Physics

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General

  • https://en.wikipedia.org/wiki/Experimental_physics - disciplines and sub-disciplines in the field of physics that are concerned with the observation of physical phenomena and experiments. Methods vary from discipline to discipline, from simple experiments and observations, such as the Cavendish experiment, to more complicated ones, such as the Large Hadron Collider.



Fields and interactions

a meeeess. still matching fields to excitations




  • https://en.wikipedia.org/wiki/Vacuum_energy - an underlying background energy that exists in space throughout the entire Universe. One contribution to the vacuum energy may be from virtual particles which are thought to be particle pairs that blink into existence and then annihilate in a timespan too short to observe. They are expected to do this everywhere, throughout the Universe. Their behavior is codified in Heisenberg's energy–time uncertainty principle. Still, the exact effect of such fleeting bits of energy is difficult to quantify.

The effects of vacuum energy can be experimentally observed in various phenomena such as spontaneous emission, the Casimir effect and the Lamb shift, and are thought to influence the behavior of the Universe on cosmological scales. Using the upper limit of the cosmological constant, the vacuum energy of free space has been estimated to be 10−9 joules (10−2 ergs) per cubic meter.[1] However, in both quantum electrodynamics (QED) and stochastic electrodynamics (SED), consistency with the principle of Lorentz covariance and with the magnitude of the Planck constant requires it to have a much larger value of 10113 joules per cubic meter. This huge discrepancy is known as the vacuum catastrophe.




  • https://en.wikipedia.org/wiki/Matter_wave - All matter can exhibit wave-like behavior. For example, a beam of electrons can be diffracted just like a beam of light or a water wave. Matter waves are a central part of the theory of quantum mechanics, being an example of wave–particle duality. The concept that matter behaves like a wave is also referred to as the de Broglie hypothesis due to having been proposed by Louis de Broglie in 1924. Matter waves are often referred to as de Broglie waves. The de Broglie wavelength is the wavelength, λ, associated with a massive particle and is related to its momentum, p, through the Planck constant

Wave-like behavior of matter was first experimentally demonstrated by George Paget Thomson's thin metal diffraction experiment, and independently in the Davisson–Germer experiment both using electrons, and it has also been confirmed for other elementary particles, neutral atoms and even molecules. The wave-like behavior of matter is crucial to the modern theory of atomic structure and particle physics.





  • https://en.wikipedia.org/wiki/Phase_velocity - of a wave is the rate at which the phase of the wave propagates in space. This is the velocity at which the phase of any one frequency component of the wave travels. For such a component, any given phase of the wave (for example, the crest) will appear to travel at the phase velocity.



  • https://en.wikipedia.org/wiki/Radiation - The gravitational field and the electromagnetic field are the only two fundamental fields in nature that have infinite range and a corresponding classical low-energy limit, which greatly diminishes and hides their "particle-like" excitations. Albert Einstein in 1905, attributed "particle-like" and discrete exchanges of momenta and energy, characteristic of "field quanta", to the electromagnetic field. Originally, his principal motivation was to explain the thermodynamics of radiation. Although the photoelectric effect and Compton scattering strongly suggest the existence of the photon, it might alternatively be explained by a mere quantization of emission; more definitive evidence of the quantum nature of radiation is now taken up into modern quantum optics as in the antibunching effect.













  • https://en.wikipedia.org/wiki/Quantum_decoherence - the loss of quantum coherence. In quantum mechanics, light particles such as electrons behave like waves and are described by a wavefunction. These waves can interfere, leading to the peculiar behaviour of quantum particles. As long as there exists a definite phase relation between different states, the system is said to be coherent. This coherence is a fundamental property of quantum mechanics, and is necessary for the function of quantum computers. However, when a quantum system is not perfectly isolated, but in contact with its surrounding, the coherence decays with time, a process called quantum decoherence. As a result of this process, the quantum behaviour is lost.

Decoherence was first introduced in 1970 by the German physicist H. Dieter Zeh and has been a subject of active research since the 1980s. Decoherence can be viewed as the loss of information from a system into the environment (often modeled as a heat bath), since every system is loosely coupled with the energetic state of its surroundings. Viewed in isolation, the system's dynamics are non-unitary (although the combined system plus environment evolves in a unitary fashion).[3] Thus the dynamics of the system alone are irreversible. As with any coupling, entanglements are generated between the system and environment. These have the effect of sharing quantum information with—or transferring it to—the surroundings.

