String Theory For Dummies book cover

String Theory For Dummies

By: Andrew Zimmerman Jones and Daniel Robbins Published: 11-16-2009

A clear, plain-English guide to this complex scientific theory

String theory is the hottest topic in physics right now, with books on the subject (pro and con) flying out of the stores. String Theory For Dummies offers an accessible introduction to this highly mathematical "theory of everything," which posits ten or more dimensions in an attempt to explain the basic nature of matter and energy. Written for both students and people interested in science, this guide explains concepts, discusses the string theory's hypotheses and predictions, and presents the math in an approachable manner. It features in-depth examples and an easy-to-understand style so that readers can understand this controversial, cutting-edge theory.

Articles From String Theory For Dummies

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String Theory For Dummies Cheat Sheet

Cheat Sheet / Updated 01-19-2022

String theory, often called the “theory of everything,” is a relatively young science that includes such unusual concepts as superstrings, branes, and extra dimensions. Scientists are hopeful that string theory will unlock one of the biggest mysteries of the universe, namely how gravity and quantum physics fit together.

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Key Events in String Theory History

Article / Updated 03-26-2016

Although string theory is a young science, it has had many notable achievements. What follows are some landmark events in the history of string theory: 1968: Gabriele Veneziano originally proposes the dual resonance model. 1970: String theory is created when physicists interpret Veneziano’s model as describing a universe of vibrating strings. 1971: Supersymmetry is incorporated, creating superstring theory. 1974: String theories are shown to require extra dimensions. An object similar to the graviton is found in superstring theories. 1984: The first superstring revolution begins when it’s shown that anomalies are absent in superstring theory. 1985: Heterotic string theory is developed. Calabi-Yau manifolds are shown to compactify the extra dimensions. 1995: Edward Witten proposes M-theory as unification of superstring theories, starting the second superstring revolution. Joe Polchinski shows branes are necessarily included in string theory. 1996: String theory is used to analyze black hole thermodynamics, matching earlier predictions from other methods.

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String Theory Features

Article / Updated 03-26-2016

String theory is a work in progress, so trying to pin down exactly what the science is, or what its fundamental elements are, can be kind of tricky. The key string theory features include: All objects in our universe are composed of vibrating filaments (strings) and membranes (branes) of energy. String theory attempts to reconcile general relativity (gravity) with quantum physics. A new connection (called supersymmetry) exists between two fundamentally different types of particles, bosons and fermions. Several extra (usually unobservable) dimensions to the universe must exist. There are also other possible string theory features, depending on what theories prove to have merit in the future. Possibilities include: A landscape of string theory solutions, allowing for possible parallel universes. The holographic principle, which states how information in a space can relate to information on the surface of that space. The anthropic principle, which states that scientists can use the fact that humanity exists as an explanation for certain physical properties of our universe. Our universe could be “stuck” on a brane, allowing for new interpretations of string theory. Other principles or features, waiting to be discovered.

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Superpartners in String Theory

Article / Updated 03-26-2016

String theory’s concept of supersymmetry is a fancy way of saying that each particle has a related particle called a superpartner. Keeping track of the names of these superpartners can be tricky, so here are the rules in a nutshell. The superpartner of a fermion begins with an “s,” so the superpartner of an “electron” is the “selectron” and the superpartner of the “quark” is the “squark.” The superpartner of a boson ends in “–ino,” so the superpartner of a “photon” is the “photino” and of the “graviton” is the “gravitino.” Use the following table to see some examples of the superpartner names. Some Superpartner Names Standard Particle Superpartner Higgs boson Higgsino Neutrino Sneutrino Lepton Slepton Z boson Zino W boson Wino Gluon Gluino Muon Smuon Top quark Stop squark

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Keeping Track of String Theory’s Many Names

