Universe and Multiverse, Part 4
Example of a Calabi-Yau manifold. Image courtesy Wikipedia commons.
Note: 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 and published by 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 the previous post, 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.
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.