Hyperspace

It is often stated that of all the theories proposed in this century, the silliest is quantum theory. In fact, some say that the only thing that quantum theory has going for it is that it is unquestionably correct.

Some people seek meaning in life through personal gain, through personal relationship, or through personal experiences. However, it seems to me that being blessed with the intellect to divine the ultimate secrets of nature gives meaning enough to life.

Srinivasa Ramanujan was the strangest man in all of mathematics, probably in the entire history of science. He has been compared to a bursting supernova, illuminating the darkest, most profound corners of mathematics, before being tragically struck down by tuberculosis at the age of 33... Working in total isolation from the main currents of his field, he was able to rederive 100 years’ worth of Western mathematics on his own. The tragedy of his life is that much of his work was wasted rediscovering known mathematics.

As Heinz Pagels has said, The challenge to our civilization which has come from our knowledge of the cosmic energies that fuels the stars, the movement of light and electrons through matter, the intricate molecular order which is the biological basis of life, must be met by the creation of a moral and political order which will accommodate these forces or we shall be destroyed. It will try our deepest resources of reason and compassion.

Just one supernova can temporarily outshine an entire galaxy of 100 billion stars.

When you listen to the beautiful sounds of stereo music, remember that you are listening to the rhythms of trillions of electrons obeying this and other bizarre laws of quantum mechanics. But if quantum mechanics were incorrect, then all of electronics including television sets, computers, radios, stereo, and so on, would cease to function. (In fact, if quantum theory were incorrect, the atoms in our bodies would collapse, and we would instantly disintegrate. According to Maxwell's equations, the electrons spinning in an atom should lose their energy within a microsecond and plunge into the nucleus. This sudden collapse is prevented by quantum theory. Thus the fact that we exist is living proof of the correctness of quantum mechanics.) This also means that there is a finite, calculable probability that "impossible" events will occur. For example, I can calculate the probability that I will unexpectedly disappear and tunnel through the earth and reappear in Hawaii. (The time we would have to wait for such an event to occur, it should be pointed out, is longer than the lifetime of the universe. So we cannot use quantum mechanics to tunnel to vacation spots around the world.)

For the ten-dimensional universe, however, there are apparemtly millions of ways in which to curl up. To calculate which state the ten-dimensional universe prefers, we need to solve the field theory of strings using the theory of phase transitions, the most difficult problem in quantum theory.

The Fate of the Earth, points

Riemann concluded that electricity, magnetism, and gravity are caused by the crumpling of our three-dimensional universe in the unseen fourth dimension. Thus a "force" has no independent life of its own; it is only the apparent effect caused by the distortion of geometry. By introducing the fourth spatial dimension, Riemann accidentally stumbled on what would become one of the dominant themes in modern theoretical physics, that the laws of nature appear simple when expressed in higher-dimensional space. He then set about developing a mathematical language in which this idea could be expressed.

In other words, a star is a nuclear furnace, burning hydrogen fuel and creating nuclear "ash" in the form of waste helium. A star is also a delicate balancing act between the force of gravity, which tends to crush the star into oblivion, and the nuclear force, which tends to blow the star apart with the force of trillions of hydrogen bombs. A star then matures and ages as it exhausts its nuclear fuel.

As all matter is crushed in the final moments before doomsday, intelligent life forms may be able to tunnel into higher-dimensional space or an alternative universe, avoiding the seemingly inevitable death of our universe.

Either this guy’s a total idiot, or he’s the biggest genius to hit physics in years!

Nature is like a work by Bach or Beethoven, often starting with a central theme and making countless variations on it that are scattered throughout the symphony. By this criterion, it appears that strings are not fundamental concepts in nature.

In other words, the reason why the string theory cannot be solved is that twenty-first mathematics has not yet been discovered.

One consequence of this formulation is that a physical principle that unites many smaller physical theories must autoomatically unite many seemingly unrelated branches of mathematics. This is precisely what string theory accomplishes. In fact, of all physical theories, string theory unites by far the largest number of branches of mathematics into a single coherent picture. Perhaps one of the by-products of the physicists' quest for unification will be the unification of mathematics as well.

