String Theory

What is theoretical physics?

Theoretical physicists use mathematics to describe certain aspects of Nature. Sir Isaac Newton was the first theoretical physicist, although in his own time his profession was called "natural philosophy".

By Newton's era people had already used algebra and geometry to build marvelous works of architecture, including the great cathedrals of Europe, but algebra and geometry only describe things that are sitting still (good for describing size, but not for describing motion). In order to describe things that are moving or changing in some way, Newton invented calculus.

The most puzzling and intriguing moving things visible to humans have always been the sun, the moon, the planets and the stars we can see in the night sky. Newton's new calculus, combined with his "Laws of Motion", made a mathematical model for the force of gravity that not only described the observed motions of planets and stars in the night sky, but also of swinging weights and flying cannonballs in England.

Today's theoretical physicists are often working on the boundaries of known mathematics, sometimes inventing new mathematics as they need it, like Newton did with calculus.

Newton was both a theorist and an experimentalist. He spent many long hours, to the point of neglecting his health, observing the way Nature behaved so that he might describe it better. The so-called "Newton's Laws of Motion" are not abstract laws that Nature is somehow forced to obey, but the observed behavior of Nature that is described in the language of mathematics. In Newton's time, theory and experiment went together.

Today the functions of theory and observation are divided into two distinct communities in physics. Both experiments and theories are much more complex than back in Newton's time. Theorists are exploring areas of Nature in mathematics that technology so far does not allow us to observe in experiments. Many of the theoretical physicists who are alive today may not live to see how the real Nature compares with her mathematical description in their work. Today's theorists have to learn to live with ambiguity and uncertainty in their mission to describe nature using math.

The story so far...particles and relativity.

In the 18th and 19th centuries, Newton's mathematical description of motion using calculus and his model for the gravitational force were extended very successfully to the emerging science and technology of electromagnetism. Calculus evolved into classical field theory. Once electromagnetic fields were throughly described using mathematics, many physicists felt that the field was finished, that there was nothin left to describe or explain. Then the electron was discovered, and particle physics was born. Through the mathematics of quantum mechanics and experimental observation, it was deduced that all known particles fell into one of two classes: bosons or fermions. Bosons are particles that transmit forces. Many bosons can occupy the same state at the same time. This is not true for fermions, only one fermion can occupy a given state at a given time, and this is why fermions are the particles that make up matter. This is why solids can't pass through one another, why we can't walk through walls -- because of Pauli Repulsion -- the inability of fermions (matter) to share the same space the way bosons (forces) can.

While particle physics was developing with quantum mechanics, increasing observational evidence indicated that light, as electromagnetic radiation, traveled at one fixed speed (in a vacuum) in every direction, according to every observer. This discovery and the mathematics that Einstein developed to describe it and model it in his Special Theory of Relativity, when combined with the later development of quantum mechanics, gave birth to the rich subject of relativistic quantum field theory. Relativistic quantum field theory is the foundation of our present theoretical ability to describe the behavior of the subatomic particles physicists have been observing and studying in the latter half of the 20th century.

But Einstein then extended his Special Theory of Relativity to encompass Newton's theory of gravitation, and the result, Einstein's General Theory of Relativity, brought the mathematics called differential geometry into physics.

General relativity has had many observational successes that proved its worth as a description of Nature, but two of the predictions of this theory have staggered the public and scientific imaginations: the expanding Universe, and black holes. Both have been observed, and both encapsulate issues that, at least in the mathematics, brush up against the very nature of reality and existence.

Why did strings enter the story?

Relativistic quantum field theory has worked very well to describe the observed behaviors and properties of elementary particles. But the theory itself only works well when gravity is so weak that it can be neglected. Particle theory only works when we pretend gravity doesn't exist.

General relativity has yielded a wealth of insight into the Universe, the orbits of planets, the evolution of stars and galaxies, the Big Bang and recently observed black holes and gravitational lenses. However, the theory itself only works when we pretend that the Universe is purely classical and that quantum mechanics is not needed in our description of Nature.

String theory is believed to close this gap.

Originally, string theory was proposed as an explanation for the observed relationship between mass and spin for certain particles called hadrons, which include the proton and neutron. Things didn't work out, though, and Quantum Chromodynamics eventually proved a better theory for hadrons.

But particles in string theory arise as excitations of the string, and included in the excitations of a string in string theory is a particle with zero mass and two units of spin.

If there were a good quantum theory of gravity, then the particle that would carry the gravitational force would have zero mass and two units of spin. This has been known by theoretical physicists for a long time. This theorized particle is called the graviton.

This led early string theorists to propose that string theory be applied not as a theory of hadronic particles, but as a theory of quantum gravity, the unfulfilled fantasy of theoretical physics in the particle and gravity communities for decades.

