Modern physics encompasses the twentieth century developments in science that arose from measurements using modern instrumentation showing that nineteenth century, or 'classical' descriptions of nature were not sufficient. The most significant developments were Einstein's general relativity, quantum theory and high energy particle physics. For the most part, relativity and high energy particle physics are not going to be tested on the MCAT, except insofar as a general, superficial sense of those subjects can help contextualize certain aspects of basic nuclear physics or atomic theory. Quantum theory is different. A good sense of the most important discoveries is an essential foundation for general chemistry. There is a lot of overlap between this chapter on Modern Physics and our chemistry chapter, Atomic Theory. While many classical approaches, such as for basic modeling of electrostatic potential energy changes, can be extremely helpful to building intuition for general chemistry, you must keep quantum theory always present to mind because without it there is no way to understand the structure of matter at the atomic and molecular level.

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Conceptual Vocabulary for Modern Physics

Special relativity

Einstein's special theory of relativity not only widened the postulate of relativity but added the second postulate - that all observers will always measure the speed of light to be the same no matter what their state of uniform linear motion is.

Einstein's special theory of relativity not only widened the postulate of relativity but added the second postulate - that all observers will always measure the speed of light to be the same no matter what their state of uniform linear motion is.

Vacuum

A vacuum is a volume of space that is essentially empty of matter, such that its gaseous pressure is much less than standard atmospheric pressure.

A vacuum is a volume of space that is essentially empty of matter, such that its gaseous pressure is much less than standard atmospheric pressure.

Albert Einstein

Albert Einstein (1879 - 1955) was a German-born theoretical physicist. He is best known for his theory of relativity and, specifically, mass-energy equivalence.

Albert Einstein (1879 - 1955) was a German-born theoretical physicist. He is best known for his theory of relativity and, specifically, mass-energy equivalence.

Quantum

Quantum theory is the branch of physics which is based on quantization, which began in 1900 when Max Planck published his theory explaining the emission spectrum of black bodies.

Quantum theory is the branch of physics which is based on quantization, which began in 1900 when Max Planck published his theory explaining the emission spectrum of black bodies.

Principle of relativity

A principle of relativity is a criterion for judging physical theories, stating that they are inadequate if they do not prescribe the exact same laws of physics in certain similar situations.

A principle of relativity is a criterion for judging physical theories, stating that they are inadequate if they do not prescribe the exact same laws of physics in certain similar situations.

Speed of light

The speed of light in vacuum is the speed in a vacuum of anything having zero rest mass.

The speed of light in vacuum is the speed in a vacuum of anything having zero rest mass.

General relativity

General relativity is the geometrical theory of gravitation published by Albert Einstein in 1915-16.

General relativity is the geometrical theory of gravitation published by Albert Einstein in 1915-16.

Black hole

A black hole is a region of space in which the gravitational field is so powerful that nothing can escape after having fallen past the event horizon.

A black hole is a region of space in which the gravitational field is so powerful that nothing can escape after having fallen past the event horizon.

Time dilation

Time dilation is the phenomenon whereby an observer finds that another's clock which is physically identical to their own is ticking at a slower rate as measured by their own clock.

Time dilation is the phenomenon whereby an observer finds that another's clock which is physically identical to their own is ticking at a slower rate as measured by their own clock.

Length contraction

Length contraction, according to the special theory of relativity, is the physical phenomenon of a decrease in length detected by an observer in objects that travel at any non-zero velocity relative to that observer.

Length contraction, according to the special theory of relativity, is the physical phenomenon of a decrease in length detected by an observer in objects that travel at any non-zero velocity relative to that observer.

Planck constant

The Planck constant is a physical constant that is used to describe the sizes of quanta, which plays a central role in the theory of quantum mechanics.

The Planck constant is a physical constant that is used to describe the sizes of quanta, which plays a central role in the theory of quantum mechanics.

Photoelectric effect

The photoelectric effect is a quantum electronic phenomenon in which electrons are emitted from matter after the absorption of energy from electromagnetic radiation.

The photoelectric effect is a quantum electronic phenomenon in which electrons are emitted from matter after the absorption of energy from electromagnetic radiation.

Antiparticle

Corresponding to most kinds of particles is an associated antiparticle with the same mass and opposite charges.

Corresponding to most kinds of particles is an associated antiparticle with the same mass and opposite charges.

Quark

The quark is one of the two basic constituents of matter in particle physics (the other is the lepton).

The quark is one of the two basic constituents of matter in particle physics (the other is the lepton).

Mass-energy equivalence

Mass-energy equivalence is the concept that any mass has an associated energy and vice versa.

Mass-energy equivalence is the concept that any mass has an associated energy and vice versa.

Event horizon

The event horizon is a general term for a boundary in spacetime, such as an area surrounding the black hole, beyond which events cannot affect an outside observer.

The event horizon is a general term for a boundary in spacetime, such as an area surrounding the black hole, beyond which events cannot affect an outside observer.

de Broglie hypothesis

The de Broglie hypothesis is the statement that all matter (any object) has a wave-like nature, in other words, wave-particle duality.