Decoherence does not generate actual wave function collapse. It only provides an explanation for the observation of wave function collapse, as the quantum nature of the system "leaks" into the environment. That is, components of the wavefunction are decoupled from a coherent system, and acquire phases from their immediate surroundings. A total superposition of the global or universal wavefunction still exists (and remains coherent at the global level), but its ultimate fate remains an interpretational issue. Specifically, decoherence does not attempt to explain the measurement problem. Rather, decoherence provides an explanation for the transition of the system to a mixture of states that seem to correspond to those states observers perceive. Moreover, our observation tells us that this mixture looks like a proper quantum ensemble in a measurement situation, as we observe that measurements lead to the "realization" of precisely one state in the "ensemble".

Decoherence represents a challenge for the practical realization of quantum computers, since such machines are expected to rely heavily on the undisturbed evolution of quantum coherences. Simply put, they require that coherent states be preserved and that decoherence is managed, in order to actually perform quantum computation.











See also Maths#Category theory




  • https://en.wikipedia.org/wiki/Weinberg%E2%80%93Witten_theorem - proved by Steven Weinberg and Edward Witten, states that massless particles (either composite or elementary) with spin j > 1/2 cannot carry a Lorentz-covariant current, while massless particles with spin j > 1 cannot carry a Lorentz-covariant stress-energy. The theorem is usually interpreted to mean that the graviton (j = 2) cannot be a composite particle in a relativistic quantum field theory.



Spacetime

  • https://en.wikipedia.org/wiki/Spacetime - any mathematical model that combines space and time into a single interwoven continuum. Since 300 BCE, the spacetime of our universe has historically been interpreted from a Euclidean space perspective, which regards space as consisting of three dimensions, and time as consisting of one dimension, the "fourth dimension". By combining space and time into a single manifold called Minkowski space in 1905, physicists have significantly simplified a large number of physical theories, as well as described in a more uniform way the workings of the universe at both the supergalactic and subatomic levels.


  • A rubber sheet can be mapped to a scalar theory of gravity
  • Relativity is a tensor field theory




  • https://en.wikipedia.org/wiki/Theory_of_relativity - or relativity in physics, usually encompasses two theories by Albert Einstein: special relativity and general relativity. (The word relativity can also be used in the context of an older theory, that of Galilean invariance.)
  • http://en.wikipedia.org/wiki/Special_relativity - the accepted physical theory regarding the relationship between space and time. It is based on two postulates: (1) that the laws of physics are invariant (i.e., identical) in all inertial systems (non-accelerating frames of reference); and (2) that the speed of light in a vacuum is the same for all observers, regardless of the motion of the light source. It was originally proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies". The inconsistency of classical mechanics with Maxwell’s equations of electromagnetism led to the development of special relativity, which corrects classical mechanics to handle situations involving motions nearing the speed of light. As of today, special relativity is the most accurate model of motion at any speed. Even so, classical mechanics is still useful (due to its simplicity and high accuracy) as an approximation at small velocities relative to the speed of light.

Special relativity implies a wide range of consequences, which have been experimentally verified including length contraction, time dilation, relativistic mass, mass–energy equivalence, a universal speed limit, and relativity of simultaneity. It has replaced the conventional notion of an absolute universal time with the notion of a time that is dependent on reference frame and spatial position. Rather than an invariant time interval between two events, there is an invariant spacetime interval. Combined with other laws of physics, the two postulates of special relativity predict the equivalence of mass and energy, as expressed in the mass–energy equivalence formula E = mc2, where c is the speed of light in vacuum.

A defining feature of special relativity is the replacement of the Galilean transformations of classical mechanics with the Lorentz transformations. Time and space cannot be defined separately from one another. Rather space and time are interwoven into a single continuum known as spacetime. Events that occur at the same time for one observer could occur at different times for another. The theory is called "special" because it applied the principle of relativity only to the special case of inertial reference frames. Einstein later published a paper on general relativity in 1915 to apply the principle in the general case, that is, to any frame so as to handle general coordinate transformations, and gravitational effects.

As Galilean relativity is now considered an approximation of special relativity valid for low speeds, special relativity is considered an approximation of the theory of general relativity valid for weak gravitational fields. The presence of gravity becomes undetectable at sufficiently small-scale, free-falling conditions. General relativity incorporates noneuclidean geometry, so that the gravitational effects are represented by the geometric curvature of spacetime. Contrarily, special relativity is restricted to flat spacetime. The geometry of spacetime in special relativity is called Minkowski space. A locally Lorentz invariant frame that abides by special relativity can be defined at sufficiently small scales, even in curved spacetime.

