- QM is a theory of interacting particles. The nature of these interactions is described in the Hamiltonian for the system. The evolution of the wavefunction is not in real space but in what is called Hilbert space.
- Two entangled quantum particles must be considered a single system. Theoretically, there’s no upper limit on how many particles can share an entangled state. The condition of nonlocality means that the system you have in front of you can be instantaneously affected by something thousands of miles away. An achievement of nonlocality in high numbers is the goal. The collapse of the wave function is an irreversible nonlinear process.
- Entanglement is an active link. There is nothing dynamic about the connection between the entangled particles, and entanglement is just a correlation expressed as operators. When two photons are entangled, they have precisely opposite momentum. We measure the acceleration of one photon by measuring its position on a CCD. We then know the position of the second photon without measuring it directly. The first measurement collapses the second photon’s wave function. The collapse means that an initially large set of possible measurement outcomes is reduced to a much smaller group.
- Quantum mechanics describes the physical properties of a system. A measurement projects a wave function into the states associated with that measurement (the eigenstates). A pixel position is the set of forms for measuring the quantity position. The chemical bond (two-electron and three-electron) is considered on the assumption that the electrons in a chemical bond can be regarded as being in an entangled quantum state; that is, the chemical bond is seen as a new indivisible particle.
- An algorithm has been provided for calculating the two-electron chemical bond. The inverse of 137.035999 is a dimensionless constant called the fine structure constant. 137 is the value of the Hebrew word Kabbala, which means “to receive wisdom. The strong force is 137 times that of the electromagnetic force over femtometer distances. The strong force drops to zero at about three femtometers. Strong force residuals bind protons and neutrons together in an atom’s nucleus. The gap is generated by complex dynamics inside atoms involving an interaction between the magnetic-dipole spin of an electron and the magnetic field it causes as it moves about the nucleus. A fine-structure constant is simply a number. Something fundamental and complicated is going on in the inner workings of atoms. The world inside an atom is impossibly small; no technological advance will ever open that world to direct observation by humans. Physicists can observe the frequencies of light that enormous collections of atoms emit. What they see is the structure in the light where none should be. For example, they see tiny gaps inside a single band of color. They call it fine structure. The vectors used in quantum mechanics are smaller; they are less than one unit long because physicists draw them to compute probabilities. An atom generates a magnetic field that rotates about its axis like a little star. Its rotational speed is limited to the speed of light. It has a diameter 137 times larger than that of a stationary electron. It has no spatial dimensions that can be measured.
- Protons have the same (but opposite) charge as electrons. Protons attract electrons but repel each other. The quarks, from which protons are made, hold themselves together in protons utilizing a strong force. A proton transfer pulls the protons together to make the atom’s nucleus. When an electron approaches velocities near the speed of light, the Lorentz transformations of Special Relativity kick in. The atom becomes less stable while the electrons take on more mass and momentum—the gravitational force between two electrons is 137.036 times greater than the electrical force. The strong force is 137 times stronger at scale than the electromagnetic force. The speed of light is 137 times greater than the speed of orbiting electrons. The electrons don’t orbit. They move around in a probability distribution.
