Isolated wavefunctions deterministically calculate future possible states. However, observing a particle measures particle position or momentum, putting particle into a definite phase-space state, and so cancels particle wavefunction {wavefunction collapse} {collapse of wavefunction}| {reduction of wave packet} {wave-packet reduction} {collapse of the wavefunction} {state vector reduction}. Wavefunction collapse is a discontinuity in physics. Collapse is time asymmetric. After observation, particle again has a wavefunction, until the nect observation.
observation and measurement
Observers and measuring instruments are too large to have observable wavefunctions, matter-wave wavelengths, matter-wave frequencies, or energy quanta. Observing and measuring cause particle interaction with a macroscopic system and make a new macroscopic system that includes the particle. Observers and instruments put particle wavefunctions into definite phase-space states {state preparation}, ready for measuring. Macroscopic systems have definite object positions and momenta.
Measuring requires that observer or instrument has definite phase-space state, and particle has definite phase-space state. Observers and instruments measure along one direction and detect particle position, time, momentum, angular momentum, or energy. Therefore, position, time, momentum, angular momentum, or energy observation/measurement operates on particle complex-number wavefunction and transforms it into a position, time, momentum, angular momentum, or energy real positive value. The value is any one of the set of possible different-probability quantum values (operator eigenfunction) described by the observer/instrument/particle wavefunction. State selection is completely random. Measurement results in a single value, not value superpositions or multiple values. The observer/instrument/particle wavefunction collapses to zero {measurement problem}. At measurement, particle phase-space state no longer exists, because particle wavefunction no longer exists.
operators
Measuring wavefunctions mathematically uses linear differential Hermitean operators.
causes
Measurements, absorptions, collisions, electromagnetic forces, and gravitational forces collapse particle wavefunctions. Gravitational effects can be gravitational waves, mass separation changes, gravitational self-energy changes, or fixed-star gravitational-field disturbances. Perhaps, measuring equipment is large and so affects wavefunction drastically (Bohr). Perhaps, collapse is large information gain (Heisenberg).
Perhaps, wavefunction collapse is due to particle and wavefunction properties. Perhaps, previous states have lingering wavefunctions that affect later wavefunctions. Perhaps, Gaussian wavefunction distributions coincide at random. Perhaps, wavefunctions have continual operators. Perhaps, wavefunctions are unstable every billion years {Ghirardi-Rimini-Weber} (GRW), so large masses collapse immediately (Giancarlo Ghirardi, Alberto Rimini, Tullio Weber).
Perhaps, wavefunction collapse is due to quantum mechanics. Perhaps, quantum fluctuations average {quantum averaging} to make definite energy states and space and time. Perhaps, cosmic inflation caused macroscopic-size quantum uncertainty and fluctuations {quantum uncertainty}.
wavefunctions and reality
Are wavefunctions just calculating devices, or do they exist in physical reality? Why do physical laws follow mathematical laws? How does perception relate to physical laws, mathematical laws, and material world? How does wavefunction collapse relate to physical laws, mathematical laws, and material world? How does wavefunction collapse relate to wavefunction time and space changes? How can observation/measurement and wavefunctions unify into a continuous explanation, rather than a discontinuous one?
alternatives: real wavefunctions
Perhaps, classical potential and quantum-mechanical potential both exist, so wavefunction is real. Measuring real wavefunction releases energy, starts wave fluctuations, and collapses wavefunction.
alternatives: undefined and defined states
Perhaps, particles have no wavefunction, so there is no collapse. Instead of wavefunctions, particles have only defined and undefined states. Undefined states can become one defined state. For example, particle density matrices represent possible different-probability physical states. Particle moves from undefined states to one state on the matrix diagonal. However, particles can be in superposed states, which matrices cannot represent. Particles can have only one or two possible states, which matrices cannot represent.
alternatives: subquanta
Perhaps, quantum levels involve even smaller properties, or quantities that cause them. However, particles have no hidden variables and so no subquanta.
alternatives: larger whole
Perhaps, physics has another conservation law about a larger whole. Observers and instruments measure only observable parts, while other parts are not observable. Whole system, observable and not observable, is deterministic, continuous, and time symmetric. For example, objects always travel at light speed, but some are time-like, and some are space-like. However, particles have no hidden variables and so no larger whole.
alternatives: two state vectors
Perhaps, quantum states have two phase-space state vectors, one starting from last wavefunction collapse and going forward in time and the other starting from next wavefunction collapse and going backward in time (Yakir Aharonov, Lev Vaidman, Costa de Beauregard, Paul Werbos) [1989]. Before and after phase-spaces are different. At events, forward-state vector happens first, and then backward-state vector happens. Their vector product makes density matrices, allowing smooth transitions between wavefunctions and collapses. This theory gives same results as quantum mechanics with one state vector. Forward and backward effects allow consistency with general relativity. However, time cannot flow backward, by general relativity.
alternatives: positivism
Perhaps, only measured results count, and wavefunctions are non-measurable things. However, experiments involving primitive measurements demonstrate that quantum state is deterministic and unique, so wavefunctions seem to have reality.