The de Broglie hypothesis is the statement that all matter (any object) has a wave-like nature, in other words, wave-particle duality.

Uncertainty principle

The Heisenberg uncertainty principle gives a lower bound on the product of the standard deviations of position and momentum for a system, implying that it is impossible for a particle to have an arbitrarily well-defined position and momentum simultaneously.

The Heisenberg uncertainty principle gives a lower bound on the product of the standard deviations of position and momentum for a system, implying that it is impossible for a particle to have an arbitrarily well-defined position and momentum simultaneously.

Standard Model

The Standard Model of particle physics is a quantum field theory developed between 1970 and 1973 which describes three of the four known fundamental interactions between the elementary particles that make up all matter.

The Standard Model of particle physics is a quantum field theory developed between 1970 and 1973 which describes three of the four known fundamental interactions between the elementary particles that make up all matter.

Positron

The positron is the antiparticle of the electron.

The positron is the antiparticle of the electron.

Lorentz transformation

The Lorentz transformation converts between two different observers' measurements of space and time in a manner consistent with special relativity, where one observer is in constant motion with respect to the other.

The Lorentz transformation converts between two different observers' measurements of space and time in a manner consistent with special relativity, where one observer is in constant motion with respect to the other.

Relativity of simultaneity

The relativity of simultaneity is the concept that simultaneity is not absolute, but dependent on the observer.

The relativity of simultaneity is the concept that simultaneity is not absolute, but dependent on the observer.

Compton scattering

Compton scattering is the decrease in energy of an X-ray or gamma ray photon, when it interacts with matter.

Compton scattering is the decrease in energy of an X-ray or gamma ray photon, when it interacts with matter.

Luminiferous ether

In the late 19th century, luminiferous ether, meaning light-bearing ether, was the term used to describe a medium for the propagation of light. Today this theory is regarded as a superseded scientific theory.

In the late 19th century, luminiferous ether, meaning light-bearing ether, was the term used to describe a medium for the propagation of light. Today this theory is regarded as a superseded scientific theory.

Planck's law

Planck's law describes the spectral radiance of electromagnetic radiation at all wavelengths from a black body at a certain temperature.

Planck's law describes the spectral radiance of electromagnetic radiation at all wavelengths from a black body at a certain temperature.

Electron diffraction

Electron diffraction is a technique used to study matter by firing electrons at a sample and observing the resulting interference pattern.

Electron diffraction is a technique used to study matter by firing electrons at a sample and observing the resulting interference pattern.

Schrödinger equation

Of central importance in non-relativistic quantum mechanics, the Schrödinger equation describes the space and time dependence of quantum mechanical systems.

Of central importance in non-relativistic quantum mechanics, the Schrödinger equation describes the space and time dependence of quantum mechanical systems.

Elementary particle

An elementary particle or fundamental particle is a particle not known to have substructure; that is, it is not known to be made up of smaller particles.

An elementary particle or fundamental particle is a particle not known to have substructure; that is, it is not known to be made up of smaller particles.

Weak interaction

The weak interaction is one of the four fundamental interactions of nature. It is due to the exchange of the heavy W and Z bosons. Its most familiar effect is beta decay.

The weak interaction is one of the four fundamental interactions of nature. It is due to the exchange of the heavy W and Z bosons. Its most familiar effect is beta decay.

Michelson-Morley experiment

The Michelson-Morley experiment, performed in 1887, is generally considered to be the first strong evidence against the theory of a luminiferous ether.

The Michelson-Morley experiment, performed in 1887, is generally considered to be the first strong evidence against the theory of a luminiferous ether.

Lorentz factor

The Lorentz factor appears in several equations in special relativity, including time dilation, length contraction, and the relativistic mass formula, generally represented with a shorthand symbol.

The Lorentz factor appears in several equations in special relativity, including time dilation, length contraction, and the relativistic mass formula, generally represented with a shorthand symbol.

Proper length

Proper length is an invariant quantity which is the rod distance between spacelike events in a frame of reference in which the events are simultaneous.

Proper length is an invariant quantity which is the rod distance between spacelike events in a frame of reference in which the events are simultaneous.

Proper time

Proper time is time measured by a single clock between events that occur at the same place as the clock.

Proper time is time measured by a single clock between events that occur at the same place as the clock.

Minkowski space

Minkowski spacetime is the mathematical setting in which Einstein's theory of special relativity is most conveniently formulated. In this setting the three ordinary dimensions of space are combined with a single dimension of time to form a four-dimensional manifold.

Minkowski spacetime is the mathematical setting in which Einstein's theory of special relativity is most conveniently formulated. In this setting the three ordinary dimensions of space are combined with a single dimension of time to form a four-dimensional manifold.

World line

The world line of an object is the unique path of that object as it travels through 4-dimensional spacetime.

The world line of an object is the unique path of that object as it travels through 4-dimensional spacetime.

Invariant mass

The invariant or intrinsic mass is a measurement or calculation of the mass of an object that is the same for all frames of reference.

The invariant or intrinsic mass is a measurement or calculation of the mass of an object that is the same for all frames of reference.

