Lithium Metal Lattice
Animated rotational perspective of a 3 x 3 x 3 unit-cell lithium metal lattice with opaque electron planes. The electron planes behave as mirror-image negative point charges to the Li+ ions such that the metallic crystal lattice bonding is Coulombic in the same way as that of an ionic compound.

Cl- CH3Cl Bound Complex and Transition State
Dynamic visualization of chloromethane (CH3Cl) receiving a chloride ion to become the Cl-CH3Cl bound complex, then the Cl.CH3.Cl transition state, then back to the bound complex, and once again to chloromethane, releasing a chloride ion.

The Hydrogen Molecular Ion
Animated rotational perspectives of the three-dimensional rendering of the exact solution of the charge-density functions of the hydrogen molecular ion.

Vibration of the Hydrogen Molecular Ion
Animated rotational perspectives of the three-dimensional rendering of the exact solution of the charge-density functions of the vibration of the hydrogen molecular ion.

The Hydrogen Molecule
Animated rotational perspectives of the three-dimensional rendering of the exact solution of the charge-density functions of the hydrogen molecule.

Vibration of the Hydrogen Molecular Ion
Animated rotational perspectives of the three-dimensional rendering of the exact solution of the charge-density functions of the vibration of the hydrogen molecule.

The H3 Molecular Ion
Animated rotational perspectives of the three-dimensional rendering of the exact solution of the charge-density functions of the H3 molecular ion.

The Water Molecule
Animated rotational perspectives of the three-dimensional rendering of the exact solution of the charge-density functions of the water molecule.

Simulation of Water Vapor

The Ammonia Molecule
Animated rotational perspectives of the three-dimensional rendering of the exact solution of the charge-density functions of the ammonia molecule.

The Methane Molecule
Animated rotational perspectives of the three-dimensional rendering of the exact solution of the charge-density functions of the methane molecule.

The Ethane Molecule
Animated rotational perspectives of the three-dimensional rendering of the exact solution of the charge-density functions of the ethane molecule.

The Propane Molecule
Animated rotational perspectives of the three-dimensional rendering of the exact solution of the charge-density functions of the propane molecule.

The Butane Molecule
Animated rotational perspectives of the three-dimensional rendering of the exact solution of the charge-density functions of the butane molecule.

The Carbon Dioxide Molecule (CO2)
Animated rotational perspectives of the three-dimensional rendering of the exact solution of the charge-density functions of the carbon dioxide molecule.

The Nitrogen Dioxide Molecule (NO2)
Animated rotational perspectives of the three-dimensional rendering of the exact solution of the charge-density functions of the nitrogen dioxide molecule.

The Benzene Molecule
Animated rotational perspectives of the three-dimensional rendering of the exact solution of the charge-density functions of the benzene molecule.

The Potassium (K) Atom
A zoom through the potassium atom showing the radii of the unpaired 4s outer electron, the three sets of paired 3p electrons, the paired 3s, three sets of paired 2p, paired 2s, and paired 1s inner electrons and the nucleus as the red solid sphere (electrons to scale, but the nucleus shown much larger than actual).

Hydrogen Molecule Charge-Density Plot (with cutout slice)
The hydrogen molecule is an orbitsphere in prolate spheroidal coordinates, completely surrounding the protons. It's non-uniform charge/current density is maximum at the ends, near the protons. Also view as Interactive Java Figure

Px or Py Orbital
Left and below. Orbitals are surface charge density waves which travel harmonically on the surface; a radial dipole moment makes them unstable. The positive and negative probability lobes of quantum mechanics become low and high electron densities (respectively). Also view as Interactive Java Figure.

High Resolution Px or Py Excited State Orbital
See above. Brightness corresponds to photon field strength.

Photon Absorption to Form a Hydrogen Excited State
See above.

Dx^2-y^2 Orbital.
See above. Also view as Interactive Java Figure

Dxz or Dyz Orbital
See above. Also view as Interactive Java Figure

Larmor Precession of a Hydrogen Atom in a Magnetic Field
Note that the rotation of the atom is several orders of magnitude faster than its revolution.

First Set of Current Loops
Left and below. Current loops rotated about specific axes are used to generate each "component." These components combine to produce the current pattern of the bound electron.

Second Set of Current Loops
See above.

Component One
Left and below. Rotating viewpoints of the "component" current patterns formed by current loops rotated about specific axes. The components are steps in the generation of the Orbitsphere Current Vector Field.