But it wasn't enough that there be a gravition predicted by string theory. One can add a graviton to quantum field theory by hand, but the calculations that are supposed to describe Nature become useless. This is because particle interactions occur at a single point of spacetime, at zero distance between the interacting particles. For gravitons, the mathematics behaves so badly at zero distance that the answers just don't make sense. In string theory, the strings collide over a small but finite distance, and the answers do make sense.

This doesn't mean that string theory is not without its deficiencies. But the zero distance behavior is such that we can combine quantum mechanics and gravity, and we can talk sensibly about a string excitation that carries the gravitational force.

This was a very great hurdle that was overcome for late 20th century physics, which is why so many young people are willing to learn the grueling complex and abstract mathematics that is necessary to study a quantum theory of interacting strings.

How many string theories are there?

There are several ways theorists can build string theories. Start with the elementary ingredient: a wiggling tiny string. Next decide: should it be an open string or a closed string? Then ask: will I settle for only bosons (particles that transmit forces) or will I ask for fermions, too (particles that make up matter)? (Remember that in string theory, a particle is like a note played on the string.)

If the answer to the last question is "Bosons only, please!" then one gets bosonic string theory. If the answer is "No, I demand that matter exist!" then we wind up needing supersymmetry, which means an equal matching between bosons (particles that transmit forces) and fermions (particles that make up matter). A supersymmetric string theory is called a superstring theory. There are five kinds of superstring theories.

The final question for making a string theory should be: can I do quantum mechanics sensibly? For bosonic strings, this question is only answered in the affirmative if the spacetime dimensions number 26. For superstrings we can whittle it down to 10. How we get down to the four spacetime dimensions we observe in our world is another story.

If we ask how to get from 10 spacetime dimensions to 4 spacetime dimensions, then the number of string theories grows, because there are so many possible ways to make six dimensions much smaller than the other four in string theory. This process of compactification of unwanted spacetime dimensions yields interesting physics on its own.

But the number of string theories has also been shrinking in recent years, because string theorists are discovering that what they thought were completely different theories were in fact different ways of looking at the same theory!

This period in string history has been given the name the second string revolution.

And now the biggest rush in string research is to collapse the table (side) into one theory, which some people want to call M theory, for it is the Mother of all theories.

(Article compliments of Superstringtheory.com)


String Theory A non-mathematical article explaining the theories used by Theoretical Physicists to measure Nature in motion by using different musical string vibrational patterns.

