Quantum mechanics can combine with general relativity to make quantum field theory {relativistic quantum mechanics}| {quantum field theory}. Relativistic quantum mechanics accounts for all force types, allows particle creation and destruction, is invariant under Lorentz transformations, requires negative energy levels, and predicts antiparticles. Quantum-field theories modify relativity with quantum mechanics and include quantum electrodynamics, quantum chromodynamics, and grand unified theories.
Non-relativistic quantum mechanics does not require particle spin and does not require Hilbert space. By relativity, observed values cannot affect each other faster than light. Relativistic quantum mechanics requires Hilbert space. In (relativistic) quantum field theory, functionals of quantum fields either commute or anti-commute, because otherwise they would interact faster than light. Relativistic quantum mechanics requires particle spin, to allow commutation and anti-commutation. Fermions anti-commute, and bosons commute. In (relativistic) quantum field theory, these are the only allowed particle types. Other non-commutative relations allow faster than light affects, because of their other components. Relativistic quantum-mechanics operator commutation properties determine Pauli exclusion principle. (Non-relativistic quantum-mechanics operator commutation properties determine Heisenberg uncertainty principle.)
Electromagnetic waves are vector waves, but non-relativistic quantum-mechanics wavefunctions are scalar waves. Scalar waves have no polarization, so non-relativistic quantum-mechanics wavefunctions cannot represent spin. Relativistic quantum-mechanics wavefunctions are scalar waves with spinors and so are vector waves. Vector waves have polarization and can be plane-polarized or circularly polarized, and spin applies to circular polarization. Relativistic quantum-mechanics wavefunctions can represent particle spin. Circular-polarization rate represents particle spin.
Theories {unified field theory}| try to unite all forces and particles. Strong, weak, and electromagnetic forces unify at 10^28 K at distances of 10^-31 meters, when universe was 10^-39 second old, if supersymmetry is true and superpartners exist. Weak and electromagnetic forces unify at 10^15 K.
Theories {grand unified theories}| {Grand Unification} (GUTS) use a new gauge boson that affects both quarks and leptons and so unifies strong and electromagnetic forces.
requirements
Complete unified theory must have perfect symmetry at high temperature, high energy, and short distances and have different and lower symmetry for current universe. Theory must relate three quark and lepton generations {horizontal symmetry}. Maintaining symmetry to preserve conservation laws requires forces.
First symmetry loss creates the twelve hyperweak-force bosons. Next symmetry loss creates the eight strong-force gluons. Next symmetry loss creates the three weak-force intermediate vector bosons. These symmetry losses give bosons their masses.
unity
Particles can have inner electric field surrounded by region with particle creations and annihilations that decrease field. Inner electric field is stronger than electromagnetism and decreases by less than radius squared.
Particles can have inner strong or weak force field surrounded by region with particle creations and annihilations that increase field. Inner field is weaker than strong or weak force and decreases by more than radius.
Decrease of strong nuclear forces and increases of electric and weak forces can meet to unify all forces.
weak and strong forces
Rotation between weak and strong forces became constant when symmetry broke at an angle {Cabibbo angle}.
weak force and electromagnetism
Weinberg-angle coupling constant for isospin and electroweak hypercharge has value close to that predicted by grand unified theory.
Strong nuclear force can unite with special relativity {quantum chromodynamics}| (QCD).
color
Long-range color force causes short-range strong nuclear force. Like electric charge, color conserves.
electric charge
Particles with integral electric charge have no color, because their colors add to white or black. Particles with fractional electric charge have color, because their colors do not add to white or black. For example, pions have up quark and down antiquark, so charge is -1 (-2/3 + -1/3), and color and complementary color add to white. Protons have two up quarks and one down quark, so charge adds to +1 (+2/3 + +2/3 + -1/3), and colors red, green, and blue add to white. In particles, two up quarks must have different colors, because same colors repel.
strength
Close quarks interact weakly, because net color is zero. Farther quarks interact more strongly, because net color is more.
free quarks
Fractional-charge colorful particles cannot exist by themselves, because they cannot break free of strong force. For high energy and temperature, distances are short, and quarks and gluons do not strongly interact {asymptotic freedom}.
vectors
Quantum chromodynamics uses three complex gauge-field vectors, for red, green, and blue, and so is non-Abelian. Cyan, magenta, and yellow are vectors in opposite directions. Colors add by vector addition, so vectors make a color wheel in complex plane.
gauge
Quantum chromodynamics is a hadron gauge theory and uses the SU(3) symmetry group. Strong force has symmetry, because quark color does not matter, only net color.
strong-force exchange particle
Strong-force field has gluons, not force lines, and can change from gluons to particles and back.
lattice
Three-dimensional lattices can approximate continuous space as discontinuous nodes. Nodes represent possible quark locations. Paths between nodes represent quark interactions, and lattice lines are forces connecting quarks. Because strong force is constant with distance after short distance, number of lines between two quarks is constant.
string theory
Strings in five-dimensional dynamic space, and particles in four-dimensional boundary of QCD-force space, have equivalent mathematics. When QCD forces are strong, strings interact weakly. In string theory, QCD viscosity is like black-hole gravity-wave absorption.