Component Two
See above.

High-Resolution Component
See above.

Point Motion - View A
Left and below. Synchronized motion of point-charges on the surface of each component.

Point Motion - View B
See above.

Sweep of Angular Momentum Vector of First Component
This animation follows the position of the angular momentum vector as two current loops are rotated about an axis to generate the first component. The resultant vector is the static sum of these rotations.

The Orbitsphere Current Vector Field
Complete coverage of the sphere is evident when both components are combined (note: this is not the final uniform function). Also view as Interactive Java Figure.

Point Motion of the Orbitsphere Current Vector Field
Synchronized motion of point-charges on the surface. See above.

Component Wobble to Generate Uniform Distribution
Wobble of a component as it is convolved about an axis to generate a uniform distribution.

Component Convolution
Formation of the uniform distribution from a component.

Uniform Current Pattern of the Bound Electron
A rotating viewpoint of (a 144-line-approximation to) the current pattern formed by convolving a component about an axis. All loops fall along great circles; patterns of convergence produce latitudinal loops. Also view as Interactive Java Figure.

High Resolution Uniform Current Pattern of the Bound Electron
See above.

The Neutron Charge Density Function
Shown in its inertial frame with positive and negative charge-density proportional to red intensity and blue intensity, respectively. The neutron is comprised of a linear combination of three orthogonal quarks, up, down, and down, of charge +2/3 e, -1/3 e, and -1/3 e, respectively, that form a two-dimensional spherical shell of charge having a radius of the Compton wavelength of the neutron. The quarks have the properties of an energy-to-matter transition state and spin about the z-axis with the centrifugal force of each quark balanced by the electric field of its gluon, a heavy photon, that is phase-locked to the spinning quark and inseparable from it.

The Neutron Mass Density Function
The neutron mass-density function in its inertial frame shown with the low and high mass-density proportional to red intensity and blue intensity, respectively. The neutron is comprised of a linear combination of three orthogonal quarks, up, down, and down, of equal mass, (1/3)*(Mn/(2*Pi)), that form a two-dimensional spherical shell of mass having a radius of the Compton wavelength of the neutron. The quarks which have the properties of an energy-to-matter transition state and spin about the z-axis with the centrifugal force of each quark balanced by the electric field of its gluon, a heavy photon, each of mass Mn(1-1/(2*Pi)), that is phase-locked to the spinning quark and inseparable from it. The brightness corresponds to the intensity of the two-dimensional radial gluon field.

The Proton Charge Density Function
Shown in its inertial frame with positive and negative charge-density proportional to red intensity and blue intensity, respectively. The proton is comprised of a linear combination of three orthogonal quarks, up, up, and down, of charge +2/3 e, +2/3 e, and -1/3 e, respectively, that form a two-dimensional spherical shell of charge having a radius of the Compton wavelength of the proton. The quarks have the properties of an energy-to-matter transition state and spin about the z-axis with the centrifugal force of each quark balanced by the electric field of its gluon, a heavy photon, that is phase-locked to the spinning quark and inseparable from it.

The Proton Mass Density Function
Shown in its inertial frame with the low and high mass-density proportional to red intensity and blue intensity, respectively. The proton is comprised of a linear combination of three orthogonal quarks, up, up, and down, of equal mass, (1/3)*(Mp/(2*Pi)), that form a two-dimensional spherical shell of mass having a radius of the Compton wavelength of the proton. The quarks have the properties of an energy-to-matter transition state and spin about the z-axis with the centrifugal force of each quark balanced by the electric field of its gluon, a heavy photon, each of mass Mp(1-1/(2*Pi)), that is phase-locked to the spinning quark and inseparable from it. The brightness corresponds to the intensity of the two-dimensional radial gluon field.

The Free Electron
Rotating view of the free electron: a disk of moving charge in the plane perpendicular to its angular momentum axis. The angular velocity of each point is constant on the disk; however the charge and current magnitude fall to zero at the edge of the disk. Also view as Interactive Java Figure.

The Precession of the Free Electron in a Magnetic Field
The angular momentum vector of the electron is shown in black.

Electron Ionization
The electron exists as a spherical shell when bound to the atom, and as a planar disk when ionized.