Article / Updated 03-26-2016

String theory has gone through many name changes over the years. This list provides an at-a-glance look at some of the major names for different types of string theory. Some versions have more specific variations, which are shown as subentries. (These different variants are related in complex ways and sometimes overlap, so this breakdown into subentries is based on the order in which the theories developed.) Now if you hear these names, you’ll know they’re talking about string theory! Bosonic string theory Superstring theory (or Supersymmetric string theory) Type I, Type IIA, Type IIB, Heterotic string theories (Type HE, Type HO) M-theory Matrix theory Brane world scenarios Randall-Sundrum models (or RS1 and RS2) F-theory

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The Successes of String Theory

Article / Updated 03-26-2016

String theory has gone through many transformations since its origins in 1968 when it was hoped to be a model of certain types of particle collisions. It initially failed at that goal, but in the 40 years since, string theory has developed into the primary candidate for a theory of quantum gravity. It has driven major developments in mathematics, and theorists have used insights from string theory to tackle other, unexpected problems in physics. In fact, the very presence of gravity within string theory is an unexpected outcome! Predicting gravity out of strings The first and foremost success of string theory is the unexpected discovery of objects within the theory that match the properties of the graviton. These objects are a specific type of closed strings that are also massless particles that have spin of 2, exactly like gravitons. To put it another way, gravitons are a spin-2 massless particle that, under string theory, can be formed by a certain type of vibrating closed string. String theory wasn’t created to have gravitons — they’re a natural and required consequence of the theory. One of the greatest problems in modern theoretical physics is that gravity seems to be disconnected from all the other forces of physics that are explained by the Standard Model of particle physics. String theory solves this problem because it not only includes gravity, but it makes gravity a necessary byproduct of the theory. Explaining what happens to a black hole (sort of) A major motivating factor for the search for a theory of quantum gravity is to explain the behavior of black holes, and string theory appears to be one of the best methods of achieving that goal. String theorists have created mathematical models of black holes that appear similar to predictions made by Stephen Hawking more than 30 years ago and may be at the heart of resolving a long-standing puzzle within theoretical physics: What happens to matter that falls into a black hole? Scientists’ understanding of black holes has always run into problems, because to study the quantum behavior of a black hole you need to somehow describe all the quantum states (possible configurations, as defined by quantum physics) of the black hole. Unfortunately, black holes are objects in general relativity, so it’s not clear how to define these quantum states. String theorists have created models that appear to be identical to black holes in certain simplified conditions, and they use that information to calculate the quantum states of the black holes. Their results have been shown to match Hawking’s predictions, which he made without any precise way to count the quantum states of the black hole. This is the closest that string theory has come to an experimental prediction. Unfortunately, there’s nothing experimental about it because scientists can’t directly observe black holes (yet). It’s a theoretical prediction that unexpectedly matches another (well-accepted) theoretical prediction about black holes. And, beyond that, the prediction only holds for certain types of black holes and has not yet been successfully extended to all black holes. Explaining quantum field theory using string theory One of the major successes of string theory is something called the Maldacena conjecture, or the AdS/CFT correspondence. Developed in 1997 and soon expanded on, this correspondence appears to give insights into gauge theories, such as those at the heart of quantum field theory. The original AdS/CFT correspondence, written by Juan Maldacena, proposes that a certain 3-dimensional (three space dimensions, like our universe) gauge theory, with the most supersymmetry allowed, describes the same physics as a string theory in a 4-dimensional (four space dimensions) world. This means that questions about string theory can be asked in the language of gauge theory, which is a quantum theory that physicists know how to work with! Like John Travolta, string theory keeps making a comeback String theory has suffered more setbacks than probably any other scientific theory in the history of the world, but those hiccups don’t seem to last that long. Every time it seems that some flaw comes along in the theory, the mathematical resiliency of string theory seems to not only save it, but to bring it back stronger than ever. When extra dimensions came into the theory in the 1970s, the theory was abandoned by many, but it had a comeback in the first superstring revolution. It then turned out there were five distinct versions of string theory, but a second superstring revolution was sparked by unifying them. When string theorists realized a vast number of solutions of string theories (each solution to string theory is called a vacuum, while many solutions are called vacua) were possible, they turned this into a virtue instead of a drawback. Unfortunately, even today, some scientists believe that string theory is failing at its goals.

