The universe began 13.72 billion years ago. What existed before multiverse and physical things {What Existed Before Universe} {What Was Before Universe} {pre-universe}?
Multiverse
Outside of universe {non-universe} is multiverse. Multiverse space-time contains all universes that were, are, or will be, over all time. Multiverse space is infinite. Multiverse-space local regions have all possible dimensions. Multiverse space-time local regions have all possible physical laws and constants.
There is only one multiverse, because multiverse includes all physical things. Outside of multiverse is nothingness and void.
Universe Beginning
Universe began at a point in multiverse space-time, as the "Big Bang".
The Non-Physical
Before physical things, only the non-physical (non-spatial, non-temporal, and non-energetic) can exist. The non-physical has no beginning or end because it exists outside of time. Because it is not temporal, the non-physical cannot be before or after multiverse. The non-physical has no location or extension because it exists outside of space. Because it is not spatial, the non-physical cannot be outside or inside multiverse.
The non-physical has no substances, structures, properties, states, or processes. The non-physical has no space, time, mass, force, field, energy, or quanta. The non-physical has no boundaries, phases, or gradients. The non-physical has no changes, movements, translations, vibrations, rotations, flows, or waves. The non-physical has no entropy, because it has no parts, forces, or spatial volume. The non-physical has no information, because it has no code and no channels. The non-physical has no causes, effects, or physical laws.
The non-physical has nothing physical and so has only one type and is homogeneous. The non-physical has no time and so has only one unchanging state. The non-physical has neither parts nor relations and so has unity.
Possible Non-Physical Things
Universe empty space has virtual particles. Perhaps, non-physical things are abstract particles or quanta.
Universe empty space has weak-force Higgs field. Perhaps, non-physical things are abstract fields or forces.
Universe empty space has quantum-mechanical waves. Perhaps, non-physical things are abstract waves or perturbations.
Universe empty space has space-time. Perhaps, non-physical things are abstract space and time.
Universe empty space has entropy, negentropy, information, order, and pattern. Perhaps, non-physical things are abstract patterns.
Non-physical things can be non-spatial, non-temporal, and non-energetic substances, structures, properties, states, or processes.
Ideas
Plato's Parmenides [Plato, -370] describes non-physical things: the Ideas or Forms. The Ideas are unified wholes that do not move, do not change, have no cause, have no possibilities, and have no purposes. The Ideas are immaterial, indivisible, a priori, perfect, absolute, unqualified, independent, eternal, necessary, and sufficient. The Ideas are abstract and never have concrete symbols or representations.
Before multiverse, there is nothing physical, so Ideas like Chair-ness or Tree-ness cannot exist. Before multiverse, there is nothing mental, so Ideas like Goodness, Beauty, or Truth cannot exist.
Mathematical Ideas
Mathematical things are not physical, because they have no location, exist before time, never end, and have non-contingent truth. Mathematical things are abstract, non-physical, non-spatial, non-temporal, and non-energetic. Mathematical things are not mental, because they exist before brain or thought (and thoughts, language, and pictorial images require space and time).
Mathematical Ideas have reality [Penrose, 2004]. They are not abstractions or concepts that people derive from perception, language, logic, or thought. However, because Ideas can be both mental categories and object essences, people can discover or intuit mathematical Ideas [Brouwer, 1927].
Before multiverse and physical things, only mathematical Ideas can exist, so non-physical things can only be mathematical things. Mathematical things can be substances, structures, properties, states, or processes.
Number Ideas
Number Ideas are about quantities and their relations. The number Idea "zero" is like nothingness and the empty set. The number Idea "one" is like one information bit, one empty set, or one number Idea zero. Number Ideas include integers, real numbers, imaginary numbers, and complex numbers. (Using only the number Ideas "zero" and "one", abstract Gödel numbering can represent any abstract number.)
Set Ideas
Set Ideas are about non-dimensional grouping relations of abstract elements. The set Idea "empty set" has no elements with no groupings. The set Idea "universal set" has all elements with all groupings. Set Ideas include set groupings (sets of sets).
Set Ideas relate to number Ideas, because numbers can represent any element, grouping, and number of set elements.
Geometric-Figure Ideas
Geometric-figure Ideas are about dimensional grouping relations of abstract elements. The geometric-figure Idea "point" is a zero-dimensional unit element, with no relations. The geometric-figure Idea "line" is a one-dimensional connected-point grouping. The geometric-figure Idea "space" is a multi-dimensional many-point grouping. Geometric-figure Ideas include all geometric-figure-combination Ideas and topological Ideas. Because both are about groupings, geometric-figure Ideas relate to set Ideas. Geometric-figure Ideas relate to number Ideas, because numbers can describe points, groupings, and number of points.
Mathematical-Operation Ideas
Mathematical-operation Ideas are about relations of abstract mathematical objects. Mathematical-operation Ideas can be unary, binary, ternary, and so on. The mathematical-operation Idea "addition" groups two number Ideas into one number Idea. The mathematical-operation Idea "union" groups two set Ideas into one set Idea. The mathematical-operation Idea "translation" relates a geometric-figure Idea to the geometric-figure Idea "space". The mathematical-operation logic Idea "and" relates two Ideas to one Idea. Mathematical-operation Ideas include mathematical-group Ideas.
