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.
Physical Sciences>Physics>Quantum Mechanics>Wavefunction>Collapse>Measurement>Operators
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Date Modified: 2022.0224