A Review.

The Elegant Universe

By Brian Greene

Nicole Feeder

String theory. Upon hearing this, a picture of the gods playing with us mortals like marionette puppets might come to mind. However amusing this thought may be, it does not attempt to explain the universe. Well, to some it might but modern scholars are of a different mindset: To them, string theory is an attempt to combine relativity with quantum mechanics into a simple, elegant theory. Brian Greene's The Elegant Universe gives an in depth discussion on sting theory and what it might mean for science.

In order to understand the necessity for string theory, we must look at both relativity and quantum mechanics and see why there is a need to bring the two together.

In June of 1905, Albert Einstein's theory of special relativity changed the course of physics. Prior to that, Newtonian physics had been the norm, along with a few smaller theories that Einstein would resolve in relativity. The principle of relativity is quite simple: "Whenever we discuss speed or velocity [...] we must specify precisely who or what is doing the measuring" (28). Green explains as follows:

Imagine that George, who is wearing a space suit with a small, red flashing light, is floating in the absolute darkness of completely empty space, far away from any planets, stars, or galaxies. From George's perspective, he is completely stationary, engulfed in the uniform, still blackness of the cosmos. Off in the distance, George catches sight of a tiny, green flashing light that appears to be coming closer and closer. Finally, it gets close enough for George to see that the light is attached to the space suit of another space-dweller, Gracie, who is slowly floating by. She waves as she passes, as does George, and she recedes in the distance. This story can be told with equal validity from Grace's perspective. It begins in the same manner with Gracie completely alone in the immense still darkness of outer space. Off in the distance, Gracie sees a red flashing light, which appears to be coming closer and closer. Finally, it gets close enough for Gracie to see that it is attached to the space suit of another being, George, who is slowly floating by. He waves as he passes, as does Gracie, and he recedes into the distance. (28)

Both George and Gracie have equally valid points of view, even though they both only describe the one situation, hence the need to specify motion relative to what is observing it. Einstein further went on to prove that light always travels at a constant speed, even if being chased. In other words, the speed of light is constant: it cannot be accelerated in any fashion. However, light will take different amounts of time to reach different points. Similar to anything moving at a constant velocity, light will reach nearer objects first. Objects moving near light speed change dramatically demonstrate special relativity.

Time is based on the notion of "perfectly regular cycles of motion" (37). Comparing two "light clocks" (a single photon bouncing between two mirrors) we can see that a stationary clock will tick faster to the observer, while a sliding clock will tick slower because the photon must travel a longer distance to reach the opposite mirror. Drawing from a stationary observer's position, we see that time moves more slowly for a moving object than a stationary clock. By the principle of relativity this implies that time moves slower for a moving object. The effects of this are only seen near light speed though.

Newton's "law of gravity" dominated the world of physics because there was agreement between the predictions and the actual forces. He observed gravity and invented formulas (calculus) to predict it's behavior, such that given the mass of two objects and the distance between them the attractive force could be found, and stated that if the a mass or distance changed, the other mass would immediately feel the effect. Special relativity came into conflict with this because special relativity ensures that nothing can travel faster than the speed of light, so an instantaneous force change would obviously violate this. This led to the discovery of general relativity.

With much thought and careful observations, Einstein concluded that gravity "is the warping of space and time" (67). He reasoned that without matter or energy space would be flat, much like a piece of paper. But since energy and mass do exist, space in a two dimensional sense would act more like a trampoline surface. If you place a bowling ball on a trampoline it stretches out to accommodate it. This is what space does around a planet. Einstein agreed with Newton however, that "gravity must be cause by an agent", but added that the "agent of gravity [...] is the fabric of the cosmos" (71). Back to the bowling ball-trampoline analogy: When you place a bowling ball on a trampoline it does not instantly stretch the fabric, it takes a small amount of time. Relating this back to space and planets, it takes some amount of time for a planet to fully bend the fabric of space. Einstein calculated that "gravitational disturbances keep pace with, but do not outrun, photons" (74). Hence the resolution of general relativity. The warping of space can be easily shown through a gravitational lens, where an object like the sun will bend the light of different stars allowing us on earth to see them at different positions. This has been experimentally shown by comparing the locations of stars to where they are in the night sky to where they appear to be when the sun is out.

(Warping of space.)

Although the conflict between special relativity and Newtonian gravity has been resolved through general relativity, another conflict that "prevents physicists from understanding what really happens to space, time, and matter when crushed together fully at the moment of the big bang or at the central point of a black hole" arises due to the incompatibility of quantum mechanics with general relativity (84).

