Past events determine, or at least constrain, future events. Because other events are too far away in space-time, only a subset of past events affects an event. In phase spaces, past states determine, or at least constrain, future states {consistent histories}. Because other states are too far away in phase space, only a subset of past states affects a state. In most systems, most states do not affect a future state. In quantum mechanics, systems have an infinite number of different consistent histories, each with a probability. Without quantum mechanics, completely determined systems have one consistent history.
In quantum mechanics, particle-system phase-space states have probabilities. States that do not happen have as much information as states that do happen. In quantum mechanics, because they had probability to happen, states that did not happen {counterfactual, quantum mechanics} can cause physical events/states on the same or other particles, because they collapse the wavefunction without interacting with the particle property/event/state. Measuring for a particle state that does not happen {null measurement} {interaction-free measurement} can gain information about another system particle or state without affecting that particle or state.
Particles simultaneously try all possible phase-space trajectories. Trajectories go directly (direct-channel) or indirectly (cross-channel) from one system energy level to another. The probability that the system reaches an energy level is the sum {sum over paths} {sum over histories} of renormalized path probabilities for direct-channel and cross-channel paths to that energy level.
Because bosons have integer spins, when previously independent identical-state bosons interchange, their wavefunctions stay the same as the other. Bosons have Bose-Einstein statistics. Therefore, interactions can bring two now-interdependent bosons to the same state. In a system, two bosons can be in the same state.
Because fermions have half-unit spins, when previously independent identical-state fermions interchange, their wavefunctions become the negative of the other. Fermions have Fermi-Dirac statistics. Therefore, no interaction can bring two now-interdependent fermions to the same state. In a system, no two fermions can be in the same state {exclusion principle} (Pauli exclusion principle).
To show directly that physics is non-local, measure entangled-electron spins {Bell experiment}. Electrons are indistinguishable. Around any measuring axis, electron spins have only two, clockwise or counterclockwise, angular-momentum states. For systems with zero total angular momentum, one electron has spin +1/2 and the other has spin -1/2. Experimenters can only measure one electron's spin, after wavefunction collapse, so system wavefunction before collapse had both electrons having both spins in superposition. Electrons 1 and 2 have spins along axes x, y, and z. If axes are indistinguishable and electrons combine randomly, states are 1x+2x-, 1x-2x+; 1x+2y-, 1x-2y+; 1x+2z-, 1x-2z+; 1y+2y-, 1y-2y+; 1y+2z-, 1y-2z+; 1z+2z-, 1z-2z+, so 6/12 of states involve x-axis, and 6/12 do not. If axes are distinguishable and electrons combine randomly, states are 1x+2x-, 1x-2x+; 1x+2y-, 1x-2y+; 1x+2z-, 1x-2z+; 1y+2x-, 1y-2x+; 1y+2y-, 1y-2y+; 1y+2z-, 1y-2z+; 1z+2x-, 1z-2x+; 1z+2y-, 1z-2y+; 1z+2z-, 1z-2z+, so 10/18 of states involve x-axis, and 8/18 do not. However, system has equal probability to start with 1x+2x- and 1x-2x+, so 2 x-axis states must be left out, making 9/18 of states involve x-axis, and 9/18 do not. If axes are indistinguishable and electrons entangle, states are xx, xy, xz, yy, yz, zz, so 3/6 of states involve x-axis, and 3/6 do not. If axes are distinguishable and electrons entangle, states are xx, xy, yx, xz, zx, yy, yz, zy, zz, so 5/9 of states involve x-axis, and 4/9 do not. Bell experiment result confirms the last conditions, so, if there are no hidden variables, electrons entangle, and physics is non-local.
In hypothetical experiments with closed boxes, particle decay triggers processes that kill cats {Schrödinger's cat} {Schrödinger cat}. If decay probability is one-half, is cat half-alive and half-dead inside box until observed? Is cat dead when particle decays, observed or not? In which state is cat after event and before observation? Less and less classical objects and events can replace cats, until replacements are quantum events and particle decay triggers a quantum state, so when does quantum-event wavefunction collapse?
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Date Modified: 2022.0225