The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory

“The discovery of the T.O.E.—the ultimate explanation of the universe at its most microscopic level, a theory that does not rely on any deeper explanation—would provide the firmest foundation on which to build our understanding of the world. Its discovery would mark a beginning, not an end. The ultimate theory would provide an unshakable pillar of coherence forever assuring us that the universe is a comprehensible place.”

The “theory of everything,” which Greene refers to here as the “T.O.E.,” is the search for a unifying theory to encompass all of physics, which relates thematically to The Unification of Physics. This is the most important theme in the book and was Greene’s motivation to write it. Thus, this theme recurs throughout. Greene argues that even if scientists find such a theory, it will not mark the end of discovery in science but a new beginning from which they can answer all the mysteries of the universe.

“Through special relativity Einstein resolved the conflict between the ‘age-old intuition’ about motion and the constancy of light speed. In short, the solution is that our intuition is wrong.”

Greene shows how Einstein’s theory of special relativity both resolved the conflict between Newtonian motion and Maxwell’s electromagnetism. In doing so, Einstein proved that human intuition about how light and motion behave was wrong. The Limitations of Intuition is a major theme of the book.

“Einstein wove gravity into the basic fabric of the universe. Rather than being imposed as an additional structure, gravity becomes part and parcel of the universe at its most fundamental level. Breathing life into space and time by allowing them to curve, warp, and ripple results in what we commonly refer to as gravity.”

This quote beautifully combines the metaphor of weaving fabric with Einstein’s idea of the fabric of spacetime. In addition, it explains that though previous ideas about gravity could merely describe the effects without understanding the causes, general relativity explained the cause of gravity for the first time.

“If you ponder the descriptions of Einstein’s work in the preceding two chapters with adequate intensity, you will—if even for just a moment—recognize the inevitability of the conclusions we have drawn. Quantum mechanics is different. […] in a real sense those who use quantum mechanics find themselves following rules and formulas laid down by the ‘founding fathers’ of the theory—calculational procedures that are straightforward to carry out—without really understanding why the procedures work or what they really mean. Unlike relativity, few if any people ever grasp quantum mechanics at a ‘soulful’ level.”

Greene argues that relativity, though complex and difficult, is comprehensible given some effort. Quantum mechanics, however, remains so abstract and strange that many physicists do not even fully understand it. This inability to understand quantum mechanics “at a ‘soulful’ level” stems partly from the human inability to physically observe reality at a microscopic level and relates thematically to The Limitations of Intuition.

“Feynman proclaimed that each electron that makes it through to the phosphorescent screen actually goes through both slits. It sounds crazy, but hang on: Things get even more wild. Feynman argued that in traveling from the source to a given point on the phosphorescent screen each individual electron actually traverses every possible trajectory simultaneously. […] the electron, according to Feynman, simultaneously ‘sniffs’ out every possible path connecting its starting location with its final destination.”

Greene explains one of the many strange aspects of quantum mechanics, which is that electrons (and other particles) inexplicably take every possible path at once. This contributes to the ideas of particle-wave duality and probability in that the waves of electrons indicate the higher or lower probabilities of the electron being in that location. This in turn demonstrates the uncertainty principle.

“You must allow nature to dictate what is and what is not sensible. As Feynman once wrote, ‘[quantum mechanics] describes nature as absurd from the point of view of common sense. And it fully agrees with experiment. So I hope you can accept nature as She is—absurd.’”

Greene, quoting Feynman, acknowledges that according to quantum mechanics, a certain level of absurdity is unavoidable. In quantum mechanics, some microscopic weirdness is not only expected but required by the physical properties of matter particles and the four forces. This contributes thematically to The Limitations of Intuition.

“Nevertheless, physicists by their nature will not be satisfied until they feel that the deepest and most fundamental understanding of the universe has been unveiled. This is what Stephen Hawking has alluded to as a first step toward knowing ‘the mind of God.’”

This passage paraphrases Hawking and neatly links two themes together: The Human Need to Understand, driven by a desire to know everything, including “‘the mind of God,’” leads physicists to search for The Unification of Physics, or a unifying theory that may explain every possible aspect of the universe.

“Music has long since provided the metaphors of choice for those puzzling over questions of cosmic concern. From the ancient Pythagorean ‘music of the spheres’ to the ‘harmonies of nature’ that have guided inquiry through the ages, we have collectively sought the song of nature in the gentle wanderings of celestial bodies and the riotous fulminations of subatomic particles. With the discovery of superstring theory, musical metaphors take on a startling reality, for the theory suggests that the microscopic landscape is suffused with tiny strings whose vibrational patterns orchestrate the evolution of the cosmos.”

