In classical physical space, particles have definite positions and momenta, not probabilities of positions and momenta. If physical space has no external forces, positions and momenta are independent. If physical space has force fields, position change changes momentum in only one way, according to energy conservation. Because particles have definite positions and momenta, and classical configuration space has only real numbers, classical configuration space has no real-number/imaginary-number interactions and so no waves. The Hamiltonian function represents energy as a function of momentum (kinetic energy) and space (potential energy) coordinates.
In quantum-mechanical physical space, particles have probabilities of positions and momenta. Quantum-mechanical physical space has energy conservation, but positions and momenta are not independent, so energy-conservation equation (Schrödinger equation) and S-matrix theory, which relate kinetic-energy change and momentum to potential-energy change and position, have complex numbers. Exponentials with complex-number exponents represent cosine and sine waves. (Maxwell's equations relate kinetic-energy change and momentum to potential-energy change and position, and solutions are electromagnetic waves.) Frequency is time derivative. Wave number is spatial derivative. The time derivative introduces an imaginary number to multiply the time derivative to give a real number.
Quantum-mechanical configuration space (phase space) has complex-number particle position and momentum coordinates. Along each configuration-space dimension, real and imaginary numbers interact to make helical scalar waves {matter wave}| {de Broglie wave} {probability wave}.
scalar
Electromagnetic waves are vector waves, because electric and magnetic forces and fields have direction, electromagnetic waves propagate in a direction, and energy travels in that direction. Matter waves are scalar, because they are not about forces or fields, have no energy, and do not propagate and so do not travel and are standing waves. Scalar waves have amplitude but no direction.
phase space
Matter waves are not in physical space.
wavelength
Wavelength determines possible particle positions and momenta, at maximum-displacement positions. Frequency and phase affect amplitude.
amplitude and probability
Amplitude determines probability that particle is at that position or momentum.
frequency and kinetic energy
Particle kinetic energy E determines matter-wave frequency f: E = h * f, where h is Planck constant. For higher energies, matter waves have higher frequencies and lower wavelengths. Particle momentum p determines matter-wave wavelength w: h = p * w. Theoretical matter-wave velocity v increases with particle kinetic energy: v = f * w = (E/h) * (h/p) = E/p.
transverse wave
Real and imaginary number interactions make transverse waves around each phase-space dimension.
length
Matter waves are in configuration space, which has infinitely-long dimensions, so matter waves are infinitely long. By uncertainty principle, matter waves extend through all space, but with low amplitude outside physical system.
no propagation and no energy
Because they are infinitely long, matter waves do not propagate, are standing waves, and have no travel, no velocity, no energy, and no leading or trailing edge. Matter waves resonate in phase space.
positions, points, and intervals
Waves require one wavelength to be a wave, so there is no definite position. For waves, positions cannot be points but are one-wavelength or half-wavelength intervals.
solidity
Matter waves have width of at least one wavelength, so they cause matter to spread over space, not be at points. Matter waves make matter have area, and matter appears solid.
momentum and position
In quantum mechanics, unlike classical mechanics, momentum and position are not independent, because amplitude relates to position, frequency relates to momentum, wave amplitude-change rate relates to wave frequency-change rate, wavelength relates to position uncertainty, and amplitude-change rate relates to momentum uncertainty.
particle sizes
Large objects have high matter-wave frequencies. At high frequencies, matter-wave properties are undetectable, because wavelengths are too small, so classical mechanics applies. Small objects have low matter-wave frequencies, so atomic particles have detectable quantum properties.
waves and quanta
Resonating waves have fundamental frequency and harmonic overtones. Particles have matter waves with harmonic frequencies. Harmonic frequencies correspond to a series of positions or energy/momentum levels, separated by equal amounts (quantum).
Waves change frequency without passing through intermediate frequencies. No intermediate frequencies means no intermediate positions or energies/momenta. Matter waves explain why particles have discrete energy levels, separated by quanta, and why, during energy-level transitions, particles never have in-between energy levels. Particles also have discrete locations, separated by quantum distances.
physical systems
In free space, particle matter waves have a small range of frequencies and superpose to make a wave packet. Particle systems superpose particle matter waves to make system matter waves. Non-interacting particles have dependent matter waves that add non-linearly (entangle). In atoms and molecules, electrons, neutrons, and protons have phase-space matter waves that represent transitions among atomic orbits.