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What String Theory Attempts to Accomplish

Article / Updated 03-26-2016

To many, the goal of string theory is to be a “theory of everything” — that is, to be the single physical theory that, at the most fundamental level, describes all of physical reality. If successful, string theory could explain many of the fundamental questions about our universe. Explaining matter and mass One of the major goals of current string theory research is to construct a solution of string theory that contains the particles that actually exist in our universe. String theory started out as a theory to explain particles, such as hadrons, as the different higher vibrational modes of a string. In most current formulations of string theory, the matter observed in our universe comes from the lowest-energy vibrations of strings and branes. (The higher-energy vibrations represent more energetic particles that don’t currently exist in our universe.) The mass of these fundamental particles comes from the ways that these string and branes are wrapped in the extra dimensions that are compactified within the theory, in ways that are rather messy and detailed. For an example, consider a simplified case where the extra dimensions are curled up in the shape of a donut (called a torus by mathematicians and physicists), as in this figure. Strings wrap around extra dimensions to create particles with different masses. A string has two ways to wrap once around this shape: A short loop around the tube, through the middle of the donut A long loop wrapping around the entire length of the donut (like a string wraps around a yo-yo) The short loop would be a lighter particle, while the long loop is a heavier particle. As you wrap strings around the torus-shaped compactified dimensions, you get new particles with different masses. One of the major reasons that string theory has caught on is that this idea — that length translates into mass — is so straightforward and elegant. The compactified dimensions in string theory are much more elaborate than a simple torus, but they work the same way in principle. It’s even possible (though harder to visualize) for a string to wrap in both directions simultaneously — which would, again, give yet another particle with yet another mass. Branes can also wrap around extra dimensions, creating even more possibilities. Defining space and time In many versions of string theory, the extra dimensions of space are compactified into a very tiny size, so they’re unobservable to our current technology. Trying to look at space smaller than this compactified size would provide results that don’t match our understanding of space-time. One of string theory’s major obstacles is attempting to figure out how space-time can emerge from the theory. As a rule, though, string theory is built upon Einstein’s notion of space-time (three space dimensions and one time dimension). String theory predicts a few more space dimensions but doesn’t change the fundamental rules of the game all that much, at least at low energies. At present, it’s unclear whether string theory can make sense of the fundamental nature of space and time any more than Einstein did. In string theory, it’s almost as if the space and time dimensions of the universe are a backdrop to the interactions of strings, with no real meaning on their own. Some proposals have been developed for how this might be addressed, mainly focusing on space-time as an emergent phenomenon — that is, the space-time comes out of the sum total of all the string interactions in a way that hasn’t yet been completely worked out within the theory. However, these approaches don’t meet some physicists’ definition, leading to criticism of the theory. String theory’s largest competitor, loop quantum gravity, uses the quantization of space and time as the starting point of its own theory. Some believe that this will ultimately be another approach to the same basic theory. Quantizing gravity The major accomplishment of string theory, if it’s successful, will be to show that it’s a quantum theory of gravity. The current theory of gravity, general relativity, doesn’t allow for the results of quantum physics. Because quantum physics places limitations on the behavior of small objects, it creates major inconsistencies when trying to examine the universe at extremely small scales. Unifying forces Currently, four fundamental forces (more precisely called “interactions” among physicists) are known to physics: gravity, electromagnetic force, weak nuclear force, and strong nuclear force. String theory creates a framework in which all four of these interactions were once a part of the same unified force of the universe. Under this theory, as the early universe cooled off after the big bang, this unified force began to break apart into the different forces we experience today. Experiments at high energies may someday allow us to detect the unification of these forces, although such experiments are well outside of our current realm of technology.

