Universe history {cosmology}| cycles between endpoints (oscillating theory), is unchanging (steady-state theory), or began by space expansion {universe, history} {universe, origin} [Greene, 1999] [Mach, 1885] [Mach, 1906] [Rees, 1997] [Rees, 1999] [Rees, 2001] [Smolin, 2001] [Weinberg, 1972] [Weinberg, 1977 and 1993] [Weinberg, 1992] [Weyl, 1952].
before universe
Perhaps, before universe origin, there was only nothingness, there was already space and/or time, or there were also mathematical and/or physical laws.
Nothingness has properties. Nothingness has no time or space and so no dimensions. It has no ground-state, zero, or complex-number energy, because it has no dimensions and so no motions or fields. It has no matter, motions, forces, fields, radiation, energy, temperature, or pressure. It is homogeneous and has only one phase. It has no quanta. It has zero entropy. Perhaps, by uncertainty principle, nothingness can create relativistic quantum-mechanical virtual particles.
Perhaps, universes spontaneously arise from empty space, if space has negative energy, which causes space expansion.
Perhaps, mathematical/physical laws cause universes to arise, if they imply space and time.
dimensions
If universe has no time dimension and any number of space dimensions, or any number of time dimensions and no space dimension, motion, energy, momentum, and space-time do not exist.
If universe has one or more time dimensions and more than three spatial dimensions, gravity and electromagnetism strength decrease more quickly with distance, so star and planet orbits and electron orbits, respectively, are too lightly bound and are unstable. With one or more time dimensions and fewer than three spatial dimensions, gravity and electromagnetism decrease less quickly with distance, so stars and planets and electrons quickly move to center, and stars, planets, and electrons do not exist.
If universe has more than one time dimension and one space dimension, fields are unstable. If universe has more than one time dimensions and more than one space dimension, physical events are unpredictable.
Electron current, magnetic field, and atom radius define three space dimensions, so electromagnetism requires at least three infinite spatial dimensions. Space cannot have more than three infinite spatial dimensions, because then electron current, magnetic field, and atom radius have two or more independent relations for electric and magnetic fields.
String theory and brane theory require three infinite spatial dimensions and seven or eight curled-up spatial dimensions. Quantum-loop theory defines three infinite spatial dimensions.
Perhaps, dimension number, length, and geometry were or are in flux. Dimension number varies from zero to infinite. Dimension lengths vary from zero to infinite length. Dimension geometries vary from linear to curved to curled up. Perhaps, dimensions evolve by physical processes to stable numbers, lengths, and geometries. Perhaps, energy and matter distributions dynamically determine dimension number, length, and geometry. Perhaps, multiverses or different universe regions have different dimensions.
Perhaps, beginning universe had zero dimensions. Perhaps, because fewer dimensions make lower entropy, universe has four-dimensional space-time because it has lowest entropy consistent with maximum energy. Perhaps, universe has optimum number, length, and geometry of space-time dimensions to allow highest number of states, most stability, and most symmetries. Perhaps, universe is like one fiber bundle, with one n-sphere as base space.
space expansion
Universe expands at same rate at all points and in all directions equally.
At its origin, universe had maximum space expansion rate. Gravity is attractive and slows expansion rate. If universe average mass-energy density is high enough, gravity eventually stops expansion, and then universe contracts back to singularity. If expansion rate had always been smaller by 10^-10 than it was, universe collapses back to singularity in one million years.
If universe average mass-energy density is low enough, gravity never stops space expansion, and universe expands at ever slower rate. If universe average mass-energy density is even lower, gases cannot condense, and galaxies and stars do not form. If expansion rate had always been greater by 10^-10 than it was, universe is like empty space in one million years. Therefore, space expansion rate has been and will be such that universe will expand to infinity, at which expansion rate will finally be zero.
entropy
At universe origin, entropy was minimum. If early-universe entropy per baryon was more, no protogalaxies form. Universe entropy is always increasing. Perhaps, universe expansion contributes to increasing universe entropy.
density variations
At neutral-charge atom formation, with matter-radiation decoupling, 300,000 years after universe origin, if universe had too-slight mass-energy density irregularities, gravity does not form galactic clusters, no protogalaxies form, and no galaxies form. If universe had slighter mass-energy density irregularities than it does, galaxies are farther apart and have fewer and smaller stars. If universe had too-great mass-energy density irregularities, galaxies are smaller and have bigger stars, so stars become dark and cool more quickly.
Cosmic microwave background radiation has variations over space. Cosmic microwave background radiation polarization has fundamental frequency and wavelength, as well as C1-dipole, C2-quadrapole, and C3-octopole multipoles. Dark energy makes ecliptic C2 and C3 multipoles align with equinoxes and solar-system-motion direction, not be random as required by inflation theory. Dark energy makes some C2 and C3 multipoles align with Milky-Way-and neighboring-galaxy supergalactic plane, not be random. Dark energy makes some C2 and C3 multipoles lower intensity than higher-C multipoles, though inflation theory requires that all multipoles have same intensity. Dark energy makes cosmic-microwave-background-radiation intensity variation over space separations greater than 60 degrees not correlate with that at smaller separations, though inflation theory requires that all separation distances have same intensity variation.
gravitation
Gravity binding-energy-to-rest-mass ratio is 10^-5, so gravity is weak. If ratio was higher, matter clustering is so great that gravity is stronger than dark energy, soon overcomes initial space expansion, and contracts matter into giant black holes. If ratio was lower, gravity is too weak to cluster matter, no galaxies or stars form, and space expands faster forever.
If dark energy was too little and gravity was too much, universe quickly re-collapses. To prevent quick contraction, matter and dark matter must be less than three times universe dark energy. If dark energy was too much and gravity was too little, universe expands before atoms can form or galaxies can form. To allow galaxy formation, dark energy must be less than 140% of universe mass.
Quantum gravity or other combination of gravitation and quantum mechanics determines universe origin. Perhaps, universe origin involved quantum-mechanical tunneling.
gravity: internal pressure
Mass m has energy E: E = m * c^2, where c is light speed. Mass can convert to kinetic energy, which causes external pressure. Increased kinetic energy increases temperature, and increased temperature pushes particles farther apart against gravity, increasing positive potential energy and making positive internal pressure. In general relativity, at space-time points, gravity G depends on mass-energy density M plus three times internal pressure P: G ~ M + 3*P. Solids do not change volume at constant temperature, so they have zero internal pressure. Hot gas has more positive potential energy than cold gas and so has more internal pressure and more gravity. Photons have zero rest mass but have radiation pressure that makes internal pressure P one-third mass-energy density M, so gravity doubles: M + 3 * (M/3) = 2*M.
electromagnetism
Electromagnetic radiation can transport energy over infinite distances. Electromagnetism determines inorganic-and-organic-chemical bonding and reactions. If electromagnetic force was stronger, electrons fall into protons, and atoms do not form. If electromagnetic force was weaker, electrons are too fast for capture in atom orbits, and atoms do not form. For example, if electromagnetism was only 4% weaker, hydrogen atoms cannot form.
If protons were 0.2 percent more massive, protons decay to neutrons. If electron and proton charge was slightly different, electrons cannot orbit protons, and atoms do not form.
strong force
Strong nuclear force holds atomic-nucleus protons together and determines fission and fusion reactions. Strong-nuclear-force strength determines star energy radiation and atomic-nuclei radioactivity levels. If strong force was stronger, only large atomic nuclei form, and no hydrogen persists. For example, if strong nuclear force was only several percent stronger, carbon cannot form from beryllium and helium. If strong nuclear force was 2% stronger, protons cannot form from quarks. If strong force was weaker, only small atomic nuclei form. For example, if strong nuclear force was 2% weaker, small nuclei are unstable.
strong nuclear and electromagnetic forces
Universe strong nuclear force and electromagnetic force have relative strengths that allow stable deuterium, stable carbon, few radioactive atoms, stable stars, and weak gravity. If strong nuclear force was stronger and electromagnetic force was same, stars explode. If strong nuclear force was weaker and electromagnetic force was same, deuterium is unstable. If strong nuclear force was same and electromagnetic force was stronger, carbon is unstable. If strong nuclear force was stronger and electromagnetic force was stronger, all atoms are radioactive.
weak force
Weak nuclear force determines fission and fusion reactions, radioactivity from nuclei, and planet melting. If weak force was stronger, nuclear fusion is faster, stars live shorter, and heavy elements cannot form. If weak force was stronger, universe has less dark matter, because, in first second of universe, dark matter stays in equilibrium with other matter longer. If weak force was weaker, nuclear fusion is slower, stars live longer, and hydrogen cannot form. If weak force was weaker weak, universe has more dark matter.
force unity
At 10^-43 seconds (Planck time) after universe origin, with universe at 10^32 K, all forces and interactions have Planck time, so all forces are the same {unity of forces}. Higher temperature makes gravitation increase greatly in strength (because internal pressure is more), weak force increase in strength (because average distance is smaller), electromagnetism change little (because radiation can have any frequency), and strong force decrease in strength (because average distance is smaller). Therefore, at universe origin, with highest temperature, all forces become equal in strength (and in other properties). Space expansion cooled universe and broke symmetry, so first strong force separated, and then electromagnetism and weak force separated.
