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.

Spacetime and fields

  • 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/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".[1] 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,[5] 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.

"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."


  • 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/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.






photons don't know time; time moves at the speed of light.

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.

Forces



  • https://en.wikipedia.org/wiki/Stress–energy_tensor - sometimes stress–energy–momentum tensor or energy–momentum tensor) is 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.


  • 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.


Electromagnetism

See also Electronics





  • 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.


Strong nuclear

Weak nuclear

Gravity

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



Other

Quantum Mechanics

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  • 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. [7]


  • 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 spaaaaaace formulation
Path integral formulation

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Quantum Field Theory

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there are no particles, only fields





  • 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


  • 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.




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



Particles

Mass

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."

Bosons

  • 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.



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






Atomic

Radiation
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


Accelerators

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

String theory

Other




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