Galileo Galilei had already postulated that there is no absolute and well-defined state of rest (no privileged reference frames), a principle now called Galileo's principle of relativity. Einstein extended this principle so that it accounted for the constant speed of light, a phenomenon that had been recently observed in the Michelson–Morley experiment. He also postulated that it holds for all the laws of physics, including both the laws of mechanics and of electrodynamics.


  • http://en.wikipedia.org/wiki/General_relativity - a theory of gravitation that was developed by Albert Einstein between 1907 and 1915, with contributions by many others after 1915. According to general relativity, the observed gravitational attraction between masses results from the warping of space and time by those masses.



  • https://en.wikipedia.org/wiki/Einstein_field_equations - a set of 10 equations in Albert Einstein's general theory of relativity which describe the fundamental interaction of gravitation as a result of spacetime being curved by matter and energy. First published by Einstein in 1915 as a tensor equation, the EFE equate local spacetime curvature (expressed by the Einstein tensor) with the local energy and momentum within that spacetime (expressed by the stress–energy tensor).


  • https://en.wikipedia.org/wiki/Stress%E2%80%93energy_tensor - a tensor quantity in physics that describes the density and flux of energy and momentum in spacetime, generalizing the stress tensor of Newtonian physics. It is an attribute of matter, radiation, and non-gravitational force fields. The stress–energy tensor is the source of the gravitational field in the Einstein field equations of general relativity, just as mass density is the source of such a field in Newtonian gravity.


"Everything, by nature of simply existing, is "moving" at the speed of light (which really has nothing to do with light: more on that later). Yes, that does include you.

"Our understanding of the universe is that the way that we perceive space and time as separate things is, to be frank, wrong. They aren't separate: the universe is made of "spacetime," all one word. A year and a lightyear describe different things in our day to day lives, but from a physicist's point of view, they're actually the exact same thing (depending on what kind of physics you're doing).

"You're (presumably) sitting in your chair right now, which means you're not traveling through space at all. Since you have to travel through spacetime at c (speed of light), though, that means all of your motion is through time."


photons don't know time; time moves at the speed of light.??? v=r or not? ish?


  • https://en.wikipedia.org/wiki/Geodetic_effect - also known as geodetic precession, de Sitter precession or de Sitter effect, represents the effect of the curvature of spacetime, predicted by general relativity, on a vector carried along with an orbiting body. The term geodetic effect has two slightly different meanings as the moving body may be spinning or non-spinning. Non-spinning bodies move in geodesics, whereas spinning bodies move in slightly different orbits. The difference between de Sitter precession and Lense–Thirring precession (frame dragging) is that the de Sitter effect is due simply to the presence of a central mass, whereas Lense–Thirring precession is due to the rotation of the central mass. The total precession is calculated by combining the de Sitter precession with the Lense–Thirring precession.
  • https://en.wikipedia.org/wiki/Geodesic - a generalization of the notion of a "straight line" to "curved spaces". The term "geodesic" comes from geodesy, the science of measuring the size and shape of Earth; in the original sense, a geodesic was the shortest route between two points on the Earth's surface, namely, a segment of a great circle. The term has been generalized to include measurements in much more general mathematical spaces; for example, in graph theory, one might consider a geodesic between two vertices/nodes of a graph.

In the presence of an affine connection, a geodesic is defined to be a curve whose tangent vectors remain parallel if they are transported along it. If this connection is the Levi-Civita connection induced by a Riemannian metric, then the geodesics are (locally) the shortest path between points in the space. Geodesics are of particular importance in general relativity. Timelike geodesics in general relativity describe the motion of free falling test particles.


  • https://en.wikipedia.org/wiki/Geodesics_in_general_relativity - generalizes the notion of a "straight line" to curved spacetime. Importantly, the world line of a particle free from all external, non-gravitational force, is a particular type of geodesic. In other words, a freely moving or falling particle always moves along a geodesic. In general relativity, gravity can be regarded as not a force but a consequence of a curved spacetime geometry where the source of curvature is the stress–energy tensor (representing matter, for instance). Thus, for example, the path of a planet orbiting around a star is the projection of a geodesic of the curved 4-D spacetime geometry around the star onto 3-D space.






  • https://en.wikipedia.org/wiki/Length_contraction - the phenomenon of a decrease in length of an object as measured by an observer who is traveling at any non-zero velocity relative to the object. This contraction (more formally called Lorentz contraction or Lorentz–FitzGerald contraction after Hendrik Lorentz and George Francis FitzGerald) is usually only noticeable at a substantial fraction of the speed of light.