Number-Array Ideas
Number-array Ideas combine number, set, geometric-figure, and mathematical-operation Ideas. Number arrays are about element relations along (non-spatial) orthogonal or dependent dimensions. Numbers represent array elements. Sets group rows and columns. Geometric figures describe square and other-shape arrays. Mathematical operations make ordered rows, columns, depths, and so on. Number-array Ideas include hypercomplex-number-array Ideas.
Abstract-Space Ideas
Abstract-space Ideas combine number, set, geometric-figure, and mathematical-operation Ideas. Abstract spaces are about elements and their relations along dimensions. Dimensions are non-spatial, continuous or discrete, orthogonal or non-orthogonal, independent or dependent, and finite or infinite. Numbers represent space points. Sets group points into lines, areas, and other geometric figures. Mathematical operations translate, rotate, vibrate, and transition points and geometric figures.
Number-Array Ideas and Abstract-Space Ideas
Both abstract spaces and number arrays combine numbers, sets, geometric figures, and mathematical operations. Abstract spaces and number arrays have elements and element relations. Abstract spaces and number arrays have dimensions. Abstract spaces and number arrays have topological features, such as warps, holes, or tears, or crystal-like flaws, insertions, omissions, translations, and rotations. Abstract spaces and number arrays have element, set, geometric-figure, topological, and operational changes. Specific number arrays correspond exactly with specific abstract spaces.
What Was before Multiverse and Physical Things
Before multiverse and physical things, only mathematical Ideas can exist. Mathematical Ideas include all mathematical objects and operations.
Specific abstract space Ideas, corresponding exactly with specific hypercomplex-number-array Ideas, have physical-thing characteristics and so began physical things and multiverse.
Before multiverse and physical things, only mathematical Ideas (Forms) can exist. Mathematical Ideas include abstract spaces and hypercomplex-number arrays. Abstract spaces and hypercomplex-number arrays can represent mathematical groups and sets of related points. Points have no dimensions and no asymmetries. Relating points can define "point sets", which have dimensions, anti-commutative relations, and anti-symmetries, and quantum-mechanically define particles, fields, space, time, and energy, making all physical things and the multiverse. Universe began from a multiverse point singularity {How Universe Began}.
Universe Beginning
The universe began 13.72 billion years ago, with highest space-expansion rate (Big Bang), at a point in multiverse space-time.
Multiverse
Multiverse space-time contains all universes that were, are, or will be, over all time. Multiverse space is infinite. Multiverse-space local regions have all possible dimensions. Multiverse space-time local regions have all possible physical laws and constants.
There is only one multiverse, because multiverse includes all physical things. Outside of multiverse is nothingness and void.
Physical Things
Physical things are subatomic and atomic particles, with associated force fields, in space-time. Particles are substances with structures and have states, properties, functions, and processes. Particles have spatial extension, size, and location. Particles are discrete (not continuous). Particles have duration, and particle events have time and order. Particles can move, translate, rotate, and invert. Particles have energy, momentum, intensity, and physical action. Particle aggregates can compress, stretch, and twist.
The Non-Physical
Before multiverse and physical things, only the non-physical (non-spatial, non-temporal, and non-energetic) can exist. The non-physical has no beginning or end because it exists outside of time. Because it is not temporal, the non-physical cannot be before or after multiverse. The non-physical has no location or extension because it exists outside of space. Because it is not spatial, the non-physical cannot be outside or inside multiverse.
The non-physical has no energy because the non-physical has no substances, structures, properties, states, functions, or processes. The non-physical has no space, time, mass, force, field, energy, or quanta. The non-physical has no boundaries, phases, or gradients. The non-physical has no changes, movements, translations, vibrations, rotations, flows, or waves. The non-physical has no entropy, because it has no parts, forces, or spatial volume. The non-physical has no information, because it has no code and no channels. The non-physical has no causes, effects, or physical laws.
The non-physical has nothing physical and so has only one type and is homogeneous. The non-physical has no time and so has only one unchanging state. The non-physical has neither parts nor relations and so has unity.
Ideas
Plato's Parmenides [Plato, -370] describes non-physical things: the Ideas or Forms. The Ideas are unified wholes that do not move, do not change, have no cause, have no possibilities, and have no purposes. The Ideas are immaterial, indivisible, a priori, perfect, absolute, unqualified, independent, eternal, necessary, and sufficient. The Ideas are abstract and never have concrete symbols or representations.
Mathematical Ideas
Before multiverse, there is nothing physical, so Ideas like Chair-ness or Tree-ness cannot exist. Before multiverse, there is nothing mental, so Ideas like Goodness, Beauty, or Truth cannot exist.