General relativity, quantum mechanics, cosmology, and logic contribute to theories of how universe began {universe-origin theories}. The universe had no beginning or began as white-hole space-time singularity, as quantum foam, as quantum branes or loops, or from nothing [Adams, 2002] [Barrow and Tipler, 1986] [Greene, 1999] [Greene, 2003] [Kauffman, 1993] [Mach, 1896] [Mach, 1906] [Price, 1996] [Rees, 1997] [Rees, 1999] [Rees, 2001] [Sklar, 1977] [Smolin, 1997] [Weinberg, 1972] [Weinberg, 1992] [Weinberg, 1993] [Weyl, 1952].
energy
By observation and calculation, at universe origin, space had smallest volume, same total energy as now, and highest energy density. Highest energy density made greatest space curvature, which is consistent with smallest 3-sphere volume. Because beginning universe was smallest volume, distances were shortest, and potential energy was lowest, so kinetic energy and temperature were highest.
energy: conservation in closed universe
By observation, universe has no energy influx from outside universe or energy outflow to outside universe. Universe total energy is constant.
energy: positive
Universe attractive forces, mainly gravity, cause positive energy, so objects have positive potential and kinetic energy. Local positive energy density varies with both rest-mass and relativistic-mass distributions.
energy: dark energy
By observation (Brian Schmidt) [1998], universe has repulsion that is expanding space, so space has negative intrinsic energy. Negative-energy causes uniform space expansion and so does work to add intrinsic negative energy to added space. Because space-expansion volume varies directly with intrinsic-energy work, space has constant negative intrinsic-energy density. Therefore, space has had constant dark-energy density since universe began. By calculation, universe has 70% dark energy and 30% matter. The future will disclose what dark energy is.
energy: amount is arbitrary
Because only energy changes have physical significance, absolute energy amount has no physical meaning. Energy level is arbitrary, so energy level is only relative, not absolute. Any physical state can be set to zero energy, and other states differ in energy from that state. For example, in earth's gravitational field, potential energy can be zero at Earth's surface or zero at infinite distance. If physical states can have arbitrary energy levels, total universe energy amount is arbitrary.
By special and general relativity, energy amounts are relative to reference-frame observer velocity. For example, for high-velocity observers, kinetic energy can be zero. If reference frame is arbitrary, total universe energy is arbitrary.
Photon energy varies directly with electromagnetic-wave frequency. Moving relative to light sources changes wave frequency and so observed photon energy. For observers moving away from source at high velocity, frequency red-shifts to near zero. For observers moving toward source at high velocity, frequency can blue-shift to arbitrarily high values. Because observer reference frame is arbitary, total universe photon energy is arbitrary.
energy: space vacuum
By observation, universe space curvature is close to zero, so universe average energy density is close to zero, meaning positive average mass-energy density and negative average intrinsic-energy density are close to equal. Closed universes do not change total energy, so average positive energy density and average negative energy density stay close to equal for closed universes.
Empty space has no energy from mass or relativistic mass, so space vacuum is set to zero average energy density. Other-states energy densities are relative to vacuum-state energy density.
energy: highest
Because shortest quantum-mechanical wavelengths mean highest frequencies, shortest spaces and times require highest energy (uncertainty principle), and universe began with shortest diameter, so universe began with highest energy density.
Universe has wide number ranges. Gravitational force has no limit in distance or amount. Strong force to gravitational force ratio is about 10^40. Because forces have wide ranges, universe can have wide energy ranges.
In empty space, positive energy density and negative energy density can be arbitrarily high, as long as positive energy density equals negative energy density so that energy density is zero. Universe can have arbitrarily high energies and energy fluctuations. Energy fluctuations can temporarily reach energy densities great enough to make particles.
general-relativity singularity
Because energy density, internal pressure, and gravity were highest, general relativity theorizes that universe began as a space-time singularity. Universe was a point both in and out of space-time. Singularities have smallest space volume and greatest space curvature. Singularities have perfect symmetry, homogeneity, unity, and order. Perhaps, all universes are similar.
quantum-mechanics closed universe
Because empty-space distances are shortest, space vacuum has uncertainty-principle energy fluctuations that can be large enough to make particles. Because both closed universes and space vacuum have zero energy flux, zero average energy density, and high energy-density variance, closed universes can arise spontaneously and randomly from space vacuum. Boundary conditions determine universe properties.
multiverse
If closed universes arise spontaneously from existing space vacuum, the number of space points is infinite. An infinite number of universes, with different laws and properties, can arise. Alternatively, each universe that has cosmic inflation has an infinite number of space points at which sub-inflations can spontaneously arise. Because space expands rapidly and separates them, the universes are independent.
quantum field theories
Quantum field theories show how particles and antiparticles arise in strong force fields, how virtual particles make force fields, and how space and time arise.
Quantum electrodynamics shows how time arises in strong force fields. Strong electromagnetic and weak-force fields make non-linear-wave time quanta (instanton), lasting for one electronic transition or one quantum tunneling.
Quantum gravity shows how space arises in strong gravitational fields. Strong gravitational fields make non-linear-wave space quanta, over one Planck distance, area, or volume, from no space and no time, and so start spaces with zero average energy density.
Therefore, strong fields can make space and time quanta and so start universes. Boundary conditions determine universe properties.
quanta
Universe space, time, energy, and momentum have non-zero minima and increase by discrete amounts (quanta). Particle energy quanta vary directly with quantum-mechanical resonating-wave harmonic frequencies (and particle momentum quanta vary inversely with quantum-mechanical resonating-wave harmonic wavelengths). Lowest-energy quanta associate with fundamental frequency. Because they have higher energy, higher-frequency quantum states have lower probability.
quanta: discrete non-zero energy levels
If protons and electrons can have zero-energy states, electrons can spiral into atomic nuclei, preventing atoms from existing. Particles and waves exist for long times and so have non-zero minimum energy.
If protons and electrons can have energy states that vary continuously, orbits can continuously decay, and electrons can spiral arbitrarily close to atomic nuclei, preventing atoms from existing. Discrete states maintain orbits, because moving from lowest orbit to no orbit cannot conserve energy, momentum, and angular momentum simultaneously. Particles and waves exist for long times and so have discrete energy levels.
If energy can vary continuously, particles and waves can have infinitesimal energy increases, each with the same small finite probability, so total energy can become infinite with measurable probability (ultraviolet catastrophe). If energy can vary only by discrete amounts, higher-energy increases have lower probability, so infinite total energy has zero probability. Higher-energies have lower probabilities, so particles and waves have discrete energy levels.
virtual particles
Physical-mathematical operators that conserve quantities, such as energy conservation, have average quantity zero. For commutative operators, operation order does not matter, so they have one more symmetry: variance quantity zero. Non-commutative operators that conserve quantities have average quantity zero but variance quantity non-zero. Action in physics multiplies energy and time non-commutatively, so action has energy fluctuations with zero averages but positive or negative variances (uncertainty principle). Space vacuum has short distances and high momenta, and short times and high energies. Therefore, space vacuum can have high enough positive or negative energy fluctuations to spontaneously create short-time energy quanta (virtual particles). Because particles are numerous, even low-probability high-energy-density states occur within moderate times, so space vacuum makes numerous virtual particles.
By observation, two positive-energy virtual particles (particle-pair) can arise spontaneously and simultaneously from empty space. Two particles allow charge and momentum conservation. The virtual particles have zero or opposite charges.
By observation, after short lifetime over small distance, virtual particles interact with zero-charge or opposite-charge virtual particles and spontaneously and simultaneously disappear, making two photons of electromagnetic energy.
The creation-and-annihilation process conserves mass-energy over long enough times and wide enough lengths.
In quantum mechanics, energy fields are streams of virtual-particle zero-rest-mass photons, zero-rest-mass gravitons, massive strong-force bosons, or massive weak-force bosons emitted from charges, masses, quarks, or leptons, respectively. Photons and gravitons are zero-rest-mass bosons that both propagate at light speed, so electromagnetism and gravity have effects over infinite distances.
antiparticles
By observation, when a particle meets its antiparticle, the particles annihilate, canceling electric charge and converting all mass to photons of electromagnetic energy. All quantum numbers become zero. Therefore, antiparticles always have charge opposite to that of their particles.
Both matter and antimatter have positive mass and attractive gravity. Antimatter does not have antimass or repulsive antigravity. Because they are the exact opposite of particles, antiparticles must have the same mass as their particles.
By special relativity, particles can only move forward in space-time. When a particle moving forward in space-time meets its antiparticle, momentum cancels, mass cancels, and only energy remains. Because particles and antiparticles have same mass and speed, momentum cannot cancel if antiparticles move forward in space-time, so antiparticles move backward in space-time. Because a particle and its antiparticle annihilate, a particle moving forward in space-time is equivalent to its antiparticle moving backward in space-time.