  • https://en.wikipedia.org/wiki/World_line - object is the unique path of that object as it travels through 4-dimensional spacetime. The concept of "world line" is distinguished from the concept of "orbit" or "trajectory" (such as an orbit in space or a trajectory of a truck on a road map) by the time dimension, and typically encompasses a large area of spacetime wherein perceptually straight paths are recalculated to show their (relatively) more absolute position states — to reveal the nature of special relativity or gravitational interactions. The idea of world lines originates in physics and was pioneered by Hermann Minkowski. The term is now most often used in relativity theories


  • https://en.wikipedia.org/wiki/Schwarzschild_metric - also known as the Schwarzschild vacuum or Schwarzschild solution, is the solution to the Einstein field equations that describes the gravitational field outside a spherical mass, on the assumption that the electric charge of the mass, angular momentum of the mass, and universal cosmological constant are all zero. The solution is a useful approximation for describing slowly rotating astronomical objects such as many stars and planets, including Earth and the Sun. The solution is named after Karl Schwarzschild, who first published the solution in 1916.















Energy

to move

  • https://en.wikipedia.org/wiki/Specific_energy - is energy per unit mass. It is used to quantify, for example, stored heat or other thermodynamic properties of substances such as specific internal energy, specific enthalpy, specific Gibbs free energy, and specific Helmholtz free energy. It may also be used for the kinetic energy or potential energy of a body. Specific energy is an intensive property, whereas energy and mass are extensive properties. The SI unit for specific energy is the joule per kilogram (J/kg).
  • https://en.wikipedia.org/wiki/Energy_condition - one of various alternative conditions which can be applied to the matter content of the theory, when it is either not possible or desirable to specify this content explicitly. The hope is then that any reasonable matter theory will satisfy this condition or at least will preserve the condition if it is satisfied by the starting conditions.

In general relativity, energy conditions are often used (and required) in proofs of various important theorems about black holes, such as the no hair theorem or the laws of black hole thermodynamics.


  • https://en.wikipedia.org/wiki/Physical_constant - a physical quantity that is generally believed to be both universal in nature and constant in time. It can be contrasted with a mathematical constant, which is a fixed numerical value, but does not directly involve any physical measurement. There are many physical constants in science, some of the most widely recognized being the speed of light in vacuum c, the gravitational constant G, Planck's constant h, the electric constant ε0, and the elementary charge e. Physical constants can take many dimensional forms: the speed of light signifies a maximum speed limit of the Universe and is expressed dimensionally as length divided by time; while the fine-structure constant α, which characterizes the strength of the electromagnetic interaction, is dimensionless.


  • https://en.wikipedia.org/wiki/Force_carrier - particles that give rise to forces between other particles. These particles are bundles of energy (quanta) of a particular kind of field. There is one kind of field for every species of elementary particle. A force between two particles can be described either as the action of a force field generated by one particle on the other, or in terms of the exchange of virtual force carrier particles between them.


Other


Particles

  • https://en.wikipedia.org/wiki/Elementary_particle - or fundamental particle is a particle whose substructure is unknown, thus it is unknown whether it is composed of other particles. Known elementary particles include the fundamental fermions (quarks, leptons, antiquarks, and antileptons), which generally are "matter particles" and "antimatter particles", as well as the fundamental bosons (gauge bosons and the Higgs boson), which generally are "force particles" that mediate interactions among fermions. A particle containing two or more elementary particles is a composite particle.

Everyday matter is composed of atoms, once presumed to be matter's elementary particles—atom meaning "unable to cut" in Greek—although the atom's existence remained controversial until about 1910, as some leading physicists regarded molecules as mathematical illusions, and matter as ultimately composed of energy. Soon, subatomic constituents of the atom were identified. As the 1930s opened, the electron and the proton had been observed, along with the photon, the particle of electromagnetic radiation. At that time, the recent advent of quantum mechanics was radically altering the conception of particles, as a single particle could seemingly span a field as would a wave, a paradox still eluding satisfactory explanation.

Via quantum theory, protons and neutrons were found to contain quarks—up quarks and down quarks—now considered elementary particles.[1] And within a molecule, the electron's three degrees of freedom (charge, spin, orbital) can separate via wavefunction into three quasiparticles (holon, spinon, orbiton). Yet a free electron—which, not orbiting an atomic nucleus, lacks orbital motion—appears unsplittable and remains regarded as an elementary particle.

Around 1980, an elementary particle's status as indeed elementary—an ultimate constituent of substance—was mostly discarded for a more practical outlook, embodied in particle physics' Standard Model, science's most experimentally successful theory. Many elaborations upon and theories beyond the Standard Model, including the extremely popular supersymmetry, double the number of elementary particles by hypothesizing that each known particle associates with a "shadow" partner far more massive, although all such superpartners remain undiscovered. Meanwhile, an elementary boson mediating gravitation—the graviton—remains hypothetical.