Relativistic Doppler effect

The relativistic Doppler effect is the change in frequency of light, caused by the relative motion of the source and the observer, when taking into account effects of the special theory of relativity.

The relativistic Doppler effect is the change in frequency of light, caused by the relative motion of the source and the observer, when taking into account effects of the special theory of relativity.

Work function

The work function is the minimum energy needed to remove an electron from a solid to a point immediately outside the solid surface.

The work function is the minimum energy needed to remove an electron from a solid to a point immediately outside the solid surface.

Light cone

A light cone is the pattern describing the temporal evolution of a flash of light in Minkowski spacetime.

A light cone is the pattern describing the temporal evolution of a flash of light in Minkowski spacetime.

Minkowski diagram

A Minkowski diagram provides an illustration of the properties of space and time in the special theory of relativity, allowing a quantitative understanding of the corresponding phenomena like time dilation and length contraction without mathematical equations.

A Minkowski diagram provides an illustration of the properties of space and time in the special theory of relativity, allowing a quantitative understanding of the corresponding phenomena like time dilation and length contraction without mathematical equations.

Transverse Doppler effect

In special relativity, the transverse Doppler effect is the nominal redshift component associated with transverse observation.

In special relativity, the transverse Doppler effect is the nominal redshift component associated with transverse observation.

Hermann Minkowski

Hermann Minkowski (1864 - 1909) was a Lithuanian-born German mathematician, of Jewish descent, who created and developed geometrical methods to solve difficult problems in number theory, mathematical physics, and the theory of relativity.

Hermann Minkowski (1864 - 1909) was a Lithuanian-born German mathematician, of Jewish descent, who created and developed geometrical methods to solve difficult problems in number theory, mathematical physics, and the theory of relativity.

Einstein field equations

The Einstein field equations are a set of ten equations in the theory of general relativity in which the fundamental force of gravitation is described as a curved spacetime caused by matter and energy.

The Einstein field equations are a set of ten equations in the theory of general relativity in which the fundamental force of gravitation is described as a curved spacetime caused by matter and energy.

Vacuum energy

Vacuum energy is an underlying background energy that exists in space even when devoid of matter.

Vacuum energy is an underlying background energy that exists in space even when devoid of matter.

Geodesic

Geodesics generalize the notion of straight lines to curved spacetime in general relativity.

Geodesics generalize the notion of straight lines to curved spacetime in general relativity.

Gravitational time dilation

Gravitational time dilation is a consequence of Albert Einstein's theories of relativity and related theories which causes time to pass at different rates in regions of a different gravitational potential.

Gravitational time dilation is a consequence of Albert Einstein's theories of relativity and related theories which causes time to pass at different rates in regions of a different gravitational potential.

Gravitational redshift

Gravitational redshift describes how light of a certain wavelength originating from a source placed in a region of stronger gravitational field are found to be of longer wavelength when received by an observer in a region of weaker gravitational field.

Gravitational redshift describes how light of a certain wavelength originating from a source placed in a region of stronger gravitational field are found to be of longer wavelength when received by an observer in a region of weaker gravitational field.

Gravitational lens

A gravitational lens is formed when the light from a very distant, bright source is bent around a massive object, such as a galaxy, between the source object and the observer.

A gravitational lens is formed when the light from a very distant, bright source is bent around a massive object, such as a galaxy, between the source object and the observer.

Gravitational singularity

A gravitational singularity is, approximately, a place where quantities which are used to measure the gravitational field become infinite.

A gravitational singularity is, approximately, a place where quantities which are used to measure the gravitational field become infinite.

Quantization

Quantization is a procedure for constructing a quantum field theory starting from a classical field theory.

Quantization is a procedure for constructing a quantum field theory starting from a classical field theory.

Fermi energy

The Fermi energy is a concept in quantum mechanics referring to the energy of the highest occupied quantum state in a system of fermions at absolute zero temperature.

The Fermi energy is a concept in quantum mechanics referring to the energy of the highest occupied quantum state in a system of fermions at absolute zero temperature.

Ultraviolet catastrophe

The ultraviolet or the Rayleigh-Jeans catastrophe was a false prediction of early 20th century classical physics that an ideal black body at thermal equilibrium will emit radiation with infinite power.

The ultraviolet or the Rayleigh-Jeans catastrophe was a false prediction of early 20th century classical physics that an ideal black body at thermal equilibrium will emit radiation with infinite power.

Compton wavelength

The Compton wavelength can be thought of as a fundamental limitation on measuring the position of a particle, taking quantum mechanics and special relativity into account.

The Compton wavelength can be thought of as a fundamental limitation on measuring the position of a particle, taking quantum mechanics and special relativity into account.

Quantum decoherence

Quantum decoherence is the mechanism by which quantum systems interact with their environments to exhibit probabilistically additive behavior and give the appearance of wavefunction collapse

Quantum decoherence is the mechanism by which quantum systems interact with their environments to exhibit probabilistically additive behavior and give the appearance of wavefunction collapse

Schrödinger's cat

Schrödinger's cat is a seemingly paradoxical thought experiment devised by Erwin Schrödinger that attempts to illustrate the incompleteness of the Copenhagen interpretation when going from subatomic to macroscopic systems.