Electrons cannot be near nucleus, because then electron matter-wave interacts with proton matter-wave, and atom collapses.
philosophy
Perhaps, matter waves are particles, only associate with particles, are mathematical descriptions, or are all that observers can know.
Matter-wave wavelength equals Planck constant divided by momentum {de Broglie relation}|.
In quantum mechanics, matter-wave amplitude determines probability that particle is at that position. Matter waves are infinite and so have positive amplitude at all space points. Therefore, unlike classical mechanics, particles have a probability of being outside potential-energy barriers {tunneling}|.
At barriers, particle waves reflect back or refract through. Particles with higher matter-wave frequency and more energy have more refraction. As difference between barrier potential energy and particle energy increases, reflection {anti-tunneling} increases.
Matter waves are infinitely long. Because particle matter waves have fundamental frequency and its harmonics, particles have an infinite number of different-frequency matter waves. Because particles interact with other universe masses and charges, particles have matter waves differing in wavelength by infinitesimally small amounts. Superposition of an infinite number of infinitely long waves, differing in wavelength by infinitesimally small amounts, makes significant amplitude {wave packet}| in one region and insignificant amplitudes in all other regions. Particles are matter-wave packets.
time
Over time, as superposition makes different results, wave packets can disappear and reappear. Wave superposition can narrow or broaden wave-packet duration. and broadening frequency range.
size
Wave packets have three to ten oscillations, with maximum amplitude in center and no amplitude at edges. Longest wavelengths are in middle and smallest wavelengths are at edges. If wavelength range is small, packet is wide. If wavelength range is large, packet is narrow.
speed
Wave packets travel at particle speed, but wave-packet component waves travel at slower and faster speeds.
frequencies
Matter-wave-packet frequency varies directly with particle energy. Wave superposition can narrow or broaden wave-packet frequency range. If wave packet has many frequencies, volume is small, but energy is big. If wave packet has few frequencies, volume is large, and energy is small.
dispersion
Due to dispersion, wave packets spread out lengthwise and transversely.
In classical mechanics, positions and momenta (and energies and times) are independent variables, but in quantum mechanics, they are dependent variables and interact in wavefunctions. In classical mechanics, when two or more particles interact, system properties sum particle properties. In quantum mechanics, when two or more particles interact, system properties multiply and sum particle properties, and particle wavefunctions combine constructively and/or destructively to make a system wavefunction {entanglement}|. If two (indistinguishable) particles entangle, they both travel together on all possible state paths available to them, and they interfere with each other's independent-particle wavefunctions along each path. For example, two particles created simultaneously form one system with one wavefunction.
Entanglement does not put particles into unchanging states (that observers measure later). Neither do particle states continually change state as they move through space-time (not like independent neutrinos, which change properties as they travel). Therefore, observation method, time, and space position and orientation do not determine observed particle state. In quantum mechanics, particles have probabilities, depending on particles and system, of taking all possible space-time and particle-interaction paths, and measurement finds that the particle has randomly gone into one of the possible particle states.
system wavefunction
When two particle wavefunctions add, system-wavefunction frequency is the beat frequency of the two particle-wavefunction frequencies, and is lower than those frequencies. System wave packet has smaller spatial extension than particle wave packets, and has higher amplitude (more energy) at beat-frequency wavelengths. Quantum-mechanical particle and system wavefunctions have non-zero fundamental frequency and its harmonic frequencies and have non-zero amplitudes over all space and time. Systems spread out over space and time.
system wavefunction decoherence
After entanglement, system wavefunction lasts until outside disturbances, such as measurement, particle collision or absorption, and electromagnetic, gravitational, or nuclear force field, interact with one or more particles. At that definite time and position, system wavefunction separates into independent particle wavefunctions (decoherence). Whole system wavefunction ends simultaneously over whole extent.
measurement
By uncertainty principle, experimenters can precisely measure either particle energy or particle time (or momentum or position) but not both. After two entangled particles separate, separate instruments can measure each particle's energy (or momentum) precisely and simultaneously and then communicate to determine the exact difference.
measurement: speculation
Perhaps, unobserved particles and systems are two-dimensional (but still in three-dimensional space). Observation then puts particles and systems into three dimensions. People observe only three-dimensional space. For example, observers see that gloves are right-handed or left-handed. Perhaps, unobserved quantum-mechanical-size gloves actually have no thickness and so have only two dimensions, so unobserved right-handed and left-handed gloves are the same, because they can rotate in three-dimensional space to superimpose and be congruent. Perhaps, unobserved clockwise and counter-clockwise particle spins are two-dimensional and so are equivalent. (Note that a two-dimensional glove appears right-handed or left-handed depending on whether the observation point is above or below the glove.)