  • https://en.wikipedia.org/wiki/Invariant_mass - rest mass, intrinsic mass, proper mass, or in the case of bound systems simply mass, is a characteristic of the total energy and momentum of an object or a system of objects that is the same in all frames of reference related by Lorentz transformations. If a center of momentum frame exists for the system, then the invariant mass of a system is simply the total energy divided by the speed of light squared. In other reference frames, the energy of the system increases, but system momentum is subtracted from this, so that the invariant mass remains unchanged.

Systems whose four-momentum is a null vector (for example a single photon or many photons moving in exactly the same direction) have zero invariant mass, and are referred to as massless. A physical object or particle moving faster than the speed of light would have space-like four-momenta (such as the hypothesized tachyon), and these do not appear to exist. Any time-like four-momentum possesses a reference frame where the momentum (3-dimensional) is zero, which is a center of momentum frame. In this case, invariant mass is positive and is referred to as the rest mass.



Bosons



Gauge field

The term gauge refers to redundant degrees of freedom in the Lagrangian. The transformations between possible gauges, called gauge transformations, form a Lie group—referred to as the symmetry group or the gauge group of the theory. Associated with any Lie group is the Lie algebra of group generators. For each group generator there necessarily arises a corresponding field (usually a vector field) called the gauge field. Gauge fields are included in the Lagrangian to ensure its invariance under the local group transformations (called gauge invariance). When such a theory is quantized, the quanta of the gauge fields are called gauge bosons. If the symmetry group is non-commutative, the gauge theory is referred to as non-abelian, the usual example being the Yang–Mills theory.

Many powerful theories in physics are described by Lagrangians that are invariant under some symmetry transformation groups. When they are invariant under a transformation identically performed at every point in the spacetime in which the physical processes occur, they are said to have a global symmetry. Local symmetry, the cornerstone of gauge theories, is a stricter constraint. In fact, a global symmetry is just a local symmetry whose group's parameters[clarification needed] are fixed in spacetime.


  • http://www.scholarpedia.org/article/Gauge_invariance - In electrodynamics, the structure of the field equations is such that the electric field E(t,x) and the magnetic field B(t,x) can be expressed in terms of a scalar field A0(t,x) (scalar potential) and a vector field A(t,x) (vector potential). The term gauge invariance refers to the property that a whole class of scalar and vector potentials, related by so-called gauge transformations, describe the same electric and magnetic fields. As a consequence, the dynamics of the electromagnetic fields and the dynamics of a charged system in a electromagnetic background do not depend on the choice of the representative (A0(t,x),A(t,x)) within the appropriate class. The concept of gauge invariance has then been extended to more general theories like, for example, Yang-Mills theories or General Relativity.





Photon (electromagnetic)

has no mass


See also Electronics



  • https://en.wikipedia.org/wiki/Electromagnetic_tensor - or electromagnetic field tensor (sometimes called the field strength tensor, Faraday tensor or Maxwell bivector) is a mathematical object that describes the electromagnetic field in space-time of a physical system. The field tensor was first used after the 4-dimensional tensor formulation of special relativity was introduced by Hermann Minkowski. The tensor allows some physical laws to be written in a very concise form.


  • https://en.wikipedia.org/wiki/Electromagnetic_stress–energy_tensor - the contribution to the stress–energy tensor due to the electromagnetic field. The stress–energy tensor describes the flow of energy and momentum in spacetime. The electromagnetic stress–energy tensor contains the classical Maxwell stress tensor that governs the electromagnetic interactions.





  • https://en.wikipedia.org/wiki/Coulomb's_law - or Coulomb's inverse-square law, is a law of physics describing the electrostatic interaction between electrically charged particles. The law was first published in 1785 by French physicist Charles Augustin de Coulomb and was essential to the development of the theory of electromagnetism. It is analogous to Isaac Newton's inverse-square law of universal gravitation. Coulomb's law can be used to derive Gauss's law, and vice versa. The law has been tested heavily, and all observations have upheld the law's principle.



W+, W− and Z0 bosons


The Z and W particles interact with the recently confirmed Higgs Boson, i.e., have mass.


Gluon (strong field)

The strong interaction is observable at two ranges: on a larger scale (about 1 to 3 femtometers (fm)), it is the force that binds protons and neutrons (nucleons) together to form the nucleus of an atom. On the smaller scale (less than about 0.8 fm, the radius of a nucleon), it is the force (carried by gluons) that holds quarks together to form protons, neutrons, and other hadron particles. In the latter context, it is often known as the color force. The strong force inherently has such a high strength that hadrons bound by the strong force can produce new massive particles. Thus, if hadrons are struck by high-energy particles, they give rise to new hadrons instead of emitting freely moving radiation (gluons). This property of the strong force is called color confinement, and it prevents the free "emission" of the strong force: instead, in practice, jets of massive particles are observed.

