# Standard Model

Elementary particles and their interactions

- relativistic quantum field theories

quantum mechanical system models

classical parameters (fields and many-body systems)

- infinite number of dynamical degrees of freedom

Perturbed quantum field theory

- forces between particles are particles

- force-carrying particles are virtual

— cannot be detected while carrying force (detection imply force not carried)

— not bound states.

Field quanta

- discrete ripples in a field

- "excitation" particles

Particles

- excited states of a field

- field quanta

Electromagnetic field (fundamental natural field)

- "infinite" range

- low-energy "limit"; quantum electrodynamics (James Clerk Maxwell (1864))

- hidden "particle-like" excitation

- discrete momenta and energy exchange; "photon" (1926)

Electromagnetic radiation

— Quantum energies

— Quantum colors

— Quantum spectral intensities

Gravitational field (fundamental natural field)

- "infinite" range

- low-energy "limit"

-hidden "particle-like" excitation

# Quantum mechanics

scientific principles

- behavior of atomic matter

- interactions with atomic energy

Copenhagen interpretation

- system is a wave function, ψ (Heisenberg's function)

- wave function, ψ, changes over time (Schrödinger's equation).

- nature is probabilistic (Max Born's rule) [probability amplitude]

- indeterminate values exist in set of all of the properties of a system during a timeframe (Heisenberg's uncertainty principle)

- matter and energy has wave-particle duality. (Bohr's complementarity principle)

- measuring devices are classical devices (classic properties)

- large systems closely approximate classical descriptions (Bohr's and Heisenberg's correspondence principle)

Quantum mechanics inverse relationships (same particle)

- increase of accuracy of one measure (position of a particle)

- decrease in accuracy another measurement (momentum)

Act of measuring first property perturbs the micro-system with additional energy

Quantum entanglement

- pairs of particles measurement

- property of its entangled twin set also [notwithstanding distance]

# Quantum Field Theory (QFT)

- particle physics

- condensed matter physics

Classical theoretical framework visualisation

- "everything is particles and fields"

— "everything is particles"

— "everything is fields"

# Wavicles

*Wave-particle duality*

Wave and particle property paradox (fundamental property)

- particles and fields

- central concept of quantum mechanics

Concept of complementarity

- phenomenon can be viewed in one way or in another, not both simultaneously

Classical concepts

- aether

- space

- time

Wavicle theory

- classical wave rotation

- local binding energy

Bound rotating wave phenomena

- charge

- relativity

- mass

- gravity

- quantum mechanics

# Quaternion

James Clerk Maxwell once declared that he had been striving all his life to be freed from the yoke of the Cartesian coordinates. He found such an instrument in the Hamiltonian quaternions, the application of which he brilliantly demonstrated in his great treatise on electricity and magnetism. Quaternions are elegant, consistent, concise and uniquely adapted to Euclidean space, but physicists have found them artificial and unnatural to their science, because the square of the quaternionic^{1} vector becomes a negative quantity.

The application of the quaternion analysis developed to the theories of elastic solids, electricity and magnetism, and hydrodynamics. It is almost wholly a translation into quaternion notation of known results: some, however, have endeavored to advance each of the theories chosen in at least one direction - The work designed to make good the following statements : first, that q*uaternions are in such a stage of development as already to justify the practically complete banishment of Cartesian geometry from physical questions of a general nature*; and second, that *quaternions will in physics produce many new results that cannot be produced by the rival and older theory*. Mathematical physicists study quaternions seriously, and it is looked forward to the time when quaternions appear in every physical text-book that assumes the knowledge of elementary plane trigonometry.

As to the estimate of the value of Hamilton's quaternion researches: they constitute a great mathematical. They contain what was long sought after — a veritable extension of algebra to space: not the, for there is more than one. The Cartesian analysis is also an extension of algebra to space, but it is fragmentary and incomplete; whereas the quaternion analysis is the true spherical trigonometry in which the axis of an angle as well as its magnitude is considered.

# String theory

## Superstring theory

# Further reading

*General*

- Weyl, H., & Brose, H. L. (1921). Space, time, matter. New York: Dutton
- Planck, M., Clarke, H. T., & Silberstein, L. (1922). The origin and development of the quantum theory. Oxford: The Clarendon Press.
- Einstein, A., & Lawson, R. W. (1921). http://books.google.com/books?id=gQ8LAAAAYAAJ Relativity: The special and general theory]. New York: Holt
- Clifford, W. K., In Rowe, R. C., & In Pearson, K. (1894). The common sense of the exact sciences. New York: D. Appleton and Co
- William H.F. Christie, The Wavicle: A Rotating Wave Theory of the Electron as a Basic Form of Matter and Its Explanation of Charge, Relativity, Mass, Gravity, and Quantum Mechanics.

*Quaternions*

- Macfarlane, A. (1891). Principles of the algebra of physics. S.l: s.n.
- McAulay, A. (1893). Utility of quaternions in physics. London, New York: Macmillan
- Hime, H. W. L. (1894). Outlines of quaternions. London: Longmans, Green.
- Joly, C. J. (1905). A manual of quaternions. London: Macmillan and Co.
- Macfarlane, A. (1906). Vector analysis and quaternions. New York: J. Wiley & Sons; [etc., etc.
- Chisholm, H. (1910). The encyclopædia britannica: A dictionary of arts, sciences, literature and general information. "Quaternions". Cambridge, Eng: At the University Press.
- Hanson, A. (2005). Visualizing quaternions. San Francisco, Calif: Morgan Kaufmann
- Doing Physics with Quaternions, Sweetser's research of standard physics done using only quaternions, a 4-dimensional division algebra.
- [PDF] Doing Physics with Quaternions - An Overview of Doing Physics with Quaternions.