Particles have finite discrete physical-property values {quantum, quantity} {quanta, quantity}. Physical-property values do not vary over a continuous range but have definite values. For example, particle energies have discrete levels and do not have intermediate energies. Discrete physical-property values differ by an amount.
particle properties
Masses are aggregations of particles and so have quanta. As they change speed, masses add or subtract relativistic mass by quanta. Charges are aggregations of electrons and protons and so have quanta. As they change speed, charges add or subtract relativistic charge by quanta. Colors are aggregations of quark colors and so have quanta. As they change speed, colors add or subtract relativistic color by quanta. Strangenesses are aggregations of strangeness and so have quanta. As they change speed, strangenesses add or subtract relativistic strangeness by quanta.
Photons, gluons, bosons, and gravitons (exchange particles) have discrete energies, momenta, and angular momenta (such as spin). Light does not change frequency or wavelength as it travels in vacuum, or as it encounters other electric charges or magnetic fields. Gluons, bosons, and gravitons do not change as they travel or encounter fields. Therefore, forces, energies, and momenta have quanta.
maximum value
Relativity limits values to below maximum, because only infinite energy can make massive particles reach light speed.
Doppler effect
Because light speed is always constant, light sources moving toward or away change light frequency and wavelength. The change occurs at the source, so light does not change frequency and wavelength. as it travels or as it encounters other electric charges or magnetic fields.
Light travels at constant speed. If wavelength decreases, frequency increases. If wavelength increases, frequency decreases. If object is moving away, Doppler effect makes wavelength increase and frequency decrease. If object is moving closer, Doppler effect makes wavelength decrease and frequency increase. Faster motions make greater Doppler effects.
Time dilation is not about Doppler effect, because light is not clock, and light travels at light speed, not lower speed.
ground-state energy
Particle energies have a minimum value (ground state) above zero, because particles have phase-space waves, and waves propagate and so have minimum motion. Particles must move so they cannot have zero energy. Propagating waves have frequency and wavelength. Waves cannot have zero frequency, so waves have a lowest frequency (fundamental frequency) and so lowest possible energy. Electromagnetic-wave energy is frequency times Planck constant.
Because waves have wavelengths, they have uncertain position. Because waves have frequencies, they have uncertain momentum, and uncertain momentum requires minimum energy (uncertainty principle).
energy levels
Waves with the same phase satisfy the Schrödinger wave equation. Therefore, particles can have phase-space waves with harmonic frequencies. Fundamental-frequency harmonics determine allowed energy levels. See Figure 1. Higher frequencies have more energy.
Adjacent wave frequencies differ by fundamental frequency. The energy quantum varies directly with a function of particle phase-space wave fundamental frequency. As frequencies increase, energy differences decrease.
frequency
Wavefunctions with harmonic frequencies solve wave equation. Waves that solve the wave equation resonate in the system, like standing waves that constructively superpose to have net amplitude. Non-standing waves have zero amplitude. Possible standing waves have harmonic frequencies.
quanta
Particle energies, momenta, orbital and spin angular momenta, masses, forces, fields, velocities, accelerations, orbital radii, orbital periods, orbital frequencies, and properties have discrete levels separated by quanta. See Figure 2.
amplitude
Quantum-mechanical waves have amplitude. For any frequency, amplitude relates to probability that particles currently have that wave frequency.
system size
High-energy systems follow quantum mechanics, but phase-space wave wavelengths are too small to detect, so such systems do not appear to have quanta. Physical systems with very small energy or momentum differences, such as subatomic particles, atoms, and molecules, have measurable phase-space wave wavelengths, and such systems require quanta to describe their behavior correctly. See Figure 3. Some quantum-mechanical systems have large space and time differences.
In quantum mechanics, fields {quantized field} have quanta. Particles are like field singularities, vortexes, or discontinuities.
In quantum mechanics, particle and field quanta are at the lowest reductionist level. There is no subquantum world {subquanta}. Subquanta are smaller than Planck time, distance, charge, and mass. Subquantum interactions occur within Planck time, distance, charge, and mass. At subquantum sizes, space, time, forces, and energies do not exist or are indistinguishable. There is no gravity, electromagnetism, stromg or weak nuclear force, distance, time, or mass.
Particle energy E and particle phase-space wave frequency f (in cycles per second) are directly proportional by constant h {Planck constant}| {Planck's constant}: E = h * f, so h = E / f. Planck constant unit is energy times time, and action in physics is energy times time, so Planck constant is quantum of action {quantum of action} {action quantum}. h = 6.626 * 10^-34 Joule-seconds or 4.136 * 10^-15 eV-s.
Particle momentum p and particle phase-space wave wavelength w are inversely proportional by Planck constant: h = p * w. For light, E = h * f = h * c / w, so h = p * w. Momentum times distance is action in physics.
