What is quantum mechanics?
It is the global zeroth-order solution to quantum electrodynamics—the ideal lowest-order electromagnetic oscillation of the complex interaction inseparable with background radiation with global boundary conditions.
“Ideal” means eigenmode and infinite speed of light. Schrödinger equation (SE) finds the ideal eigenmodes. No gap exists between quantum mechanics and classical physics or quantum field theory. At the atomic and molecular scale, it is a good approximation. It is deterministic. However, considering measurement is interactive, we will have a relative reality (different from nihilism, idealism, and mechanical materialism).
Quantum coherencing
Quantum is a wave (abstract ideal matter-wave) and must be globally coherent.
Decoherence leads to the disappearance of quantum properties. Coherencing leads to the establishment of quantum coherence.
If there are no constraints, the wave propagates freely, as plane wave, or develop eigenmodes. Eigenmodes depend only on frequency (energy). Frequencies with unfavorable coherence situations damp out.
For microscopic electromagnetic systems, eigenmodes are the eigenstates (energy levels) of atoms, molecules, or solids.
The eigenmode establishment requires a certain time related to the size of the system and the propagation speed (period) of the wave. It can take several periods.
Establishing global coherence (coherencing) can appear as interference, resonance, and synchronization.
Any signal (disturbance) has a wide frequency composition (spectrum) in a wave system. With no dissipation, the energy concentrate on the eigenmode due to dispersion and coherence feedback.
The Schrödinger equation is a global equation, the boundary condition is the global coherence restriction, and the wave (frequency, energy) chosen by the boundary condition is the eigenstate. "Solving" the Schrödinger equation is finding the boundary conditions' limitations or selecting the favorable frequencies (energy).
Schrödinger equation holds all the secrets
SE is the core of quantum mechanics formulation. Its physical meaning is not apparent and requires interpretation. However, it is absent in almost all interpretations of quantum mechanics. Schrödinger himself didn't explain it, nor do all textbooks.
Almost all the mysteries of quantum mechanics reside in SE. Analyzing SE gives an intuitive understanding of nearly all quantum phenomena.
SE is a wave diffusion equation in form, not a wave equation. SE is the operator form of the Hamiltonian (energy). It is an identical equation and needs no solution.
"Solving" SE is finding the eigenmodes according to the boundary conditions. The mechanism of the eigenmode formation is globally coherencing, interfering, and damping out of the non-favorable frequencies.
The wave function in the Schrödinger equation is abstract, with only amplitude and no physical dimension. The abstract wave amplitude gives the correct energy density to get the probability of occurrence of local events, which was interpreted as wave-particle duality.
The solution of SE only gives the information of the system, not the quantum (wave).
SE assumes that the wave traveling and interaction propagation speeds are infinite. In an electromagnetic system, it is equivalent to the infinite speed of light (non-relativistic assumption)
Non-relativistic assumption leads to the global nature of the quantum. Any local change leads to instantaneous global changes, or quantum non-locality (quantum entanglement). It is the origin of instantaneous measurement collapse.
The globality of the quantum wave and the boundary conditions lead to quantization (discreteness) of the wave pattern.
Global quantum waves must be globally coherent, which can produce complex interference patterns that depend on global conditions (double-slit interference, quantum eraser)
The fact that constraint global quantum waves lead to quantization hints that if quantization happens, it should be a global mode or a property that emerges in interaction, such as electron spin (not an intrinsic property).
Quantum entanglement -- a trick got everyone
Quantum entanglement is a misnomer.
All Bell experiments can only prove the existence of correlation, not entanglement (interaction, mutual influence, or causality)
There is one way for correlation -- coherence.
Global (nonlocal) coherence is an essential property of any (ideal) waves.
Quanta are waves (matter waves).
Coherence is established (coherencing, interfering, and resonation). The system concentrates energy on the dominant modes (eigenmodes).
The NV centers in diamonds are "entangled" in that they resonate through the connecting optic fiber. Resonance is coherence.
The "entanglement" experiment of polarized light is because the polarizers at both ends reflect light parallel to the polarizers, which becomes the dominant mode of the photon "entanglement" system. Dominant modes vary with polarizer settings, formerly interpreted as incomprehensible "space-like" correlations.
Light is at least an electromagnetic wave, and low-energy photons are not point particles. Because the speed of light is high, quantum entanglement experiments are little magic tricks where dominant modes quickly establish. Even if the distance is significant, as long as the optical path setup ensures the influence of the polarizers at both ends on the "entangled photon generation", the dominant mode can quickly establish. Correlation establishes when the polarizers are in place unless we design the optical path to eliminate the reflection enhancement.
Quantum entanglement is common global coherence.
More on youtube: google “Lei Yian youtube”. Email: yalei@pku.edu.cn
Book: Lei Yian, Liu Yiwen, A Global Approximation Interpretation of Quantum Mechanics, Cambridge Scholars, 2022.