Before multiverse and physical things, only mathematical Ideas can exist, so non-physical things can only be mathematical things. Mathematical things are not physical, because they have no location, exist before time, never end, and have non-contingent truth. Mathematical things are abstract, non-physical, non-spatial, non-temporal, and non-energetic.
Mathematical things are not mental, because they exist before brain or thought (and thoughts, language, and pictorial images require space and time).
Mathematical Ideas have reality [Penrose, 2004]. They are not abstractions or concepts that people derive from perception, language, logic, or thought. (However, because Ideas can be both mental categories and object essences, people can discover or intuit mathematical Ideas [Brouwer, 1927].)
Number-Array Ideas
Number arrays combine numbers, sets, geometric figures, and mathematical operations. Number arrays are about element relations along (non-spatial) orthogonal or dependent dimensions. Numbers represent array elements. Sets group rows and columns. Geometric figures describe square and other-shape arrays. Mathematical operations make ordered rows, columns, depths, and so on. Number arrays include hypercomplex-number arrays.
Properties
Hypercomplex-number arrays can represent scalars, vectors, spinors, tensors, and matrices. They can represent relations and relation uncertainties. They can have parts, structures, shapes, and patterns, with symmetries. They can have curvatures, densities, viscosities, and fields. They can be homogeneous or have phases. They have order and entropy.
Changes
Hypercomplex-number arrays can change numbers, dimensions, orientations, and patterns to represent commutative and non-commutative mathematical linear and non-linear operations, transformations, translations, rotations, spins, inversions, vibrations, and transverse and longitudinal waves. Vibration components have hypercomplex-number abstract frequencies, resonances, and harmonics.
Dimensions
Hypercomplex-number arrays can have any number and all types of dimensions. Dimensions can be orthogonal or dependent, continuous or discrete, abstract or spatial, finite or infinite, straight or curled up, isotropic or non-isotropic, fractional or whole-number, and static or dynamic. Dimensions can have relative magnitudes, orientations, and direction senses.
Combinations
Hypercomplex-number arrays can combine, overlap, and interact.
Abstract-Space Ideas
Abstract spaces combine numbers, sets, geometric figures, and mathematical operations. Abstract spaces are about elements and their relations along (non-spatial) dimensions. Numbers represent space points. Sets group points into lines, areas, and other geometric figures. Mathematical operations translate, rotate, vibrate, and transform points and geometric figures.
Properties
Abstract spaces have scalars, vectors, spinors, and tensors. They can represent relations and relation uncertainties. They have parts, structures, shapes, and patterns, with symmetries. They have curvatures, densities, viscosities, and fields. They can be homogeneous or have phases. They have order and entropy. They have boundaries, where interactions can occur.
Changes
Abstract spaces can change points, dimensions, orientations, and patterns to represent commutative and non-commutative mathematical linear and non-linear operations, transformations, translations, rotations, spins, inversions, vibrations, and transverse and longitudinal waves. Vibration components have frequencies, resonances, and harmonics.
Dimensions
Abstract spaces can have any number and all types of dimensions. Dimensions can be orthogonal or dependent, continuous or discrete, abstract or spatial, finite or infinite, straight or curled up, isotropic or non-isotropic, fractional or whole-number, and static or dynamic. Dimensions can have relative magnitudes, orientations, and direction senses.
Combinations
Abstract spaces can combine, overlap, and interact.
Hypercomplex-Number Arrays and Abstract Spaces
Abstract spaces and hypercomplex-number arrays both combine numbers, sets, geometric figures, and mathematical operations. They both have elements and element relations, with dimensions. They both have topological features, such as warps, holes, or tears, or crystal-like flaws, insertions, omissions, translations, and rotations. They both have element, set, geometric-figure, topological, and operational changes.
Abstract spaces can have same-dimension point arrays with relative hypercomplex-number coordinates. Abstract spaces and their same-dimension hypercomplex-number arrays represent points, positions, position relations, and position uncertainties. Hypercomplex-number arrays list abstract-space point coordinates. Abstract spaces are geometric representations of hypercomplex-number arrays.
Symmetry
Points have no relations, no dimensions, no substances, no structures, no properties, no processes, no states, and no functions. Points have no asymmetries.
Sets of unrelated points have no dimensions, no substances, no structures, no properties, no processes, no states, and no functions.
Sets of points can have relative point motions, translations, vibrations, rotations, periodic chaotic orbits, and harmonic longitudinal and transverse vibrations/rotations, with topological constraints. Mathematical groups can represent sets of points whose relations have symmetries. Hypercomplex-number arrays (and their abstract spaces) can represent mathematical groups.
Point Sets and Anti-symmetry
Quantum mechanics has anti-commutative relations. Sets of related points can have anti-commutative relations and so anti-symmetries. These "point sets" follow quantum-mechanical laws and so are substances and structures and have properties, processes, states, and functions.
Point sets have the first spontaneous symmetry breaking.
Point sets have a 3-sphere boundary, with Planck-length-multiple diameter. Point-set points are somewhat like M-theory string endpoints confined to branes.
