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String theory

String theory is a model of fundamental physics whose building blocks are one-dimensional extended objects called strings, rather than the zero-dimensional point particles that form the basis for the Standard Model of particle physics. The phrase is often used as shorthand for Superstring theory, as well as related theories such as M-theory. String theorists are attempting to adjust the Standard Model by removing the assumption in quantum mechanics that particles are point-like. By removing this assumption and replacing the point-like particles with strings, it appears that a sensible quantum theory of gravity naturally emerges. Moreover, string theory may be able to “unify” the known natural forces (gravitational, electromagnetic, weak nuclear and strong nuclear) by describing them with the same set of equations. (See Theory of everything)

Very few avenues for experimental verification of the theory have been claimed.[1] With the construction of the Large Hadron Collider in CERN some scientists hope to produce relevant data. However, it is generally expected that any theory of quantum gravity would require much higher energies to probe.

There are different versions of string theory, depending on factors such as whether or not supersymmetry is incorporated into the formulation. These versions are thought to be related to each other as different limits of one theory, coined M-theory. However, there is a huge number of possible solutions to string theory as it is currently understood.[2] Thus it has been claimed by some scientists that string theory may not be falsifiable and may have no predictive power.[3][4][5][6]

Studies of string theory have revealed that it predicts higher-dimensional objects called branes. String theory strongly suggests the existence of ten or eleven (in M-theory[7]) spacetime dimensions, as opposed to the usual four (three spatial and one temporal) used in relativity theory; however the theory can describe universes with four effective (observable) spacetime dimensions by a variety of methods.

An important branch of the field is dealing with a conjectured duality between string theory as a theory of gravity and gauge theory. It is hoped that research in this direction will lead to new insights on quantum chromodynamics, the fundamental theory of strong nuclear force. This direction of research has better hopes to make contact with experiment, compared to string theory as a quantum theory of gravity,[8][9][10][11] though currently the alternative, Lattice QCD, is doing a much better job and has already made contact with experiments at various fields with good results [12], though the computations are numerical rather than analytic.

The basic idea behind all string theories is that the constituents of reality are strings of extremely small size (possibly of the order of the Planck length, about 10−35 m) which vibrate at specific resonant frequencies.[13] Thus, any particle should be thought of as a tiny vibrating object, rather than as a point. This object can vibrate in different modes (just as a guitar string can produce different notes), with every mode appearing as a different particle (electron, photon, etc.). Strings can split and combine, which would appear as particles emitting and absorbing other particles, presumably giving rise to the known interactions between particles.

In addition to strings, this theory also includes objects of higher dimensions, such as D-branes and NS-branes. Furthermore, all string theories predict the existence of degrees of freedom which are usually described as extra dimensions. String theory is thought to include some 10, 11, or 26 dimensions, depending on the specific theory and on the point of view.

Interest in string theory is driven largely by the hope that it will prove to be a consistent theory of quantum gravity or even a theory of everything. It can also naturally describe interactions similar to electromagnetism and the other forces of nature. Superstring theories include fermions, the building blocks of matter, and incorporate supersymmetry, a conjectured (but unobserved) symmetry of nature. It is not yet known whether string theory will be able to describe a universe with the precise collection of forces and particles that is observed, nor how much freedom the theory allows to choose those details.

String theory as a whole has not yet made falsifiable predictions that would allow it to be experimentally tested, though various planned observations and experiments could confirm some essential aspects of the theory, such as supersymmetry and extra dimensions. In addition, the full theory is not yet understood. For example, the theory does not yet have a satisfactory definition outside of perturbation theory; the quantum mechanics of branes (higher dimensional objects than strings) is not understood; the behavior of string theory in cosmological settings (time-dependent backgrounds) is still being worked out; finally, the principle by which string theory selects its vacuum state is a hotly contested topic (see string theory landscape).

String theory is thought to be a certain limit of another, more fundamental theory - M-theory - which is only partly defined and is not well understood.[14]

Quantum

The word “quantum” (Latin, “how much”) in quantum mechanics refers to a discrete unit that quantum theory assigns to certain physical quantities, such as the energy of an atom at rest (see Figure 1, at right). The discovery that waves have discrete energy packets (called quanta) that behave in a manner similar to particles led to the branch of physics that deals with atomic and subatomic systems which we today call Quantum Mechanics. It is the underlying mathematical framework of many fields of physics and chemistry, including condensed matter physics, solid-state physics, atomic physics, molecular physics, computational chemistry, quantum chemistry, particle physics, and nuclear physics. The foundations of quantum mechanics were established during the first half of the twentieth century by Werner Heisenberg, Max Planck, Louis de Broglie, Niels Bohr, Erwin Schrödinger, Max Born, John von Neumann, Paul Dirac, Wolfgang Pauli and others. Some fundamental aspects of the theory are still actively studied.