Convolution of the Free Electron in a Magnetic Field
Time-averaged, the quickly wobbling free electron in a magnetic field forms a pattern identical to a “component” for each radius. The spin-flip transition forms the uniform pattern for each radius.

Classical Electron Diffraction
Simulation of the double-slit experiment with electrons. As the electron passes through the slits, it absorbs and emits photons, interacting with both slits. The photon far field pattern of the two-slit shape is imprinted on the electron beam pattern.

Top View Detail of Classical Electron Diffraction
See above.

Classical Photon Diffraction
Simulation of the double-slit experiment with photons. The impinging photon's electric and magnetic fields give rise to currents at both slits (blue). The currents then reemit the photon, and the variation of intensity in the far field is due to the conservation of angular momentum of the source currents. (There is no constructive or destructive interference of electromagnetic fields.) For more details see Chapter 8.

Photon Absorption to Form an Excited State Electron Bubble in Superfluid Helium
Free electrons may be trapped as hollow bubbles in superfluid helium. The surrounding helium atoms maintain the bubble through Van der Waals forces at a fixed initial radius. The bubble may act as a resonator cavity to absorb certain frequencies of photons, resulting in long-lived metastable states wherein the electron radii are 1/integer times that of the initial radius. Applying an electric field causes the electrons to migrate, and the radius of the bubble influences its mobility through the fluid. (Note that angular velocity of the excited state orbital has been dramatically reduced for visual purposes.) More details...

Linearly Polarized Photon
Spinning viewpoint of the electric and magnetic vector field (e&mvf) of a single linearly polarized photon. Also view as Interactive Java Figure.

Simulation of Pair Production
A linearly polarized photon of energy 1.02 MeV comprising the superposition of two oppositely circularly-polarized photons collides with a third body such as a proton. The photon transforms into a transition state intermediate between matter and energy, then forms a two-dimensional spherical shell with twice the mass of the electron and with the same radius as the photon, the electron Compton-wavelength bar. The shell comprises the superposition of the positron and the electron of opposite charges and each having h-bar of total angular momentum. This transition state ionizes, and the free particles propagate in different directions with linear momentum conserved. 

Formation and Annihilation of Positronium
A free positron and electron are mutually attracted by the Coulombic force. A positron and an electron form a bound state called positronium that exists as a two-dimensional spherical shell of twice the mass of the electron with a radius of twice the Bohr radius. The particle provides the central force for the antiparticle. The shell comprises the superposition of the positron and the electron of opposite charges and each having h-bar of total angular momentum. Transitions between ortho and para magnetic states may occur. The pair transforms into a transition state intermediate between matter and energy. The annihilation is complete as two oppositely circularly-polarized photons each of 510 keV and having a radius of twice the electron Compton-wavelength bar (not to scale) propagate in opposite directions.

Right-Hand-Circularly-Polarized Photon
A surface rendering of the electric field lines of a right-handed circularly polarized photon e&mvf as seen along the axis of propagation as it passes a fixed point in the lab frame. The axis of propagation in the animation is vertical. Also see Interactive Java Figure of the vectors that form the surface.

Neutrino Function
A surface rendering of the electric field lines of a neutrino e&mvf as seen along the axis of propagation as it passes a fixed point in the lab frame. The axis of propagation in the animation is vertical. (Thumbnail on left is top view.)

Aspect Experiment (A)
The polarization correlation (coincidence count rate) of visible photons emitted in a two-photon- calcium-atomic cascade from a state pumped using two lasers are measured using independently rotated polarizers. The exactly-correlated photons are both transmitted when the mutually aligned polarizers are aligned sufficiently with each photon's optical axis to cause a coincidence count. 

Aspect Experiment (B)
See above. The exactly correlated photons are both blocked when the mutually aligned polarizers are aligned sufficiently perpendicular to each photon's optical axis to cause the absence of a coincidence count.

Expansion of Spacetime as Matter is Converted to Energy in a Star
The conversion of matter into energy causes spacetime, and thus the universe, to expand, since light has inertial but no gravitational mass. The acceleration of the expansion of the presently observed universe was predicted by Mills in 1995 and has since been confirmed experimentally.

Expansion and Contraction of the Universe
External view of the evolution of the cosmos as a function of time, showing the expansion and contraction cycle over a thousand-billion years. Expansion is due to the conversion of matter into energy in stars, and contraction is due to the conversion of energy to matter.

Animations  |  Interactive Book Figures