According to some Christian outlooks we were made for another world. Perhaps, rather, we were made for this world to recreate, reclaim, redeem, and renew unto God's future aspiration by the power of His Spirit. - R.E. Slater
Secularization theory has been massively falsified. We don't live in an age of secularity. We live in an age of explosive, pervasive religiosity... an age of religious pluralism. - Peter L. Berger
Exploring the edge of life and faith in a post-everything world. - Todd Littleton
I don't need another reason to believe, your love is all around for me to see. – anon
Thou art our need; and in giving us more of thyself thou givest us all. - Khalil Gibran, Prayer XXIII
Be careful what you pretend to be. You become what you pretend to be. - Kurt Vonnegut
Religious beliefs, far from being primary, are often shaped and adjusted by our social goals. - Jim Forest
People, even more than things, need to be restored, renewed, revived, reclaimed, and redeemed; never throw out anyone. – anon
Certainly God's love has made fools of us all. - R.E. Slater
An apocalyptic Christian faith doesn't wait for Jesus to come, but for Jesus to become in our midst. - R.E. Slater
Christian belief in God begins with the cross and resurrection of Jesus, not with rational apologetics. - Eberhard Jüngel, Jürgen Moltmann
Our knowledge of God is through the 'I-Thou' encounter, not in finding God at the end of a syllogism or argument. There is a grave danger in any Christian treatment of God as an object. The God of Jesus Christ and Scripture is irreducibly subject and never made as an object, a force, a power, or a principle that can be manipulated. - Emil Brunner
Ehyeh Asher Ehyeh means "I will be that who I have yet to become." - God (Ex 3.14)
Our job is to love others without stopping to inquire whether or not they are worthy. - Thomas Merton
The church is God's world-changing social experiment of bringing unlikes and differents to the Eucharist/Communion table to share life with one another as a new kind of family. When this happens we show to the world what love, justice, peace, reconciliation, and life together is designed by God to be. The church is God's show-and-tell for the world to see how God wants us to live as a blended, global, polypluralistic family united with one will, by one Lord, and baptized by one Spirit. – anon
The cross that is planted at the heart of the history of the world cannot be uprooted. - Jacques Ellul
The Unity in whose loving presence the universe unfolds is inside each person as a call to welcome the stranger, protect animals and the earth, respect the dignity of each person, think new thoughts, and help bring about ecological civilizations. - John Cobb & Farhan A. Shah
If you board the wrong train it is of no use running along the corridors of the train in the other direction. - Dietrich Bonhoeffer
God's justice is restorative rather than punitive; His discipline is merciful rather than punishing; His power is made perfect in weakness; and His grace is sufficient for all. – anon
Our little [biblical] systems have their day; they have their day and cease to be. They are but broken lights of Thee, and Thou, O God art more than they. - Alfred Lord Tennyson

Wednesday, April 11, 2012

Biologos: Particle Physics of the Universe & Multiverse, Parts 1-4

Universe and Multiverse, Part 1
March 26, 2012

~  An Autobiography of the Author  ~

Universe and Multiverse, Part 2
 April 2, 2012

Today's entry was written by Gerald Cleaver. Gerald Cleaver is an Associate Professor of Physics at Baylor University. He is a member of the Physics Department's High Energy Physics group and also heads the Early Universe Cosmology and String Theory division of Baylor's Center for Astrophysics, Space Physics, and Engineering Research. Gerald earned his Ph.D. at Caltech in 1993, where he studied under John H. Schwarz, one of the founders of string theory. His research interests focus on elementary particles, fundamental forces, and superstring theory. His hobbies include radio-controlled model aviation, small-boat sailing, and tae kwon do.        
Universe and Multiverse, Part 2
Example of a Calabi-Yau manifold. Image courtesy Wikipedia commons.

This essay is Part 2 of a series from Gerald Cleaver’s chapter in the book Delight in Creation: Scientists Share Their Work with the Church , edited by Deborah Haarsma & Scott Hoezee, from the Center for Excellence in Preaching at Calvin College, Grand Rapids, Michigan. Another version of the essay appeared at the Ministry Theorem, as part of their “What I Wish My Pastor Knew About. . .” series.

In Part 1, Cleaver described his own path to science through the Church. Today, in Part 2, he suggests that fellow Christians should seek to reconcile science and the Scriptures, and begins a short history our changing views of cosmology.