It is necessary to use quantum mechanics to understand the behavior of systems at atomic length scales and smaller. For example, if Newtonian mechanics governed the workings of an atom, electrons would rapidly travel towards and collide with the nucleus. However, in the natural world the electrons normally remain in an unknown orbital path around the nucleus, defying classical electromagnetism.

Quantum mechanics was initially developed to explain the atom, especially the spectra of light emitted by different atomic species. The quantum theory of the atom developed as an explanation for the electron’s staying in its orbital, which could not be explained by Newton’s laws of motion and by Maxwell’s laws of classical electromagnetism.

In the formalism of quantum mechanics, the state of a system at a given time is described by a complex wave function (sometimes referred to as orbitals in the case of atomic electrons), and more generally, elements of a complex vector space. This abstract mathematical object allows for the calculation of probabilities of outcomes of concrete experiments. For example, it allows one to compute the probability of finding an electron in a particular region around the nucleus at a particular time. Contrary to classical mechanics, one cannot ever make simultaneous predictions of conjugate variables, such as position and momentum, with arbitrary accuracy. For instance, electrons may be considered to be located somewhere within a region of space, but with their exact positions being unknown. Contours of constant probability, often referred to as “clouds” may be drawn around the nucleus of an atom to conceptualize where the electron might be located with the most probability. It should be stressed that the electron itself is not spread out over such cloud regions. It is either in a particular region of space, or it is not. Heisenberg’s uncertainty principle quantifies the inability to precisely locate the particle.

The other exemplar that led to quantum mechanics was the study of electromagnetic waves such as light. When it was found in 1900 by Max Planck that the energy of waves could be described as consisting of small packets or quanta, Albert Einstein exploited this idea to show that an electromagnetic wave such as light could be described by a particle called the photon with a discrete energy dependent on its frequency. This led to a theory of unity between subatomic particles and electromagnetic waves called wave-particle duality in which particles and waves were neither one nor the other, but had certain properties of both. While quantum mechanics describes the world of the very small, it also is needed to explain certain “macroscopic quantum systems” such as superconductors and superfluids.

Broadly speaking, quantum mechanics incorporates four classes of phenomena that classical physics cannot account for: (i) the quantization (discretization) of certain physical quantities, (ii) wave-particle duality, (iii) the uncertainty principle, and (iv) quantum entanglement. Each of these phenomena will be described in greater detail in subsequent sections.

Theory

There are numerous mathematically equivalent formulations of quantum mechanics. One of the oldest and most commonly used formulations is the transformation theory invented by Cambridge theoretical physicist Paul Dirac, which unifies and generalizes the two earliest formulations of quantum mechanics, matrix mechanics (invented by Werner Heisenberg)[2] and wave mechanics (invented by Erwin Schrödinger).

In this formulation, the instantaneous state of a quantum system encodes the probabilities of its measurable properties, or “observables”. Examples of observables include energy, position, momentum, and angular momentum. Observables can be either continuous (e.g., the position of a particle) or discrete (e.g., the energy of an electron bound to a hydrogen atom).

Generally, quantum mechanics does not assign definite values to observables. Instead, it makes predictions about probability distributions; that is, the probability of obtaining each of the possible outcomes from measuring an observable. Naturally, these probabilities will depend on the quantum state at the instant of the measurement. There are, however, certain states that are associated with a definite value of a particular observable. These are known as “eigenstates” of the observable (”eigen” meaning “own” in German). In the everyday world, it is natural and intuitive to think of everything being in an eigenstate of every observable. Everything appears to have a definite position, a definite momentum, and a definite time of occurrence. However, quantum mechanics does not pinpoint the exact values for the position or momentum of a certain particle in a given space in a finite time, but, rather, it only provides a range of probabilities of where that particle might be. Therefore, it became necessary to use different words for (a) the state of something having an uncertainty relation and (b) a state that has a definite value. The latter is called the “eigenstate” of the property being measured.