In quantum mechanics, all possible particle and antiparticle trajectories have wavefunctions and probabilities, and space-vacuum quantum energy fluctuations make virtual particles and antiparticles with measurable probabilities. By observation, a real particle can disappear at one location, and then a real particle can re-appear at the same time at a nearby location. Space-vacuum quantum energy fluctuations made the particle's virtual antiparticle arise earlier in space-time where the particle re-appeared. The virtual antiparticle went backward in space-time to where the particle disappeared and annihilated it at the observed time, the same time as the particle re-appeared at the nearby location.
antiparticles: antimatter
At universe beginning, because matter and antimatter have same physical laws and processes, universe had equal matter and antimatter amounts. Matter-antimatter annihilations made radiation, which is part of cosmic microwave background radiation. During annihilation, weak-force parity-and-time asymmetries left one part matter (and no antimatter) after every billion annihilations, so universe has only some matter: one proton for every billion radiation photons.
electric charge
At universe origin, very high temperature unified the strong force, weak force, and electromagnetism, so quark creation and lepton creation coupled. That coupling balanced positive and negative charge creation, so universe has no net charge.
dark matter
By calculation, stars move faster in their galactic orbits than galaxy visible and non-visible ordinary matter can make them move, and galactic-cloud ordinary-matter mass does not make enough gravity to form galaxies, so galaxies must have more matter (dark matter) than just ordinary matter. By calculation, universe has nine times more dark matter than ordinary matter. Dark matter is invisible, because it does not interact with electromagnetic radiation. The future will disclose what dark matter is.
time
Universe began a definite time ago, and observations indicate that universe will keep expanding indefinitely, so past time was not infinitely long ago, but future time will be or approach infinite time.
space
By observation, space is isotropic and homogeneous and probably began that way.
By calculation and observation, universe began with finite volume, and space has expanded ever since. Space expansion has reduced object gravitational attraction, space curvature, and outward kinetic energy. By observation, space expansion rate is increasing, so space will expand faster. Universe has large volume now and will approach infinite volume.
space: curvature
By general relativity, positive space curvature reduces distances, and negative space curvature increases distances. Because observed cosmic-microwave-background-radiation irregularities equal expected cosmic-microwave-background-radiation irregularities [1997], space on average has no curvature.
By calculation, universe average mass-energy density (positive and attractive) equals average dark-energy density (negative and repulsive), so space on average has no curvature.
space-time
Space and time unite in continuous space-time. By special relativity and experiment, time dimension relates to space dimensions by light speed: time-dimension time times light speed is space-dimension length. All objects move through space-time at light speed. Space-time has no time flow or direction, so space-time represents all previous and future times in the same way as spatial dimensions represent all points in all directions.
space-time: why was space three-dimensional?
Space is where energy is, so energy makes space. More space dimensions means more energy but less energy density. Zero space dimension has no energy and no energy density. One space dimension makes energy be one-dimensional longitudinal waves, so energy is too low and energy density is too high. Two space dimensions make energy be longitudinal and one-plane-transverse waves, so energy is too low and energy density is too high. Three space dimensions make energy be longitudinal and two-coordinate transverse waves, so energy density not too low or too high. Four space dimensions make energy be longitudinal and three-coordinate transverse waves, so energy is too high and energy density is too low.
Continuous four-dimensional space-time is stable and allows motion, potential, and energy. Space-time is unstable with more than three spatial dimensions and/or more than one time dimension, because gravity is too weak. With two or fewer space dimensions, kinetic energy is too small, and space does not expand. With four or more space dimensions, kinetic energy is too great, and space expands rapidly to make near vacuum.
space: expansion
At universe origin, although energy density and internal pressure were highest and so gravity was highest, space had smallest possible volume, and random-motion kinetic energy was highest and overcame gravity greatest, so space expansion rate was highest. However, because gravity was highest, expansion-rate decrease rate was greatest.
entropy
Planck-size discrete units have information bits. At universe origin, volume was smallest, so entropy was lowest.
Beginning universe had smallest volume, fewest allowable number of dimensions, fewest states, fewest information bits, most force symmetries, no matter, highest energy, and highest temperature, all of which make entropy lower, so total universe entropy was lowest.
Continuous systems have infinitesimal energy increases, each with the same small finite probability, and so infinitely many possible states. Discrete systems have lower-probability higher-energy states, so entropy is lower.
entropy: fractal processes
Perhaps, to minimize volume and dimension number, beginning universe had fractal processes. Fractal processes have high order and so low entropy. Moreover, fractal processes can make unlimited energy and energy ratios, because they repeat indefinitely.
symmetries and conservation laws
At universe origin, space-time, general relativity, quanta, and quantum mechanics began. Beginning universe had deterministic physical laws with time, space, and handedness symmetries.
Because physical laws are the same for forward and backward time (isochrony), space-time has energy conservation (least action over time), so universe total energy stays constant.
Because physical laws are the same for any space direction (isotropy), space-time has momentum conservation (least action over distance), so universe has no net motion.
Because physical laws are the same for right-handed and left-handed systems (symmetry), space-time has angular-momentum conservation (least action over rotation), so universe has no net rotation.
Future physical theories will account for all universe properties, including universe origin and its properties.
Immediately after universe beginning, space itself expanded equally at all points in all directions at highest rate (the "Big Bang"). Why did space expand at universe origin {space-expansion, causes} {Big Bang, causes}?
beginning-universe properties
By observation and calculation, at universe origin, space had smallest volume, and universe had same energy as now, so space had highest energy density. Because space had shortest distances, universe had lowest potential energy and highest kinetic energy and temperature. At highest temperature, forces unify and have greatest strength, so beginning universe had only radiation of one unified type, with zero rest mass, light speed, highest wave frequency, shortest wavelength, and highest radiation internal and external pressure. Because mass-energy density and internal pressure were highest, universe had highest gravity and space curvature, consistent with smallest 3-sphere volume. Because entropy varies directly with volume and inversely with gravity, beginning universe had lowest entropy.
space filling
Space is where matter and radiation are. Radiation-wave random reflections, refractions, and diffractions, and particle random motions and collisions, send waves and particles in all directions, so particles and waves fill space homogeneously and isotropically.
expanding space
In systems, most particle random motions and collisions, and most radiation-wave reflections, refractions, and diffractions, move particles and radiation apart, where they are less likely to encounter other particles and radiation and so less likely to change direction, so they continue moving apart. As particles and radiation move apart, space volume increases, mass-energy density decreases, potential energy increases, kinetic energy decreases, temperature decreases, internal pressure decreases, gravity decreases, and space curvature decreases.
Space expansion stretches lengths between particles and radiation. Space expansion adds quantum lengths between particles and waves.
expanding space: waves and particles remain intact
If particles are points, they have no insides, so space-expansion forces do not change point-particles. If particles have internal forces, those forces are much greater than space-expansion forces and particle-collision forces, so space-expansion forces do not change particles. Wave electromagnetic forces are very much stronger than gravity, and waves do not have collisions, so space-expansion forces do not change wave internal structure.
forces
Gravity is attractive and has infinite range, so it always opposes particle and radiation separation. Electromagnetism has infinite range but is attractive and repulsive and so has no overall effect on particle and radiation separation. Strong and weak nuclear forces have short range and so do not affect particle and radiation separation.
general relativity
Object random motions are mostly outward and so separate objects, increasing potential energy and decreasing kinetic energy, temperature, mass-energy density, and space curvature. Outward force varies directly with temperature (and so with mass and speed). If object kinetic energy overcomes gravity, kinetic energy decreases, and gravitational potential energy increases, by the same amounts. Total energy stays constant.
Matter, antimatter, and radiation have positive mass, positive energy, positive mass-energy density, and positive internal pressure, so gravity is positive and attractive, and gravitational energy is positive energy. Attractive gravity makes positive space curvature. Masses gravitationally attract each other at any distance less than infinite distance, so masses tend to move relatively closer, decreasing potential energy and increasing kinetic energy, temperature, mass-energy density, and space-time curvature. Gravitational force varies directly with mass and varies inversely with distance squared. General relativity adds internal pressure as a relativistic source of gravity, so objects with higher temperature have more gravity.
Objects with higher temperature also have greater outward motion. Because increased gravity is a relativistic effect of higher temperature and increased outward motion is a direct effect of higher temperature, higher temperature increases outward motion more than it increases gravity, and so increases space expansion. At universe origin, temperature was highest, and radiation external pressure was highest, so space expansion rate was highest.
Gravity and temperature vary directly with total energy at universe origin, but in different ratios. Because space expansion decreases temperature and gravity unequally, space expansion rate decreases over time.
Because gravity and temperature vary with energy at different rates, space has zero probability of neither expanding nor contracting. Universe is always changing.
quantum mechanics and vacuum intrinsic energy
By observation, space has a constant negative intrinsic-energy (dark-energy) density that causes repulsion (antigravity) and uniform space expansion. Dark energy can do negative work. Negative work decreases negative kinetic energy as it pushes space apart, and increases negative potential energy in the added space. (Positive work decreases positive kinetic energy and increases positive potential energy.) Dark energy adds intrinsic energy and adds space in exact proportion, so space always has constant dark-energy density.
Dark-energy strength was much lower than object random motions at universe origin and contributed little to original rapid space expansion.
quantum mechanics and vacuum intrinsic energy: expansion rate
Dark-energy repulsion also pushes particles and radiation apart, increasing positive potential energy and decreasing positive kinetic energy, decreasing mass-energy density and space curvature. Total energy stays constant, as required for closed systems.