Perhaps, unobserved particles and systems randomly, continually, and instantaneously turn inside out (and outside in), in three-dimensional space. Observation stops the process. For example, turning a right-handed glove inside out makes a left-handed glove, and vice versa. Perhaps, unobserved quantum-mechanical-size gloves continually and instantaneously turn inside out in three-dimensional space and so are equally right-handed and left-handed. Perhaps, unobserved clockwise and counter-clockwise particle spins continually interchange. (Note that a glove appears right-handed or left-handed depending on when the process stops.)
Perhaps, unobserved quantum-mechanical-size particle and system states are indeterminate and follow quantum-mechanical rules because space-time is not conventional four-dimensional space-time. Observation requires conventional three-dimensional space, and randomly makes definite three-dimensional particle and system states, with probabilities. Perhaps, time is not real-number time, but complex-number or hypercomplex-number time. Real-number times are separate, but imaginary-number times are not. Perhaps, space is not real-number space, but complex-number or hypercomplex-number space. Real-number distances are separate, but imaginary-number distances are not.
Observations measure real-number part of complex-number variables. Perhaps, wavefunction imaginary-number part continues after observation.
Perhaps, Necker cubes illustrate the effects of observation. Observer angle to Necker cube determines whether observer sees right-facing or left-facing Necker cube. Effects may be linear with angle or depend on cosine of angle.
interacting electrons and spin
If a process creates two electrons, momentum sum is the same before and after creation, by momentum conservation, and electrons move away from each other at same velocity along a straight line. Angular-momentum sum is the same before and after creation, by angular-momentum conservation. (If two separate electrons entangle, momentum sum and angular-momentum sum are the same before and after interaction.)
By quantum mechanics, measured spin is always +1/2 or -1/2. Because the electrons are in a system, one cannot know which has +1/2 spin and which -1/2 spin. Both electrons share a system wavefunction that superposes the state (wavefunction) in which first electron has spin +1/2 unit and second has spin -1/2 unit and the state (wavefunction) in which first electron has spin -1/2 unit and second has spin +1/2 unit, with zero total angular momentum in any direction. Two wavefunctions can superpose constructively (add) or destructively (subtract). Because two electrons are distinguishable, the two wavefunctions add, so system wavefunction is anti-commutative.
One possibility is that one particle has positive 1/2 unit spin along z-axis (motion line), and other particle has negative 1/2 unit spin along z-axis. See Figure 1.
After two particles interact and move apart, separate spin detectors can measure around any axis for first particle and around any axis for second particle, simultaneously or in succession. For example, the axes can be z-axis (motion line), x-axis, and y-axis. See Figure 2. Measuring spin around an axis fixes one electron's spin at +1/2 (or -1/2) and fixes the other electron's spin around an axis at -1/2 (or +1/2), to conserve angular momentum.
spin: possible axis and spin combinations
By quantum mechanics, left electron has spin +1/2 half the time and spin -1/2 half the time, around any axis, say z-axis. Around same z-axis, right electron always has opposite spin: left=z+ right=z- or left=z- right=z+. Around x-axis, right electron has opposite spin (while y-axis has same spin), same spin (while y-axis has opposite spin), opposite spin (while y-axis has opposite spin), or same spin (while y-axis has same spin): x-y+z-, x+y-z-, x-y-z-, x+y+z-; x-y+z+, x+y-z+, x-y-z+, x+y+z+. For right-electron z-axis compared to left-electron z-axis, spins are opposite all of the time: z+z-, z+z-, z+z-. z+z-. For right-electron x-axis or y-axis compared to left-electron z-axis, spins are same 1/2 of time and opposite 1/2 of time: z+x-, z+y+; z+x+, z+y-; z+x-, z+y-; z+x+, z+y+. See Figure 3. Because quantum mechanics has random probabilities, left and right electrons have same spin half the time and opposite spin half the time.