Point sets, unlike string-theory strings, have no string, no string tension, and no string-vibration modes. Point-set points do not form a compact group.
Hypercomplex-number arrays (and their abstract spaces) can represent mathematical groups with anti-commutative and anti-symmetric relations and so can represent point sets.
Space-Time Dimensions
Point-set point configurations and motions make extension, direction, and orientation, as well as density, viscosity, and phase, and so define dimensions. Starting from zero dimensions, point sets combine and overlap dynamically to make fractional dimensions and "quantum foam", and later build three independent spatial dimensions and one time dimension, united in space-time. (Because they do not have strings, and so do not have tensions or too many points, point sets can have no net vibration and so can have zero rest mass without using compactified dimensions, with no need for more than three spatial dimensions.)
Particles and Particle Properties
Hypercomplex-number arrays can be matrices that represent tensors that account for general-relativity mass-energy densities and space curvatures. Abstract spaces have densities and curvatures that account for general-relativity mass-energy densities and space curvatures.
Hypercomplex-number arrays and their abstract spaces can have (quantum-mechanical) waves that account for particle energies and motions and for uncertainty principle. Hypercomplex-number arrays can be quantum-mechanical transition matrices (with matrix mechanics) that account for particle states and physical processes. Abstract spaces have states and trajectories that account for particle states and physical processes.
Point-set points share a wavefunction and so entangle. Point-set relative internal motions have longitudinal and transverse complex-number-frequency vibrations along and across all space dimensions. Discrete wave frequencies represent energy quanta, which account for particle masses, energies, spins, and orientations. Point sets can combine, overlap, and interact (like superposed wavefunctions) to make continuous fields.
Point-set point configurations and motions have symmetries that account for all particles, exchange particles, force fields, and conservation laws. Point sets make particles, space, time, and energy. Point sets combine and overlap to make all physical things. Point-set interactions define physical objects, physical fields, and space-time dimensions.
How Universe Began
After physical things and multiverse began, multiverse had new space-time points as space-time singularities. Universe began as a multiverse white-hole space-time singularity, with very high positive radiation (kinetic) energy. (Because total energy there was zero, a paired space-time singularity had negative energy, and a negative-energy universe began.)
According to general relativity and quantum mechanics, smaller spaces have larger energy fluctuations, so the smallest spaces can reach energy levels of any amount. By starting as a space-time singularity, universe began with highest energy level and so highest temperature.
According to thermodynamics and statistical mechanics, the smallest spaces have lowest entropy. By starting as a space-time singularity, universe began with lowest entropy.
Therefore, universe began with smallest volume, highest energy, highest energy density, highest temperature, and lowest entropy.
In those conditions, particles repulse. Because particles have space between them, universe space expanded. Because repulsion was the highest possible, space expanded most rapidly at universe beginning.
Particle theories must be consistent with the particle Standard Model and its Yang-Mills gauge group, as well as account for space-time and general relativity, energy quanta and quantum mechanics, and conservation laws.
Quantum Field Theories
General relativity has continuous fields with electromagnetic and gravitational waves. Quantum mechanics has discrete particles with energy quanta, quantum-mechanical waves, and transition matrices. Quantum field theories try to unify general-relativity fields and quantum-mechanics particles. For example, virtual-particle streams make continuous field lines.
In string theories and M-theory, particles are Planck-length one-dimensional strings or p-dimensional p-branes. In quantum-loop theories, particles are Planck-length two-dimensional quantum loops that make spin networks. In point-particle theories, particles are zero-length zero-dimensional points.
Strings
Strings have length or diameter and can have different lengths or diameters. Strings have internal rotations and vibrations.
Strings: Particle Properties
String rotations account for particle spins and orientations. Closed strings have two rotation modes and so can make spin-2 bosons (gravitons).
Strings: Space Dimensions
Special relativity and space conformal symmetry require that some particles have zero rest mass, so that they travel at light speed. Strings must have non-zero lengths and fundamental-frequency vibrations, so they cannot have zero rest mass by being only points or by having no motions. Zero-rest-mass-particle strings have string-vibration superpositions that cancel positive and negative components to make net vibration energy zero.
Because strings have many points and vibration modes, string-vibration superpositions can cancel only when space has a specific number of compactified dimensions, allowing special compactified-dimension configurations. Compactified dimensions have transverse vibrations both along axis and around axis, and these dual vibrations can cancel. More compactified dimensions increase positive energy. Fewer compactified dimensions increase negative energy. Four-dimensional space-time has no compactified dimensions, so in string theory it cannot have conformal symmetry {conformal anomaly}.
For bosonic string theory, conformal symmetry requires 26 space-time dimensions (22 compact space dimensions). For supersymmetric string theory, conformal symmetry requires 10 dimensions (6 compact space dimensions), because superstring theory has fermion-boson symmetries that cancel 16 dimensions. M-theory has supersymmetric string theories as subspaces, so conformal symmetry requires 11 dimensions (7 compact space dimensions).
Therefore, string theories require too many (and perhaps unobservable) dimensions.