Entangled particle wavefunctions depend on each other, maintain phase relations, and have coherence. In isolated systems with entangled particle wavefunctions, system wavefunction continues to evolve deterministically. In non-isolated systems with entangled particle wavefunctions, measurements, absorptions, collisions, electromagnetic forces, and gravitational forces disturb particles and cause entangled superposed particle states to become independent {decoherence}|. System wavefunctions become non-coherent, and particle waves no longer interfere with each other {decoherent histories}, though observers only know this afterwards. System-state phase-space vector reduces to zero. Each particle is independent and has one position and one momentum.
Non-local large-scale gravitational processes eventually collapse all system wavefunctions {objective reduction}. Particle systems cannot remain isolated, because universe gravitation is at all space points.
For macroscopic systems without observers, macroscopic observation can separate states, so system states are distinct {state distinction principle} {principle of state distinction}.
Entangled particles stay in immediate and direct contact, by sharing the same system wavefunction, over any-size space or time interval {non-locality}|. Changes in one particle immediately affect the other particle, seemingly sending information faster than light speed. Conservation laws hold, because particle travels as fast as information, and same particle can go to both detectors. Perhaps, non-locality is due to quantum-mechanical space and time being discrete, foam-like, and looping.
Particles, energies, fields, and quanta are always in space-time. Physical objects and events happen only in space-time.
Wavefunctions are abstract non-physical mathematical objects that describe possible particle or system states and their probabilities. Particle and particle-system wavefunctions are not physical forces, are not energy exchanges, and are not objects in space-time. Wavefunctions describe all space-time points simultaneously. Waves have wavelength, and so are not about only one point, but all wave points at once. Wavefunctions account for and connect all space points, and so appear infinitely long.
As particles interact (and so form an interacting-particle system), the particle wavefunctions superpose to make a system wavefunction, in which all particle states depend on each other. Because wavefunctions connect all space, particles separated by arbitrary distances have states that affect each other. If one particle changes state, the other particle instantaneously changes state, no matter how far apart in space the particles are, because the system wavefunction (and all waves) collapse at all points simultaneously. Experiments that measure energy and time differences, or momentum and position differences, show that particles can remain entangled over far distances and long times, and that wavefunction collapse immediately affects all system particles, fields, and points, no matter how distant. (Because later times involve new wavefunctions, wavefunction collapse never changes particles at same place at different times.) State-vector reduction seemingly violates the principle that all physical effects must be local interactions, because coordinated changes happen simultaneously at different places.
Particle and system wavefunctions are about particles in indefinite states. Observation of one particle's definite state instantaneously collapses the system wavefunction and puts all system particles in definite states, no matter how far apart they are. No physical force or energy at the other particle causes the definite state, but the no-definite-state simultaneously changes to definite state {action at a distance}. The cause seemingly travels faster than light speed to make an effect. Therefore, the cause is non-physical.
Physical causes and effects must occur at one event in space-time. All physical communications, forces, and energies require local interactions through field-carrying particle exchanges in space-time. Physical interactions can have no action at a distance.
theories
Perhaps, wavefunctions reflect something physical that can account for action at a distance. Perhaps, particles can travel backward in time, from measured position to previous position, to make cause and effect at same space-time point. Perhaps, wavefunctions have retrograde wave components, so particles are always interacting at same space-time point. For example, in double-slit experiments, backward-flowing waves (from detectors to incoming particles) determine particle paths and explain whether wave or particle phenomena appear. However, general relativity does not allow time to flow backward. Furthermore, space-time points cannot have different times simultaneously.
theories: no-space-time
Perhaps, every space-time point touches an abstract outside-space-time structure. Perhaps, quantum foam has no-space-time in it. Perhaps, just as all sphere points touch sphere interior, all space-time points touch a no-space-time interior. By whatever method, every space-time point communicates with all others through no-space-time. No-space-time has no distances or time intervals, so space and time do not matter, and action at a distance can occur.
No-space-time is an abstract mathematical object, just as are quantum-mechanical waves. Perhaps, no-space-time carries quantum-mechanical waves.
Before measurement, particles can be said to be everywhere {Copenhagen interpretation}|, not necessarily close to the observed position. Because particle is everywhere, measured particle is always adjacent to other system particles, so there is no non-locality.