However, quantum mechanics with non-randomness (due to local real hidden factors) makes a different prediction. Non-random hidden factors correlate right and left spins, to conserve angular momentum. If left=x+y+z+, right=x-y-z-. If left=x-y+z+, right=x+y-z-. If left=x+y-z+, right=x-y+z-. If left=x-y-z+, right=x+y+z-. If left=x-y-z-, right=x+y+z+. If left=x+y-z-, right=x-y+z+. If left=x-y+z-, right=x+y-z+. If left=x+y+z-, right=x-y-z+. See Figure 4. For right-electron z-axis compared to left-electron z-axis, spins are opposite all the time. For right-electron x-axis or y-axis compared to left-electron z-axis, spins are same 4/9 of time and opposite 5/9 of time, higher than the 1/2 level for quantum mechanics. Local hidden variable theories correlate events through hidden variable(s), making probabilities non-random. Quantum mechanics has no more-fundamental factors and introduces uncertainties, and so is random. Therefore, correlated outcomes in classical theories have different probabilities than in quantum mechanics. Experiments show that outcomes are random, so there are no local hidden factors and/or no real hidden factors.
if infinite light speed
Perhaps, entanglement over large distances and times has no non-locality problems if light speed is infinite, as in Newton's gravitational theory. Assume that relativity is true but with light speed infinite. Time is zero for light, and speed is always infinite for all observers, so all objects are always in contact. However, light speed is finite.
action at distance
Wavefunctions do not represent physical forces or energy exchanges, so space and time do not matter. If system wavefunction does not decohere, system particles and fields remain connected, even over long duration and far distances. Experiments that measure energy and time differences, or momentum and position differences, show that particles remained entangled over far distances and long times, and that wavefunction collapse immediately affects all system particles and fields, no matter how distant (action at a distance). Seemingly, new information about one particle travels instantly to second particle. See Particle Interference, Scientific American 269(August): 52-60 [1993].
However, information about collapse only travels at light speed, preserving special relativity theory that physical effects faster than light speed are not possible. Observers must wait for light to travel to them before they become aware of information changes. All physical laws require local interaction through field-carrying particle exchanges, which result in space curvatures. All physical communication happens when particles are in contact and interact, so there is no actual action at a distance.
teleportation
After particle entanglement, particle wavefunctions have specific relations. By manipulating particle properties at interaction and at wavefunction collapse, experimenters can transfer particle properties from one particle to another particle, even far away, though the particles have no physical connection at collapse time.
Bombs can have photon or light pressure triggers. Bombs explode if trigger does not jam, but jamming happens often. How can testers find at least one working bomb without exploding it {Elitzur-Vaidman bomb-testing problem} [1993] (Avshalom C. Elitzur and Lev Vaidman)? Using photon entanglement can find good bomb without triggering it.
Particles can seemingly move from one place to another without ever being between the two places {teleportation}|. Teleportation requires that both locations share a particle pair {EPR pair}. Particles are identical, with entangled properties. For example, if one photon splits into two photons, new photons can be same-state superpositions. If instrument observes one particle's state later, it then knows other particle's state. If EPR pair exists, putting one pair member into one state can result in property disappearance at one location and other-pair-member property appearance at another location.
Instruments can measure momentum, position, energy, and time by absorbing energy and using clocks and rulers. However, instruments cannot simultaneously or precisely measure both particle momentum and position {uncertainty principle}| {Heisenberg uncertainty principle} {indeterminacy principle}, because measuring one alters information about the other. Instruments cannot simultaneously or precisely measure both particle energy and time, because they relate to momentum and position.
situation
The uncertainty principle is about measurement precision on one particle at one time and place. The uncertainty principle does not apply to different measurements on same particle over time. The uncertainty principle does not apply to simultaneous momentum and position, or energy and time, measurements on different particles.
wave packet
Particles have wavefunctions, so measurements are about wave packets. As particle moves through time and space, total uncertainty increases, because wave packet spreads out.
wave properties
Uncertainty follows from wave properties, because wave position and momentum, or time and energy, inversely relate. Energy and momentum depend on wave frequency. Position and time depend on wave amplitude. Measuring wave frequency or wavelength precisely prevents measuring wave amplitude precisely. Measuring wave amplitude precisely prevents measuring wave frequency or wavelength precisely. If momentum or position is specific, position or momentum must be uncertain. If energy or time is specific, time or energy must be uncertain.