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The Basic Elements of String Theory

Article / Updated 03-26-2016

Five key ideas are at the heart of string theory. Become familiar with these key elements of string theory right off the bat. Read on for the very basics of these five ideas of string theory in the sections below. Strings and membranes When the theory was originally developed in the 1970s, the filaments of energy in string theory were considered to be 1-dimensional objects: strings. (One-dimensional indicates that a string has only one dimension, length, as opposed to say a square, which has both length and height dimensions.) These strings came in two forms — closed strings and open strings. An open string has ends that don’t touch each other, while a closed string is a loop with no open end. It was eventually found that these early strings, called Type I strings, could go through five basic types of interactions, as shown this figure. Type I strings can go through five fundamental interactions, based on different ways of joining and splitting. The interactions are based on a string’s ability to have ends join and split apart. Because the ends of open strings can join together to form closed strings, you can’t construct a string theory without closed strings. This proved to be important, because the closed strings have properties that make physicists believe they might describe gravity. Instead of just being a theory of matter particles, physicists began to realize that string theory may just be able to explain gravity and the behavior of particles. Over the years, it was discovered that the theory required objects other than just strings. These objects can be seen as sheets, or branes. Strings can attach at one or both ends to these branes. A 2-dimensional brane (called a 2-brane) is shown in this figure. In string theory, strings attach themselves to branes. Quantum gravity Modern physics has two basic scientific laws: quantum physics and general relativity. These two scientific laws represent radically different fields of study. Quantum physics studies the very smallest objects in nature, while relativity tends to study nature on the scale of planets, galaxies, and the universe as a whole. (Obviously, gravity affects small particles too, and relativity accounts for this as well.) Theories that attempt to unify the two theories are theories of quantum gravity, and the most promising of all such theories today is string theory. Unification of forces Hand-in-hand with the question of quantum gravity, string theory attempts to unify the four forces in the universe — electromagnetic force, the strong nuclear force, the weak nuclear force, and gravity — together into one unified theory. In our universe, these fundamental forces appear as four different phenomena, but string theorists believe that in the early universe (when there were incredibly high energy levels) these forces are all described by strings interacting with each other. Supersymmetry All particles in the universe can be divided into two types: bosons and fermions. String theory predicts that a type of connection, called supersymmetry, exists between these two particle types. Under supersymmetry, a fermion must exist for every boson and vice versa. Unfortunately, experiments have not yet detected these extra particles. Supersymmetry is a specific mathematical relationship between certain elements of physics equations. It was discovered outside of string theory, although its incorporation into string theory transformed the theory into supersymmetric string theory (or superstring theory) in the mid-1970s. Supersymmetry vastly simplifies string theory’s equations by allowing certain terms to cancel out. Without supersymmetry, the equations result in physical inconsistencies, such as infinite values and imaginary energy levels. Because scientists haven’t observed the particles predicted by supersymmetry, this is still a theoretical assumption. Many physicists believe that the reason no one has observed the particles is because it takes a lot of energy to generate them. (Energy is related to mass by Einstein’s famous E = mc2 equation, so it takes energy to create a particle.) They may have existed in the early universe, but as the universe cooled off and energy spread out after the big bang, these particles would have collapsed into the lower-energy states that we observe today. (We may not think of our current universe as particularly low energy, but compared to the intense heat of the first few moments after the big bang, it certainly is.) Scientists hope that astronomical observations or experiments with particle accelerators will uncover some of these higher-energy supersymmetric particles, providing support for this prediction of string theory. Extra dimensions Another mathematical result of string theory is that the theory only makes sense in a world with more than three space dimensions! (Our universe has three dimensions of space — left/right, up/down, and front/back.) Two possible explanations currently exist for the location of the extra dimensions: The extra space dimensions (generally six of them) are curled up (compactified, in string theory terminology) to incredibly small sizes, so we never perceive them. We are stuck on a 3-dimensional brane, and the extra dimensions extend off of it and are inaccessible to us. A major area of research among string theorists is on mathematical models of how these extra dimensions could be related to our own. Some of these recent results have predicted that scientists may soon be able to detect these extra dimensions (if they exist) in upcoming experiments, because they may be larger than previously expected.