Gluons can have eight colour charges so there are eight fields, in contrast to photons which are neutral and so there is only one photon field.


Scalar field

  • https://en.wikipedia.org/wiki/Scalar_field - associates a scalar value to every point in a space. The scalar may either be a mathematical number or a physical quantity. Scalar fields are required to be coordinate-independent, meaning that any two observers using the same units will agree on the value of the scalar field at the same absolute point in space (or spacetime) regardless of their respective points of origin. Examples used in physics include the temperature distribution throughout space, the pressure distribution in a fluid, and spin-zero quantum fields, such as the Higgs field. These fields are the subject of scalar field theory.



Higgs field

"the mass of almost all matter that we are used to is basically independent of the Higgs mechanism. Over 99% of all the mass that we ever interact with is due to the mass of the protons and neutrons in atomic nuclei, and the masses of protons and neutrons, which are in turn made out of very light quarks, is determined by quantum chromodynamics (nuclear strong force interactions), not the Higgs mechanism, which only applies to elementary particles!"

"It's often said that mass bends space-time, but in reality it's more complex than that: energy density bends space-time (and even that is a simplification...). The gravitational field of a massless photon is just as real and extant as the gravitational field of a planet; one is just hugely larger than the other. A photon with 100 Joules of energy has the same gravitational pull as an ecoli bacterium weighing 1 picogram."

"Higgs field interacts with certain fundamental particles (i.e. quarks, electrons) and gives them mass. All particles (even massless ones that never interact with the higgs field) have some energy and gravity acts on energy (not just mass!). So the higgs field give some things more mass which makes gravity affect them more, but gravity affects all things and would even if there was no higgs field."

Fermions

  • https://en.wikipedia.org/wiki/Fermion - any particle characterized by Fermi–Dirac statistics and following the Pauli exclusion principle; fermions include all quarks and leptons, as well as any composite particle made of an odd number of these, such as all baryons and many atoms and nuclei. spin-1⁄2 particle. Composite fermions, such as protons and neutrons, are key building blocks of everyday matter





  • https://en.wikipedia.org/wiki/Spinor - elements of a (complex) vector space that can be associated with Euclidean space. Like geometric vectors and more general tensors, spinors transform linearly when the Euclidean space is subjected to a slight (infinitesimal) rotation. When a sequence of such small rotations is composed (integrated) to form an overall final rotation, however, the resulting spinor transformation depends on which sequence of small rotations was used: unlike vectors and tensors, a spinor transforms to its negative when the space is rotated through a complete turn from 0° to 360° (see picture). This property characterizes spinors. It is also possible to associate a substantially similar notion of spinor to Minkowski space in which case the Lorentz transformations of special relativity play the role of rotations. Spinors were introduced in geometry by Élie Cartan in 1913. In the 1920s physicists discovered that spinors are essential to describe the intrinsic angular momentum, or "spin", of the electron and other subatomic particles.


  • https://en.wikipedia.org/wiki/Spinor_field - particles with spin s are described by 2s-dimensional spinor field, where s is an integer or a half-integer. Fermions are described by spinor field, while bosons by tensor field.
  • https://en.wikipedia.org/wiki/Spin_structure - on an orientable Riemannian manifold (M,g) allows one to define associated spinor bundles, giving rise to the notion of a spinor in differential geometry. Spin structures have wide applications to mathematical physics, in particular to quantum field theory where they are an essential ingredient in the definition of any theory with uncharged fermions. They are also of purely mathematical interest in differential geometry, algebraic topology, and K theory. They form the foundation for spin geometry.
  • https://en.wikipedia.org/wiki/Spinor_bundle - the complex vector bundle associated to the corresponding principal bundle of spin frames over and the spin representation of its structure group on the space of spinors. A section of the spinor bundle is called a spinor field.