Schrödinger's cat is a seemingly paradoxical thought experiment devised by Erwin Schrödinger that attempts to illustrate the incompleteness of the Copenhagen interpretation when going from subatomic to macroscopic systems.

Quantum entanglement

Quantum entanglement is a quantum mechanical phenomenon in which the quantum states of two or more objects have to be described with reference to each other, even though the individual objects may be spatially separated.

Quantum entanglement is a quantum mechanical phenomenon in which the quantum states of two or more objects have to be described with reference to each other, even though the individual objects may be spatially separated.

Probability amplitude

A probability amplitude is a complex-valued function that describes an uncertain or unknown quantity such as the position of a particle in the form of a wave function, expressed as a function of position.

A probability amplitude is a complex-valued function that describes an uncertain or unknown quantity such as the position of a particle in the form of a wave function, expressed as a function of position.

Wave packet

A wave packet is an envelope containing an arbitrary number of wave forms. In quantum mechanics this is interpreted to be a probability wave describing the probability that a particle or particles in a particular state will be measured to have a given position or momentum.

A wave packet is an envelope containing an arbitrary number of wave forms. In quantum mechanics this is interpreted to be a probability wave describing the probability that a particle or particles in a particular state will be measured to have a given position or momentum.

Quantum chromodynamics

Quantum chromodynamics is the theory of the strong interaction, a fundamental force describing the interactions of the quarks and gluons found in hadrons such as the proton, neutron or pion.

Quantum chromodynamics is the theory of the strong interaction, a fundamental force describing the interactions of the quarks and gluons found in hadrons such as the proton, neutron or pion.

Color confinement

Color confinement is the physics phenomenon that color charged particles such as quarks cannot be isolated but are confined with other quarks by the strong interaction to form pairs or triplets so that the net color is neutral.

Color confinement is the physics phenomenon that color charged particles such as quarks cannot be isolated but are confined with other quarks by the strong interaction to form pairs or triplets so that the net color is neutral.

Fermion

Fermions are particles with half-integer spin, such as protons and electrons.

Fermions are particles with half-integer spin, such as protons and electrons.

Flavor

Flavor is a quantum number of elementary particles related to their weak interactions.

Flavor is a quantum number of elementary particles related to their weak interactions.

Lepton

A lepton is a fermion that does not experience the strong interaction such as the electron, the muon, and the tau, distinct from the other known family of fermions, the quarks.

A lepton is a fermion that does not experience the strong interaction such as the electron, the muon, and the tau, distinct from the other known family of fermions, the quarks.

Bremsstrahlung

Bremsstrahlung is electromagnetic radiation produced by the acceleration of a charged particle, such as an electron, when deflected by another charged particle, such as an atomic nucleus.

Bremsstrahlung is electromagnetic radiation produced by the acceleration of a charged particle, such as an electron, when deflected by another charged particle, such as an atomic nucleus.

Boson

Distinguished from fermions, which are matter particles, by their integer spin, bosons are force carrier particles such as the photon, for example.

Distinguished from fermions, which are matter particles, by their integer spin, bosons are force carrier particles such as the photon, for example.

Strong interaction

The strong interaction is the fundamental force mediated by gluons, acting upon quarks, antiquarks, and the gluons themselves.

The strong interaction is the fundamental force mediated by gluons, acting upon quarks, antiquarks, and the gluons themselves.

Poincaré group

The Poincaré group is the group of isometries of Minkowski spacetime.

The Poincaré group is the group of isometries of Minkowski spacetime.

Causal spacetime structure

Causal spacetime structure refers to the description of spacetime using curves that describe the temporal relation between events.

Causal spacetime structure refers to the description of spacetime using curves that describe the temporal relation between events.

Lorentz covariant

A physical quantity is said to be Lorentz covariant if it transforms under a given representation of the Lorentz group.

A physical quantity is said to be Lorentz covariant if it transforms under a given representation of the Lorentz group.

Vacuum solution

A vacuum solution is a Lorentzian manifold whose Einstein tensor vanishes identically, so that no matter or non-gravitational fields are present.

A vacuum solution is a Lorentzian manifold whose Einstein tensor vanishes identically, so that no matter or non-gravitational fields are present.

Schwarzschild metric

The Schwarzschild in Einstein's theory of general relativity describes the gravitational field outside a spherical, non-rotating mass such as a non-rotating star, planet, or black hole.

The Schwarzschild in Einstein's theory of general relativity describes the gravitational field outside a spherical, non-rotating mass such as a non-rotating star, planet, or black hole.

Schwarzschild radius

The Schwarzschild radius is a characteristic radius associated with every mass where, if that mass could be compressed to fit within that radius, no known force or degeneracy pressure could stop it from continuing to collapse into a gravitational singularity.

The Schwarzschild radius is a characteristic radius associated with every mass where, if that mass could be compressed to fit within that radius, no known force or degeneracy pressure could stop it from continuing to collapse into a gravitational singularity.