Strings: Singularities
If particles are strings, particles have at least Planck length, so space cannot have point singularities.
Strings: Gauge Group
Strings have infinitely many points and many vibration modes. Therefore, strings allow many possible gauge groups, not just the Yang-Mills gauge group.
Strings: Fermion-Boson Unity
Bosonic string theory is a vector gauge theory that accounts for only open strings and spin-1 bosons. Supersymmetric string theory is a tensor gauge theory that accounts for open and closed strings and spin-1 and spin-2 bosons and has supersymmetry to unify fermions and bosons.
Strings: No Tachyons
Because strings have many points, and string-theories require compactified space dimensions, strings have complex-number vibration components, so particles can have negative (and positive) energies and masses. In special relativity, negative-mass particles travel faster than light speed. Bosonic string theory has negative mass particles. Superstring theory accounts for both fermions and bosons, and their interactions cancel any negative masses, so superstring theory has only positive-mass particles.
Quantum Loops
Quantum loops have diameter and can have different diameters. Quantum loops have internal rotations and vibrations.
Quantum Loops: Particle Properties
Quantum-loop rotations account for particle spins and orientations. Quantum loops can have two rotation modes and so can make spin-1 and spin-2 bosons.
Quantum Loops: Space Dimensions
Spin-network spins define three space directions and so define four-dimensional space-time. Therefore, quantum-loop theories do not require compactified dimensions.
Quantum Loops: Singularities
If particles are quantum loops, particles have at least Planck-length diameter, so space cannot have point singularities.
Quantum Loops: Gauge Group
Quantum loops have infinitely many points and many vibration modes. Therefore, quantum loops allow many possible gauge groups, not just the Yang-Mills gauge group.
Quantum Loops: Fermion-Boson Unity
Quantum loops and spin networks can have supersymmetry and so unify fermions and bosons.
Quantum Loops: No Tachyons
Quantum-loop theory accounts for both fermions and bosons, and their interactions cancel any negative masses, so superstring theory has only positive-mass particles.
Point Particles
Point particles have zero diameter and do not change diameter. Points have no rotations or vibrations.
Point Particles: Space Dimensions
Point particles have only real-number properties, so point-particle theories do not require compactified dimensions to make zero-rest-mass particles.
Point Particles: Singularities
If particles are points, space can have point singularities, violating space-time field continuity.
Point Particles: Particle Properties
Point particles have no mechanism for particle spin or orientation, and so no mechanism to make spin-2 bosons (gravitons).
Point Particles: Gauge Group
Point particles can have zero rest mass and account for all Standard-Model particles. However, point-particle theory has no mechanism to account for the Standard-Model Yang-Mills gauge group.
Point Particles: Fermion-Boson Unity
Point particles have no mechanism for unifying bosons and fermions.
Point Particles: No Tachyons
Points have no rotations or vibrations, and so no complex-number vibration modes, so point particles have only positive energies and masses.
Enlarged Points
Enlarging points makes three dimensions and Planck-length-multiple diameters. However, enlarged points have no parts or structure inside, so they are essentially the same as point particles.
Point Groups
Putting points together in compact groups makes three dimensions and Planck-length-multiple diameters. Point groups have more than one point and so parts and structures. If points have no forces or tension among them, point groups are essentially the same as point particles. If points have forces or tension among them, point groups are essentially the same as strings or p-branes.
Toruses
Tori have inside radius, outside radius, and cross-section, making three dimensions.
Reducing torus radius to zero makes a two-dimensional cross-section. If cross-section has Planck-length-multiple diameter and internal tension, zero-radius-torus particles are essentially the same as 2-branes. With no internal tension, zero-radius-torus particles are essentially the same as point particles.
Reducing torus cross-section to zero makes a one-dimensional radius. If radius has Planck-length and internal tension, zero-cross-section-torus particles are essentially the same as closed strings. With no internal tension, zero-cross-section-torus particles are essentially the same as point particles.
Geometric Fractals
Fragmenting straight or curved line segments into a series of separated shorter line segments makes dimension greater-than-zero and less-than-one. If line-segment lengths are Planck-length multiples and line segments have internal tension, fractal segments are essentially the same as open strings. With no internal tension, fractal segments are essentially the same as point particles.
Perhaps, fractals can overlap and interact to fill in missing points and make continuous whole-number space dimensions.
Vectors
Giving line segments direction and orientation makes one-dimensional directed line segments in three-dimensional space. Vectors involve only real-number energies and spins. Bivectors, trivectors, and so on, combine vectors. If they have no tension (and no vibration components), vector particles are essentially the same as point particles. If they have tension (and vibration components), vector particles are essentially the same as directed open strings.
Quaternions and Octonions
Giving line segments direction and orientation and adding a scalar makes one-dimensional directed line segments in multi-dimensional abstract space. Quaternions and octonions involve complex-number energies and spins. If they have no tension (and no vibration components), quaternion and octonion particles are essentially the same as point particles. If they have tension (and vibration components), quaternion and octonion particles are essentially the same as directed open strings.