Advice for Christians

My path to a Christian vocation as a scientist is not unique. While each of our lives is different, I know from conversations with numerous Christian colleagues that they faced similar quandaries regarding apparent conflicts between scripture and science. In many Protestant churches I have encountered Christians who fear science because of this seeming conflict. On the other hand, I have also encountered Christians with a desire to better understand modern science and its interplay with scripture, but little opportunity to do so. Likely there are some scientists or young people in your congregation dealing with similar issues.

I encourage churches to develop and teach a consistent Christian worldview in which scientific and theological understandings of the universe are viewed as mutually supportive and complementary. The historic “two books” view of nature and scripture reminds us that God’s revelation comes not just through the Bible, but through the physical world as God’s book of general revelation to us. In line with Augustine, Aquinas, and Pascal, we must not reject outright the testimony of scientists, since they speak truths about God’s creation. Nor can we afford to ignore the controversial aspects of this debate. Churches should instead invite scientists who are Christian to share their knowledge with the congregation and come alongside them to wrestle with difficult passages. Churches can lead in-depth studies of the scriptures, helping everyone to better understand the historical aspects and cultural milieu of the text. Often a misunderstanding of the context can create a false conflict between scripture and science.

Churches can also remind Christians of the many ways that science enhances faith. Learning about science and scientific discovery can deepen our understanding of God’s creation and of God’s creative nature. It can renew and deepen our awe and reverence for God. Science can also shed new light on scripture and on theological issues. In the rest of this essay, I want to share with you the beauty, order, and wonder of creation displayed in my own field, elementary particle physics and cosmology. In order to understand these discoveries, I will start with a brief history of the human views of the universe.

Expanding Views of the Universe

Over the last few thousand years, the human perception of physical reality has gone through several stages. Each shift has illuminated a larger, grander creation, and for Christians, each advance should signify a fuller representation of God’s eternal power. The Middle Eastern world of one to two millennia B.C. perceived reality essentially as a three-tiered structure (Fig. 1). Center stage was the flat surface of the earth and the ground below containing the underworld of the dead (e.g., the Sheol of the Old Testament). Beneath this level was a primeval ocean upon which the earth floated and into which the pillars of the earth descended. Far above were the split levels of the heavens: the firmament of the stars and the sun and moon and the watery expanse of the heavens kept separated above by a cover (as in Gen. 1:7), and often beyond that was the heaven of heavens. This was the setting in which Genesis 1 was written.

The Greek civilization brought about a significant paradigm shift, one that lasted almost one and a half millennia—the geocentric picture, in which both the sun and the other planets were believed to orbit around the earth (Fig. 2).

Then, in the 1600s astronomical discoveries by scientists such as Galileo resulted in the realization that the earth and all of the rest of the planets orbit the sun. Thus was born the helio-centric era. Simultaneously, the law of gravity was developed by Isaac Newton and proven to apply both on the earth and throughout the whole helio-centric system (Fig. 3).

By the 1800s, astronomers discovered the existence of gaseous nebula beyond the solar system and found that our sun was but one of hundreds of billions of stars within the so-named Milky Way galaxy. Thus, a galactic-centric perception replaced the helio-centric (Fig. 4). Our galaxy and its contents were believed to compose the entirety of the universe.

By the 1920s, many of the objects identified during the preceding century as “spiral nebulae” inside our Milky Way galaxy were discovered by astronomers such as Edwin Hubble to be independent galaxies, located vast distances (millions to billions of light years) away from the Milky Way and of comparable size to it. Thus, after little more than a century the galactic-centric paradigm was transformed into a universe-centric paradigm, with our universe comprising the entire stage (Fig. 5). Over the following decades, around a trillion visible galaxies were identified in our visible universe, each possessing hundreds of billions to trillions of stars (Fig. 6).

In the next installment, Cleaver follows up this quick walk through the history of cosmology with a discussion of its next, modern stages, when scientists began to ask anew, “How came the universe?”

Universe and Multiverse, Part 3
April 9, 2012

This essay is Part 3 of a series from Gerald Cleaver’s chapter in the book Delight in Creation: Scientists Share Their Work with the Church , edited by Deborah Haarsma & Scott Hoezee, forthcoming from the Center for Excellence in Preaching at Calvin College, Grand Rapids, Michigan. Another version of the essay appeared at the Ministry Theorem, as part of their “What I Wish My Pastor Knew About. . .” series.