Greene ties together the use of music as a metaphor for describing the motions of the universe to the literal physical properties of string theory. Like violin strings that vibrate at different rates to create different notes, Greene argues that the tiny strings of string theory have specific patterns of vibrations that create the universe as humans know it.

“But it is certainly the case that some decisions made by theoretical physicists are founded upon an aesthetic sense—a sense of which theories have an elegance and beauty of structure on par with the world we experience. Of course, nothing ensures that this strategy leads to truth.”

Although Greene argues that aesthetics can never be the definitive judge for the validity of any scientific theory, he admits that scientists throughout history have relied on a sense of aesthetics to guide their intuition and make judgments about which ideas have merit. For instance, Einstein’s insistence on a unifying theory was inspired largely by the belief that the laws of physics should be elegant and simple. However, just as intuition is often flawed, this aesthetic sense does not guarantee that the judgment is correct.

“In physics, as in art, symmetry is a key part of aesthetics. But unlike the case in art, symmetry in physics has a very concrete and precise meaning. In fact, by diligently following this precise notion of symmetry to its mathematical conclusion, physicists during the last few decades have found theories in which matter particles and messenger particles are far more closely intertwined than anyone previously thought possible.”

Echoing the importance of aesthetics, Greene argues for the importance of symmetry. According to Greene, symmetry is an organizing principle within physics that has held true through many theories and guides physicists toward new concepts. Many kinds of symmetry appear in the book, including equivalence, mirror symmetry, and supersymmetry.

“Here is a theory that resolves the central dilemma confronting contemporary physics—the incompatibility between quantum mechanics and general relativity—and that unifies our understanding of all nature’s fundamental material constituents and forces. But to accomplish these feats, it turns out that string theory requires that the universe have extra space dimensions.”

Greene summarizes the main thrust of his argument, which is that string theory is the solution to the conflict between relativity and quantum mechanics. In doing so, however, string theory also suggests and even requires many more spatial dimensions beyond the three that humans are familiar with. This is an important aspect of all the ideas that follow in Part 4.

“And so, string theory proclaims that the family organization observed experimentally, rather than being some unexplainable feature of either random or divine origin, is a reflection of the number of holes in the geometrical shape comprising the extra dimensions! This is the kind of result that makes a physicist’s heart skip a beat.”

Part of Greene’s argument for a unifying theory is that such a theory should be able to answer the question of why the principles of physics are what they are. Accordingly, he demonstrates how the dimensions and holes of Calabi-Yau shapes, a component of string theory, may do precisely that. This is one piece of evidence in favor of string theory’s validity.

“The history of physics is filled with ideas that when first presented seemed completely untestable but, through various unforeseen developments, were ultimately brought within the realm of experimental verifiability.”

Greene acknowledges the current shortcomings of string theory, particularly the inability to experimentally test the theory due to insufficient technology. However, he points out that in many cases in the history of physics, wild theories outpaced the technology necessary to prove them. Eventually, technological advancements catch up and prove theories.

“The beautiful simplicity of string theory, the way in which it tames the conflict between gravity and quantum mechanics, its ability to unify all of nature’s ingredients, and its potential of limitless predictive power all serve to provide rich inspiration that makes the risk worth taking.”

This quote echoes the continual call for a unifying theory, and thematically reflects The Human Need to Understand and explain all aspects of the universe. Greene summarizes the main points of Part 3 and argues that string theory is the best current solution to the search for unification. He also argues that the potential of string theory motivates theorists to continue despite many obstacles.

“In the physical framework of string theory, and, correspondingly, in the realm of the emerging discipline of quantum geometry, there are two notions of distance. By judiciously making use of both we find a concept of distance that meshes with both our intuition and with general relativity when distance scales are large, but that differs from them dramatically when distance scales are small. Specifically, sub-Planck-scale distances are inaccessible.”

This is an important aspect of string theory and the concepts that follow. Distances can be described and measured in two different ways, and by using both, string theory shows that the miniscule distances that cause so much difficulty for general relativity and quantum mechanics have no bearing on the equations of string theory. This opens new avenues for mathematical formulation.

“Physicists are more like avant-garde composers, willing to bend traditional rules and brush the edge of acceptability in the search for solutions. Mathematicians are more like classical composers, typically working within a much tighter framework, reluctant to go to the next step until all previous ones have been established with due rigor. […] Like modern and classical music, it’s not that one approach is right and the other wrong—the methods one chooses to use are largely a matter of taste and training.”