Spinors
Giving line segments direction, orientation, and rotation makes one-dimensional rotating directed line segments in three-dimensional space. Spinors involve complex-number energies, spins, and orientations. Non-commutative spinors have non-symmetric opposite orientations.
Relativistic electron-spin theory (Dirac) and supersymmetric-string theory use spinors. Relativistic quantum-mechanics wavefunctions use spinor waves.
Bispinors are bivectors involving hypercomplex numbers. Bispinors (and antisymmetric tensors) can represent quark-antiquark pairs, such as pions and other bosons, because their four components have parity-violating gauge group SO(1,3) for relativistic half-integer-spin quantum fields.
Trispinors can represent three-quark particles, such as protons and other fermions, because their eight components have gauge group SO(3) for electroweak interactions and strong-nuclear-force interactions (Weinberg) (Salam).
However, spinor and twistor theories have inconsistencies with general relativity [Penrose, 2004].
Point Sets
Point sets {Point-Set Theory of Particles} are one or more separated points inside a Planck-length-diameter 3-sphere boundary. Rather than one point, point sets have any number of separate points (points are not a compact group). Rather than two endpoints connected by a string, point sets have points but no string, no string tension, and no string-vibration modes. Point sets can have different Planck-length-multiple diameters. Point sets have internal translations, vibrations, and rotations. Point-set points are somewhat like M-theory string endpoints confined to branes.
Point sets are intermediate among points, strings, and quantum loops, so they have the good results of point-particle, string, and quantum-loop theories and do not have the bad results. Like point-particle, string, and quantum-loop theories, point sets account for particles, particle properties, particle motions, quanta, fields, space-time, quantum-mechanical waves and transition matrices, and general-relativity energy-density and curvature tensors. Point sets account for initial-universe "quantum foam" and later universe properties.
Point Sets: Constraints
Point-set point motion constraints are like strong nuclear force, which increases strength with distance, keeping quarks in a "bag".
Point Sets: Mini-Atoms
Point sets are not mini-atoms, with central point and orbiting points, because they do not have central forces.
Point Sets: Mini-Molecules
Point sets are not mini-molecules, with bonds between points, because they do not have radial forces.
Point Sets: Dimensions
Because points have zero dimensions, point sets have zero dimensions. However, point-set point configurations (and motions) make extension, direction, and orientation, as well as density, viscosity, and phase, and so define dimensions. Point-set structures and motions first define fractional dimensions from zero up to one dimension. Point-set dynamic dimensions account for "quantum foam".
Point sets combine and overlap to build up to three independent spatial dimensions and one time dimension, united in space-time. Perhaps, dynamic dimensions hybridize three space dimensions and one time dimension to make space-time. Perhaps, dynamic dimensions resonate three space dimensions and one time dimension to make quantum-mechanical waves in space-time.
Because they do not have strings, and so do not have tensions or too many points, point sets do not require compactified dimensions.
Perhaps, point-set interiors have no space-time and no metric.
Point Sets: Motions
Point-set points can have random motions, periodic chaotic orbits, and harmonic longitudinal and transverse vibrations/rotations. Internal motions have topological constraints. Point-set relative internal motions account for particle spins and orientations.
Point Sets: Vibration Components
Point sets have internal parts and structures and so have longitudinal and transverse complex-number-frequency vibrations along and across all space dimensions. Point configurations determine resonance frequencies and make point-set particles have only positive energies and masses.
Point sets must have more than one point and so cannot have zero diameter. However, because they do not have tension, point-set points can have no net vibration, so point-set particles can have zero rest mass without using compactified dimensions.
Point Sets: Quanta and Quantum Mechanics
Point-set vibration-wave equations have harmonic-frequency wavefunction solutions. Discrete wave frequencies represent energy quanta, which account for particle masses. Point-set wavefunctions are essentially the same as particle quantum-mechanical wavefunctions.
Point-set particle distributions determine total system energy.
Point Sets: Quantum Mechanics and General Relativity
Point sets can combine, overlap, and interact (like superposed wavefunctions) to make continuous fields and other structures. Point-set virtual-particle streams make continuous field lines. Point-set combinations can be both quantized and continuous and so unite quantum mechanics and general relativity.
Point Sets: Gauge Group
Similar to string theories, point-set theory accounts for all Standard-Model particles. Unlike strings with too many points, and single points with too few points, point sets can have just the right number of points, point structures, and motions to allow only one gauge group, the SU(3) x SU(2) x U(1) Yang-Mills gauge group. Like strings, point sets allow zero-rest-mass spin-2 bosons (gravitons).
Point Sets: Particle Masses
Like strings and quantum loops, point-set Planck-multiple-length diameters and constraining forces, which depend on electric charge and on point configurations and motions, determine vibration modes that account for particle energies and masses. Shorter diameters correspond to higher frequencies and energies. Point sets can have no net vibration energy, so particles can have zero-point lowest-energy state and zero rest mass.