For example, consider a free particle. In quantum mechanics, there is wave-particle duality so the properties of the particle can be described as a wave. Therefore, its quantum state can be represented as a wave, of arbitrary shape and extending over all of space, called a wavefunction. The position and momentum of the particle are observables. The Uncertainty Principle of quantum mechanics states that both the position and the momentum cannot simultaneously be known with infinite precision at the same time. However, one can measure just the position alone of a moving free particle creating an eigenstate of position with a wavefunction that is very large at a particular position x, and zero everywhere else. If one performs a position measurement on such a wavefunction, the result x will be obtained with 100% probability. In other words, the position of the free particle will be known. This is called an eigenstate of position. If the particle is in an eigenstate of position then its momentum is completely unknown. An eigenstate of momentum, on the other hand, has the form of a plane wave. It can be shown that the wavelength is equal to h/p, where h is Planck’s constant and p is the momentum of the eigenstate. If the particle is in an eigenstate of momentum then its position is completely blurred out.

Usually, a system will not be in an eigenstate of whatever observable we are interested in. However, if one measures the observable, the wavefunction will instantaneously be an eigenstate of that observable. This process is known as wavefunction collapse. It involves expanding the system under study to include the measurement device, so that a detailed quantum calculation would no longer be feasible and a classical description must be used. If one knows the wavefunction at the instant before the measurement, one will be able to compute the probability of collapsing into each of the possible eigenstates. For example, the free particle in the previous example will usually have a wavefunction that is a wave packet centered around some mean position x0, neither an eigenstate of position nor of momentum. When one measures the position of the particle, it is impossible to predict with certainty the result that we will obtain. It is probable, but not certain, that it will be near x0, where the amplitude of the wavefunction is large. After the measurement is performed, having obtained some result x, the wavefunction collapses into a position eigenstate centered at x.

Wave functions can change as time progresses. An equation known as the Schrödinger equation describes how wave functions change in time, a role similar to Newton’s second law in classical mechanics. The Schrödinger equation, applied to the aforementioned example of the free particle, predicts that the center of a wave packet will move through space at a constant velocity, like a classical particle with no forces acting on it. However, the wave packet will also spread out as time progresses, which means that the position becomes more uncertain. This also has the effect of turning position eigenstates (which can be thought of as infinitely sharp wave packets) into broadened wave packets that are no longer position eigenstates.

Some wave functions produce probability distributions that are constant in time. Many systems that are treated dynamically in classical mechanics are described by such “static” wave functions. For example, a single electron in an unexcited atom is pictured classically as a particle moving in a circular trajectory around the atomic nucleus, whereas in quantum mechanics it is described by a static, spherically symmetric wavefunction surrounding the nucleus (Fig. 1). (Note that only the lowest angular momentum states, labeled s, are spherically symmetric).

The time evolution of wave functions is deterministic in the sense that, given a wavefunction at an initial time, it makes a definite prediction of what the wavefunction will be at any later time. During a measurement, the change of the wavefunction into another one is not deterministic, but rather unpredictable, i.e., random. It should be noted, however, that in quantum mechanics, “random” has come to mean “random for all practical purposes,” and not “absolutely random.” Those new to quantum mechanics often confuse quantum mechanical theory’s inability to predict exactly how nature will behave with the conclusion that nature is actually random.

The probabilistic nature of quantum mechanics thus stems from the act of measurement. This is one of the most difficult aspects of quantum systems to understand. It was the central topic in the famous Bohr-Einstein debates, in which the two scientists attempted to clarify these fundamental principles by way of thought experiments. In the decades after the formulation of quantum mechanics, the question of what constitutes a “measurement” has been extensively studied. Interpretations of quantum mechanics have been formulated to do away with the concept of “wavefunction collapse”; see, for example, the relative state interpretation. The basic idea is that when a quantum system interacts with a measuring apparatus, their respective wavefunctions become entangled, so that the original quantum system ceases to exist as an independent entity. For details, see the article on measurement in quantum mechanics.

Relativity and quantum mechanics
The modern world of physics is notably founded on two tested and demonstrably sound theories of general relativity and quantum mechanics —theories which appear to contradict one another. The defining postulates of both Einstein’s theory of relativity and quantum theory are indisputably supported by rigorous and repeated empirical evidence. However, while they do not directly contradict each other theoretically (at least with regard to primary claims), they are resistant to being incorporated within one cohesive model.

Einstein himself is well known for rejecting some of the claims of quantum mechanics. While clearly inventive in his field, he did not accept the more exotic corollaries of quantum mechanics, such as the lack of deterministic causality, and the assertion that a single subatomic particle can occupy numerous areas of space at one time. He also noticed some of the more exotic consequences of entanglement and used them to formulate the Einstein-Podolsky-Rosen paradox, in the hope of showing that quantum mechanics has unacceptable implications. The Einstein-Podolsky-Rosen paradox shows that measuring the state of one particle can instantaneously change the state of its entangled partner, although the two particles can be an arbitrary distance apart. However, this effect does not violate causality, since no transfer of information is possible.