For angular frequency, radians per second, Planck constant divides by 2 * pi {reduced Planck constant} {Dirac constant} {h-bar}: h-bar = h / (2 * pi). h-bar is the quantum of angular momentum.
In quantum mechanics, phase space includes particle positions and momenta and so includes physical space. Particle systems have phase-space waves that determine probabilities of particle positions and momenta at times. In bounded space regions, such as atoms, molecules, and boxes, particles have resonating phase-space waves, with stationary points at boundaries, whose frequencies are harmonics. For example, a particle in a box has phase-space waves, with stationary points at box walls, which have fundamental frequency, twice fundamental frequency, thrice fundamental frequency, and so on. Phase-space wave frequencies determine energies, so system energies are discrete and in series: E0, E1, E2, and so on. Energy-level differences are quanta that are functions of fundamental frequency.
Because energy has quanta, momentum and angular momentum (including spin) have quanta. Electron experiments have determined the angular-momentum quantum unit to be h-bar / (2)^0.5. Momentum has quantum: h / (phase-space wave wavelength). Energy has quantum: h * (phase-space wave frequency). Electron experiments have determined that action has quanta, so energy times time, and momentum times distance, have quanta.
Because a continuous quantity times a discontinuous quantity would make a continuous quantity, for action to have quanta, time and length must have quanta. The quantum-mechanical uncertainty principle depends on particle-wave properties, relates indeterminacies in particle energy and time (or momentum and position), and so relates energy uncertainty to time uncertainty: dE * dt >= h. In space-time, maximum particle energy is where particle gravity has quantum effects and makes space-time discontinuous: 1.22 * 10^19 GeV. By the uncertainty principle, minimum time is then 10^-43 seconds (and minimum length is 10^-35 meters).
Maximum particle energy, 1.22 * 10^19 GeV, is where gravity has quantum effects and makes space and time discontinuous. Field theory no longer applies. Space is foam-like and loops and distorts, due to spin, and has no dimensionality.
Particles have phase-space waves. Particle momentum varies directly with particle-wave wavelength. Wavelength varies directly with time. Because momentum uncertainty times length uncertainty must be less than Planck constant, by the uncertainty principle, at maximum particle energy, quantum length unit {Planck length} is 1.6 * 10^-33 centimeters (1.6 x 10^-35 meters). Because space-time is no longer continuous, phase-space waves cannot have frequency greater than 10^43 Hz and wavelength less than 10^-35 meters.
Planck length depends on gravity strength and so gravitational constant g, electromagnetism strength and so light speed c, and action quantum Planck constant h: (h-bar * g / c^3)^0.5, where h-bar is Planck constant h divided by (2 times pi). h is the quantum of action, and h-bar is the quantum of angular momentum, so Planck length is the quantum of length. Planck length is distance light travels in Planck time.
Planck area quantum is 10^-66 cm^2. Planck volume quantum is 10^-99 cm^3.
Planck-length-diameter black-hole mass {Planck mass} is 10^-5 gram. Particle gravity has quantum effects and makes space-time discontinuous. Because particles are waves, if position uncertainty equals Planck length, gravity uncertainty is highest. Field theory no longer applies. Space is foam-like, due to spin, and has no dimensionality.
At universe origin or soon after, universe had Planck-length diameter. Space-time was discontinuous. Field theory no longer applies. Space is foam-like, due to spin, and has no dimensionality. When universe grew larger than Planck-length diameter, space became continuous, and temperature {Planck temperature} was 10^32 K.
Maximum particle energy, 1.22 * 10^19 GeV, is where gravity has quantum effects and makes space and time discontinuous. Field theory no longer applies. Time loops and distorts, due to spin, and has no dimensionality.
Particles have phase-space waves. Particle energy varies directly with particle-wave frequency. Frequency varies inversely with time. Because energy uncertainty times time uncertainty must be less than Planck constant, by the uncertainty principle, at maximum particle energy, minimum time unit {Planck time} is 5.391 * 10^-44 seconds. Because space-time is no longer continuous, phase-space waves cannot have frequency greater than 10^43 Hz and wavelength less than 10^-35 meters.
Planck time depends on gravity strength and so gravitational constant g, electromagnetism strength and so light speed c, and action quantum Planck constant h: (h-bar * g / c^5)^0.5, where h-bar is Planck constant h divided by (2 times pi). h is the quantum of action, and h-bar is the quantum of angular momentum, so Planck time is the quantum of time. Planck time is time light travels Planck length.
Time {chronon}| {time quantum} for light to travel (classical) electron radius is 10^-24 seconds.
Event-quantum time intervals {instanton}| are non-linear waves, lasting for one electronic transition or one quantum tunneling.
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Date Modified: 2022.0225