Closed timelike curve

A closed timelike curve is a worldline of a material particle in spacetime that returns to its starting point. If CTCs exist, their existence would seem to imply at least the theoretical possibility of making a time machine.

A closed timelike curve is a worldline of a material particle in spacetime that returns to its starting point. If CTCs exist, their existence would seem to imply at least the theoretical possibility of making a time machine.

Hawking radiation

Hawking radiation is a thermal radiation predicted to be emitted by black holes due to quantum effects.

Hawking radiation is a thermal radiation predicted to be emitted by black holes due to quantum effects.

Micro black hole

A micro black hole, also called a quantum mechanical black hole and inevitably a mini black hole, is simply a tiny black hole for which quantum mechanical effects play an important role.

A micro black hole, also called a quantum mechanical black hole and inevitably a mini black hole, is simply a tiny black hole for which quantum mechanical effects play an important role.

Quantum gravity

Quantum gravity is the field of theoretical physics attempting to unify quantum mechanics with general relativity.

Quantum gravity is the field of theoretical physics attempting to unify quantum mechanics with general relativity.

Supermassive black hole

A supermassive black hole is a black hole with a mass of an order of magnitude between hundreds of thousands and tens of billions of solar masses.

A supermassive black hole is a black hole with a mass of an order of magnitude between hundreds of thousands and tens of billions of solar masses.

Gravitational collapse

Gravitational collapse in astronomy is the inward fall of a massive body under the influence of the force of gravity.

Gravitational collapse in astronomy is the inward fall of a massive body under the influence of the force of gravity.

Einstein ring

A Chwolson ring or Einstein ring is the deformation of the light from a source such as a galaxy or star into a ring through gravitational deflection of the source's light by a lens such as another galaxy, or a black hole.

A Chwolson ring or Einstein ring is the deformation of the light from a source such as a galaxy or star into a ring through gravitational deflection of the source's light by a lens such as another galaxy, or a black hole.

Photon gas

The photon gas is a framework for treating electromagnetic radiation as having many of the same properties of a conventional gas like hydrogen or neon - including pressure, temperature, and entropy.

The photon gas is a framework for treating electromagnetic radiation as having many of the same properties of a conventional gas like hydrogen or neon - including pressure, temperature, and entropy.

Phonon

A phonon is a quantized mode of vibration occurring in a rigid crystal lattice, such as the atomic lattice of a solid.

A phonon is a quantized mode of vibration occurring in a rigid crystal lattice, such as the atomic lattice of a solid.

Quantum field theory

Quantum field theory provides a theoretical framework in which to formulate consistent quantum theories of many-particle systems, especially in situations where particles may be created and destroyed.

Quantum field theory provides a theoretical framework in which to formulate consistent quantum theories of many-particle systems, especially in situations where particles may be created and destroyed.

Davisson-Germer experiment

In the Davisson-Germer experiment, which provided a critically important confirmation of the de Broglie hypothesis, the angular dependence of reflected electron intensity was measured, and was determined to have a predictable diffraction pattern.

In the Davisson-Germer experiment, which provided a critically important confirmation of the de Broglie hypothesis, the angular dependence of reflected electron intensity was measured, and was determined to have a predictable diffraction pattern.

Correspondence principle

The correspondence principle of Bohr and Heisenberg states that the quantum mechanical description of large systems should closely approximate to the classical description.

The correspondence principle of Bohr and Heisenberg states that the quantum mechanical description of large systems should closely approximate to the classical description.

Copenhagen interpretation

The Copenhagen interpretation is a very influential interpretation of quantum mechanics formulated by Niels Bohr and Werner Heisenberg while collaborating around 1927.

The Copenhagen interpretation is a very influential interpretation of quantum mechanics formulated by Niels Bohr and Werner Heisenberg while collaborating around 1927.

Many-worlds interpretation

Viewing history as a many-branched tree where every possible branch is realized, the many-worlds interpretation of quantum mechanics explains the appearance of wavefunction collapse with the mechanism of quantum decoherence.

Viewing history as a many-branched tree where every possible branch is realized, the many-worlds interpretation of quantum mechanics explains the appearance of wavefunction collapse with the mechanism of quantum decoherence.

Perturbation theory

Perturbation theory is a set of approximation schemes for describing a complicated quantum system in terms of a simpler one, starting with a simple system and gradually turning on an additional perturbing Hamiltonian representing a weak disturbance to the system.

Perturbation theory is a set of approximation schemes for describing a complicated quantum system in terms of a simpler one, starting with a simple system and gradually turning on an additional perturbing Hamiltonian representing a weak disturbance to the system.

Asymptotic freedom

Asymptotic freedom is the property of some gauge theories in which the interaction between the particles, such as quarks, becomes arbitrarily weak at ever shorter distances.

Asymptotic freedom is the property of some gauge theories in which the interaction between the particles, such as quarks, becomes arbitrarily weak at ever shorter distances.

Up quark

The up quark is a particle described by the Standard Model theory of physics. It is a first-generation quark with a charge of +(2/3)e. It is the lightest of all quarks.

The up quark is a particle described by the Standard Model theory of physics. It is a first-generation quark with a charge of +(2/3)e. It is the lightest of all quarks.