Mass and energy are scalars and are always positive. Anti-mass and anti-energy are scalars and are always positive, but have opposite electric charge.
Point Sets: Particle Electric Charges
Positive charge comes from directed-point-set orientation. Negative charge comes from opposite directed-point-set orientation. Electric anti-charge is exactly opposite charge.
Point Sets: Particle Spins
Point-set points rotate around center or two-point axes. Point-set axes have two opposite orientations that represent clockwise and counterclockwise spins. Point sets can have more than one rotation mode.
Spin comes from clockwise or counterclockwise transverse-wave amplitude-vector rotation around oriented-point-set long axis. Boson spin 0 comes from two opposite-orientation spins. Boson spin 1 comes from two same-orientation spins. Graviton spin 2 comes from two perpendicular-orientation spins, one around each tensor axis. Fermion half-integer spins come from three clockwise or counterclockwise spins.
Point Sets: Particle Color Charges
Point-set complex-number oriented-point axes can be three vectors that add to zero, corresponding to an equiangular triangle. Anti-colors have opposite electric charge and opposite color charge.
Point Sets: Particle Strangeness
Point-set points can have configurations that represent non-opposite directions and orientations, so a pattern (strangeness) is present or absent, allowing parity or no parity. Anti-strangeness is pattern absence.
Point Sets: Structures
Point sets can have two points separated by Planck-length multiples. Two points with unsynchronized motions are like open strings. Two points with synchronized motions are like closed strings. Two-point point sets have shape and symmetry.
Point sets can have three points separated by Planck-length multiples. Points can be at three of seven possible positions and can have synchronized or unsynchronized motions. Three-point point sets have shape and symmetries. See Figure 1.
For point sets with more than two points, distances have ratios. For point sets with three points, square-line to vector-line ratio is 2:1, and triangle-line to square-line ratio is 3:2 (same as 4:3), so three-point point sets have harmonic lengths (and vibration frequencies).
Point sets do not have four points, because points have too many motion modes and too many gauge-group possibilities.
Point Sets: Particles
Point-set point configurations have symmetries that account for particles, exchange particles, forces, and conservation laws. Like strings and points, point sets can exist for real-particle lifetimes. Real-particle point sets have longer diameters, lower energies, and longer lifetimes.
Point Sets: Photons and Electrons
For U(1) photons, one point is at center point, second point has orientation away from center point, and third point is along same line in opposite direction, plus the points have unsynchronized motions. Photon three-point point sets make vectors with spin 1, no charge, and zero rest mass. Photons have photons as antiparticles, so both have the same three-point point sets.
Electron three-point point sets have spin 1/2, one negative electric charge, and non-zero rest mass. Electrons have positrons as antiparticles, so positron three-point point sets have spin 1/2, exactly opposite positive electric charge, and non-zero rest mass.
Point Sets: Intermediate Vector Bosons and Pions
For SU(2) intermediate vector bosons, one point is at center point, second point has orientation away from center point, and third point has perpendicular orientation to center-point and second-point line, plus the points have unsynchronized motions. Intermediate-vector-boson three-point point sets are vectors with spin 1, charge or no charge, strangeness, and rest mass. Intermediate-vector-boson antiparticles have spin 1, opposite charge, strangeness, and same rest mass.
Pion three-point point sets are vectors with half-integer spins, charge, strangeness, and rest mass. Pion antiparticles have half-integer spins, opposite charge, strangeness, and same rest mass.
Point Sets: Gluons and Quarks
For SU(3) gluons, three points are not at center and have orientations to center point that differ by 120 degrees, so the three points form an equilateral triangle around center point, plus the points have unsynchronized motions. Gluon three-point point sets are vectors with spin 1, no electric charge, color charge, and rest mass. Gluon antiparticles have spin 1, no electric charge, opposite color charge, and same rest mass.
Quark three-point point sets are vectors with half-integer spins, electric charge, color charge, and rest mass. Anti-quark three-point point sets are vectors with half-integer spins, opposite electric charge, opposite color charge, and rest mass.
Point Sets: Gravitons
For gravitons, three points are not at center and have orientations to center point that differ by 120 degrees, so the three points form an equilateral triangle around center point, plus the points have synchronized motions, making a circle. Flipping the circle makes the same figure, so figure has spin 2. See Figure 1. Graviton three-point point sets are single-symmetry tensors with spin 2, no electric charge, and zero rest mass. Gravitons have gravitons as antiparticles, so both have the same three-point point sets.
Point Sets: Other Bosons
Dilaton two-point point sets are scalars with spin 0. Axion three-point point sets are antisymmetric tensors with spin 0. Zero-rest-mass un-oriented point sets are SO(n) or Sp(n) bosons.
Point Sets: Uncertainty Principle
Point sets represent relations and can represent relation uncertainties. For spatial dimensions, point sets represent positions, position relations, and position uncertainties.