The problem is that while twenty-first-century physics fell accidentally into the twentieth century, twenty-first-century mathematics hasn't been invented yet. It seems that we may have to wait for twenty-first-century mathematics before we can make any progress, or the current generation of physicists must invent twenty-first-century mathematics on their own.

Of course, the set of logically consistent mathematical structures is many times larger than the set of physical principles. Therefore, some mathematical structures, such as number theory (which some mathematicians claim to be the purest branch of mathematics), have never been incorporated into any physical theory. Some argue that this situation may always exist: Perhaps the human mind will always be able to conceive of logically consistent structures that cannot be expressed through any physical principle. However, there are indications that string theory may soon incorporate number theory into its structure as well.

Unforunately, string theorists are, at present, at a loss to explain why ten dimensions are singled out. The answer lies deep within mathematics, in an area called modular functions. Whenever we manipulate the KSV loop diagrams created by interacting strings, we encounter these strange modular functions, where the number ten appears in the strangest places. These modular functions are as mysterious as the man who invented them, the mystic from the East. Perhaps if we better understood the work of this Indian genius, we would understand why we live in our present universe.

Some people seek meaning in life through personal gain, through personal relationships, or through personal experiences. However, it seems to me that being blessed with the intellect to divine the ultimate secrets of nature gives meaning enough to life.

These fields, which govern the interaction of all subatomic particles, are now called Yang-Mills fields. However, the puzzle that has stumped physicists within this century is why the subatomic field equations look so vastly different from the field equations of Einstein-that is, why the nuclear force seems so different from gravity. Some of the greatest minds in physics have tackled this problem, only to fail. Perhaps the reason for their failure is that they were trapped by common sense. Confined to three or four dimensions, the field equations of the subatomic world and gravitation are difficult to unify. The advantage of the hyperspace theory is that the Yang-Mills field, Maxwell's field, and Einstein's field can all be placed comfortably within the hyperspace field. We see that these fields fit together precisely within the hyperspace field like pieces in a jig-saw puzzle. The other advantage of field theory is that it allows us to calculate the precise energies at which we can expect space and time to foem wormholes.

A quantum theory of gravity that unites it with the other forces is the Holy Grail of physics.

Since the speed of light squared (c^2) is an astronomically large number, a small amount of matter can release a vast amount of energy. Locked within the smallest particles of matter is a storehouse of energy, more than 1 million times the energy released in a chemical explosion. Matter, in some sense, can be seen as an almost inexhaustible storehouse of energy; that is, matter is condensed energy.

In summary, the rather obscure laws of the weather are easy to understand once we view the earth from space. Thus the solution to the problem is to go up into space, into the third dimension. Facts that were impossible to understand in a flat world suddenly become obvious when viewing a three-dimensional earth. Similarly, the laws of gravity and light seem totally dissimilar. They obey different physical assumptions and different mathematics. Attempts to splice these two forces have always failed. However, if we add one more dimension, a fifth dimension, to the previous four dimensions of space and time, then the equations governing light and gravity appear to merge together like two pieces of a jigsaw puzzle. Light, in fact, can be explained as vibrations in the fifth dimension. In this way, we see that the laws of light and gravity become simpler in five dimensions.

The key point is now this: If the wave function of a particle vibrates along this surface, it will inherit this SU(N) symmetry. Thus the mysterious SU(N) symmetries arising in subatomic physics can now be seen as by-products of vibrating hyperspace! In other words ,we now have an explanation for the origin of the mysterious symmetries of wood: They are really the hidden symmetries coming from marble.

In the work of Ramanujan, the number 24 appears repeatedly. This is an example of what mathematicians call magic numbers, which continually appear, where we least expect them, for reasons that no one understands. Miraculously, Ramanujan's function also appears in string theory. The number 24 appearing in Ramanujan's function is also the origin of the miraculous cancellations occurring in string theory. In string theory, each of the 24 modes in the Ramanujan function corresponds to a physical vibration of the string. Whenever the string executes its complex motions in space-time by splitting and recombining, a large number of highly sophisticated mathematical identities must be satisfied. These are precisely the mathematical identities discovered by Ramanujan. (Since physicists add two more dimensions when they count the total number of vibrations appearing in a relativistic theory, this means that space-time must have 24 + 2 = 26 space-time dimensions.)