At space points, wavefunctions that have high amplitude have precise position and timing. However, wavefunction slope is steep, so amplitude change between nearby points is large, so velocity change, momentum change, and energy change are large and so uncertain at that position. See Figure 1.
Wavefunctions with wide wave packets have large uncertainty. Wavefunction slopes are not steep, and amplitude change at nearby points is small, so velocity change, momentum change, and energy change are small in that region. Momentum is precise, while position is imprecise. Alternatively, energy is precise, while timing is imprecise. See Figure 2.
Waves that have just one frequency and wavelength have one momentum and energy. Only one wave can have no superposition and no cancellation anywhere in space or time, making wave equally present throughout all space and time, and so completely uncertain in position and time. See Figure 3.
Wavefunctions that have almost all frequencies and wavelengths have precise position and time, because waves cancel everywhere, except one space or time point. Wavefunctiond that have almost all frequencies and wavelengths have almost all momentum and energy levels, making wave momentum and energy very uncertain. See Figure 4.
Waves that have some frequencies and wavelengths have moderate uncertainty in momentum and energy and moderate uncertainty in position and time, because waves cancel, except at moderate-size wave packet.
Waves with two or three frequencies and wavelengths have beat frequencies where waves superpose. Beat frequency makes precise momentum and energy, but time and position are uncertain. See Figure 5.
Waves with harmonic frequencies and wavelengths have beat frequencies where waves superpose. Beat frequencies make precise momentum and energy, but time and position are uncertain.
measurement processes
Besides wavefunction effects, physical processes limit precision. To find precise frequency for energy and momentum takes time and space, so position and time information are uncertain. To find precise position and time takes high amplitude, so position and time information are uncertain. Uncertainty's physical cause is discontinuity, whereas uncertainty's quantum-mechanical cause is wave-particle duality, because particles are about momentum and energy and waves are about position and time, as shown above.
mathematics
Quantum of action is h, and energy over time is action. Therefore, energy uncertainty dE times time uncertainty dt equals at least Planck constant divided by 4 * pi: dE * dt >= h / (4 * pi).
dE = F * dx = (dp / (4 * pi * dt)) * dx, so dE * dt * (4 * pi) = dp * dx. Position uncertainty dx times momentum uncertainty dp equals at least Planck constant: dx * dp >= h.
dx = 4 * pi * dF, and dp = dN / 2. Phase uncertainty dF times phonon number uncertainty dN equals Planck constant divided by 2 * pi: dF * dN = h / (2 * pi).
energy levels
Electrons in lower atomic orbitals have higher frequency, kinetic energy, and angular momentum and lower time period and orbital diameter. Electrons in higher atomic orbitals have lower frequency, kinetic energy, and angular momentum and higher time period and orbital diameter. Therefore, higher orbitals have higher position uncertainty and lower momentum uncertainty.
For low-orbital and high-orbital electrons, photon absorption can cause electronic transition to adjacent higher energy level, increasing position uncertainty and decreasing momentum uncertainty. For low-orbital and high-orbital electrons, photon emission can cause electronic transition to adjacent lower energy level, decreasing position uncertainty and increasing momentum uncertainty.
For low-orbital and high-orbital electrons, photon absorption can cause electronic transition to non-adjacent higher energy levels, increasing position uncertainty and decreasing momentum uncertainty. For low-orbital and high-orbital electrons, photon emission can cause electronic transition to non-adjacent lower energy levels, decreasing position uncertainty and increasing momentum uncertainty.
Besides fundamental Heisenberg uncertainty, electron, proton, and neutron configuration changes affect measured amounts. Electronic transitions conserve energy, momentum, and angular momentum, so absorption and emission do not necessarily have the same photon frequency. Electrons cannot transition to same orbital.
two particles
Though instruments cannot measure either's time or energy, instruments can measure two particles' energy difference and time difference precisely and simultaneously. Such measurement can define one-ness and two-ness.
confinement
By uncertainty principle, particles confined to smaller regions or times have greater momentum and energy. In confined regions, even in vacuum, energy is high, allowing particle creation and annihilation.
matrices
In quantum mechanics, particle position and momentum are quantized and so are matrices (not scalars or vectors), with complex-number elements. Because particles have probabilities of being anywhere in space, matrix rows and columns have infinite numbers of elements, and matrices are square matrices. In quantum mechanics, position and momentum are not necessarily independent, but depend on the whole particle system.