For closed universes, because positive energy changes and negative energy changes always offset, universe positive energy and negative energy can be any amount. Mass-energy density and intrinsic-energy density can be any value, so space expansion rate can be any value for closed universes. By observation, universe has had periods of greatly differing space-expansion rates, such as initial expansion rate, the very high cosmic-inflation rate, and ever-slower expansion rates.
gravity at very short distances
Perhaps, gravity is repulsive at very short distances and very high temperatures.
string theory at very short distances
String theory theorizes that, when universe diameter was Planck length or less, strings repulsed, making gravity repulsive and space curvature negative, so space expanded rapidly.
string-theory inflatons
Perhaps, spontaneous symmetry breaking disunified forces, phase transition made string/brane scalar (inflaton) field, and inflaton-field repulsions caused space expansion.
space-expansion rate
At universe origin, unified force was greatest, and space expansion decreased at highest rate.
At any instant, space-expansion rate depends on initial radiation-velocity-driven space-expansion rate, initial unified-force/gravity space-contraction rate, and constant dark-energy antigravity space-expansion rate.
As space expands over time, distances between objects increase, so gravitational potential energy increases and object kinetic energy decreases, so object average speed becomes less, temperature decreases, and space-expansion rate decreases.
Gravity space-contraction rate depends on mass-energy density and on internal pressure, so it decreases as space volume increases. As space expands over time, gravity always decreases space-expansion rate, but ever more slowly.
Universe dark-energy density is constant, so it constantly increases space-expansion rate.
After initial expansion, object kinetic-energy expansion force decreases, gravity contraction force decreases, and dark-energy expansion force is small compared to them, so space-expansion rate decreases.
Eventually, dark-energy expansion force, plus object kinetic-energy expansion force, overcome gravity contraction force, and space expands ever faster.
entropy
Space expansion makes more volume, more states, more information bits, fewer force symmetries (as forces separated from other forces), more matter, same energy, lower temperature, and higher entropy, and so more entropy.
Gravity slows universe expansion rate {deceleration parameter}.
The universe began 13.72 billion years ago {universe history}.
before Planck time
Quantum mechanics and general relativity theorize that universe began with smallest 3-sphere volume, densest energy, highest pressure, greatest space curvature, and highest temperature. Because volume was smallest, universe had lowest entropy. Because temperature and external pressure were highest, space had highest expansion rate (Big Bang).
Before elapsed time was Planck time, 10^-43 seconds, time had quanta, random perturbations, expansions, contractions, and inhomogeneities. Space volume had diameter less than Planck length, 10^-35 meters. Indeterminate space and time dimensions superimposed and interchanged, with no distance metric, so things had indeterminate sizes. Quantized space had random expansions and contractions; tears and joins; loops, handles, holes, nodes, knots, links, kinks, and entanglements; rotations, spins, twists, and windings; phases, boundaries, inhomogeneities, and overlaps; asymmetries, anisotropies, and discontinuities; and relaxations, nonstandard fields, and nonstandard forces. This "quantum foam" was like periodic orbits in chaotic systems.
before Planck time: energy
Total universe energy was same as now. Because space volume was smallest, energy density was highest. Because universe had shortest size and time, by uncertainty principle, universe had highest energy and energy fluctuations. Because many bosons can occupy the same space, even the smallest universe can have any number of high-energy real and virtual bosons and can have any energy level.
before Planck time: temperature and pressure
Because kinetic energy was highest, temperature and pressure were highest. Radiation frequency was highest, so radiation energy and pressure were highest.
after Planck time
From 10^-43 seconds after universe origin (diameter 10^-35 meters) to 10^-39 seconds after (diameter 10^-15 meters), space expansion pushed masses farther apart and increased potential energy, so kinetic energy decreased and universe cooled. Quantum mechanics and general relativity theorize that quantum foam became continuous four-dimensional space-time as universe temperature and pressure decreased. Space, time, energy, and momentum had discrete quanta, and physical processes followed quantum-mechanics and general-relativity laws.
after Planck time: radiation only
Because gravitation, electromagnetism, strong nuclear force, and weak nuclear force differentiate only at lower temperatures, universe had only one unified force. Supersymmetry united bosons and fermions. Because distances were short, potential energy was low, and kinetic energy was high. Because temperature was too hot to allow matter formation, universe had only zero-rest-mass radiation, traveling at light speed at high frequency with short wavelength.
after Planck time: physical laws
Universe had special relativity, general relativity, and quantum mechanics. Because universe had only radiation, universe had no particles and so no particle Standard Model. Because forces had not yet differentiated, universe did not have quantum electrodynamics or quantum chromodynamics. Energy, momentum, and angular momentum conservation began.
cosmic inflation
After 10^-39 seconds after universe origin, space expansion rate became extra-fast for less than one second, after which time it returned to regular space expansion rate.
particle formation
After that, protons, neutrons, and electrons formed, and then helium atomic nuclei formed.
atom formation
When universe was 300,000 years old, neutral-charge hydrogen and helium atoms formed, leaving 3000-K (visible-wavelength) radiation.
galaxies
Between 12 and 9 billions years ago, galaxies formed, and since then supernovas have made carbon, oxygen, and other atomic nuclei.
now
Now, universe has 400 billion galaxies, about 3 million light-years apart, averaging 100 billion stars. Universe has more than 100 billion planets.
Universe has 75% hydrogen nuclei and atoms and 25% helium nuclei and atoms.
The 3000-K radiation has become 3-K (microwave) radiation, streaming almost uniformly from all space directions, proving that universe began hot and then space expanded.
future
One hundred fifty billion years from now, recession velocity of the galaxy cluster nearest to the Milky Way Galaxy (in the Virgo Cluster) will exceed light speed. Light from galaxy-cluster stars (small ones will still be shining) will have red-shifted to frequency 5000 times lower. Cosmic microwave background radiation will have temperature near absolute zero.
Two trillion years from now, recession velocity of the very-small-so-still-shining stars closest to the sun will exceed light speed, and its light will have red-shifted to frequency near zero, so those photons will have lowest energy, and cosmic microwave background radiation will have temperature essentially absolute zero.
Much longer than two trillion years from now, solar system, earth, and molecule particles and radiation will spread apart to almost infinite distances, and universe will have absolute zero temperature.
If multiverse does not exist, adjacent to universe {outside universe} is only non-physical nothingness. If multiverse exists, outside universe is empty space-time, and an unlimited number of other universes, with the same or different properties, are farther away in space and time.
Religions, mythologies, and traditions have universe creation and origin theories {cosmogony}|. Cosmology is a science.
If, due to space expansion, Earth observers are moving away from a light source faster than light speed, that light cannot reach Earth. Earth observers can see cosmic microwave background radiation, which was emitted 13.72 billion years ago and has redshift 1000 times. However, light sources 16 billion light-years away are expanding away at light speed, so that is the current maximum distance {horizon, cosmic} {cosmic horizon} from which light will eventually reach Earth. Because space expansion is exponentially increasing, in future cosmic horizon will decrease.
From universe origin to 300,000 years later, from any space point most other space points had space expansion rate faster than light speed. Because universe radius was larger than cosmic horizon, light from most early-universe space points did not reach most other space points, and space did not reach thermal equilibrium {thermalization}. Space was non-homogeneous, and space regions had different temperatures, mass-energy densities, and space curvatures. However, cosmic microwave background radiation has same temperature to 1 part in 10,000, showing that universe is almost homogeneous. How did space regions beyond each other's cosmic horizons become almost homogeneous {horizon problem}? Perhaps, beyond current cosmic horizon, universe is not really homogeneous. Perhaps, random quantum-mechanical processes kept variations to 1 part in 10000. Perhaps, in-phase sound waves caused compressions and rarefactions of 1 part in 10000. Perhaps, early-universe space inflation greatly decreased space curvature, mass-energy density, and temperature, so variations greatly decreased.
If universe is infinite and static, galaxies are at all sky directions, so night sky is bright, but night sky is dark {Olber's paradox} {Olber paradox}. Because universe is finite and expanding, galaxies separate far, and night sky is dark.
Perhaps, space regions can tunnel {wormhole}| through space-time to other space regions. Wormholes require energy to warp space-time. Gravity collapses wormholes. Negative energy resists gravity, so wormholes with negative-energy particles are stable. Positive energy assists gravity, so wormholes with positive-energy particles are unstable. Perhaps, wormholes allow energy from future and past to interchange, with positive feedback, and/or allow travel to future and past. In string theory, strings can tear space-time.
Massive objects strongly attract atoms gravitationally. In large stars, gravity pulls atoms into each other up to maximum hot-gas density, which is about 0.5 g/cm^3. Uncertainty principle prevents distances from being zero. Pauli exclusion principle prevents particles from having same location (state). In matter, uncertainty principle and Pauli exclusion principle cause quantum-mechanical resistance pressure {degeneracy pressure}, so matter resists further compression. Degeneracy pressure varies directly with gravitational force and with mass-energy density, not with temperature. In white-dwarf stars, gravity decreases electron distances causing electron degeneracy pressure. In neutron stars, gravity overcomes electron degeneracy pressure, and decreases neutron distances, causing neutron degeneracy pressure.
About 10^-11 seconds after universe origin, electromagnetic force and weak nuclear force decoupled {electroweak phase transition} at temperature 10^15 K.
Perhaps, trillions of years from now, universe will be near absolute zero temperature and in thermal equilibrium {heat death}, when space expansion is much larger than now.
Space has intrinsic negative energy {dark energy}|. Dark energy is 70% of universe mass-energy (ordinary matter and dark matter are 30%). Perhaps, dark energy is virtual particles that have negative energy {vacuum energy} and repulse masses. Perhaps, dark energy involves new forces and interactions, such as quintessence. Perhaps, dark energy uses hidden space dimensions.