Electromagnetism can unite with special relativity {quantum electrodynamics}| (QED) {relativistic quantum field theory}. From electron charge and mass, quantum electrodynamics can predict all charged-particle interactions. Quantum electrodynamics describes electromagnetic photon-electron/proton/ion interactions using quantum mechanics. Possible paths have amplitudes and probabilities. Path number is infinite, but some cancel and some end (sum over histories). Feynman diagrams illustrate paths.
field
Electric field has photons, not force lines. Electromagnetic force has symmetry.
photons
Photons are electric-field excitations. Sources emit photons, and sinks absorb photons. Field can change from photons to particles and back.
quasiparticle
Electrons {quasiparticle, electron} move through material with higher or lower mass than rest mass, because they interact more or less with material electric fields. Electrons moving at relativistic speed tunnel through barriers {Klein paradox}. Electrons {Dirac quasiparticle} moving at relativistic speeds have low effective mass, because they have accompanying virtual antiparticles, which subtract mass, that materialize from vacuum. In vacuum, time is short, so frequency and energy are high enough to make particle-antiparticle pairs. Antiparticles attract to fields that repel particles, so Dirac quasiparticles tunnel.
string theory
String theory derives from quantum-electrodynamics approximation methods {perturbation theory}.
special relativity
Quantum mechanics can combine with special relativity, for use in flat space-time or in time-independent space-time. Time can include imaginary time, which rotates time axis {Wick rotation} and transforms Minkowski into Euclidean space. Gravitons have features that are not gravitational-field excitations.
At energy levels that are low compared to interacting-particle mass, forces are negligible {effective field theory}. Gravitation has negligible force.
Quantum electrodynamics, quantum chromodynamics, and quantum electroweak theory form unified theory {particle physics standard model} {standard model of particle physics} {standard theory}.
particles
Quarks, leptons, and intermediate vector bosons are wave bundles in fields. Top quark has 175 GeV. Proton has 1 GeV.
Why are there three particle generations, rather than just one? The first generation makes consistent theory with need for higher-mass particles.
Particle masses, charges, and spins relate by the Yang-Mills gauge group in the particle Standard Model. That gauge group is the direct product of the Special Unitary group for three gluons, Special Unitary group for two intermediate vector bosons, and Unitary group for one photon: SU(3) x SU(2) x U(1). Therefore, the Yang-Mills gauge group has SU(3), SU(2), and U(1) as subgroups. SU(3) is for strong-force quark and gluon color, is non-Abelian, and has no invariant subgroups, so its matrix is traceless. SU(2) is for weak-force pion and W-and-Z boson strangeness, is non-Abelian, and has no invariant subgroups, so its matrix is traceless. U(1) is for electromagnetic electron and positron electric charge and is Abelian and normal. Unitary groups have unitary square matrices, as generators. Special groups have square-matrix determinants = 1.
field
Standard theory is renormalizable quantum-field theory. Quantum-field theory is for energies that are high compared to particle mass, so it is not about gravitation.
gauge symmetry
Only quantum differences are important, not absolute values.
gauge symmetry: renormalization
Redefining 18 physical constants {renormalizable} can remove infinite quantities.
other forces: mass
Gravitation is about mass. Standard Model does not predict quark and lepton masses, unless it adds a scalar field. Scalar field probably has quanta and so Higgs particles, with masses of 100 to 300 GeV.
other forces: supersymmetry
Perhaps, a new force allows protons to be unstable with half-life 10^31 to 10^34 years. Perhaps, new force gives mass 10^-11 GeV to neutrinos.
In quantum-field theories, matter positive frequencies can go forward in time, and antimatter negative frequencies can go backward in time {twistor, quantum mechanics}| (Penrose). In Minkowski space, twistors are spinors and complex-conjugate spinors.
Riemann sphere
Complex numbers graph to planes. Plane can be at Riemann sphere equator. Pole point can be at infinity. Line from pole through plane can intersect Riemann sphere. Real numbers are on equator. Positive frequencies are in upper hemisphere. Riemann sphere is twistor space. Twistor space has two plane dimensions and three space-time-point dimensions. Adding spin makes six real dimensions {projective twistor space}.
space-time and quantum mechanics
Perhaps, general relativity and quantum mechanics unify using twistors. Space-time relates to quantum-mechanics complex amplitudes through Riemann spheres. Riemann-sphere space-time points have light-ray sets. Space-time events are Riemann-sphere directions, showing which past events can affect future event. In twistor space, light rays are points, so twistor space is not local. Photons have right or left circular polarization {helicity}. Half-spin particles have up and down spin superpositions, as observer sees Riemann sphere. Riemann spheres can have inscribed icosahedrons, which define 20 sphere points. Points join three edges, which can be like three space dimensions. Points combine two independent entangled fermion spins, with spin +1/2 or -1/2. Riemann tensor has 20 components in flat space-time. Perhaps, complex numbers can relate general relativistic space-time to spin quantum mechanics [Penrose, 2004]. At different velocities, transformation groups {Möbius transformation, twistor} can find curvature.
5-Physics-Quantum Mechanics-Theory-Quantum Relativity-Theories
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Date Modified: 2022.0225