Lepton

Quark


  • https://en.wikipedia.org/wiki/Eightfold_way_(physics) - a term coined by American physicist Murray Gell-Mann for a theory organizing subatomic baryons and mesons into octets (alluding to the Noble Eightfold Path of Buddhism). The theory was independently proposed by Israeli physicist Yuval Ne'eman and led to the subsequent development of the quark model. In addition to organizing the mesons and spin -1/2 baryons into an octet, the principles of the Eightfold Way also applied to the spin -3/2 baryons, forming a decuplet. However, one of the particles of this decuplet had never been previously observed. Gell-Mann called this particle the Ω− and predicted in 1962 that it would have a strangeness −3, electric charge −1 and a mass near 1680 MeV/c2. In 1964, a particle closely matching these predictions was discovered[1] by a particle accelerator group at Brookhaven. Gell-Mann received the 1969 Nobel Prize in Physics for his work on the theory of elementary particles.



Composite

Hadron

Baryon
    • https://en.wikipedia.org/wiki/Baryon - a composite subatomic particle made up of three quarks (as distinct from mesons, which are composed of one quark and one antiquark). Baryons and mesons belong to the hadron family of particles, which are the quark-based particles. The name "baryon" comes from the Greek word for "heavy" (βαρύς, barys), because, at the time of their naming, most known elementary particles had lower masses than the baryons.


Meson





Quantum Mechanics

to reorder, merge with above

Quanta is the plural of quantum.



  • Notes: Quantum Mechanics - This short lecture series has two main goals: 1. To introduce you to quantum mechanics at a level necessary for a good understanding of the fundamentals of nuclear magnetic resonance (NMR) and 2. To present the quantum mechanical description of NMR in sufficient detail so that you can understand multiple quantum coherence effects. [16]



  • https://en.wikipedia.org/wiki/Uncertainty_principle - also known as Heisenberg's uncertainty principle, is any of a variety of mathematical inequalities asserting a fundamental limit to the precision with which certain pairs of physical properties of a particle known as complementary variables, such as position x and momentum p, can be known simultaneously. Introduced first in 1927, by the German physicist Werner Heisenberg, it states that the more precisely the position of some particle is determined, the less precisely its momentum can be known, and vice versa.




  • https://en.wikipedia.org/wiki/Quantum_spacetime - a generalization of the usual concept of spacetime in which some variables that ordinarily commute are assumed not to commute and form a different Lie algebra. The choice of that algebra still varies from theory to theory. As a result of this change some variables that are usually continuous may become discrete. Often only such discrete variables are called "quantized"; usage varies. The idea of quantum spacetime was proposed in the early days of quantum theory by Heisenberg and Ivanenko as a way to eliminate infinities from quantum field theory. The germ of the idea passed from Heisenberg to Rudolf Peierls, who noted that electrons in a magnetic field can be regarded as moving in a quantum spaaaaaace-time, and to Robert Oppenheimer, who carried it to Hartland Snyder, who published the first concrete example. Snyder's Lie algebra was made simple by C. N. Yang in the same year.



Interpretations

Copenhagen
  • https://en.wikipedia.org/wiki/Copenhagen_interpretation - a loosely-knit informal collection of axioms or doctrines that attempt to express in quotidian language the mathematical formalism of quantum mechanics. The interpretation was largely devised in the years 1925–1927 by Niels Bohr and Werner Heisenberg. It is fundamental to the Copenhagen interpretation that the results of experiments must be reported in ordinary language, not relying on arcane terminology or words that refer only to clusters of mathematical symbols.
De_Broglie–Bohm


Formulations


Matrix mechanics
  • https://en.wikipedia.org/wiki/Matrix_mechanics - Matrix mechanics was the first conceptually autonomous and logically consistent formulation of quantum mechanics. It extended the Bohr Model by describing how the quantum jumps occur. It did so by interpreting the physical properties of particles as matrices that evolve in time. It is equivalent to the Schrödinger wave formulation of quantum mechanics, and is the basis of Dirac's bra–ket notation for the wave function.
Schrödinger picture
  • https://en.wikipedia.org/wiki/Schrödinger_equation - a partial differential equation that describes how the quantum state of a physical system changes with time. It was formulated in late 1925, and published in 1926, by the Austrian physicist Erwin Schrödinger.

In quantum mechanics, the analogue of Newton's second law of motion is Schrödinger's equation for a quantum system (usually atoms, molecules, and subatomic particles whether free, bound, or localized). It is not a simple algebraic equation, but in general a linear partial differential equation, describing the time-evolution of the system's wave function (also called a "state function").

Solutions to Schrödinger's equation describe not only molecular, atomic, and subatomic systems, but also macroscopic systems, possibly even the whole universe. The Schrödinger equation, in its most general form, is consistent with both classical mechanics and special relativity, but the original formulation by Schrödinger himself was non-relativistic.

Heisenberg picture
  • https://en.wikipedia.org/wiki/Heisenberg_picture - a formulation (largely due to Werner Heisenberg in 1925) of quantum mechanics in which the operators (observables and others) incorporate a dependency on time, but the state vectors are time-independent, an arbitrary fixed basis rigidly underlying the theory.