What general relativity is to the very large things in the universe, quantum mechanics is to the small; it is "a conceptual framework for understanding the microscopic properties of the universe" (86). Plank reasoned (and receives a Nobel Peace Prize for) that energy is transferred in discrete packages. He further found a "proportionality factor between the frequency of a wave and the minimal lump of energy it can have" (93.) This is know as Plank's constant or (h-bar) and is equal to about 6.63 x 10-34 Jsec, which means that each "lump of energy" is very small. This can be observed through the photoelectric effect where a photon cannot excite an electron unless it carries the correct amount, or quanta, of energy. This also shows both particle and wave like properties of light.

At the heart of quantum mechanics is the Heisenburg Uncertainty Principle which states that you cannot know both a particle's velocity and location at the same time. Adding to this, the more you know of one, the less you know of the other. This also gives rise to quantum tunneling which allows, for example, a rubber ball to pass through a concrete wall that it is thrown at. Although this does not seem possible to our everyday experience, there is a certain amount of probability with respect to Plank's constant that will allow each of the rubber ball's individual particles to pass through an area that previously did not have enough energy. But due to the extremely small size of Plank's constant, this has a very small probability of happening.

When this concept of quantum mechanics is "applied to the fabric of spacetime", gravity thus becomes imperfect and a new theory is needed (116). According to general relativity, a massless space would be flat. However, looking at Plank length pieces of space (those 10-33 cm in length), space appears to be full of violent undulations (Imagine looking at the Great Plains then zooming in and seeing the Rocky Mountians). Some scientists choose to ignore these different views of space because the Plank length is so small, and many have tried to figure a way to combine both equally valid theories. The most "bold and ingenious" theory thus far has been superstring theory (131).

(Quantum space.)

Supersting theory, in short, is the unifying of general relativity and quantum mechanics by supposing the most basic element of the universe is not zero-dimensional point particles, but rather one dimensional strings. Let us take a step back and fully explain what this means.

To picture these fundamental elements, imagine "tiny, one-dimensional filaments somewhat like infinitely thin rubber bands, vibrating to and fro" (136). On average, each sting is about Plank length (10-33 cm) and are too small to be detected by any instruments available today. To visualize these vibrations, imagine a simple harmonic wave on the string of a violin being played. Each different wave corresponds to a different pitch. So on the string level, each different "pitch" that is "played" on a sting corresponds to a different type of particle. This forms the base for all elementary particles.

All elementary particles have certain intrinsic properties. The most common are mass and electrical charge, but also a spin. A particle's spin is its actual rotational motion that never changes: "If an electron were not spinning, it would not be an electron" (171). To a string theorist, different particles arise due to different excitations of strings. Included in this is the possibility for a particle of zero mass and a spin of two, which is the theoretical particle responsible for the transmission of gravity; the graviton.

Along with the property of spin comes one additional law of nature known as supersymmetry. This implies that particles in nature must come in pairs whose respective spins differ by 1/2. The pairs are made up of a boson (a force transmitting particle) and a fermion (a particle that makes up matter). The partners to all of the fundamental particles have not yet been detected, but there are reasons to back up their existence. Their equal yet opposite quantum jitters "significantly calm some of the frenzied quantum effects" allowing space to exist with a low Plank's constant (175). Supersymmetry also allows for the notion of "grand unification", where the three non-gravitational forces (strong, weak, and electromagnetic) have the same strengths when measured operating on small distances. Without supersymmetry the forces almost meet, but there is a "tiny but undeniable discrepancy" that for all logical purposes must be accounted for (178).

As the strings move in different ways, they also give rise to different branes. Strings are one-dimensional so are zero-branes, and so on. The 9 spatial dimensions are referred to as p-branes, which are individually defined as "a spacetime object that is a solution to the Einstein equation in the low energy limit of superstring theory, with the energy density of the non gravitational fields confined to some p-dimensional subspace of the nine space dimensions in the theory" (www.superstringtheory.com). These branes are vital to the development of string theory.

We live in a 4 dimensional world; one consisting of the up-down, right to left, forward to back, and time, or do we? Well, Greene points out that "experience informs intuition" but furthermore it "sets the frame within which we analyze and interpret what we perceive" (184). In 1919 Theodor Kaluza from the University of K�nigsburg suggested that the universe may have more than just the three normal spatial dimensions. Oskar Klein, a Swedish mathematician, refined Kaluza's work and in 1926 proposed that "the spatial fabric of our universe may have both extended and curled-up dimensions" (188). This Kaluza-Klein Theory has become a very important part of string theory because it means that "extradimensional geometry determines fundamental physical attributes like particle masses and charges that we observe in the usual three large space dimensions of common experience" (206). The image is of a Calabi-Yau space, a shape in which the six extra dimensions are curled up into, which is consistent with the equations behind string theory. Since these dimensions are so small, is means that "there is not much room for a large object like your hand to move-- it all averages out so that after sweeping your arm, you are completely unaware of the journey you took through the curled-up Calabi-Yau dimensions" (208).

