Weak force and electromagnetic force can unite with special relativity {quantum electroweak theory}. Field has photons and has Z and W particles, not force lines. Field can change from photons and Z and W particles to particles and back. Weak force has symmetry.
Perhaps, space-time averages all possible 4-simplex matter-wave superpositions {Euclidean quantum gravity}. If space and time are equivalent dimensions, time has no direction, and physics has no causality. If space and time are not equivalent dimensions, time has direction, and physics has causality, so simplexes connect {causal dynamical triangulations}.
Quantum mechanics can unify with general relativity {quantum gravity}|. Quantum gravity is unitary.
gravity
Gravity curves space-time, and space-time determines mass motions {Wheeler-DeWitt equation}. Gravitons and interactions among gravitons determine curvature, but interactions are small if curvature is much larger than Planck length. Interactions take all possible paths, because no information is available about interaction.
gravity: metrics
For cosmology, measurements must be from within and so local. Metrics can have no singularities. Euclidean metrics can be local and can have two types, connected and disconnected.
Connected metrics are broad bounded space-time regions, with a local measurement region. Connected metrics have a boundary, and so boundary conditions. Connected metrics have few paths.
Disconnected metrics are compact unbounded space-time regions, with all local measurements. Disconnected metrics have no boundary, and so no boundary conditions. Disconnected metrics have almost all paths.
wavefunction
Universe wavefunction determines particle positions and depends on three spatial-dimension metrics and on particle. It does not depend on time, because compact metric has no preferred time. It does not depend on coordinate choice, becasue coordinates are equivalent.
Observers can see only part of space, so universe has mixed quantum state, which implies decoherence and classical physics. Superpositions do not happen, because gravitational effects cancel superpositions.
Fermions have Fermi-Dirac statistics, and bosons have Bose-Einstein statistics, and there are no other particle types {spin statistics theorem}, because quantum field theory functionals either commute or anti-commute.
To relate fermions to bosons, theories {supergravity}| can use three spatial dimensions, one time dimension, and seven more spatial dimensions to form high-curvature and high-energy-density seven-spheres. Supergravity is supersymmetry using curved spatial dimensions, seven curled-up dimensions, and gravity.
To describe phenomena that involve massive objects at short distances, such as black holes and Big Bang, theories {theory of everything}| {final theory} must unite general relativity and quantum mechanics. String theory derives from quantum mechanics.
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.
Quantum mechanics can combine with special relativity {gauge theory}.
boson
Forces have force fields and exchange bosons. Bosons are quanta. Field quanta are bosons. Gauge transformations are boson exchanges. Boson exchange carries energy and momentum quanta between fermions. Field is for relativity, and quanta are for quantum mechanics.
Higgs particles are bosons that generate masses for particles. Hadrons are bosons in multiplets for charge and isotopic spin.
groups
Conservation laws determine symmetries and gauge transformations, which form mathematical groups. Quantum electrodynamics is lepton gauge theory and uses symmetry group U(1). Quantum chromodynamics is hadron gauge theory and uses symmetry group SU(3). Electroweak theory [1973] is gauge theory for weak interactions and electromagnetism and uses symmetry group SU(2) x U(1).
Symmetry {gauge symmetry}| requires that only quantum differences are important, not absolute values.
Continuous point sets are manifolds {base space}. Manifold points can have internal spaces {fiber space}, with internal dimensions {fiber, mathematics}. Fiber spaces are manifolds. Fibers do not intersect. Fibers project to points {canonical projection}.
fiber bundles
Combined base and fiber space {fiber bundle}| {bundle} has dimension number equal to sum of fiber-space and base-space dimensions. Base space can be curve. Curve points have line tangents to curve. Tangents are fiber spaces.