In Part 1, Cleaver described his own path to science through the Church; in Part 2, he suggested that fellow Christians should seek to reconcile science and the Scriptures and began a short history our changing views of cosmology.

Today, in Part 3, Cleaver discusses the way evidence for the Big Bang widened the horizons of our cosmology again, while scientists were simultaneously searching to understand the fundamental building blocks of matter.

Evidence for the Big Bang

The universe-centric paradigm naturally raised the question, “How came the universe?” Not only does modern science show us the extent of the universe, but its understanding of the history of the universe is also highly detailed and exact. In 1929, Edwin Hubble proved that the universe was expanding. By observing distant galaxies and the light they emit, he showed that the further away a galaxy was from ours, the more rapidly it was moving away from it. As an analogy, consider a spherical balloon being blown up (Figure 1). The dots on the surface of the balloon are analogous to galaxies, and the inflating balloon is analogous to the stretching of space between the galaxies. An observer on any one of the dots would perceive the other dots to all be moving away from him at rates proportional to their distance away.

This expansion means that in the distant past the universe was much smaller than it is today. So, following Hubble’s discovery, scientists began to consider a model in which the universe started out extremely small, with all of the matter packed close together. Near the very beginning, the entire universe would have been extremely hot (at least 1032 degrees) and extremely small (10-33 cm, which is much smaller than an atom, in fact 1/100000000000000000000 times smaller than the tiny nucleus inside an atom). This model was called the Big Bang. Although some people use the term “Big Bang” as if it were a replacement for God, it is merely a scientific explanation of how the universe developed after the first instant (immediately after time t = 0).

The Big Bang was confirmed by several independent pieces of evidence. The first and best known is the verification of a specific Big Bang prediction, that the heat of the early universe should still be visible today as low energy radiation from all over the sky. This cosmic microwave background radiation was discovered unintentionally by two IBM employees in 1963.

Several independent lines of evidence point to billions of years of history since the Big Bang. Astronomers understand much of this history and have found no serious gaps, other than what happened to start the Big Bang. I understand this detailed history of the universe as the ongoing process by which God continually creates the universe.

Forces and Particles

Parallel to the development of modern cosmology in the twentieth century, physicists began a concerted drive to understand the forces of nature in a consistent, interrelated manner. Long before this, in 1687, Newton had worked out a basic understanding of the force of gravity. Two centuries later, in 1864, James Clerk Maxwell derived the fundamental equations of electromagnetism, thereby proving that electricity and magnetism were manifestations of a second force, one associated with light. From then until the 1930s, gravity and electromagnetism were believed to be the only forces. But with the discovery of the neutron in 1932, physicists learned of additional forces (what became known as the strong and weak nuclear forces). Although the first attempts to explain the strong nuclear force appeared in 1935, the first true models of the nuclear forces did not develop until the 1950s. Then in the 1960s, a way to combine electromagnetism with the weak nuclear force was discovered and referred to as electroweak theory. Simultaneously, understanding of the strong nuclear force was accomplished during 1963 to 1965. The related theory was named quantum chromodynamics (QCD). These theories showed that all the fundamental forces (with the exception of gravity) were related.

As the understanding of forces developed, physicists were also learning about the elementary particles that compose all matter. Around 1870, the periodic table of the elements was developed by Dmitri Mendeleev and others as a systematic way to organize the dozens of known atoms; today 117 types of atoms are known. In the early 1900s, physicists discovered that each atom is not solid like a billiard ball, but is made of more fundamental particles: protons and neutrons in a nucleus with electrons swirling around the nucleus.

Yet the protons and neutrons are still not the most fundamental: high- speed collisions in particle accelerators hinted at the existence of even more elementary particles. Experiments also began to reveal many particles besides protons, neutrons, and electrons. For a time, physicists were discovering new types of particles faster than they could explain them— there seemed to be a “zoo” of particles rather than orderly categories (see Figure 2).

Gradually a more orderly picture came together. Protons and neutrons were each discovered to be made of elementary particles called “quarks.” The two most common types of quarks are called up and down, and come in three varieties (called red, green, and blue) [2x3=6]. When you add in the electron and the electron neutrino, you get a family of eight elementary particles. All of the atoms in the periodic table can be explained with just those eight particles. That’s a lot simpler than 117!