It stands in contrast to the Schrödinger picture in which the operators are constant, instead, and the states evolve in time. The two pictures only differ by a basis change with respect to time-dependency, which corresponds to the difference between active and passive transformations. The Heisenberg picture is the formulation of matrix mechanics in an arbitrary basis, in which the Hamiltonian is not necessarily diagonal.

Interaction picture
Phase space formulation
Path integral formulation

Quantum Field Theory

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there are only field waveforms, and particles are waveform excitations





  • YouTube: Understanding Quantum Field Theory - Dr. Rodney Brooks, author of "Fields of Color: The theory that escaped Einstein", shows why the answer is quantum field theory. He shows how quantum field theory, so often overlooked or misunderstood, resolves the weirdness of quantum mechanics and the paradoxes of relativity . Once the concepts of quantum field theory are grasped, understanding physics is within anyone's grasp.






  • https://en.wikipedia.org/wiki/False_vacuum - a false vacuum is a metastable sector of space that appears to be a perturbative vacuum, but is unstable due to instanton effects that may tunnel to a lower energy state.


  • https://en.wikipedia.org/wiki/Lagrangian_mechanics - is a re-formulation of classical mechanics using the principle of stationary action (also called the principle of least action, and applies to systems whether or not they conserve energy or momentum, and it provides conditions under which energy, momentum or both are conserved


https://en.wikipedia.org/wiki/Lie_derivative

Quantum electrodynamics

Richard Feynman - 1979 Sir Douglas Robb Memorial Lectures:

Quantum chromodynamics

Standard Model









Statistics

  • https://en.wikipedia.org/wiki/Quantum_statistical_mechanics - a statistical ensemble (probability distribution over possible quantum states) is described by a density operator S, which is a non-negative, self-adjoint, trace-class operator of trace 1 on the Hilbert space H describing the quantum system
  • https://en.wikipedia.org/wiki/Hilbert_space - generalizes the notion of Euclidean space, extends the methods of vector algebra and calculus from the two-dimensional Euclidean plane and three-dimensional space to spaces with any finite or infinite number of dimensions, an abstract vector space possessing the structure of an inner product that allows length and angle to be measured



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  • https://en.wikipedia.org/wiki/Weinberg_angle - a parameter in the Weinberg–Salam theory of the electroweak interaction, part of the standard model of particle physics, and is usually denoted as θW. It is the angle by which spontaneous symmetry breaking rotates the original W0 and B0 vector boson plane, producing as a result the Z0 boson, and the photon. It also gives the relationship between the masses of the W and Z bosons (denoted as mW and mZ).

Ions

  • https://en.wikipedia.org/wiki/Ion - an atom or molecule in which the total number of electrons is not equal to the total number of protons, giving the atom a net positive or negative electrical charge



Matter





  • https://en.wikipedia.org/wiki/Ion - an atom or molecule in which the total number of electrons is not equal to the total number of protons, giving the atom a net positive or negative electrical charge


Quasiparticle



Atomic

http://www.periodictable.com/





Molecular

Cosmology

See also Space




  • https://en.wikipedia.org/wiki/Cosmological_principle - an axiom that embodies the working assumption or premise that the distribution of matter in the universe is homogeneous and isotropic when viewed on a large enough scale, since the forces are expected to act uniformly throughout the universe


  • https://en.wikipedia.org/wiki/Interstellar_cloud - the generic name given to an accumulation of gas, plasma and dust in our and other galaxies. Put differently, an interstellar cloud is a denser-than-average region of the interstellar medium





Quasar

Beyond the Standard Model




  • https://en.wikipedia.org/wiki/Unified_field_theory - occasionally referred to as a uniform field theory, is a type of field theory that allows all that is usually thought of as fundamental forces and elementary particles to be written in terms of a single field. There is no accepted unified field theory, and thus it remains an open line of research. The term was coined by Einstein, who attempted to unify the general theory of relativity with electromagnetism. The "theory of everything" and Grand Unified Theory are closely related to unified field theory, but differ by not requiring the basis of nature to be fields, and often by attempting to explain physical constants of nature.




  • arxiv: Physics in 100 Years - Frank Wilczek. "Here I indulge in wide-ranging speculations on the shape of physics, and technology closely related to physics, over the next one hundred years. Themes include the many faces of unification, the re-imagining of quantum theory, and new forms of engineering on small, intermediate, and large scales." [30]


Georgi-Glashow model

Supersymmetry

String theory

Loop quantum gravity

E8

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