As they travel, electron, muon, and tau neutrinos, which have different masses, interconvert. Perhaps, neutrino-mass changes make dark energy, as they oscillate matter quark flavors. Dark-energy density is similar to neutrino density.
Perhaps, supernova changes or distant-particle effects cause space expansion, so there is no dark energy. Perhaps, rippling long-wavelength waves still travel after cosmic inflation and increase in intensity, expanding universe indefinitely, so there is no dark energy. Perhaps, non-linear mass interactions (backreaction) contribute to space expansion.
density
Dark energy density is 10^-26 kg/m^3. Dark-energy density variation over space is zero, because dark-energy particles do not attract each other, so space has constant dark-energy density over time and space.
When energy is negative, force is repulsive, so positive space expansion amount equals added negative energy amount, keeping dark-energy density same when universe is small or large.
space expansion
After cosmic inflation ended, 1 second after universe origin, dark energy causes universe space expansion.
internal pressure
Rubber membranes resist stretching (expansion) and compressing (contraction). Stretched rubber membranes try to contract (like gravity) and have positive (attractive) restoring force, potential energy, and internal pressure. Compressed rubber membranes try to expand (like antigravity) and have negative (repulsive) restoring force, potential energy, and internal pressure. Quantum vacuum has negative (repulsive) force that expands space, increasing negative potential energy (dark energy) by subtracting universe positive kinetic energy, and so cooling the universe. Quantum vacuum has negative internal pressure between one-third and one of mass-energy density, so repulsive antigravity is between zero and negative two times mass-energy density: M + 3 * -(M/3) = 0 and M + 3 * -M = -2*M.
universe
In early universe, dark-energy repulsion and gravitational attraction clustered matter into protogalaxy filaments. Filaments formed galaxy clusters. Galaxy clusters stopped forming six billion years ago, as space expansion made mass-energy density lower and gravity less, while dark-energy density stayed constant. Clusters allow galaxy collisions, so older galaxies have irregular shapes (while younger galaxies are spirals). Colliding galaxies increase star formation. Star formation became low six billion years ago.
Before five billion years ago, mass-energy density was higher than dark-energy density, so universe initial expansion slowed. Five billion years ago, mass-energy density became equal to dark-energy density. After five billion years ago, mass-energy density became less than dark-energy density, and universe expansion accelerated. In the future, dark energy will cause faster separation of galaxy clusters, then galaxies, then stars and planets, then molecules, and finally atoms.
heavy elements
If dark energy was stronger, filaments are fewer, clustering is less, and star formation is less, so fewer supernovas make fewer heavy elements. If dark energy was weaker, filaments are more numerous, and clustering is more, but star formation makes smaller stars, which do not supernova to make heavy elements. Universe dark-energy density maximizes heavy-element formation.
Perhaps, non-linear mass interactions {backreaction} contribute to space expansion.
For ordinary matter, average vacuum fluctuation energy is zero {average weak energy condition}. For exotic matter, average can be negative.
When calculations showed that general-relativity equations require that universe expand forever, Einstein introduced extra space-time force {cosmological constant}|, whose attractive force balanced space expansion and maintained static and infinite universe. However, recent observations show that, though gravity slows expansion, space expansion is accelerating, requiring repulsive cosmological constant. Perhaps, dark energy or quintessence supplies cosmological constant. Perhaps, universe angular momentum causes cosmological constant (but universe does not rotate).
By virtual-particle quantum mechanics, space contains very high vacuum energy. If so, universe has very high curvature. By virtual-particle quantum mechanics, cosmological constant is 120 orders of magnitude greater than cosmological constant that balances gravity, but observations show that space has zero curvature {cosmological constant problem}. Perhaps, space has negative pressure to counterbalance vacuum energy. Perhaps, constant negative dark energy counterbalances vacuum energy.
Observed universe mass-energy density is the density (critical density) that makes space curvature zero. If early-universe mass-energy density was 10^-14 more than early-universe critical density, later-universe density becomes much higher than later-universe critical density, and space becomes more curved and more closed. If early-universe mass-energy density was 10^-14 less than early-universe critical density, later-universe density becomes much lower than later-universe critical density, as space becomes less curved and more open. Therefore, because universe space curvature is zero now, early-universe space had zero curvature, an unlikely situation {flatness problem}. Perhaps, though early universe did not have critical density, early-universe cosmic inflation reduces space curvature.
Perhaps, dark energy can become more repulsive energy {phantom energy} as time increases.
Perhaps, dark energy is repulsive field {quintessence, field}|, not virtual particles or vacuum energy. Quintessence is higher at higher potential energy and zero at lowest potential energy, so quintessence (and cosmological constant) decrease over time as universe expands. Perhaps, space negative pressure or quantum effects cause quintessence.
Quintessence field strength is almost zero. If strength was more, space expansion is so great that only radiation can exist. If strength was less, space expansion is so small that only matter can exist.
When rock hits another rock, pressure waves spread from surface and from inside. When inside pressure wave reaches surface, reflection changes phase by 180 degrees. At a thin layer {spall zone} at surface, pressure wave from surface and pressure wave from reflection almost cancel, and surface pressure is near zero. However, pressure just below surface is high, and rock erupts through surface. In cosmology, expanding universe has spall zones.
In universe's first second, gravity and weak force formed baryon and non-baryon subatomic particles {dark matter}| that do not interact with electromagnetic radiation and move much slower than light speed {cold dark matter}. Because they do not interact with electromagnetic radiation, dark-matter particles are invisible. (Planets, cool gas, dust, and black holes interact with electromagnetic radiation and, though not visible, are not dark matter.)
Dark matter has mass. Dark matter is 23% of universe mass. Observed galaxy star (and gas) rotation rates show that dark-matter mass is nine times visible-matter mass.
Dark-matter particles have irregular mass differences. Because they do not have smooth small-scale mass differences, dark matter is not subatomic particles that move at near light speed {hot dark matter}.
About 900 million years after universe origin, 12.8 billion years ago, dark matter formed clouds, with masses million times Sun mass. From then until 7 billion years ago, clouds contracted and merged and made evenly spaced spherical clouds, with masses five to ten times more than visible and non-visible ordinary matter there. These clouds have enough matter to make gravity form galaxies. If matter was only ordinary matter, density is not enough to let gravity form galaxies. Because galaxies have five to ten times smaller volume than dark-matter clouds, dark-matter density and ordinary-matter density are approximately equal.
Because they have mass, dark-matter particles exchange potential and kinetic energy with gravitational fields, which change as particles move, so dark-matter particles and gravitation fields settle into virial equilibrium.
Dark-matter particles never collide.
Universe matter distribution is more even than expected by particle statistics {smoothness problem}.
Perhaps, real particles {ylem} can come from virtual-particle pairs, making universe more homogeneous.
Perhaps, new subatomic-particle types {ghost condensate} can make outward pressure that prevents gravitational collapse.
Perhaps, cold-dark-matter particles are superpartner particles {lightest superpartner particle} (LSP).
Perhaps, dark matter is neutrinos or supersymmetric particles {photino} {Zino} {Higgsino}.
Perhaps, cold dark matter is subatomic particles {weakly interacting massive particles} (WIMP) {neutralino} from universe origin that do not interact with electromagnetic radiation and move slowly.
Microwave radiation {cosmic microwave background}| (CMB) {microwave background} {background radiation, microwave} comes from all universe directions. Cosmic microwave background radiation is same visible-light-frequency radiation that was in hot plasma before plasma cooled enough, to 3000 K, for neutral-charge atoms to form, 300,000 years after universe origin, and comes from 13.72 billion light years away.
temperature
At that distance, recession velocity is near light speed, and redshift divides frequency by 1000, so radiation is now microwaves, with effective temperature 2.7 K.
temperature fluctuations
Cosmic-microwave-background temperature varies over space by less than 1 part in 10000. Temperature variations have Gaussian distribution. Temperature fluctuations arose from early-universe in-phase acoustic waves, density differences, and gravity waves. Gravitational waves cause red-shift and blue-shift. Gravitational-wave handedness causes polarization curls. Gravitational lensing affects CMB.
Largest same-temperature structures have one-degree diameter. Temperature variations depend on in-phase acoustic-wave wavelength, such as the largest spatial distance {first Doppler peak}. The four largest spatial distances have same intensity differences {scale-invariance}.
Gravity affects photon trajectories and energies. About 300,000 years after universe origin, when neutral-charge atoms formed, photons in higher-density regions lost more energy than photons in lower-density regions {Sachs-Wolfe effect}, because they had to overcome more potential energy. Sachs-Wolfe effect cancels gravity-photon effects.
If photons enter higher-energy-density regions and then exit them, universe space-expansion energy makes photons have higher energies than before {integrated Sachs-Wolfe effect}.
Galaxy-cluster plasma scatters cosmic microwave background radiation {Sunyaev-Zel'dovich effect}.
Perhaps, universe is homogeneous because light can go faster than light speed {varying-speed-of-light theory} {varying speed of light} (VSL). Fast light can bring all universe regions into contact, making one closed system (with nothing outside, before, or after), and so make thermal equilibrium, so there was no need for cosmic inflation.
During universe first seconds, subatomic-particle creation made x-rays {background radiation, x-ray} {x-ray background radiation} that still travel through universe.