What is theoretical physics? Theoretical physicists use mathematics to describe certain aspects of Nature. Sir Isaac Newton was the first theoretical physicist, although in his own time his profession was called "natural philosophy". By Newton's era people had already used algebra and geometry to build marvelous works of architecture, including the great cathedrals of Europe, but algebra and geometry only describe things that are sitting still (good for describing size, but not for describing motion). In order to describe things that are moving or changing in some way, Newton invented calculus. The most puzzling and intriguing moving things visible to humans have always been the sun, the moon, the planets and the stars we can see in the night sky. Newton's new calculus, combined with his "Laws of Motion", made a mathematical model for the force of gravity that not only described the observed motions of planets and stars in the night sky, but also of swinging weights and flying cannonballs in England. Today's theoretical physicists are often working on the boundaries of known mathematics, sometimes inventing new mathematics as they need it, like Newton did with calculus. Newton was both a theorist and an experimentalist. He spent many long hours, to the point of neglecting his health, observing the way Nature behaved so that he might describe it better. The so-called "Newton's Laws of Motion" are not abstract laws that Nature is somehow forced to obey, but the observed behavior of Nature that is described in the language of mathematics. In Newton's time, theory and experiment went together. Today the functions of theory and observation are divided into two distinct communities in physics. Both experiments and theories are much more complex than back in Newton's time. Theorists are exploring areas of Nature in mathematics that technology so far does not allow us to observe in experiments. Many of the theoretical physicists who are alive today may not live to see how the real Nature compares with her mathematical description in their work. Today's theorists have to learn to live with ambiguity and uncertainty in their mission to describe nature using math. The story so far...particles and relativity. In the 18th and 19th centuries, Newton's mathematical description of motion using calculus and his model for the gravitational force were extended very successfully to the emerging science and technology of electromagnetism. Calculus evolved into classical field theory. Once electromagnetic fields were throughly described using mathematics, many physicists felt that the field was finished, that there was nothin left to describe or explain. Then the electron was discovered, and particle physics was born. Through the mathematics of quantum mechanics and experimental observation, it was deduced that all known particles fell into one of two classes: bosons or fermions. Bosons are particles that transmit forces. Many bosons can occupy the same state at the same time. This is not true for fermions, only one fermion can occupy a given state at a given time, and this is why fermions are the particles that make up matter. This is why solids can't pass through one another, why we can't walk through walls -- because of Pauli Repulsion -- the inability of fermions (matter) to share the same space the way bosons (forces) can. While particle physics was developing with quantum mechanics, increasing observational evidence indicated that light, as electromagnetic radiation, traveled at one fixed speed (in a vacuum) in every direction, according to every observer. This discovery and the mathematics that Einstein developed to describe it and model it in his Special Theory of Relativity, when combined with the later development of quantum mechanics, gave birth to the rich subject of relativistic quantum field theory. Relativistic quantum field theory is the foundation of our present theoretical ability to describe the behavior of the subatomic particles physicists have been observing and studying in the latter half of the 20th century. But Einstein then extended his Special Theory of Relativity to encompass Newton's theory of gravitation, and the result, Einstein's General Theory of Relativity, brought the mathematics called differential geometry into physics. General relativity has had many observational successes that proved its worth as a description of Nature, but two of the predictions of this theory have staggered the public and scientific imaginations: the expanding Universe, and black holes. Both have been observed, and both encapsulate issues that, at least in the mathematics, brush up against the very nature of reality and existence. Why did strings enter the story? Relativistic quantum field theory has worked very well to describe the observed behaviors and properties of elementary particles. But the theory itself only works well when gravity is so weak that it can be neglected. Particle theory only works when we pretend gravity doesn't exist. General relativity has yielded a wealth of insight into the Universe, the orbits of planets, the evolution of stars and galaxies, the Big Bang and recently observed black holes and gravitational lenses. However, the theory itself only works when we pretend that the Universe is purely classical and that quantum mechanics is not needed in our description of Nature. String theory is believed to close this gap. Originally, string theory was proposed as an explanation for the observed relationship between mass and spin for certain particles called hadrons, which include the proton and neutron. Things didn't work out, though, and Quantum Chromodynamics eventually proved a better theory for hadrons. But particles in string theory arise as excitations of the string, and included in the excitations of a string in string theory is a particle with zero mass and two units of spin. If there were a good quantum theory of gravity, then the particle that would carry the gravitational force would have zero mass and two units of spin. This has been known by theoretical physicists for a long time. This theorized particle is called the graviton. This led early string theorists to propose that string theory be applied not as a theory of hadronic particles, but as a theory of quantum gravity, the unfulfilled fantasy of theoretical physics in the particle and gravity communities for decades. But it wasn't enough that there be a gravition predicted by string theory. One can add a graviton to quantum field theory by hand, but the calculations that are supposed to describe Nature become useless. This is because particle interactions occur at a single point of spacetime, at zero distance between the interacting particles. For gravitons, the mathematics behaves so badly at zero distance that the answers just don't make sense. In string theory, the strings collide over a small but finite distance, and the answers do make sense. This doesn't mean that string theory is not without its deficiencies. But the zero distance behavior is such that we can combine quantum mechanics and gravity, and we can talk sensibly about a string excitation that carries the gravitational force. This was a very great hurdle that was overcome for late 20th century physics, which is why so many young people are willing to learn the grueling complex and abstract mathematics that is necessary to study a quantum theory of interacting strings. How many string theories are there? There are several ways theorists can build string theories. Start with the elementary ingredient: a wiggling tiny string. Next decide: should it be an open string or a closed string? Then ask: will I settle for only bosons (particles that transmit forces) or will I ask for fermions, too (particles that make up matter)? (Remember that in string theory, a particle is like a note played on the string.) If the answer to the last question is "Bosons only, please!" then one gets bosonic string theory. If the answer is "No, I demand that matter exist!" then we wind up needing supersymmetry, which means an equal matching between bosons (particles that transmit forces) and fermions (particles that make up matter). A supersymmetric string theory is called a superstring theory. There are five kinds of superstring theories. The final question for making a string theory should be: can I do quantum mechanics sensibly? For bosonic strings, this question is only answered in the affirmative if the spacetime dimensions number 26. For superstrings we can whittle it down to 10. How we get down to the four spacetime dimensions we observe in our world is another story. If we ask how to get from 10 spacetime dimensions to 4 spacetime dimensions, then the number of string theories grows, because there are so many possible ways to make six dimensions much smaller than the other four in string theory. This process of compactification of unwanted spacetime dimensions yields interesting physics on its own. But the number of string theories has also been shrinking in recent years, because string theorists are discovering that what they thought were completely different theories were in fact different ways of looking at the same theory! This period in string history has been given the name the second string revolution. And now the biggest rush in string research is to collapse the table (side) into one theory, which some people want to call M theory, for it is the Mother of all theories. (Article compliments of Superstringtheory.com)	In String Theory, a particle is like a note played on a string. Type: Bosonic Spacetime Dimensions: 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. Type: I Spacetime Dimensions: 10 Supersymmetry between forces and matter, with both open and closed strings, no tachyon. Type: IIA Spacetime Dimensions: 10 Supersymmetry between forces and matter, with closed strings only, no tachyon, massless fermions spin both ways (nonchiral). Type: IIB Spacetime Dimensions: 10 supersymmetry between forces and matter, with closed strings only, no tachyon, massless fermions only spin one way (chiral). Type: HO Spacetime Dimensions: 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(16)x SO(16) Type: HE Spacetime Dimensions: 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
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