Matrices represent electronic transitions between energy levels. Matrix rows are one energy level, and matrix columns are the other energy level. Matrix elements represent the probability of that electronic transition. Matrix elements are periodic to represent the possible quanta. The diagonal represents transitions between the same energy level and so has value zero. Near the diagonal represents transitions between adjacent energy levels and so has higher values. Far from the diagonal represents transitions between non-adjacent energy levels and so has lower values. Energy levels have ground state and no upper limit, so the matrices have infinite numbers of elements. There is no zero energy level.
For non-infinite-dimension square matrices with real elements, PQ = QP (commutative). For infinite-dimension and/or non-square and/or complex-number-element matrices, PQ <> QP (non-commutative). Matrix multiplication is typically non-commutative.
In quantum mechanics, particle action is the product of the momentum P and position Q matrices: action = PQ. For infinite-dimension square matrices with complex-number elements, PQ - QP = -i*h*I, where I is identity matrix and h is Planck constant, because action has Planck-constant units and complex number multiplication rotates the axes by pi/2 radians.
Though electrons and protons have strong electrical attraction, and outside electrical attractions and repulsions can disturb atom orbitals, electrons do not spiral into protons and collapse atoms. Because particles have matter waves, by the uncertainty principle, orbiting electrons cannot spiral into atomic nucleus {atom, stability}. See Figure 1.
waves
Particles have matter waves, whose harmonic frequencies relate to particle energy levels.
uncertainty
Waves by definition must be at least one wavelength long. Therefore, particle waves have location uncertainty of at least one wavelength. Particle waves have time uncertainty of at least one period, which is one wavelength divided by light speed. Particle waves have momentum uncertainty of at least Planck constant divided by wavelength. Particle waves have energy uncertainty of at least Planck constant divided by period. Particle waves make the uncertainty principle.
energy
By uncertainty principle, particles must move, and so they cannot have zero energy. Particles cannot have zero energy because they cannot have zero motion, because that violates conservation of both energy and momentum. Lowest particle energy is first-quantum-level ground-state energy.
orbits
Electron orbits have quantum distances from nucleus and take quantum durations to orbit nucleus. In lowest orbital, electron position uncertainty has same diameter as orbital. Electron can be anywhere in that region around nucleus. In lowest orbital, electron time uncertainty is same period as orbital rotation. Electron can be anywhere in that interval. In lowest orbital, electron is already at closest possible distance and smallest possible time.
transitions
From lowest orbital, electrons cannot go to lower orbits, because there are no lower energy levels. They cannot lose more energy, because if energy decreases then time increases, by uncertainty principle, making orbital go higher. They cannot lose more distance because if distance decreases then energy must increase, by uncertainty principle, making orbital go higher. Therefore, lowest orbital has lowest energy, smallest distance, and shortest time. Lowest orbital already includes nucleus region, so it cannot be smaller.
kinetic and potential energy
In quantum mechanics and classical mechanics, electric-field positions relate to potential energies. In quantum mechanics, unlike classical mechanics, kinetic energy cannot completely convert to potential energy, and vice versa. Kinetic energy and potential energy have minimum energy level and cannot be zero.
energy quantum
First energy quantum is difference between ground-state energy and next-highest-orbital energy. Second energy quantum is difference between next-highest-orbital energy and third-orbital energy. Energy quanta are not equal. Energy quanta decrease at higher orbitals. Energy quanta relate to wave harmonic frequencies. Higher adjacent wave frequencies have smaller energy differences.
atom nucleus
Atomic nucleus occupies only 10^-5 volume inside lowest-electron-orbital volume. Nucleus protons and neutrons have energy, momentum, position, and time uncertainty and so have ground-state energies. Nucleus protons and neutrons have quantum energy levels.