Moreover, there do exist quantum theories which incorporate special relativity—for example, quantum electrodynamics (QED), which is currently the most accurately-tested physical theory [1] —and these lie at the very heart of modern particle physics. Gravity is negligible in many areas of particle physics, so that unification between general relativity and quantum mechanics is not an urgent issue in those applications. However, the lack of a correct theory of quantum gravity is an important issue in cosmology.

Quantum mechanics and classical physics
Predictions of quantum mechanics have been verified experimentally to a very high degree of accuracy. Thus, current logic of correspondence principle between classical and quantum mechanics is that all objects obey laws of quantum mechanics, and classical mechanics is just a quantum mechanics of a large system (or a statistical quantum mechanics of a large collection of particles). Laws of classical mechanics thus follow from laws of quantum mechanics at the limit of large system or large quantum numbers.

Many “macroscopical” properties of “classic” systems are direct consequences of quantum behavior of its parts. For example, stability of bulk matter (which consists of atoms and molecules which would quickly collapse under electric forces alone), rigidity of this matter, mechanical, thermal, chemical, optical and magnetic properties of this matter - they are all results of interaction of electric charges under rules of quantum mechanics.

Because seemingly exotic behavior of matter posited by quantum mechanics and relativity theory become more apparent when dealing with extremely fast-moving or extremely tiny particles, the laws of classical “Newtonian” physics still remain accurate in predicting the behavior of surrounding us (”large”) objects - of the order of the size of large molecules and bigger.

Despite the proposal of many novel ideas, the unification of quantum mechanics—which reigns in the domain of the very small—and general relativity—a superb description of the very large—remains a tantalizing future possibility. (See quantum gravity, string theory.)

In the mathematically rigorous formulation of quantum mechanics, developed by Paul Dirac and John von Neumann, the possible states of a quantum mechanical system are represented by unit vectors (called “state vectors”) residing in a complex separable Hilbert space (variously called the “state space” or the “associated Hilbert space” of the system) well defined up to a complex number of norm 1 (the phase factor). In other words, the possible states are points in the projectivization of a Hilbert space. The exact nature of this Hilbert space is dependent on the system; for example, the state space for position and momentum states is the space of square-integrable functions, while the state space for the spin of a single proton is just the product of two complex planes. Each observable is represented by a densely defined Hermitian (or self-adjoint) linear operator acting on the state space. Each eigenstate of an observable corresponds to an eigenvector of the operator, and the associated eigenvalue corresponds to the value of the observable in that eigenstate. If the operator’s spectrum is discrete, the observable can only attain those discrete eigenvalues.

The time evolution of a quantum state is described by the Schrödinger equation, in which the Hamiltonian, the operator corresponding to the total energy of the system, generates time evolution.

The inner product between two state vectors is a complex number known as a probability amplitude. During a measurement, the probability that a system collapses from a given initial state to a particular eigenstate is given by the square of the absolute value of the probability amplitudes between the initial and final states. The possible results of a measurement are the eigenvalues of the operator - which explains the choice of Hermitian operators, for which all the eigenvalues are real. We can find the probability distribution of an observable in a given state by computing the spectral decomposition of the corresponding operator. Heisenberg’s uncertainty principle is represented by the statement that the operators corresponding to certain observables do not commute.

The Schrödinger equation acts on the entire probability amplitude, not merely its absolute value. Whereas the absolute value of the probability amplitude encodes information about probabilities, its phase encodes information about the interference between quantum states. This gives rise to the wave-like behavior of quantum states.

It turns out that analytic solutions of Schrödinger’s equation are only available for a small number of model Hamiltonians, of which the quantum harmonic oscillator, the particle in a box, the hydrogen-molecular ion and the hydrogen atom are the most important representatives. Even the helium atom, which contains just one more electron than hydrogen, defies all attempts at a fully analytic treatment. There exist several techniques for generating approximate solutions. For instance, in the method known as perturbation theory one uses the analytic results for a simple quantum mechanical model to generate results for a more complicated model related to the simple model by, for example, the addition of a weak potential energy. Another method is the “semi-classical equation of motion” approach, which applies to systems for which quantum mechanics produces weak deviations from classical behavior. The deviations can be calculated based on the classical motion. This approach is important for the field of quantum chaos.