High-enough mass-energy density makes high-enough gravity to make space curvature so high that radial matter and radiation curve back into the region and so cannot leave. Space-time singularities have a surface {event horizon} beyond which no particles or radiation can escape. Therefore, outside observers cannot detect physical processes in the space {hidden region} inside event horizon. For black holes and other spherical objects with no charge and no angular momentum, event-horizon radius is two times object mass. For such spherically symmetric singularities, space-time has Schwarzschild metric. For non-spherically-symmetric singularities, space-time has Kerr metric.
photon layer
At event horizon, gravity potential energy equals light kinetic energy, so photons orbit singularity in stable and unstable circular orbits, making a photon layer.
inside horizon
To observers inside event horizon, all matter and radiation appear to move toward singularity center. Observers inside event horizon see nothing outside horizon, because high gravity slows time so much that radiation frequency red-shifts to very low, so photons have almost no energy and are undetectable.
outside horizon
To observers outside event horizon, objects falling toward singularity appear to slow to a stop at horizon, because time slows greatly in high gravity. Because high gravity makes object part closer to singularity have much more acceleration than farther part, objects falling toward singularity elongate perpendicular to event-horizon surface. Outside event horizon, observers can measure only electric charge, mass (monopole moment), and angular momentum (dipole moment).
Outside observers cannot see universe singularities {cosmic censorship hypothesis}. Universe has no singularities without an event horizon ("naked" singularities). All singularities have an event horizon. Outside observers cannot see space-time time-like singularities (ideal points) {strong cosmic censorship hypothesis}. Universe singularities can be space-like or light-like (null) but not time-like. Outside observers far away in space-time cannot see time-like singularities {weak cosmic censorship hypothesis}.
Universe can have singularities without an event horizon. Spinning or charged black holes can lose event horizons after small charge or spin increases or small mass decreases. Exploding black holes can expose singularities. Perhaps, cosmic censorship is true only if cosmological constant is zero or negative.
Some singularities {white hole}| emit particles and/or radiation. In quantum theory, small singularities emit particles and/or radiation rapidly, while black holes emit slowly. Perhaps, universe has large white holes.
Supernova remnant stars and galaxy centers {black hole}| have high-enough mass-energy density to cause high-enough gravity so that object escape velocity is higher than light speed, so matter and radiation cannot leave the black hole. Outside observers receive no radiation, so black holes are not visible. Gravity is so strong that space curvature is so high that it curves moving matter and radiation back into the black hole or into orbit around the black hole.
stars
Some stars with more than 2.25 Sun mass become supernovas. After supernova, remaining neutron star has mass two times Sun mass and diameter 2000 meters. When neutron-star nuclear fusion slows, black holes form in one second, with no measurable diameter but with close event horizon. Galaxies average 10^6 star black holes.
galaxies
Galactic centers, including Milky Way and Cygnus X-1, have one large black hole. Galactic centers have high star concentrations and stars collide and merge to make larger mass, until mass is so high, black hole forms. Then black hole attracts more mass and grows larger. Galactic-center black holes contain mass from 10 million stars and have no measurable diameter but distant event horizon.
mass
Black holes can have unlimited mass and gravity.
density
High-enough gravity can overcome neutron-degeneracy pressure, so neutrons compress into each other, making density greater than in atomic nuclei.
diameter
Black holes are space-time singularities. Black holes have no measurable diameter. Black holes are outside space and so are one point in time.
rotation
Non-rotating black holes far from matter have a point singularity. Space around non-rotating black holes far from matter has Kerr metric.
Black holes probably rotate with angular momentum equal to mass. Rotating black holes have ring-shaped singularity, perpendicular to rotation axis. Perhaps, objects can go through ring center and come out into negative or antigravity space. Spinning black holes produce long gamma-ray bursts.
electric charge
Black holes can have positive or negative electric charge. Black holes can have only small charge {no hair}, because they rapidly attract or repel nearby charges and become neutral.
sizes and lives
Early universe probably had enough radiation pressure to create tiny black holes. Planck-size black holes have mass 10^-8 kilograms, density 10^97 kg/m^3, and radius 10^-35 meters. Smaller black holes compress neutrons more, as inverse square of mass. Hawking radiation evaporates them quickly.
Ball-size black holes are hotter than the hottest star center.
Mountain-mass black holes have mass 10^12 kilograms and proton-sized radius. Hawking radiation evaporates them in 10^12 years at 10^12 K.
Sun-mass black holes have mass 10^30 kilograms, density 10^19 kg/m^3, and radius 3000 meters. Hawking radiation evaporates them in 10^64 years at temperature 10^-6 K.
radiation
Black-hole event horizons have high space curvature and high tidal forces, and so form virtual-particle pairs. Sometimes, one virtual particle enters black hole, and the other escapes and becomes a real particle (Hawking radiation). It is like quantum tunneling. In-falling and escaping particles carry energy. Negative energy flows into black hole, reducing mass-energy density, and positive energy escapes, reducing mass-energy, so energy conservation energy holds overall, but black-hole mass and energy decrease. Hawking radiation decreases black-hole mass and energy, so event horizon has shorter radius and smaller surface area.
Spatial-surface gravity determines particle-creation amount. Mass-energy-loss rate varies inversely with mass squared, so smaller black holes radiate more rapidly and lose mass faster. Smallest ones can explode. Smallest ones radiate particles with no spin. Small ones radiate neutrons and other neutral particles with spin in equatorial plane. Large ones radiate protons, electrons, and other charged particles. Largest ones radiate photons and gravitons. Equal numbers of baryons and anti-baryons leave black holes.
However, outside space also creates virtual photons, and some enter black holes, so typical black holes probably are in thermal equilibrium with surrounding space and do not evaporate.
temperature
Hot objects radiate to cooler objects. Warm objects radiate infrared light. Light-frequency distribution depends on object temperature. Black holes radiate Hawking radiation, and event-horizon temperature determines frequency distribution. Event-horizon temperature varies inversely with black-hole surface area and mass. Smaller black holes have higher energy-to-mass ratio and so higher temperature. Large black holes have event-horizon temperatures near absolute zero. Tiny-black-hole event-horizon temperatures are 10^21 K.
Black holes have high gravity and attract outside particles. In-falling particles add heat and increase event-horizon temperature.
Hawking radiation reduces black-hole mass more than it reduces energy, so energy-to-mass ratio increases, and so event-horizon temperature rises.
Black-hole event-horizon temperature results from quark and gluon motions. Black holes have strongly interacting quarks and gluons, which have low shear viscosity. Temperature T varies directly with acceleration a: T = (h / (2 * pi * c)) * a, where c is light speed, and h is Planck constant. T = kappa / (2 * pi), where kappa = (h/c) * a. Particles have high acceleration at event horizon. Larger black holes have smaller particle accelerations, and so lower event-horizon temperatures. Temperature represents quantum-fluctuation strength.
Classically, emitting thermal radiation from hot bodies removes energy and makes surface have lower temperature, because hotter-than-average particles preferentially leave. Does only cooler-than-average radiation leave black holes, so they get hotter? Is virtual radiation thermal emission or another radiation kind?
entropy
Black holes have entropy proportional to star information that becomes lost when star collapses. From outside, only black-hole event horizons are observable, so event horizons carry all information. Black-hole entropy S depends on event-horizon surface area A: S = A * k * c^(3/4) * h * G, where k is Boltzmann constant, c is light speed, h is Planck constant, and G is gravitational constant.
In cosmological units, entropy S varies directly with event-horizon surface area A divided by four: S = A / (4 * h * G), where h is Planck constant and G is gravitational constant in Planck units. Partition-function P logarithm is negative of free energy FE divided by temperature T: ln(P) = - FE / T. Free energy FE is energy E plus temperature T times entropy S: FE = E + T*S.
Because things can only go into black holes, and nothing can come out except Hawking radiation, event-horizon surface area and entropy typically increase. If black hole and space are in thermal equilibrium, surface area and entropy stay constant. If Hawking radiation is more than photon and particle entry from space, surface area and entropy decrease. Black-hole entropy relates thermodynamics and quantum gravity.
entropy: information
When black holes form, where does information about matter type and distribution {multipole moment} go? Information can be at event horizon, below event horizon, in black hole, or at singularity. Outside observers never see information loss, because they see time slow and light red-shift but never see black hole form.
Information has quantum-mechanical limits.
By string theory, black holes seem to destroy information but actually just transfer it {AdS/CFT correspondence}.
gravity
Gravity strength is the same at all event-horizon points {zeroth law of black-hole mechanics}. The zeroth thermodynamics law says all points in contact are at same temperature (thermal equilibrium).
energy
Mass or energy change dE is event-horizon spatial-area change dA times constant kappa / (8 * pi), plus angular-momentum change dJ times omega constant, plus charge change dQ times psi constant {first law of black hole mechanics}: dE = (kappa / (8 * pi)) * dA + omega * dJ + psi * dQ, where kappa is event-horizon gravity strength. The first thermodynamics law says total energy is constant.
temperature
Event-horizon gravity strength is like thermodynamic temperature. Event-horizon spatial area is like thermodynamic entropy. Because null geodesics have no observable future and can never converge, event-horizon spatial-area change dA never decreases over time {second law of black hole mechanics}: dA >= 0. The second thermodynamics law says entropy never decreases.