Down quark

The down quark is a first-generation quark with a charge of -(1/3)e. It is the second-lightest of all quarks. This particle and the up quark are the fundamental constituents of the nucleons

The down quark is a first-generation quark with a charge of -(1/3)e. It is the second-lightest of all quarks. This particle and the up quark are the fundamental constituents of the nucleons

Charm quark

The charm quark is a second-generation quark with a charge of +(2/3)e. It is the third most massive of the quarks, at 1.3 GeV (a bit more than the mass of the proton).

The charm quark is a second-generation quark with a charge of +(2/3)e. It is the third most massive of the quarks, at 1.3 GeV (a bit more than the mass of the proton).

Strange quark

The strange quark is a second-generation quark with a charge of -(1/3)e. It is the third lightest quark after the up and down quarks, with a mass of somewhere between 80 and 130 MeV.

The strange quark is a second-generation quark with a charge of -(1/3)e. It is the third lightest quark after the up and down quarks, with a mass of somewhere between 80 and 130 MeV.

Top quark

The top quark is the third-generation up-type quark with a charge of +(2/3)e. It is by far the most massive of known elementary particles. Its mass is nearly as great as a gold nucleus.

The top quark is the third-generation up-type quark with a charge of +(2/3)e. It is by far the most massive of known elementary particles. Its mass is nearly as great as a gold nucleus.

Bottom quark

The bottom quark is a third-generation quark with a charge of -(1/3)e. This quark possesses a distinctive signature that makes it relatively easy to identify experimentally

The bottom quark is a third-generation quark with a charge of -(1/3)e. This quark possesses a distinctive signature that makes it relatively easy to identify experimentally

Gauge boson

Gauge bosons are bosonic particles which act as carriers of the fundamental forces of nature.

Gauge bosons are bosonic particles which act as carriers of the fundamental forces of nature.

Gauge theory

Gauge theories are a class of physical theories based on the idea that symmetry transformations can be performed locally as well as globally.

Gauge theories are a class of physical theories based on the idea that symmetry transformations can be performed locally as well as globally.

W and Z bosons

The W and Z bosons are the elementary particles that mediate the weak force.

The W and Z bosons are the elementary particles that mediate the weak force.

String theory

String theory is a model of fundamental physics, whose building blocks are one-dimensional extended entities rather than the zero-dimensional point particles that form the basis for the standard model of particle physics.

String theory is a model of fundamental physics, whose building blocks are one-dimensional extended entities rather than the zero-dimensional point particles that form the basis for the standard model of particle physics.

Gluon

Gluons are elementary particles that cause quarks to interact, and are indirectly responsible for the binding of protons and neutrons together in atomic nuclei.

Gluons are elementary particles that cause quarks to interact, and are indirectly responsible for the binding of protons and neutrons together in atomic nuclei.

Baryon

The baryons are the family of subatomic particles which are made of three quarks. The family notably includes the proton and neutron, which make up the atomic nucleus.

The baryons are the family of subatomic particles which are made of three quarks. The family notably includes the proton and neutron, which make up the atomic nucleus.

Fermionic condensate

A fermionic condensate is a superfluid phase formed by fermionic particles at low temperatures.

A fermionic condensate is a superfluid phase formed by fermionic particles at low temperatures.

Trouton-Rankine experiment

The Trouton-Rankine experiment was an experiment designed to measure if the Lorentz-FitzGerald contraction of an object according to one frame produced a measurable effect in the rest frame of the object.

The Trouton-Rankine experiment was an experiment designed to measure if the Lorentz-FitzGerald contraction of an object according to one frame produced a measurable effect in the rest frame of the object.

Einstein tensor

The Einstein tensor is a mathematical entity expressing the curvature of spacetime in the Einstein field equations, thus describing gravitation according to the theory of general relativity.

The Einstein tensor is a mathematical entity expressing the curvature of spacetime in the Einstein field equations, thus describing gravitation according to the theory of general relativity.

Riemannian manifold

A Riemannian manifold is a real differentiable manifold in which each tangent space is equipped with an inner product in a manner which varies smoothly from point to point.

A Riemannian manifold is a real differentiable manifold in which each tangent space is equipped with an inner product in a manner which varies smoothly from point to point.

Hilbert space

The concept of a Hilbert space generalizes the notion of Euclidean space extending methods of vector algebra from the two-dimensional plane and three-dimensional space to infinite-dimensional spaces.

The concept of a Hilbert space generalizes the notion of Euclidean space extending methods of vector algebra from the two-dimensional plane and three-dimensional space to infinite-dimensional spaces.

Einstein-Hilbert action

The Einstein-Hilbert action is a mathematical object that is used to derive Einstein's field equations of general relativity.

The Einstein-Hilbert action is a mathematical object that is used to derive Einstein's field equations of general relativity.

Einstein-Cartan theory

Einstein-Cartan theory in theoretical physics extends general relativity to the problem of spin angular momentum.

Einstein-Cartan theory in theoretical physics extends general relativity to the problem of spin angular momentum.