Point Sets: Virtual Particles
At small distances, the energy-time uncertainty principle allows virtual particles. Like strings and points, point-set pairs can arise spontaneously from space vacuum and exist for times inversely proportional to energy before virtual-particle annihilation. Virtual-particle point sets have short diameters, high energies, and short lifetimes.
Point sets always change to point sets, never to no point sets, because, by uncertainty principle, zero-length point sets have infinite energy. One zero-point-energy point set can become two virtual-particle point sets (particle creation). Two virtual-particle point sets can become one zero-point-energy point set (particle annihilation). The no-point-set (vacuum) state cannot exist. Point-set particle creations and annihilations preserve all symmetries and conservation laws.
Point Sets: Conformal Symmetry
Because point sets have no strings and so no tensions, point sets do not require compactified dimensions and can have conformal symmetry in four-dimensional space-time.
Point Sets: Density
Point sets can combine, overlap, and interact. Point-set combinations can make density, viscosity, and phase.
Point Sets: Fields
Point-set combinations can make scalar fields.
Point Sets: Boundary
Point-set point structures and motions define a boundary. At the boundary, point sets can combine, overlap, and interact to define new boundaries and change physical effects.
Point Sets: Space Curvature
Point-set combinations have boundary interactions that change point-set point structures and motions and make energy density and space curvature.
Point Sets: No Singularities
Point sets have at least Planck-length diameter, so space has no point singularities.
Point Sets: Dark Matter and Dark Energy
Perhaps, point-set points, point structures, and motions define dark matter and dark energy.
Point Sets: Microtextures
Point sets are nanoscopic three-dimensional structures. Point-set surface boundaries combine, overlap, and interact to make microscopic two-dimensional surface textures (microtextures).
Point Sets: Microtextures and Sensations
Perhaps, brain has pattern recognition of microtextures and interprets them as sensations.
Point Motions and Interactions
Particle points are Planck distance apart. Particle points move with Planck-time periods. Particle points have Planck energies. Particle points interact but do not have conventional forces.
Space at Planck distances is "quantum foam". Quantum-foam has Planck distances. Quantum-foam straight lines last less than Planck time. Quantum-foam has random kinetic energy.
Particle points move in "quantum foam". Point interactions always change distance and direction and so do not have separable transverse or longitudinal components. Point interactions oscillate but at random.
Point space-time positions and interactions define the point-set surface and its configuration. Points are always on the point-set surface. Point-set surfaces always change, and point interactions are along surfaces. Points can have different distances and interactions. For example, points can be equidistant or not. Points can have the same or different interactions. Point-set surfaces add structure to quantum foam.
Point interactions are attractive, neutral, or repulsive, depending on distance and point-set-surface configuration.
Points are discrete. Point interactions are continuous. Point sets are both discrete and continuous, so they can account for both quantum mechanics and general relativity.
Particles have three points, so they have unpredictable behavior, just like the gravitational three-body problem. Unpredictability accounts for quantum-mechanical uncertainties and probabilities.
In classical mechanics, momentum and position are independent, but in quantum mechanics, they are dependent. Particle points account for this.
Abstract Spaces
Abstract mathematical Ideas exist non-physically [Penrose, 2004] and include abstract-space Ideas.
Abstract spaces have states and trajectories that define point-set point numbers, configurations, and motions (which account for particle states and physical processes). Abstract spaces can change and have waves that define point-set quantum-mechanical waves that account for particle energies and motions and for uncertainty principle. Abstract spaces have densities and curvatures that define point-set densities and curvatures that account for general-relativity mass-energy densities and space curvatures. Abstract spaces are discrete but can overlap to make continuous structures, so point sets can unify quantum mechanics and general relativity.
Hypercomplex-Number Arrays
Abstract mathematical Ideas include hypercomplex-number-array Ideas.
Hypercomplex-number arrays represent abstract-space point numbers, configurations, and motions. Hypercomplex-number arrays can be quantum-mechanical transition matrices (with matrix mechanics) that account for abstract-space states and trajectories. Hypercomplex-number arrays can have waves that account for abstract-space quantum-mechanical waves. Hypercomplex-number arrays can be matrices that represent tensors that account for abstract-space densities and curvatures. Hypercomplex-number arrays are discrete but can overlap to make continuous structures, so abstract spaces can have discrete points and continuous fields.
Point Sets, Abstract Spaces, and Hypercomplex-Number Arrays
Specific abstract-space Ideas, corresponding exactly with specific hypercomplex-number-array Ideas, have physical-thing characteristics. Special hypercomplex-number-array Ideas define special abstract-space Ideas that define point sets and begin physical things. Point-set point numbers, configurations, and motions account for particle energy states and motions, quantum-mechanical waves, uncertainty principle, mass-energy densities, space curvatures, general relativity, and quantum mechanics.
Point sets are both non-physical and physical. Point sets have abstract properties that come from non-physical special mathematical Ideas. Point sets have physical points and constraining boundaries required mathematically by physical-thing characteristics of special abstract-space Ideas and their hypercomplex-number-array Ideas.
5-Astronomy-Universe-Cosmology
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Date Modified: 2022.0225