If double stars have one black hole and one ordinary star, black hole can pull gas from star, making a disk {accretion disk}. Gas has fast-moving charged particles, whose magnetic interactions cause turbulence (magnetorotational instability). Gas particles closer to black hole are faster. Magnetic attractions slow near-black-hole gas particles, so they move closer to black hole. Magnetic attractions speed far particles, so they move farther from black hole. Overall potential energy decreases, and kinetic energy increases (generating heat), providing energy for accretion disk to radiate.
Black holes have maximum entropy and information. Outside observers cannot see inside event horizons, so black-hole information is in event-horizon surface area. More massive black holes have larger event-horizon surface areas. By quantum-loop theory, event-horizon surfaces have area quanta, which hold one information bit. Larger event-horizon surfaces have more area quanta, hold more bits, and represent more entropy. Event-horizon surface area varies directly with black-hole entropy. Event-horizon surfaces have maximum entropy {Bekenstein bound}. If mass-energy falls into black hole, black-hole mass-energy increases, event-horizon surface area increases, and entropy increases. regions bounded by event horizons have limited information amounts.
Rotating black holes have a region beyond event horizon but inside stationary limit {ergosphere}. Ergosphere particles appear to have negative energy to outside observers.
For charged rotating stationary black holes, angular momentum and magnetic moment are in same direction and their ratio {gyromagnetic ratio} is 2. Angular momentum is 2*m*e*w, and magnetic moment is m*e*w, where m = mass, e = charge, and w = angular velocity. (Electrons also have gyromagnetic ratio 2.)
Black-hole event horizons have high space curvature and high tidal forces, and so form virtual-particle pairs. Sometimes, one virtual particle enters black hole, and the other escapes and becomes a real particle {Hawking radiation}. It is like quantum tunneling. In-falling and escaping particles carry energy. Negative energy flows into black hole, reducing mass-energy density, and positive energy escapes, reducing mass-energy, so energy conservation energy holds overall, but black-hole mass and energy decrease {black hole evaporation}. Hawking radiation decreases black-hole mass and energy, so event horizon has shorter radius and smaller surface area.
Spatial-surface gravity determines particle-creation amount. Mass-energy-loss rate varies inversely with mass squared, so smaller black holes radiate more rapidly and lose mass faster. Smallest ones can explode. Smallest ones radiate particles with no spin. Small ones radiate neutrons and other neutral particles with spin in equatorial plane. Large ones radiate protons, electrons, and other charged particles. Largest ones radiate photons and gravitons. Equal numbers of baryons and anti-baryons leave black holes.
However, outside space also creates virtual photons, and some enter black holes, so typical black holes probably are in thermal equilibrium with surrounding space and do not evaporate.
temperature
Hot objects radiate to cooler objects. Warm objects radiate infrared light. Light-frequency distribution depends on object temperature. Black holes radiate Hawking radiation, and event-horizon temperature determines frequency distribution. Event-horizon temperature varies inversely with black-hole surface area and mass. Smaller black holes have higher energy-to-mass ratio and so higher temperature. Large black holes have event-horizon temperatures near absolute zero. Tiny-black-hole event-horizon temperatures are 10^21 K.
Black holes have high gravity and attract outside particles. In-falling particles add heat and increase event-horizon temperature.
Hawking radiation reduces black-hole mass more than it reduces energy, so energy-to-mass ratio increases, and so event-horizon temperature rises. Thermal emission reduces black-hole mass and makes black hole hotter.
Black-hole event-horizon temperature results from quark and gluon motions. Black holes have strongly interacting quarks and gluons, which have low shear viscosity. Temperature T varies directly with acceleration a: T = (h / (2 * pi * c)) * a, where c is light speed, and h is Planck constant. T = kappa / (2 * pi), where kappa = (h/c) * a. Particles have high acceleration at event horizon. Larger black holes have smaller particle accelerations, and so lower event-horizon temperatures. Temperature represents quantum-fluctuation strength.
Classically, emitting thermal radiation from hot bodies removes energy and makes surface have lower temperature, because hotter-than-average particles preferentially leave. Does only cooler-than-average radiation leave black holes, so they get hotter? Is virtual radiation thermal emission or another radiation kind?
If double stars have one black hole and one ordinary star, black hole can pull gas from star, making an accretion disk. Gas has fast-moving charged particles, whose magnetic interactions cause turbulence {magnetorotational instability} (MRI).
At a radius {Roche limit} around black holes, gravity equals electric force.
From black-hole center, the farthest distance {Schwarzschild limit} {Schwarzschild radius} from which light cannot escape is 2 * G * m / c^2, where G is gravitational constant, m is mass, and c is light speed. Larger-mass black holes have farther Schwarzschild limit.
After objects fall into black holes, outside observers cannot observe object properties, because nothing can come out except Hawking radiation, which is random and has no information. Outside observers can only measure total black-hole mass, charge, and angular momentum. All object information is lost, but there should be information conservation {black hole information paradox}. By string theory and quantum-loop theory, because strings are unitary, information is constant {unitarity} {unitary process}, and object information goes into event-horizon surface area. Perhaps, when black holes evaporate and so have no event horizon, outside observers can see all information again.
Perhaps, universe physical parameters require life {strong anthropic principle} {anthropic cosmological principle} [Barrow and Tipler, 1986], because universe properties must be such that humans can observe them. Perhaps, universe physical parameters allow life {weak anthropic principle}, because universe properties must be such that life exists.
Universe began with small volume, high energy, high mass-energy density, high temperature, high pressure, and high spatial curvature, and then rapidly expanded {Big Bang}, increasing spatial volume, decreasing mass-energy density, decreasing temperature, decreasing pressure, and decreasing spatial curvature.
All space points moved away from each other, so farther points moved away faster. From any space point (at any time), if a second point is at distance x and moves away from first point at velocity v, and a third point is at twice that distance 2*x, third point moves away from first point at velocity 2*v. If second point is between first and third points, first and third points move away from second point at same velocity v. Space has no central point or region. Big Bang was space expansion, not an explosion into existing space.
Universes that make more black holes propagate more universes similar to themselves and so come to dominate {cosmological natural selection}. (The universe reached its low-probability parameters by self-organization and other selection mechanisms.)
Perhaps, universe distribution came from one quantum path over infinite space. Perhaps, universe distribution came from decoherence making quantum mechanics approximate classical mechanics. Both scenarios result in same universe distribution {ergodicity}.
Issues that science cannot answer require outside agents to resolve them {God of the Gaps argument}.
Universe regions have information. Total is 10^60 bits. Universe regions have boundary surfaces, such as sphere around galaxy dark matter or event-horizon around black holes. For outside observers, all region information flows through boundary surface to observer, so boundary surface holds region information, though surface has lower dimension than region. If observer is far away, bounding-surface physics can represent region physics {holographic principle}. Perhaps, region physics projects onto boundary surface, and boundaries are like holograms {strong holographic principle}. Perhaps, region information projects onto boundary surface, and bounding surface has information channels {weak holographic principle}.
hologram
Just as surfaces can hold holograms, from which coherent light can make three-dimensional images, two-dimensional surface boundaries can contain all information needed to describe three-dimensional space regions. For example, superstring theory for anti-de-Sitter space-time five-dimensional regions is equivalent to conformal quantum-field theory of four-dimensional surface-boundary-point particles.
string theory
Hyperbolic-space regions have constant surface boundary. In string theory, boundary-surface gluon strings represent one quantum information bit and have thickness and strong-force color. String thickness represents space-point distance from boundary surface. Color represents information about space-point's quantum state. String number varies directly with space-region radius, so larger radius makes large boundary surface. Surface-string interactions represent gravitons.
Newtonian dynamics modifications {Modifications of Newtonian dynamics} (MOND) {Newtonian dynamics modification} do not require dark matter to provide extra gravity needed to form galaxies.
Perhaps, space {multiverse} has separate independent universes, with different phases. Perhaps, multiverse is still making and ending universes.
Level I multiverse
If space is infinite (or sufficiently large), and matter has even spatial distribution, universe objects and events repeat {Level I multiverse}.
Level II multiverse
Perhaps, if Level-I-multiverse universes are infinite in number, each universe has different dimension numbers and physical constants {Level II multiverse}. In string theory, quantum-field inflatons make space expand. For small quantum-field fluctuations, local bubbles form in universes. For example, if space starts with nine dimensions, only three expand, Alternatively, matter is in only three dimensions. Local bubbles become different universes, with different properties. Space inflation continues, making distances between bubbles expand faster than light, so universes are separate. Perhaps, vibrations between parallel three-dimensional universes along fourth dimension create and destroy universes. Perhaps, universes begin and end at black holes.
Level III multiverse
In quantum-mechanics many-worlds interpretation, all possible events occur (with different probabilities), making universe branches, which repeat {Level III multiverses}, and so do not become infinite in number. Observers see only one world by decoherence. All possible worlds are wavefunction-solution superpositions. Number of universes does not increase exponentially as time goes forward but stays constant, because they only repeat.
Level IV multiverse
Universes can vary in physical laws. Perhaps, all possible mathematical structures and universes exist {Level IV multiverse}.
Universe cycles between Big Bang and Big Crunch {oscillating theory}.
Perhaps, other universes {parallel universes} exist simultaneously with, or before or after, universe.