Gibbons-Hawking-York boundary term

The Gibbons-Hawking-York boundary term is a term that needs to be added to the Einstein-Hilbert action when the underlying spacetime manifold has a boundary.

The Gibbons-Hawking-York boundary term is a term that needs to be added to the Einstein-Hilbert action when the underlying spacetime manifold has a boundary.

Reissner-Nordström metric

The Reissner-Nordström metric is a solution to the Einstein field equations in empty space, which corresponds to the gravitational field of a charged, non-rotating, spherically symmetric body.

The Reissner-Nordström metric is a solution to the Einstein field equations in empty space, which corresponds to the gravitational field of a charged, non-rotating, spherically symmetric body.

Kerr metric

The Kerr metric describes the geometry of spacetime around a rotating massive body in general relativity.

The Kerr metric describes the geometry of spacetime around a rotating massive body in general relativity.

Cauchy horizon

A Cauchy horizon is a light-like boundary of the domain of validity of a Cauchy problem. One side contains closed space-like geodesics and the other side contains closed time-like geodesics.

A Cauchy horizon is a light-like boundary of the domain of validity of a Cauchy problem. One side contains closed space-like geodesics and the other side contains closed time-like geodesics.

Stress-energy tensor

The stress-energy tensor is a tensor quantity in physics that describes the density and flux of energy and momentum in spacetime.

The stress-energy tensor is a tensor quantity in physics that describes the density and flux of energy and momentum in spacetime.

Stellar black hole

A stellar black hole is a black hole formed by the gravitational collapse of a star of three or more solar masses at the end of its lifetime. The process is observed as a supernova explosion or as a gamma ray burst.

A stellar black hole is a black hole formed by the gravitational collapse of a star of three or more solar masses at the end of its lifetime. The process is observed as a supernova explosion or as a gamma ray burst.

No-hair theorem

The no-hair theorem postulates that all black hole solutions of the Einstein-Maxwell equations can be completely characterized by three externally observable classical parameters: mass, electric charge, and angular momentum.

The no-hair theorem postulates that all black hole solutions of the Einstein-Maxwell equations can be completely characterized by three externally observable classical parameters: mass, electric charge, and angular momentum.

Photon sphere

A photon sphere is a spherical region of space where gravity is strong enough that photons of light are forced to travel in orbits.

A photon sphere is a spherical region of space where gravity is strong enough that photons of light are forced to travel in orbits.

Naked singularity

In general relativity, a naked singularity is a theoretically postulated gravitational singularity without an event horizon.

In general relativity, a naked singularity is a theoretically postulated gravitational singularity without an event horizon.

Geodetic effect

The geodetic effect represents the effect of the curvature of spacetime on a spinning, moving body.

The geodetic effect represents the effect of the curvature of spacetime on a spinning, moving body.

Frame-dragging

Frame-dragging is the term for the prediction of general relativity that rotating bodies drag spacetime around themselves.

Frame-dragging is the term for the prediction of general relativity that rotating bodies drag spacetime around themselves.

Klein-Nishina formula

The Klein-Nishina formula provides an accurate prediction of the angular distribution of x-rays and gamma-rays incident upon a single electron.

The Klein-Nishina formula provides an accurate prediction of the angular distribution of x-rays and gamma-rays incident upon a single electron.

Neutron interferometer

A neutron interferometer is a device capable of diffracting neutrons.

A neutron interferometer is a device capable of diffracting neutrons.

Ehrenfest theorem

The Ehrenfest theorem relates the time derivative of the expectation value for a quantum mechanical operator to the commutator of that operator with the Hamiltonian of the system.

The Ehrenfest theorem relates the time derivative of the expectation value for a quantum mechanical operator to the commutator of that operator with the Hamiltonian of the system.

Dirac equation

The Dirac equation is a relativistic quantum mechanical wave equation providing a description of elementary half-spin particles, such as electrons, consistent with both quantum mechanics and special relativity.

The Dirac equation is a relativistic quantum mechanical wave equation providing a description of elementary half-spin particles, such as electrons, consistent with both quantum mechanics and special relativity.

Quantum Monte Carlo

Quantum Monte Carlo is a large class of computer algorithms that simulate quantum systems with the idea of solving the many-body problem.

Quantum Monte Carlo is a large class of computer algorithms that simulate quantum systems with the idea of solving the many-body problem.

Density functional theory

Density functional theory is a quantum mechanical theory used in physics and chemistry to investigate the ground state of many-body systems, in particular atoms, molecules and the condensed phases.

Density functional theory is a quantum mechanical theory used in physics and chemistry to investigate the ground state of many-body systems, in particular atoms, molecules and the condensed phases.

WKB approximation

The WKB approximation is the most familiar example of a semiclassical calculation in quantum mechanics in which the wavefunction is recast as an exponential function, semiclassically expanded, and then either the amplitude or the phase is taken to be slowly changing.

The WKB approximation is the most familiar example of a semiclassical calculation in quantum mechanics in which the wavefunction is recast as an exponential function, semiclassically expanded, and then either the amplitude or the phase is taken to be slowly changing.