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Considering String Theory’s Setbacks

Article / Updated 03-26-2016

Because string theory has made so few specific predictions, it’s hard to disprove it, but the theory has fallen short of some of the hype about how it will be a fundamental theory to explain all the physics in our universe, a “theory of everything.” This failure to meet that lofty goal seems to be the basis of many (if not most) of the attacks against it. Here are three issues that even most string theorists aren’t particularly happy about: Because of supersymmetry, string theory requires a large number of particles beyond what scientists have ever observed. This new theory of gravity was unable to predict the accelerated expansion of the universe that was detected by astronomers. A vastly large number of mathematically feasible string theory vacua (solutions) currently exist, so it seems virtually impossible to figure out which could describe our universe. The following sections cover these dilemmas in more detail. The universe doesn’t have enough particles For the mathematics of string theory to work, physicists have to assume a symmetry in nature called supersymmetry, which creates a correspondence between different types of particles. One problem with this is that instead of the 18 fundamental particles in the Standard Model, supersymmetry requires at least 36 fundamental particles (which means that nature allows 18 particles that scientists have never seen!). In some ways, string theory does make things simpler — the fundamental objects are strings and branes or, as predicted by matrix theory, zero-dimensional branes called partons. These strings, branes, or possibly partons make up the particles that physicists have observed (or the ones they hope to observe). But that’s on a very fundamental level; from a practical standpoint, string theory doubles the number of particles allowed by nature from 18 to 36. One of the biggest possible successes for string theory would be to experimentally detect these missing supersymmetric partner particles. The hope of many theoretical physicists is that when the Large Hadron Collider particle accelerator at CERN in Switzerland goes fully online, it will detect supersymmetric particles. Even if successful, proof of supersymmetry doesn’t inherently prove string theory, so the debate would continue to rage on, but at least one major objection would be removed. Supersymmetry might well end up being true, whether or not string theory as a whole is shown to accurately describe nature. Dark energy: The discovery string theory should have predicted Astronomers found evidence in 1998 that the expansion of the universe was actually accelerating. This accelerated expansion is caused by the dark energy that appears so often in the news. Not only did string theory not predict the existence of dark energy, but attempts to use science’s best theories to calculate the amount of dark energy comes up with a number that’s vastly larger than the one observed by astronomers. The theory just absolutely failed to initially make sense of dark energy. Claiming this as a flaw of string theory is a bit more controversial than the other two, but there’s some (albeit questionable) logic behind it. The goal of string theory is nothing less than the complete rewriting of gravitational law, so it’s not unreasonable to think that string theory should have anticipated dark energy in some way. When Einstein constructed his theory of general relativity, the mathematics indicated that space could be expanding (later proved to be true). When Paul Dirac formulated a quantum theory of the electron, the mathematics indicated an antiparticle existed (later proved to actually exist). A profound theory like string theory can be expected to illuminate new facts about our universe, not be blind-sided by unanticipated discoveries. Of course, no other theory anticipated an accelerating expansion of the universe either. Prior to the observational evidence (some of which is still contested), cosmologists (and string theorists) had no reason to assume that the expansion rate of space was increasing. Years after dark energy was discovered, it was shown that string theory could be modified to include it, which string theorists count as a success (although the critics continue to be unsatisfied). Where did all of these “fundamental” theories come from? Unfortunately, as string theorists performed more research, they had a growing problem (pun intended). Instead of narrowing in on a single vacuum (solution) that could be used to explain the universe, it began to look like there were an absurdly large number of vacua. Some physicists’ hopes that a unique, fundamental version of string theory would fall out of the mathematics effectively dissolved. In truth, such hype was rarely justified in the first place. In general relativity, for example, an infinite number of ways to solve the equations exist, and the goal is to find solutions that match our universe. The overly ambitious string theorists (the ones who expected a single vacuum to fall out of the sky) soon realized that they, too, would end up with a rich string theory landscape, as Leonard Susskind calls the range of possible vacua. The goal of string theory has since become to figure out which set of vacua applies to our universe.

