One-dimensional vibrating loops or line segments {string, physics} account for matter, force, and energy. Strings vibrate at specific frequencies, amplitudes, phases, and modes {superstring theory}| {string theory} to represent particles.
length and mass
String lengths are multiples of Planck length. Uncertainty principle requires strings to be longer than Planck length.
particles
Strings are fundamental particles and have no sub-structure or sub-particles. String vibration modes make elementary particles. String theory requires an infinite series of elementary particles with increasing masses. High-mass elementary particles are unstable. Particle interactions merge two strings into one string or split one string into two strings.
particles: dilaton
Force strengths depend on string 11th-space-time-dimension length (dilaton). Short dilatons represent weak nuclear forces. Long dilatons represent strong nuclear forces. Dilaton lengths represent electromagnetism, and dilaton length variations change electromagnetic fields.
Before universe origin, dilatons are long, and forces are strong. At universe origin, dilatons are short, and forces are weak. Observing intergalactic magnetic-field changes is a test for dilatons and so can indicate universe-origin conditions.
mass
String mass is proportional to string length. Shorter strings have higher vibration frequencies and so higher masses.
waves and resonance
Strings vibrate at light speed as high-frequency waves. Shorter strings have higher vibration frequencies. String waves dampen Planck-scale quantum fluctuations. Waves have Planck lengths and so are not observable. String-wave resonances make particles and forces.
space
Strings have dimension and vibrate, so strings occupy space. Strings require background space.
energy
Strings have high energy and mass, because they are stiff vibrators, with 10^39 tons tension {Planck tension}. However, quantum fluctuations decrease this energy.
In zero-rest-mass particles, string rest masses cancel, leaving low-energy vibrations. Zero-rest-mass strings have relativistic mass and so can have momentum and angular momentum.
In elementary particles with mass, almost all string rest masses cancel.
spatial dimensions
Uncertainty principle causes strings to have a smallest length, equal to Planck length. Strings occupy space because they vibrate.
String waves vibrate in three extended spatial dimensions, seven curled-up Planck-size spatial dimensions (Joyce manifolds), and one time dimension. Physical scalar and vector fields determine the number and properties of infinite and curled-up dimensions. String waves can vibrate in dimensions, wrap around dimensions, and travel around dimensions. Winding around large dimensions takes more energy, because string stretches. Moving around large dimensions takes less energy, because frequency is less. The effects balance each other.
spatial dimensions: winding
In a curled-up dimension, string vibrations occur along the dimension (dimensional vibration) and go around the dimension {winding mode}. They can go around more than once. Curled-up dimensions cannot be smaller and their vibrations have a minimum, so waves have quantum size and energy.
spatial dimensions: size
Curled-up dimensions have two radii, one across curl and one around dimension. Because vibrations increase as quantum fluctuations increase, if one dimension becomes smaller, other dimension becomes larger. Winding-mode vibrations depend directly on dimension radius. Dimensional vibrations depend inversely on radius. Because winding mode vibrations and dimensional vibrations are reciprocal, curled-up dimensions have same physics as dimensions with exchanged winding-mode and dimensional-vibration radius.
spatial dimensions: physical forces
Electromagnetic waves, matter waves, gluons, and W and Z particles travel only in three-dimensional space, not curled-up dimensions. Gravity waves can travel in all dimensions.
interactions
Strings can split into two strings, or two strings can merge into one string. Splitting and merging probabilities depend on a positive-number constant {string coupling constant}. Constant is less than one for weak coupling or greater than one for strong coupling.
finite
String theory has finite quantities and so removes field-theory infinity problems and quantum-mechanics renormalization problems. (However, eleven-dimensional quantum-field theory can have finite particles and quantities.)
strings
Strings are one-dimensional Planck-length-multiple line segments or circles, and M-theory p-branes are multi-dimensional Planck-length-multiple areas. Particles are Planck-length-multiple strings that harmonically vibrate in dimensions.
strings: general relativity
At greater-than-Planck-length distances and larger-than-energy-quantum energies, string theory and general relativity have same form.
strings: quantum mechanics
String-vibration wave equations have harmonic-frequency wavefunction solutions. Discrete wave frequencies represent energy quanta, which account for particle masses. String wavefunctions are essentially the same as particle quantum-mechanical wavefunctions.
strings: dimensions
Space has three infinite dimensions and some number of compactified dimensions. Compactified dimensions have relations.
strings: vibration components
As fundamental units, strings have no internal parts, structure, or forces. Because longitudinal vibrations require internal parts, structure, or forces, strings have no longitudinal vibrations.
Strings vibrate transversely across all dimensions, so vibrations have many components. For curled-up dimensions, vibration frequency varies directly with radius inverse, so shorter strings have wave higher frequencies. For curled-up dimensions, strings can also vibrate transversely around the dimension (wind), and winding-vibration frequency varies directly with radius, so longer strings have higher winding-wave frequencies. Therefore, winding vibrations are duals to the other transverse vibrations.