Physicists also found that associated with each of these eight particles is an anti-particle. Anti-matter is commonly referred to in science fiction, as in Star Trek, making it sound very exotic. Yet the essential difference between anti-matter and regular matter is just the sign of the electric charge: if a particle is positively charged, its anti-matter partner carries a negative charge (or vice versa). The existence of anti-particles doubles the number of elementary particles in a family to sixteen.

As all of the elementary matter particles were discovered, physicists were also learning more about forces and discovered the existence of another category of particle: a “force-carrying” particle. This is difficult to picture, but you have already heard of one such particle, the photon. The photon is the force-carrying particle for electricity and magnetism. QCD is associated with eight (8) force-carrying particles (called gluons, because like a glue, they cause quarks to stick together) and the electroweak force with four (4) force-carrying particles (including the photon), making a set of twelve (12) force-carrying particles (see Figure 3).

File:Elementary particle interactions.svg
Summary of interactions between particles described by the Standard Model.

The left three columns show three families (“generations”) of matter particles (quarks and leptons, shaded purple and green). The right column shows force carrying particles (bosons, shaded pink). In addition to the particles shown, each quark comes in three so-called colors (red, green, blue), and each of those has an antiparticle with opposite color (anti-red, anti-green, or anti-blue) and opposite electric charge. Each lepton also has an anti-particle of opposite electric charge. Thus, there are 16 = 2*3 + 2*3 + 2 + 2 matter particles in each generation. The force carrying particles also come in more varieties than shown (a total of 12). This set of forces and matter particles became known as the Standard Model of Elementary Particle Physics.

Next week we'll talk a bit more about the Standard Model and then turn to the relationships between the very small and the very large aspects of the cosmos.

From Wikipedia

The Standard Model of particle physics is a theory concerning the electromagnetic, weak, and strong nuclear interactions, which mediate the dynamics of the known subatomic particles. Developed throughout the mid to late 20th century, the current formulation was finalized in the mid 1970s upon experimental confirmation of the existence of quarks. Since then, discoveries of the bottom quark (1977), the top quark (1995) and the tau neutrino (2000) have given further credence to the Standard Model. Because of its success in explaining a wide variety of experimental results, the Standard Model is sometimes regarded as a theory of almost everything.

Still, the Standard Model falls short of being a complete theory of fundamental interactions because it does not incorporate the physics of dark energy nor of the full theory of gravitation as described by general relativity. The theory does not contain any viable dark matter particle that possesses all of the required properties deduced from observational cosmology. It also does not correctly account for neutrino oscillations (and their non-zero masses). Although the Standard Model is believed to be theoretically self-consistent, it has several apparently unnatural properties giving rise to puzzles like the strong CP problem and the hierarchy problem.

Nevertheless, the Standard Model is important to theoretical and experimental particle physicists alike. For theorists, the Standard Model is a paradigmatic example of a quantum field theory, which exhibits a wide range of physics including spontaneous symmetry breaking, anomalies, non-perturbative behavior, etc. It is used as a basis for building more exotic models which incorporate hypothetical particles, extra dimensions and elaborate symmetries (such as supersymmetry) in an attempt to explain experimental results at variance with the Standard Model, such as the existence of dark matter and neutrino oscillations. In turn, experimenters have incorporated the Standard Model into simulators to help search for new physics beyond the Standard Model.

Universe and Multiverse, Part 4
April 16, 2012

This essay is Part 4 of a series from Gerald Cleaver’s chapter in the book Delight in Creation: Scientists Share Their Work with the Church , edited by Deborah Haarsma & Scott Hoezee, forthcoming from the Center for Excellence in Preaching at Calvin College, Grand Rapids, Michigan. Another version of the essay appeared at the Ministry Theorem, as part of their “What I Wish My Pastor Knew About. . .” series.

In Part 1, Cleaver described his own path to science through the Church; in Part 2, he suggested that fellow Christians should seek to reconcile science and the Scriptures and began a short history our changing views of cosmology. Last week, Cleaver discussed the way evidence for the Big Bang widened the horizons of our cosmology again, while scientists were simultaneously searching to understand the fundamental building blocks of matter. Today we turn to the relationships between the very small and the very large aspects of the cosmos.