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Einstein's Special Relativity

Article / Updated 03-26-2016

In 1905, Albert Einstein published the theory of special relativity, which explains how to interpret motion between different inertial frames of reference — that is, places that are moving at constant speeds relative to each other. Einstein explained that when two objects are moving at a constant speed as the relative motion between the two objects, instead of appealing to the ether as an absolute frame of reference that defined what was going on. If you and some astronaut, Amber, are moving in different spaceships and want to compare your observations, all that matters is how fast you and Amber are moving with respect to each other. Special relativity includes only the special case (hence the name) where the motion is uniform. The motion it explains is only if you’re traveling in a straight line at a constant speed. As soon as you accelerate or curve — or do anything that changes the nature of the motion in any way — special relativity ceases to apply. That’s where Einstein’s general theory of relativity comes in, because it can explain the general case of any sort of motion. Einstein’s theory was based on two key principles: The principle of relativity: The laws of physics don’t change, even for objects moving in inertial (constant speed) frames of reference. The principle of the speed of light: The speed of light is the same for all observers, regardless of their motion relative to the light source. (Physicists write this speed using the symbol c.) The genius of Einstein’s discoveries is that he looked at the experiments and assumed the findings were true. This was the exact opposite of what other physicists seemed to be doing. Instead of assuming the theory was correct and that the experiments failed, he assumed that the experiments were correct and the theory had failed. In the latter part of the 19th century, physicists were searching for the mysterious thing called ether — the medium they believed existed for light waves to wave through. The belief in ether had caused a mess of things, in Einstein’s view, by introducing a medium that caused certain laws of physics to work differently depending on how the observer moved relative to the ether. Einstein just removed the ether entirely and assumed that the laws of physics, including the speed of light, worked the same regardless of how you were moving — exactly as experiments and mathematics showed them to be! Unifying space and time Einstein’s theory of special relativity created a fundamental link between space and time. The universe can be viewed as having three space dimensions — up/down, left/right, forward/backward — and one time dimension. This 4-dimensional space is referred to as the space-time continuum. If you move fast enough through space, the observations that you make about space and time differ somewhat from the observations of other people, who are moving at different speeds. You can picture this for yourself by understanding the thought experiment depicted in this figure. Imagine that you’re on a spaceship and holding a laser so it shoots a beam of light directly up, striking a mirror you’ve placed on the ceiling. The light beam then comes back down and strikes a detector. (Top) You see a beam of light go up, bounce off the mirror, and come straight down. (Bottom) Amber sees the beam travel along a diagonal path. However, the spaceship is traveling at a constant speed of half the speed of light (0.5c, as physicists would write it). According to Einstein, this makes no difference to you — you can’t even tell that you’re moving. However, if astronaut Amber were spying on you, as in the bottom of the figure, it would be a different story. Amber would see your beam of light travel upward along a diagonal path, strike the mirror, and then travel downward along a diagonal path before striking the detector. In other words, you and Amber would see different paths for the light and, more importantly, those paths aren’t even the same length. This means that the time the beam takes to go from the laser to the mirror to the detector must also be different for you and Amber so that you both agree on the speed of light. This phenomenon is known as time dilation, where the time on a ship moving very quickly appears to pass slower than on Earth. As strange as it seems, this example (and many others) demonstrates that in Einstein’s theory of relativity, space and time are intimately linked together. If you apply Lorentz transformation equations, they work out so that the speed of light is perfectly consistent for both observers. This strange behavior of space and time is only evident when you’re traveling close to the speed of light, so no one had ever observed it before. Experiments carried out since Einstein’s discovery have confirmed that it’s true — time and space are perceived differently, in precisely the way Einstein described, for objects moving near the speed of light. Unifying mass and energy The most famous work of Einstein’s life also dates from 1905 (a busy year for him), when he applied the ideas of his relativity paper to come up with the equation E=mc2 that represents the relationship between mass (m) and energy (E). In a nutshell, Einstein found that as an object approached the speed of light, c, the mass of the object increased. The object goes faster, but it also gets heavier. If it were actually able to move at c, the object’s mass and energy would both be infinite. A heavier object is harder to speed up, so it’s impossible to ever actually get the particle up to a speed of c. Until Einstein, the concepts of mass and energy were viewed as completely separate. He proved that the principles of conservation of mass and conservation of energy are part of the same larger, unified principle, conservation of mass-energy. Matter can be turned into energy and energy can be turned into matter because a fundamental connection exists between the two types of substance.

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