In each dimension, strings vibrate at resonant frequencies, determined by string length and tension. Vibration components have complex-number frequencies, which determine real and imaginary wave-energy components, which determine real and imaginary particle-mass components. Because complex-number operations can result in positive or negative values, superpositions of wave components can make positive or negative wave energies and positive or negative particle masses. Quantum energy fluctuations can also be positive or negative, so virtual particles can have positive or negative masses.
Strings cannot have zero length, because then they are not strings, which must have tension between endpoints. Strings cannot have no vibrations, because they must have tension and endpoints and so fundamental frequency.
strings: particles
String theory accounts for all Standard-Model particles.
Electric charge is at open-string endpoints or spread around closed string. Zero-rest-mass oriented open strings are U(n) bosons. Photons are open strings, are vectors with spin 1, and have wave amplitude zero. For local interactions, photons have clockwise or counterclockwise transverse-wave amplitude-vector rotation around oriented-string long axis to account for integer spin. Photons have no mass, so strings have zero-point lowest-energy state. Photons have photons as antiparticles. For global interactions, electric charge can be positive or negative and that corresponds to orientation, requiring otherwise-same opposite oriented open strings or otherwise-same clockwise and counterclockwise motions around closed strings. Electric charge does not have anti-charge, only exactly opposite positive and negative charge. Electrons and positrons have clockwise or counterclockwise transverse-wave amplitude-vector rotation around long axis to account for half-integer spin.
Strangeness is at open-string endpoints or spread around closed string. Vector bosons are open strings and are vectors with spin 1. Strangeness can be zero or one, corresponding to absence or presence, requiring non-opposite oriented open strings or non-opposite clockwise and counterclockwise motions around closed strings (violating parity). Strangeness does not have anti-strangeness. For local interactions, Z intermediate vector bosons have clockwise or counterclockwise transverse-wave amplitude-vector rotation around oriented-string long axis to account for integer spin. W intermediate vector bosons have both clockwise and counterclockwise transverse-wave amplitude-vector rotation around oriented-string long axis to account for zero spin. Intermediate vector bosons have mass, so strings have intermediate-energy state. Intermediate vector bosons have intermediate vector bosons as antiparticles. For global interactions, pions have clockwise or counterclockwise transverse-wave amplitude-vector rotation around oriented-string long axis to account for half-integer spin.
Color charge is at open-string endpoints or spread around closed string. Gluons are open strings and are vectors with spin 1. Color has three vectors that add to zero, corresponding to an equiangular triangle, requiring complex-number oriented open strings or complex-number clockwise and counterclockwise motions around closed strings. Colors have anti-colors. For local interactions, gluons have clockwise or counterclockwise transverse-wave amplitude-vector rotation around long axis to account for integer spin. Gluons have mass, so strings have high-energy state. Gluons have gluons as antiparticles. For global interactions, quarks have clockwise or counterclockwise transverse-wave amplitude-vector rotation around long axis to account for half-integer spin.
Gravitons are closed strings, are symmetric tensors with spin 2, and have wave amplitude zero. Mass-energy is positive and scalar. Mass has negative scalar anti-mass. For local interactions, gravitons have two clockwise or counterclockwise transverse-wave amplitude-vector spins, one around each tensor axis. Gravitons have no mass, so strings have zero-point energy. Gravitons have gravitons as antiparticles. Fermion and boson waves together make tensor that has one symmetry, which makes tensor gauge and so closed string with spin 2.
Dilatons are closed strings and are scalars with spin 0. Axions are closed strings and are antisymmetric tensors with spin 0. Zero-rest-mass unoriented open strings are SO(n) or Sp(n) bosons.
strings: virtual particles
At small distances, string-theory quantum mechanics allows virtual particles. Strings always change to strings, never to no strings, because, by uncertainty principle, zero-length strings have infinite energy. The no-string (vacuum) state cannot exist.
One zero-point-energy string can become two virtual-particle strings. Two virtual-particle strings can become one zero-point-energy string.
Strings preserve all symmetries and conservation laws.
Real-particle strings have longer lengths, lower energies, and longer lifetimes. Virtual-particle strings have short lengths, high energies, and short lifetimes.
strings: particle properties
String (Planck-multiple) lengths and (high) tensions determine transverse vibration modes and account for particle energies, masses, rotations, and other properties.
String endpoints rotate around center, or closed strings rotate, so strings account for particle spin. String orientations that differ only in direction can represent clockwise and counterclockwise spin. String orientations that differ in direction and other properties can represent parity or no parity. Closed strings can account for zero-rest-mass spin-2 particles (graviton).
matrix theory
Perhaps, space is intertwined strings or zero-branes {matrix theory} and so is not background-independent.
quantum loop
Perhaps, quantum loops are the background for strings. Larger loops can be strings. Perhaps, strings are waves in spin networks.
comparison to points
Strings have one dimension, are Planck length or higher, and have waves. Points have zero dimension, are smaller than Planck scale, and have no waves.
Physical Sciences>Physics>String Theory
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Date Modified: 2022.0224