Spin-zero-particle decay can make two entangled coupled spin-1/2 particles, one +1/2 and one -1/2, which have one coherent system wavefunction {Einstein-Podolsky-Rosen experiment} {EPR experiment}. After particle-pair production, one particle always has spin opposite to the first, by conservation of angular momentum, but observation has not yet determined which particle has which spin. If an instrument detects one particle's spin direction and collapses the system wavefunction, the other particle immediately has the opposite spin, even over long distances. Einstein, Podolsky, and Rosen said instantaneous information transmission was impossible, so particles changed to the measured spins when the particles separated. Experiments showed that both particles have no definite spin until measured, so particles had superposed states until measured. By quantum mechanics, neither particle has definite spin-axis direction, so particles have superposition of +1/2 and -1/2 states until measured.
Experimenters must choose direction around which to measure spin and can measure in any direction. If they measure opposite direction, they can observe opposite spin. Therefore, particle production alone does not determine measured spin, and realism does not happen. Measuring system and particle together, as a new system, determine measured spin.
spin detection
If two spin-1/2 particles are in singlet state, three detectors oriented at -120, 0, and +120 degree angles perpendicular to moving-particle path can measure one particle's spin. Probability that both spins have opposite values is cos^2(A/2), where A is angle.
Named things have unique values {nominal level} {level of measurement} {measurement level} {absolute, measurement}. Name and value have one-to-one correspondence. Origin and units do not matter.
Different named things have value differences {interval level}. Affine linear transformations, such as t(m) = c * m + d, where m is value and c and d are constants, maintain differences.
For many named things, values have positions {ordinal level} in order. Monotone increasing transformations maintain order.
Values have ratios {ratio level} {log-interval level}. Power transformations, such as t(m) = c * m^d, where m is value and c and d are constants, maintain ratios. Linear transformations maintain ratio relations.
Interaction with matter collapses wavefunctions {measurement postulate}.
How do wavefunctions, such as electron fields, collapse everywhere simultaneously {quantum mechanical measurement problem}. Collapse is absolute, with no relativity.
Measurements can map directly to object properties {scale, measurement} {measurement scale}. Measurement relations can map directly to object-property relations.
Perhaps, measurement theory needs special prohibitions {superselection rules} on measurements.
For objective measurement, events {observable} must be independent of where or when they happen. Objective measurements cannot be functions of space or time coordinates.
Measurements need reference points, such as x=0, and measurement units, such as meter. By relativity, objective measurements cannot be functions of reference points or units.
Measured state is orthogonal to all other possible states, because if one state happens, others do not. Measured state can be along coordinate {primitive measurement}.
Measurements in systems with no waves, or with waves with no phase differences, can have any order {commuting measurement}. Primitive measurements commute, because they are not about phase, only about yes or no. Measurements in systems with waves and phase differences depend on sequence {non-commuting measurement}. Most measurements do not commute, because they find value or probability.
subjective measurement
In quantum mechanics, time and space are not continuous but have quanta. In phase space, momenta relate to positions, and energies relate to times, so events are functions of space and time coordinates. Because positions and lengths relate to momenta, events are functions of reference points and units. Objective measurement is not possible. Quantum mechanics has only subjective measurement.
interaction
To measure particle size, light must have wavelength less than particle diameter and so high frequency and energy. High energy can change particle momentum. Higher energy increases momentum uncertainty.
To measure particle momentum, light must have low energy, to avoid deflecting particle, and so long wavelength. Longer wavelength increases location uncertainty.
Measuring position requires different-frequency light wave than measuring momentum, so experiments cannot find both position and momentum simultaneously (uncertainty principle).
wavefunction collapse
Measuring disturbs particle and creates a new system of observer, instrument, and particle, with a new wavefunction. At actual measurement, the new system wavefunction collapses to zero. Measuring allows observing only one particle property.
operator
Momentum, energy, angular momentum, space, or time functions {operator, wavefunction} operate on wavefunction to find discrete positive real values (eigenvalue) of momentum, energy, angular momentum, space, or time, which are all possible outcomes, each with probability. Direct measurements project onto space or time coordinate or energy or momentum vector.
Projection operators operate on wavefunction and project onto space or time coordinate, or energy or momentum vector, to give discrete positive real values (eigenvalue) {direct measurement}, which are all possible outcomes, each with probability. Experimenters can know possible measured values and predict probabilities. However, values may be less than quantum sizes and so not measurable. Operators have same dimensions as particle.
Alternatively, experimenters can prepare a quantum system in a known initial state, have particle interact with prepared quantum system, separate particle and prepared quantum system, and then measure quantum-system state {indirect measurement}. Indirect measurements require entangling particle and prepared quantum system, to couple their states. Wavefunction collapse puts quantum system into a state that indirectly determines particle state. Quantum system can have same or more dimensions as particle.
Operators on wavefunctions produce discrete positive real values (eigenvalue) {positive-operator-valued measure} {positive operator-valued measure} (POVM).
Operators {projection operator, measurement} on wavefunctions can project values onto measurement axis.
5-Physics-Quantum Mechanics-Wavefunction
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Date Modified: 2022.0225