Once again relying on the metaphor of music, Greene compares the difference in methods that physicists and mathematicians use. Their ways of thinking and approaching a problem are different, but one is not better than the other. Most importantly, these different methods and styles can be complementary, allowing each to go farther than they could alone.

“In his long search for a unified theory, Einstein reflected on whether ‘God could have made the Universe in a different way; that is, whether the necessity of logical simplicity leaves any freedom at all.’ With this remark, Einstein articulated the nascent form of a view that is currently shared by many physicists: If there is a final theory of nature, one of the most convincing arguments in support of its particular form would be that the theory couldn’t be otherwise. […] Such a theory would declare that things are the way they are because they have to be that way.”

As before, this quote points to the power of aesthetics and intuition in driving theorists toward a unifying theory. Additionally, this quote introduces the idea of inevitability, which physicists believe would be one important aspect of any unifying theory.

“Establishing such inevitability in the structure of the universe would take us a long way toward coming to grips with some of the deepest questions of the ages. These questions emphasize the mystery surrounding who or what made the seemingly innumerable choices apparently required to design our universe. Inevitability answers these questions by erasing the options. Inevitability means that, in actuality, there are no choices. Inevitability declares that the universe could not have been different.”

This passage further explores and explains the concept of inevitability. Greene argues that a unifying theory would be capable of explaining every single aspect of the universe, thus removing chance or choice from the equation. He even claims that the inevitability of a true unifying theory would imply that choices do not even exist.

“The pre-string theory conflict between general relativity and quantum mechanics was an affront to our visceral sense that the laws of nature should fit together in a seamless, coherent whole. But this antagonism was more than a towering abstract disjunction. The extreme physical conditions that occurred at the moment of the big bang and that prevail within black holes cannot be understood without a quantum mechanical formulation of the gravitational force. With the discovery of string theory, we now have a hope of solving these deep mysteries.”

This quote summarizes Greene’s argument that string theory is necessary to resolve the conflicts between relativity and quantum mechanics. It is not merely an add-on but an inherent part of the physical universe. Additionally, his claim that humans have a “visceral sense” that the laws of physics should be unified again implies the influence of intuition on scientific exploration.

“This line of argument is a version of an idea with a long history known as the anthropic principle. As presented, it is a perspective that is diametrically opposed to the dream of a rigid, fully predictive, unified theory in which things are the way they are because the universe could not be otherwise. Rather than being the epitome of poetic grace in which everything fits together with inflexible elegance, the multiverse and the anthropic principle paint a picture of a wildly excessive collection of universes with an insatiable appetite for variety. It will be extremely hard, if not impossible, for us ever to know if the multiverse picture is true.”

The anthropic principle basically argues that if the properties of the universe were different than they are, humans would not have evolved to observe the universe. The concept of the multiverse deeply connects to this principle; it suggests that the properties of the universe could be any number of things and that each configuration creates its own universe, but the anthropic principle indicates that humans will never be able to know this for certain.

“The history of science teaches us that each time we think that we have it all figured out, nature has a radical surprise in store for us that requires significant and sometimes drastic changes in how we think the world works.”

Echoing the earlier passage in which the history of physics shows that theories often arrive before the technology to prove them, this statement admits that the reverse is true too. Just as often as people dismiss theories that are later proven, some theories that people accept as fact eventually fall apart in the face of new information, requiring scientists to alter what they believed true.

“But in the raw state, before the strings that make up the cosmic fabric engage in the orderly, coherent vibrational dance we are discussing, there is no realization of space or time. Even our language is too coarse to handle these ideas, for, in fact, there is even no notion of before. In a sense, it’s as if individual strings are ‘shards’ of space and time, and only when they appropriately undergo sympathetic vibrations do the conventional notions of space and time emerge.”

Greene discusses one intriguing and confusing aspect of the big bang that applies not only to string theory but to quantum mechanics as well. Physicists posit that before the big bang, space and time did not exist and that the word “before” is thus misleading. Unfortunately, human language and understanding is not currently capable of usefully describing what this means.

“And, moreover, might it be that this failing does not mean that we need to look for an even deeper theory, but simply reflects that there is no explanation for these observed properties of reality?”

In discussing the obstacles and shortcomings of string theory, Greene explores one possibility: that no explanation even exists. Although science has so far overcome virtually every obstacle of knowledge it has encountered, the possibility remains that science will eventually hit a limit beyond which theories and logic fail. This does not, however, deter Greene or any other scientist from trying.