(Calabi-Yau space.)

With all of the stretching of space, one might imagine it eventually tearing. General relativity does not allow for this, but the concept of wormholes has captured the thoughts of many physics. Wormholes are small tunnels that are thought to connect one part of the universe to another. Black holes are similar in nature in that space actually appears to be "pinched or punctured at the [...] center" (265). String theory shows that there are ways that space can tear, although they differ from wormholes and black holes.

Space can tear in string theory, and it undergoes flop transitions where it rips then repairs itself. The tearing is acceptable because the ripped area of space is protected by a world-sheet, which is "a two dimensional surface that a string sweeps out as it moves through space", thus allowing for very minimal side effects (279). Since Feynman reasoned that the resulting motion of an object is the combination of all possible trajectories, then if a tear were to occur no where near a string quantum mechanics would still take into "account of [the] physical effects from all possible string trajectories and among there are numerous (infinite, in fact) protective paths that encircle the tear" (280). Thus the "cosmic calamity" of torn space through topology-changing transitions are canceled out.

(Space changes.)

However promising string theory may be, there has not been experimental data to confirm its possibilities. Too little is known about the strings themselves. For example, are they closed vibrating loops, or open-ended wavelike strings? Without amazing technology that obviously does not exist now we will never be able to actually look at a string. So for now, physicists can only work on the math and try to grapple with their theories.

The second superstring revolution has led physicists to believe that all five current string theories (Type I, Type IIA, Type IIB, Heteroic-O, and Heteroic-E) are all part of a single, unified theory called M-Theory. Many believe that all contain truth but are all just a small part of the whole picture. Green describes this as five separate groups of people looking at a different arm of a starfish, not yet able to see how they are connected. Some progress has been made in finding "dual symmetries", which are situations "in which two or more theories appear to be completely different, yet actually give rise to identical physical consequences" (415). Symmetry plays a large role in this because it allows for "significant constraints on the properties [string theory] can have" (302).

The table below from www.superstringtheory.com summarizes the different branches of string theory and how many dimensions each one believes to have.

A Brief Table of String Theories
Type Spacetime Dimensions Details
Bosonic

26 Only bosons, no fermions means only forces, no matter, with both open and closed strings. Major flaw: a particle with imaginary mass, called the tachyon
I 10 Supersymmetry between forces and matter, with both open and closed strings, no tachyon, group symmetry is SO(32)
IIA 10 Supersymmetry between forces and matter, with closed strings only, no tachyon, massless fermions spin both ways (nonchiral)
IIB 10 Supersymmetry between forces and matter, with closed strings only, no tachyon, massless fermions only spin one way (chiral)
HO 10 Supersymmetry between forces and matter, with closed strings only, no tachyon, heterotic, meaning right moving and left moving strings differ, group symmetry is SO(32)
HE 10 Supersymmetry between forces and matter, with closed strings only, no tachyon, heterotic, meaning right moving and left moving strings differ, group symmetry is E8 x E8

Along with explaining the base of the universe, string theory also allows for a reasonable theory of the Big Bang and how the universe came to evolve in its current state. Added to the current observations of cosmic background radiation and the red-shirt, a string theorists view of time at the beginning of well, time itself, puts things into perspective and offers further explanation of the immense, unimaginable density of the universe at the beginning. Imagine all of the mass of the universe smashed into a small Plank size nugget. It is impossible to image this, but yet probable that it is how it all began. And yet there are other theories that suggest each universe yields another after it, each having different physical laws and such. And yet some like Lee Smolin of Penn State University even go as far to think that "every black hole is the seed for a new universe that erupts into existence through a big bang-like explosion, but is forever hidden from our view by the black hole's event horizon" (369). Whatever the truth of the universe may be, we may never know the answer if it is forever hidden like Smolin's universes.

Many years from now, or even tomorrow, evidence may be found and tested to prove these theories either true or false. Many, like Edward Witten are very optimistic: "I imagine that any day, the final form of the theory might drop out of the sky and land in someone's lap. But more realistically, I feel that we are now in the process of constructing a much deeper theory than anything we have had before" (373). And so with this type of inspiration, starry-eyed students stretch into their intuition and continue to learn what their predecessors have learned and also discovered, each one contributing their best to a theory of universal unification so everything can be described in its most basic form and in a common language.

Greene describes this well: "We are all, each in out own way, seekers of the truth and we each long for an answer to why we are here. As we collectively scale the mountain of explanation, each generation stands firmly on the shoulders of the previous, bravely reaching for the peak. [...] And as our generation marvels at out new view of the universe-- our new way of asserting the world's coherence-- we are fulfilling our part, contributing our rung to the human ladder reaching for the stars" (387).

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