Universe probably is just one of many possible universes {plurality of worlds}. Because bosons have unique quantum-number sets, and space-time is relative, not absolute, many universes exist [Sklar, 1993]. Space-time quantum-mechanical and statistical fluctuations determine each universe's physical laws.
Universe is unchanging {steady-state theory}.
Gravity curves space-time, and space-time curvature accelerates mass. In one quantum-mechanical cosmology {Wheeler-DeWitt equations} {quantum-constraints equations}, universe wavefunction depends on gravity and space-time curvature [DeWitt, 1965].
Deriving general relativity from quantum-loop-theory supergravity makes universe wave equations have infinite numbers of exact solutions. Solutions are non-intersecting no-kink quantum loops or are intersecting symmetric quantum loops. Quantum-loop area represents energy, so quantum loops have quantum area, and minimum area is ground state. Using quantum-loop theory, solutions can be independent of space-time {diffeomorphism constraints}. With those constraints, quantum-loop intersection topology, knots, and kinks define space dimensions, so quantum loops determine space dimensions.
In non-expanding empty space, radiation from sources decreases proportional to distance-from-source squared. In expanding universes, expansion reduces net distances, so radiation from sources decreases less than distance-from-source squared. It is like space absorbs less radiation {Wheeler-Feynman absorption theory}.
Perhaps, 10^-36 to 10^-34 seconds after universe origin, starting at temperature 10^28 K, space-expansion rate increased exponentially, and universe expanded 10^28 to 10^30 times in 1 second {inflationary cosmological model} {theory of inflation} {inflation, cosmology}| {inflation scenario} {cosmic inflation}. From initial singularity, universe can go to any state, so expansion or no-expansion probabilities are not determinable. Perhaps, inflation was only in the universe. Perhaps, inflation was in a region (multiverse) millions of times bigger than universe and so affected many universes.
before
At universe origin, universe had light-speed maximum-frequency radiation that made maximum temperature and pressure. Immediately after, universe had space expansion. Space expansion cooled universe evenly, except for quantum fluctuations (which correspond to observed cosmic-microwave-background-radiation density fluctuations) that averaged 1 part in 10000. Immediately, high gravitation, due to high mass-energy density, decreased space-expansion rate.
phase transition
Perhaps, as universe cooled, it did not change phase, but entered a "supercooled" state, prolonging the phase, so vacuum of space {false vacuum} had higher stored potential energy. That potential energy was gravitationally repulsive and exponentially increased space-expansion rate, causing exponential volume increase. Space expansion exceeded light speed.
end
After one second, high-expansion phase ended. Uncertainty-principle gravitation-and-electromagnetic-field quantum fluctuations made different space regions, of different sizes, stop inflation at slightly different times. Stopping inflation released false-vacuum energy, and uncertainty-principle quantum fluctuations made local regions have different matter and radiation densities, and perhaps different physical laws and constants. Inflation continued between stopped-inflation regions, spreading those regions far apart, so they became completely separate.
More likely, uncertainty-principle gravitation-and-electromagnetic-field quantum fluctuations made different space regions, of different sizes, increase or prolong inflation (chaotic inflation). In those inflating regions, local regions stopped inflation and made separate universes with different matter and radiation densities, and perhaps different physical laws and constants. Space inflation continued indefinitely in most space regions. Perhaps, some are still inflating.
Perhaps, space has hidden dimensions, so separate universes are at the same space point.
after
After one second, universe had matter and radiation, with density variations of 1 part in 10000.
effects
If universe had cosmic inflation, initial universe was small enough so that all points were within each other's cosmic horizon, so space was in thermal equilibrium, explaining why cosmic microwave background radiation is almost homogeneous. After inflation ended, temperature, density, magnetic-field, electric-field, and gravity differences were still 1 part in 10000. Temperature fluctuations have Gaussian distribution. Inflation affected all sizes, except the smallest, equally, so cosmic-microwave-background temperature fluctuations have same amplitude over different large-size space regions.
Inflation makes space curvature much flatter than otherwise.
Inflation caused gravity waves but few high-frequency gravity waves.
cause
Perhaps, antimatter has negative gravity and caused cosmological inflation.
If space dimensions are dynamic, high-dimensional spaces rapidly expand or contract.
zero total energy
Matter and radiation have positive mass and positive kinetic energy. Masses and charges in (infinite) fields have potential energy, which can scale from zero at object surface to infinite at infinite distance. At infinity, if total energy is zero, kinetic energy is zero, and potential energy is zero. At object surface, if total energy is zero, kinetic energy is positive, and potential energy is negative. By this convention, in infinite fields, total object energy is always zero.
In expanding universes, galaxies are moving apart while gravitation tries to pull them together. Space expansion gives galaxies positive kinetic energy, and gravitational attraction gives galaxies negative potential energy. Mass-energy density causes gravitation field strength, which is space curvature. In a flat universe, space curvature is zero, so total galaxy energy can be zero.
By relativity, gravity depends on sum of mass-energy density M and on internal pressure P: G ~ M + 3 * P. Hot gas has slightly more internal pressure than cold gas, and so has slightly more gravity. Photon gas has radiation (internal) pressure equal to one-third its energy density, doubling gravity: M + 3 * P = M + 3 * (M/3) = 2*M. Objects can have negative internal pressure. For example, compressed rubber membranes tend to repulse molecules, by negative internal restoring force, so internal potential energy is negative. Quantum vacuum has negative (repulsive) force that expands space, increasing negative potential energy (dark energy) by subtracting universe positive kinetic energy, and so cooling the universe. Quantum vacuum has negative internal pressure between one-third and one of mass-energy density, so repulsive antigravity is between zero and negative two times mass-energy density: M + 3 * -(M/3) = 0 and M + 3 * -M = -2*M.
Kinetic energy makes positive pressure, which can do work, reducing kinetic energy and pressure. Potential energy makes no pressure. Quantum vacuum has negative potential energy and so negative internal pressure, which causes repulsion and makes space expand. During expansion, negative internal pressure does negative work on quantum vacuum to expand space, and negative potential energy becomes negative kinetic energy, which is the same as subtracting positive kinetic energy. Space expansion increases total negative energy, by subtracting positive energy, because total energy is constant. Because space expansion causes negative-energy density, space expansion increases at same rate as negative energy addition, so quantum vacuum has constant negative-energy density. Starting at universe origin, space expands with constant negative energy density. During this process, total-energy quantum fluctuations cause a small fraction of positive kinetic energy to become matter and radiation.
The Higgs field can reach higher-energy levels {inflaton field}. Perhaps, high potential energy from Higgs-field particles {inflaton} caused gravitational repulsion and accelerated universe expansion. Higher-energy levels are unstable. However, because initial universe is precisely homogeneous, universe does not change phase (supercooling) as it expands and cools, but prolongs inflation before changing phase. (If liquids have no nucleation sites as they cool, they supercool below temperature at which crystallization typically occurs, then they crystallize at lower temperature.) Perhaps, if supercooling delayed force decoupling, later decoupling released extra energy, which worked like antigravity and caused 10^100 times more space-vacuum negative pressure than before.
Perhaps, one inflaton falls, in one quantum jump, from supercool to zero energy, which acts as a seed for other inflatons to fall, so inflation-stopping spreads at light speed {bubble nucleation}. Perhaps, inflatons have different energies and fall through many quantum jumps. Some high-energy inflatons cannot fall back down, because other inflatons already fill lower energy levels. Inflation-stopping does not spread, prolonging inflation. Different space points have different periods of inflation (chaotic inflation).
String theories describe what cosmology was like before universe origin and what happened to begin universe. String theory allows more high-frequency gravity waves than inflation theory or ekpyrotic theory, so observing gravity waves can test string theories {pre-big-bang theory}. In fact, universe has few high-frequency gravity waves and some low-frequency gravity waves. Perhaps, universe has small-scale and large-scale strings. Perhaps, universe origins involve quantum-mechanical tunneling.
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.
axion
Magnetic-field photons can make dilaton-related strings (axion) that have less than one millionth electron mass, no charge, and zero average quantum field. Magnetic-field axions can make photons. Therefore, axions allow strong nuclear forces to maintain charge-parity (CP) symmetry between antiparticles and particles.
Cosmic-microwave-background temperature fluctuations are small, have Gaussian distribution, and have same amplitude for large space regions. Cosmic-microwave-background temperature fluctuations arise mostly from density differences and partly from gravity waves. However, string theories without axions allow no density differences. Axions determine large-scale universe temperature fluctuations [Adams, 2002].
Smaller strings have higher vibration frequencies and so higher masses. The smallest strings have highest mass and smallest size and so can be like black holes {string hole}.
Because many D-branes occupy high-dimensional space and D-branes attract each other, D-brane pairs collided, making universes' origins {ekpyrotic scenario} {conflagration scenario}. As D-branes mutually move closer, space contracts. If D-branes mutually move farther, space expands. Adjacent D-branes can repeatedly collide and separate, in contraction and expansion cycles.
Perhaps, before universe origin, time reversal and T-duality caused universe contraction, with matter accreting into string holes (pre-big-bang theory) {pre-big-bang scenario}. As space filled with string holes, universe was like string-hole gas. String-hole gas had smooth string-size distribution (unlike chaotic conditions at black-hole surfaces). Smooth size distribution allowed large string holes to form. Inside the largest string hole, matter reached maximum allowable density and temperature, causing an emission-singularity white-hole.
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.
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Date Modified: 2022.0225