape Theory in 2003 CE

Background
According to Superstring Theory, Calabi-Yau Manifold was an account of the extra 6 dimensions. Calabi-Yau Manifold has 10^150 through 10^500 kinds in configuration. In relation to Dark Energy, diversity of Calabi-Yau Manifolds and energy levels were disputed.

Susskind's Anthropic Landscape
Susskind presented the concept of Anthropic Landscape representing diversity of physical constants involving vacua. The diverse energy levels on graphs seemed like landscapes of mountain ranges. The concept also represents myriad universes.
* "String Theory Landscape in Wikipedia" http://en.wikipedia.org/wiki/String_theory_landscape
* "The Anthropic Landscape of String Theory" http://arxiv.org/abs/hep-th/0302219

2.5.11.2.18 Zeilinger's Quantum Entanglement over 144km in 2007 CE

Zeilinger verified Quantum Entanglement on photons over 144km. It means waves (particles) of photons are related simultaneously regardless of 144km distance.






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