Lowest-orbital electrons and highest-orbital neutrons and protons never collide, because electrons have lower orbiting energies, and higher orbital radii, than neutrons and protons.
electron-proton collision
At high-enough energy and beam collimation, electrons can collide with atomic nuclei, because increased energy can narrow position, by uncertainty principle. Such electrons are not orbiting, so this situation is not about atom stability.
Particle in enclosed space {particle in box} must have velocity, because particle has fixed position, so uncertainty is in momentum. If enclosed space is smaller, velocity must be more.
Electric field and magnetic field cannot be at rest {quantum fluctuation}, because then they have precise position and precise zero momentum and so violate uncertainty principle. All fields have random motion, even in vacuum where net energy is zero.
At quantum level, empty-space field fluctuation {vacuum polarization}| is infinite.
Two parallel uncharged metal plates attract each other by reducing vacuum-energy fluctuations and number of wavelengths between them {Casimir effect} {Casimir force}: energy density = c / d^4, where c is constant and d is plate distance. Energy at plate is zero. Interior energy density decreases, so exterior energy density increases and pushes plates together. Fewer particle histories with closed time-like loops are between plates.
Particles cannot be at rest {zero point motion}|, because then they have precise position and precise zero momentum and so violate uncertainty principle. All particles have random motion, even in vacuum where net energy is zero.
For energy transfers, particles act like particles. For determining locations, particles act like waves {wave-particle duality}|.
Matter waves have spatial/momentum effects and time/energy effects, which instruments cannot detect simultaneously {complementarity, quantum mechanics}. Particles have energy, and waves have positions. Instruments cannot determine particle properties and wave properties simultaneously. Experiments can be only complementary, because particles always have both wave and particle properties.
Wave, photon, or particle sources can send collimated beams through one or two slits, to a measuring surface {slit experiment, quantum mechanics} {two-slit experiment}. For one slit, beam makes medium intensity line across from slit. For two slits, beam makes line with four times medium intensity across from slit. It makes alternating intense and clear lines on both sides. First intense line to side has two times medium intensity. Second intense line has medium intensity. Third intense line has lower intensity, and so on. Beam waves constructively and destructively interfere.
quanta
Particles sent through two consecutive pinholes create concentric rings on screen, as waves do. Particles sent through two adjacent pinholes make stripes perpendicular to line between pinholes on far screen, as waves do. If one slit closes, ring pattern appears. If slits alternate between closed and open, two ring patterns appear. If detector is at one slit, ring pattern appears. If detectors are poor, feeble stripe pattern appears. If half-silvered mirror is after one slit in particle-stream path, and both paths reflect from mirrors, stripe pattern appears.
wave
Particle motions are not single trajectories but diffract, as waves do. Wave theory accounts for all results. Matrix theory can account for results if slits act together to make periodicity.
Paths entangle, so electrons that pass through beam splitter and go past solenoid coil have quantum interference {Aharonov-Bohm effect}, though no electromagnetic field is outside solenoid coil.
Detectors can be after location at which particles must choose which path to take and can turn on after particles pass decision point {delayed-choice experiment} (Wheeler) [1980].
In two-slit experiments (Scully and Drühl) [1982], tagger {quantum eraser} can be in front of each slit to make spin clockwise or counterclockwise along axis. Screen can detect particle location and spin. There is no interference. Waves are present, but they cancel. Before screen, place spin tagger that always results in same spin. There is interference. Waves do not cancel.
down conversion
A photon can become two photons, each with half the energy {down-converter}. In beam-splitter experiments (Scully and Drühl) [1982], a down-converter can be on each path, to make one photon that continues on that path {signal photon} and one photon {idler photon} that is detected {delayed-choice quantum eraser}. Waves do not interfere.
When information about idler photon is random, because idler photon splits and goes on ambiguous paths, waves interfere. Instruments can receive the information before or after signal photons hit, by any amount of time or space. Waves are always present, but they can cancel.
detector
In two-slit experiments, particles make interference pattern when observed. If detector capable of knowing if particle went through left, right, none, or both slits is after slits, and it indicates that each particle goes only through either left or right slit, never both or none, there is no interference pattern.
If detector can operate without affecting particle in any way, and observer observes it, there is still no interference pattern.
If observer does not observe detector, there is interference pattern, even if detector puts the information in memory awhile and then deletes memory. This suggests that just gaining information is enough to end interference [Seager, 1999].
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