The Standard Model

The set of forces and matter particles discussed last week became known as the Standard Model of Elementary Particle Physics. This includes the combination of twelve electroweak and QCD force-carrying particles, plus the sixteen particles making up ordinary matter. It also includes two additional exotic matter families, containing another sixteen particles each. Each particle in an exotic family is nearly identical to a corresponding one in the more ordinary first family of particles. The primary difference between the first family of particles and the exotic second and third families is that particles in the latter two families are more massive.

Two additional particles called the Higgs (named after the physicist who first theorized their existence) are also believed to exist and are included in the Standard Model. The two Higgs particles apparently give mass to all matter particles. They are expected to be produced at the Large Hadron Collider (LHC) at CERN, Switzerland, within the next few years. In total, the Standard Model contains sixty-two elementary particles.

Mathematical aspects of the Standard Model further suggest that each of these 62 elementary particles has associated with it another particle, called its supersymmetric partner. While none of these supersymmetric particles have been found to date at either Fermilab or CERN, if they exist, they should also soon be discovered. Their existence would increase the number of elementary particles to 124. This set of 124 particles is called the Minimal Supersymmetric Standard Model (MSSM).

Beginning in the 1980s, some elementary particle physicists suggested that the Standard Model might not be the underlying fundamental theory. First, a theory with either sixty-two or 124 elementary particles doesn’t seem that simple or fundamental, even if it is more orderly than the earlier “zoo.” Also, why are there two exotic copies of the everyday set of sixteen particles? There is also no explanation why QCD or the electroweak force took the respective form that each did. Further, neither the Standard Model nor the MSSM offers a connection between these forces and gravity.

String Theory: One Particle and Ten Dimensions

A possible resolution to issues with the Standard Model first appeared in the mid-1980s, called string theory. It is a theory that unifies the strong and electroweak forces of the Standard Model, while it simultaneously reduces the number of elementary particles from 124 to 1. This is an amazing accomplishment—it offers the possibility to finally achieve the “holy grail” of physics, to unify all the forces into a single picture (sometimes nicknamed the Theory of Everything, but better called the Theory of Everything Physical). String theory simplifies the understanding of particles by showing that all particles are fundamentally the same and have the same origin.

According to string theory, there is only one fundamental particle from which both force-carrying particles and matter particles are formed. This particle is essentially a closed string (or loop) of pure energy (Fig. 1).

The string is tiny with a length of 10-33 cm (recall this length was discussed prior—the universe started out no larger than this size). The string of energy can produce all the other particles by vibrating in different ways. Just as vibrations travel up and down on a violin string, so vibrations travel around the string of energy. A violinist changes the way the violin string vibrates in order to produce a different musical note. Similarly, when the vibration of the string changes, the string appears as a different type of particle. There are many ways the energy string can vibrate, including all sorts of combinations of clockwise and counter-clockwise vibrations— in fact, enough different combinations of vibrations to explain all of the elementary particles in the Standard Model.

Thus, string theory solves several difficulties of the Standard Model. But it does much more. It opens new vistas in our understanding of nature, including multiple universes (discussed further in this essay) and whole new dimensions of space in our universe. Our everyday lives exist in three spatial dimensions (height, width, depth) and one time dimension. We can speak of these together as spacetime and say that we live in 3+1 spacetime dimensions. In order for string theory to be mathematically consistent, however, spacetime instead must be exactly 9+1 dimensional. That is, six additional spatial directions beyond height, width, and depth must exist!

Since we can only perceive the spatial dimensions of height, width, and depth, scientists immediately realized that these extra dimensions must be very small (referred to as compact). Not only are the extra dimensions much too small to see, they are much smaller than an atom. In fact they are of the same length scale as the string itself, that is, around 10-33 cm. These compact dimensions differ in another way from the three large dimensions we are used to: they are closed. This means that in moving along a compact direction, you would return to the starting point after traversing a distance of only 10-33 cm. Picture an infinitely long rope (Figure 2). A tightrope walker can travel infinitely far along the long direction of the rope (like one of the three large dimensions), but a small ant crawling around the circumference of the rope will quickly return to where it started (like one of the six compact dimensions).

Astonishingly, the existence of these compact directions is the reason that all forces and matter are related. In fact, without compact directions, the types of particles in string theory would be vastly reduced to only those that carry the gravitational force. That’s because such particles involve vibrations only in the three large spatial directions. The electroweak and strong force-carrying particles are produced when the vibration is also in the compact directions. Matter particles are produced when the string vibrates only in the compact dimensions. Thus, in string theory, without extra compact spatial dimensions, the matter particles making up our bodies (and all other objects) could not exist. This is a stunning conclusion: although we exist in the three large dimensions, each elementary particle in our bodies is a tiny energy string vibrating in extra compact spatial dimensions!

