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

The four forces are gravitation, electromagnetism, weak force, and strong force. Each force has a particle associated with the smallest possible “packet” of that force. Each known matter particle has a kind of charge (negative or positive) that relates to each kind of force. Each force has a corresponding particle: strong force and gluon; electromagnetic force and photon; weak force and weak gauge boson; gravity and graviton. (See Table 1.2 on page 11 of the book.)

Einstein’s theory of gravity, general relativity shows that the gravitational force is communicated through the curvature of spacetime by objects with mass. In addition, general relativity posits the symmetry of all viewpoints, regardless of their accelerated motion, if observations include a suitable gravitational force.

Emerging from the second superstring revolution, M-theory, proposed by Edward Witten, argues that the five distinct versions of string theory can (and should) be united within a single overarching framework and may therefore constitute a true unifying theory. M-theory requires 11 spacetime dimensions; however, many of its properties have yet to be determined.

A framework that allows physicists to simplify highly complicated, difficult equations by ignoring details, perturbation theory enables approximate solutions that can be refined closer and closer to reality as previously excluded details are slowly added to a system. Perturbation theory is required for studying string theory because the precise equations required have not yet been discovered.

A series of proportions and measurements, Planck units (based on the work of Max Planck) represent the smallest possible scales at which quantum mechanics and string theory apply. These include Planck’s constant (the fundamental parameter in quantum mechanics that determines the units of mass, energy, spin, etc. possessing a value of 1.05x10^-27 grams-cm/sec), Planck length (the distance scale below which quantum fluctuations become enormous, with a value of about 10^-33 centimeters), Planck mass (the typical mass of a vibrating string in string theory, with a value of about ten billion billion times the mass of a proton), and Planck time (the miniscule time duration during which the size of the universe was roughly one Planck length, with a value of about 10^-43 seconds).

The framework of laws that govern the universe at the microscopic level, quantum mechanics includes such features as the uncertainty principle, quantum fluctuations, and wave-particle duality. These features become apparent only at Planck scales.

A theory proposed by Albert Einstein in 1905, special relativity describes the principle of relativity, which states that observers in relative constant-velocity motion will always have “different perceptions of distance and of time” (25). Additionally, special relativity established the constancy of light speed and the equation E=mc².

A guiding principle in physics, symmetry is a property of a system that ensures that viewpoints/results remain the same regardless of how that system is transformed. Several vital kinds of symmetry are at work in physics, including the principles of relativity and equivalence, proposed by Einstein; gauge symmetry, which applies to the three nongravitational forces and ensures that the system does not change as force charge values shift; supersymmetry, which relates to the properties of spin in particles; and mirror symmetry, a concept in string theory in which Calabi-Yau shapes exist in mirror pairs, which give rise to identical physics.

The 12 known matter particles are organized into three groups, or families, each containing two quarks, an electron or “cousin” (muon or tau), and the corresponding neutrino. The particles in each successive family differ from those before it by possessing more mass, while carrying the same electric and nuclear charges. Family 1 consists of electron, electron-neutrino, up quark, and down quark. Family 2 consists of muon, muon-neutrino, charm quark, and strange quark. Family 3 consists of tau, tau-neutrino, top quark, and bottom quark. (See Table 1.1 on page 9 of the book.)