Hinton spent most of his adult years trying to visualize higher spatial dimensions. He had no interest in finding a physical interpretation for the fourth dimension. Einstein saw, however, that the fourth dimension can be taken as a temporal one. He was guided by a conviction and physical intuition that higher dimensions have a purpose: to unify the principles of nature. By adding higher dimensions, he could unite physical concepts that, in a three-dimensional world, have no connection, such as matter and energy.

When the Ramanujan function is generalized, the number 24 is replaced by the number 8. Thus the critical number for the superstring is 8 + 2, or 10. This is the origin of the tenth dimension. The string vibrates in ten dimensions because it requires these generalized Ramanujan functions in order to remain self-consistent. In other words, physicists have not the slightest understanding of why ten and 26 dimensions are singled out as the dimension of the string. It's as though there is some kind of deep numerology being manifested in these functions that no one understands. It is precisely these magic numbers appearing in the elliptic modular function that determines the dimension of space-time to be ten.

Because both quantum theory and Einstein's theory of gravity are united in ten-dimensional space, we expect that the question of time travel will be settled decisively by the hyperspace theory. As in the case of wormholes and dimensional windows, the final chapter will be written when we incorporate the full power of the hyperspace theory.

Three of the four forces (excluding gravity) are therefore united by quantum theory, giving us unification without geometry, which appears to contradict the theme of this book and everything we have considered so far.

This solves a long-standing mystery in cosmology. Our bodies are made of heavy elements beyond iron, but our sun is not hot enough to forge them. If the earth and the atoms of our bodies were originally from the same gas cloud, then where did the heavy elements of our bodies come from? The conclusion is inescapable: the heavy elements in our bodies were synthesized in a supernova that blew up before our sun was created. In other words, a nameless supernova exploded billions of years ago, seeding the original gas cloud that created our solar system.

We recall that the warping of the bedsheet was determined by the presence of the rock. Einstein summarized this analogy by stating: The presence of matter-energy determines the curvature of the space-time surrounding it.

The geometry of a universe is very like the grammatical structure of a sentence. Just as a sentence has no structure and no existence apart from the relationships between the words, space has no existence apart from the relationships that hold between the things in the universe. If you change a sentence by taking some words out, or changing their order, its grammatical structure changes. Similarly, the geometry of space changes when the things in the universe change their relationships to one another.

Men imagine gods to be born, and to have clothes and voices and shapes like theirs....Yea, the gods of the Ethiopians are black and flat-nosed, and the gods of the Thracians are red-haired and blue-eyed.

String theory, therefore, is rich enough to explain all the fundamental laws of nature. Starting from a simple theory of a vibrating string, one can extract the theory of Einstein, Kaluza-Klein theory, supergravity, the Standard Model, and even GUT theory. It seems nothing less than a miracle that, starting from some purely geometric arguments from a string, one is able to rederive the entire progress of physics for the past 2 milleninia. All the theories so far discussed in this book are automatically included in string theory.

According to string theory, if we could somehow magnify a point particle, we would actually see a small vibrating string. In fact, according to this theory, matter is nothing but the harmonies created by this vibrating string. Since there are an infinite number of harmonies that can be composed for the violin, there are an infinite number of forms of matter that can be constructed out of vibrating strings. This explains the richness of the particles in nature. Likewise, the laws of physics can be compared to the laws of harmony allowed on the string. The universe itself, composed of countless vibrating strings, would then be comparable to a symphony.

If we now take a Kaluza-Klein theory defined in 4+N dimensions and then curl up N dimensions, we will find that the equations split into two pieces. The first piece is Einstein's usual equations, which we retrieve as expected. But the second piece will not be the theory of Maxwell. We find that the remainder is precisely the Yang-Mills theory, which forms the basis of all subatomic physics! This is the key to turning the symmetries of wood into the symmetries of marble.