Curved-surface points have planes tangent to surface. Tangent planes are fiber spaces.
vector bundle
Fiber spaces can be vector spaces {vector bundle}.
twisting
If fiber spaces are the same for all base-space points, base space and fiber space can make product space {untwisted bundle}. If fiber spaces are not all the same, base space and fiber space can make a symmetrical locally untwisted product space {twisted bundle} with a mathematical group. For example, particle spins can be fiber bundles. Base-space spins go to fiber-space phase relations.
curvature
Curvature can be connections between fibers in fiber bundles, with rule {path-lifting rule} for getting to fiber-space point from base-space point.
gauge fields
Gauge fields can be connections between fiber-bundle fibers. Bundles can have locally constant values {bundle connection}, which are like gauge connections. Connections represent field phase shifts {path lift}.
tangent bundle
Base spaces can have tangent vectors as fiber spaces {tangent bundle} or covectors as fiber spaces {cotangent bundle}. Base spaces can be two-dimensional spheres. Fiber spaces can be circles. Bundles {Hopf fibration} {Clifford bundle} can be three-dimensional spheres.
Quantum mechanics can combine with general relativity by gauge-theory extension {relativistic gauge theory}. Base field or space represents physical space-time events. Total field or space represents quantum wavefunctions or symmetry transformations. Base-space points project to total-space points to make fibers.
Perhaps, fermions and bosons can interchange using a new force {technicolor theory}| {supersymmetry} {Supersymmetric Standard Model} (SSM). Fermions and bosons have quarks, which are fermions. Supersymmetry unites half-integer-spin fermions and integer-spin bosons.
fermion
Particles with odd number of quarks are fermions, which have half-integer spins. Fermions have negative ground-state energy.
boson
Particles with even number of quarks are bosons, which have integer spins. Bosons have positive ground-state energy.
stability
Fermion-boson interaction can cancel ground-state energies, leaving small stable energies.
force
Fermions and bosons can have a new force. The new exchange particles have 1000-GeV energies, with range from 10^2 GeV to 10^16 GeV. Because force strength depends on particle energy, the new force is the strongest force.
spin: superpartner
Particles pair with massive superpartners with spin 1/2 more or less than particle spin. Fermions have boson superpartners, such as squark, sneutrino, and selectron. Bosons have fermion superpartners, such as gravitino, higgsino, photino, gluino, wino, and zino.
spin: change and symmetry
Perhaps, besides space, time, and orientation symmetries, angular-momentum components {spin symmetry} can unite all forces and particles.
spin: space dimensions
Supersymmetry spin change requires extra spatial dimensions {Grassmann dimension, spin}.
spin: symmetry
Supersymmetry uses graded Lie algebra {superalgebra}.
detection
Instruments have not yet detected superpartners or fermion decay to bosons. Perhaps, universe origin had supersymmetry but universe now has broken symmetry.
hierarchy problem
At 10^16 GeV, all forces except gravitation are equal in strength. At 10^18 GeV, all forces are equal in strength. Why is this unifying energy so high (hierarchy problem)? Supersymmetry uses high energies and can resolve this problem.
supergravity
Supersymmetry applies to flat space-time Yang-Mills-field strong and weak nuclear forces and to electromagnetic fields, but can extend to gravity.
Standard Model
Supersymmetry can add to Standard Model. Standard-Model particles have superpartners {Minimal Supersymmetric Standard Model}.
In a supersymmetry model {interacting boson model}| [Arima and Iachello, 1975], atomic nuclei can have nucleon pairs. Even numbers of protons and neutrons, as in platinum, can have three dynamical-symmetry classes. Even numbers of protons and odd numbers of neutrons, and vice versa, and odd numbers of protons and numbers, relate to even-even case. Interacting bosons make nuclei behavior independent of particles and of special relativity, except for mass. If boson and fermion numbers are constant, supersymmetry can predict odd-odd case for heavy atoms, such as gold 196 with 79 p and 117 n, which has doublet ground state.
5-Physics-Quantum Mechanics-Theory-Quantum Relativity
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Date Modified: 2022.0225