Spontaneous parametric down conversion

Spontaneous parametric down-conversion is an important process in quantum optics in which a nonlinear crystal splits incoming photons into pairs of photons of lower energy whose combined energy and momentum are equal to the energy and momentum of the original photon.

Spontaneous parametric down-conversion is an important process in quantum optics in which a nonlinear crystal splits incoming photons into pairs of photons of lower energy whose combined energy and momentum are equal to the energy and momentum of the original photon.

Pauli equation

The Pauli equation is a Schrödinger equation which describes the time evolution of spin 1/2 particles. It is the non-relativistic border case of the Dirac equation and can be used where particles are slow enough that relativistic effects can be neglected.

The Pauli equation is a Schrödinger equation which describes the time evolution of spin 1/2 particles. It is the non-relativistic border case of the Dirac equation and can be used where particles are slow enough that relativistic effects can be neglected.

CP-violation

CP violation is a violation of the postulated symmetry of the laws of physics which plays an important role in theories of cosmology that attempt to explain the dominance of matter over antimatter in the present Universe.

CP violation is a violation of the postulated symmetry of the laws of physics which plays an important role in theories of cosmology that attempt to explain the dominance of matter over antimatter in the present Universe.

Cabibbo-Kobayashi-Maskawa matrix

In the standard model of particle physics the Cabibbo-Kobayashi-Maskawa matrix is a unitary matrix which contains information on the strength of flavour-changing weak decays.

In the standard model of particle physics the Cabibbo-Kobayashi-Maskawa matrix is a unitary matrix which contains information on the strength of flavour-changing weak decays.

QCD matter

Quark or QCD matter refers to any of a number of theorized phases of matter whose degrees of freedom include quarks and gluons, postulated to occur at extremely high temperatures and densities.

Quark or QCD matter refers to any of a number of theorized phases of matter whose degrees of freedom include quarks and gluons, postulated to occur at extremely high temperatures and densities.

Strangelet

A strangelet or strange nugget is a hypothetical object, consisting of a bound state of roughly equal numbers of up, down, and strange quarks.

A strangelet or strange nugget is a hypothetical object, consisting of a bound state of roughly equal numbers of up, down, and strange quarks.

Quarkonium

Quarkonium designates a flavorless meson whose constituents are a quark and its own antiquark.

Quarkonium designates a flavorless meson whose constituents are a quark and its own antiquark.

Muon

The muon is an elementary particle with negative electric charge and a spin of 1/2. It's a mean lifetime of 2.2 microseconds is longer than any other unstable lepton, meson or baryon except for the neutron.

The muon is an elementary particle with negative electric charge and a spin of 1/2. It's a mean lifetime of 2.2 microseconds is longer than any other unstable lepton, meson or baryon except for the neutron.

Glueball

A glueball is a strongly-interacting particle containing no valence quarks. It is composed entirely of gluons. Such a state is possible because gluons carry color charge and experience the strong interaction.

A glueball is a strongly-interacting particle containing no valence quarks. It is composed entirely of gluons. Such a state is possible because gluons carry color charge and experience the strong interaction.

Higgs boson

The Higgs boson, also known as the God particle, is a hypothetical massive scalar elementary particle predicted to exist by the Standard Model of particle physics.

The Higgs boson, also known as the God particle, is a hypothetical massive scalar elementary particle predicted to exist by the Standard Model of particle physics.

Graviton

The graviton is a hypothetical elementary particle that mediates the force of gravity in the framework of quantum field theory.

The graviton is a hypothetical elementary particle that mediates the force of gravity in the framework of quantum field theory.

Hadron

A hadron is any strongly interacting composite subatomic particle such as a baryon (proton or neutron) or meson.

A hadron is any strongly interacting composite subatomic particle such as a baryon (proton or neutron) or meson.

Meson

A meson is a strongly interacting boson, in other words, a hadron with integral spin.

A meson is a strongly interacting boson, in other words, a hadron with integral spin.

Hyperon

A hyperon is any subatomic particle which is a baryon with non-zero strangeness, but with zero charm and zero bottomness.

A hyperon is any subatomic particle which is a baryon with non-zero strangeness, but with zero charm and zero bottomness.

Pion

Pions are the lightest mesons and play an important role in explaining low-energy properties of the strong nuclear force.

Pions are the lightest mesons and play an important role in explaining low-energy properties of the strong nuclear force.

Kaon

A kaon is any one of a group of four mesons distinguished by the fact that they carry a quantum number called strangeness. In the quark model they are understood to contain a single strange quark (or antiquark).

A kaon is any one of a group of four mesons distinguished by the fact that they carry a quantum number called strangeness. In the quark model they are understood to contain a single strange quark (or antiquark).

Deconfinement

Deconfinement refers to a phase of matter in which quarks and gluons are free to move over distances larger than a femtometer.

Deconfinement refers to a phase of matter in which quarks and gluons are free to move over distances larger than a femtometer.

Gluon condensate

The gluon condensate is a non-perturbative property of the QCD vacuum which could be partly responsible for giving masses to certain hadrons.

The gluon condensate is a non-perturbative property of the QCD vacuum which could be partly responsible for giving masses to certain hadrons.