In addition to automatically producing all of the forces and all of the matter particles, string theory also explains why they have their specific properties. On a violin, the length of the string and the shape of the soundboard determine what vibrations are possible and thus what musical notes can be played. In string theory, the size and shape of the six compact dimensions determine what vibrations the string can have and thus what particles are produced. Therefore, the shape of compact space itself determines the types of matter particles allowed and types of the non-gravitational forces. Much of the work of string theory involves figuring out how the six compact dimensions might be shaped. It turns out there are around 100 trillion (very complicated) possible shapes, called Calabi-Yau manifolds—an example of which is given as the illustration for this series, at the top of the post.

A primary effort of string theorists was to determine which of the 100 trillion Calabi-Yau shapes for the extra six compact directions corresponded to the space of our universe. If the correct compact shape could be found, string theory had the potential to be the actual Theory of Everything (Physical). A handful of Calabi-Yau shapes were eventually found that came very close to producing exactly the forces and matter particles of this universe. Nevertheless, each of these shapes resulted in at least a few incorrect predictions, such as wrong masses for some particles. This search continued full scale for roughly a decade, with significant progress made in some cases. Still, an underlying nagging issue of string theory was that it wasn’t actually a single theory, but five alternative theories, with slightly different properties of the energy string in each.

 Next week, we’ll look at how physicists address that issue and how we may be on the verge of another paradigm shift in our understanding of the cosmos—and the immense scope of God’s creativity.

From Wikipedia

String theory is an active research framework in particle physics that attempts to reconcile quantum mechanics and general relativity. It is a contender for a theory of everything (TOE), a self-contained mathematical model that describes all fundamental forces and forms of matter.

String theory posits that the electrons and quarks within an atom are not 0-dimensional objects, but rather 1-dimensional oscillating lines ("strings"). The earliest string model, the bosonic string, incorporated only bosons, although this view developed to the superstring theory, which posits that a connection (a "supersymmetry") exists between bosons and fermions. String theories also require the existence of several extra dimensions to the universe that have been compactified into extremely small scales, in addition to the four known spacetime dimensions.

The theory has its origins in an effort to understand the strong force, the dual resonance model (1969). Subsequent to this, five different superstring theories were developed that incorporated fermions and possessed other properties necessary for a theory of everything. Since the mid-1990s, in particular due to insights from dualities shown to relate the five theories, an eleven-dimensional theory called M-theory is believed to encompass all of the previously-distinct superstring theories.[citation needed]

Many theoretical physicists (e.g., Stephen Hawking, Witten, Maldacena and Susskind) believe that string theory is a step towards the correct fundamental description of nature. This is because string theory allows for the consistent combination of quantum field theory and general relativity, agrees with general insights in quantum gravity (such as the holographic principle and Black hole thermodynamics), and because it has passed many non-trivial checks of its internal consistency.[1][2][3][4] According to Hawking in particular, "M-theory is the only candidate for a complete theory of the universe."[5] Nevertheless, other physicists, such as Feynman and Glashow, have criticized string theory for not providing novel experimental predictions at accessible energy scales.[6]

* * * * * * * *

A Calabi–Yau manifold is a special type of manifold that shows up in certain branches of mathematics such as algebraic geometry, as well as in theoretical physics. Particularly in superstring theory, the extra dimensions of spacetime are sometimes conjectured to take the form of a 6-dimensional Calabi–Yau manifold.

Calabi–Yau manifolds are complex manifolds that are higher-dimensional analogues of K3 surfaces. They are sometimes defined as compact Kähler manifolds whose canonical bundle is trivial, though many other similar but inequivalent definitions are sometimes used. They were named "Calabi–Yau spaces" by Candelas et al. (1985) after E. Calabi (1954, 1957) who first studied them, and S. T. Yau (1978) who proved the Calabi conjecture that they have Ricci flat metrics. In superstring theory the extra dimensions of spacetime are sometimes conjectured to take the form of a 6-dimensional Calabi–Yau manifold, which led to the idea of mirror symmetry.


to conclude this discussion on
multi-universes go here -

Universe and Multiverse, Part 5
April 23, 2012

Calabi - Yau Manifolds with string Vibes

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