An alternative formulation of quantum mechanics is Feynman’s path integral formulation, in which a quantum-mechanical amplitude is considered as a sum over histories between initial and final states; this is the quantum-mechanical counterpart of action principles in classical mechanics.

[edit] Interactions with other scientific theories
The fundamental rules of quantum mechanics are very broad. They state that the state space of a system is a Hilbert space and the observables are Hermitian operators acting on that space, but do not tell us which Hilbert space or which operators. These must be chosen appropriately in order to obtain a quantitative description of a quantum system. An important guide for making these choices is the correspondence principle, which states that the predictions of quantum mechanics reduce to those of classical physics when a system moves to higher energies or equivalently, larger quantum numbers. In other words, classic mechanics is simply a quantum mechanics of large systems. This “high energy” limit is known as the classical or correspondence limit. One can therefore start from an established classical model of a particular system, and attempt to guess the underlying quantum model that gives rise to the classical model in the correspondence limit.

Unsolved problems in physics: In the correspondence limit of quantum mechanics: Is there a preferred interpretation of quantum mechanics? How does the quantum description of reality, which includes elements such as the superposition of states and wavefunction collapse, give rise to the reality we perceive?When quantum mechanics was originally formulated, it was applied to models whose correspondence limit was non-relativistic classical mechanics. For instance, the well-known model of the quantum harmonic oscillator uses an explicitly non-relativistic expression for the kinetic energy of the oscillator, and is thus a quantum version of the classical harmonic oscillator.

Early attempts to merge quantum mechanics with special relativity involved the replacement of the Schrödinger equation with a covariant equation such as the Klein-Gordon equation or the Dirac equation. While these theories were successful in explaining many experimental results, they had certain unsatisfactory qualities stemming from their neglect of the relativistic creation and annihilation of particles. A fully relativistic quantum theory required the development of quantum field theory, which applies quantization to a field rather than a fixed set of particles. The first complete quantum field theory, quantum electrodynamics, provides a fully quantum description of the electromagnetic interaction.

The full apparatus of quantum field theory is often unnecessary for describing electrodynamic systems. A simpler approach, one employed since the inception of quantum mechanics, is to treat charged particles as quantum mechanical objects being acted on by a classical electromagnetic field. For example, the elementary quantum model of the hydrogen atom describes the electric field of the hydrogen atom using a classical Coulomb potential. This “semi-classical” approach fails if quantum fluctuations in the electromagnetic field play an important role, such as in the emission of photons by charged particles.

Quantum field theories for the strong nuclear force and the weak nuclear force have been developed. The quantum field theory of the strong nuclear force is called quantum chromodynamics, and describes the interactions of the subnuclear particles: quarks and gluons. The weak nuclear force and the electromagnetic force were unified, in their quantized forms, into a single quantum field theory known as electroweak theory.

It has proven difficult to construct quantum models of gravity, the remaining fundamental force. Semi-classical approximations are workable, and have led to predictions such as Hawking radiation. However, the formulation of a complete theory of quantum gravity is hindered by apparent incompatibilities between general relativity, the most accurate theory of gravity currently known, and some of the fundamental assumptions of quantum theory. The resolution of these incompatibilities is an area of active research, and theories such as string theory are among the possible candidates for a future theory of quantum gravity.

Thermodynamics

Thermodynamics (from the Greek θερμη, therme, meaning “heat” and δυναμις, dunamis, meaning “power”) is a branch of physics that studies the effects of changes in temperature, pressure, and volume on physical systems at the macroscopic scale by analyzing the collective motion of their particles using statistics.[1][2] Roughly, heat means “energy in transit” and dynamics relates to “movement”; thus, in essence thermodynamics studies the movement of energy and how energy instills movement. Historically, thermodynamics developed out of need to increase the efficiency of early steam engines.[3]

Typical thermodynamic system - heat moves from hot (boiler) to cold (condenser), (both not shown) and work is extracted, in this case by a series of pistons.The starting point for most thermodynamic considerations are the laws of thermodynamics, which postulate that energy can be exchanged between physical systems as heat or work.[4] They also postulate the existence of a quantity named entropy, which can be defined for any system.[5] In thermodynamics, interactions between large ensembles of objects are studied and categorized. Central to this are the concepts of system and surroundings. A system is composed of particles, whose average motions define its properties, which in turn are related to one another through equations of state. Properties can be combined to express internal energy and thermodynamic potentials, which are useful for determining conditions for equilibrium and spontaneous processes.

With these tools, thermodynamics describes how systems respond to changes in their surroundings. This can be applied to a wide variety of topics in science and engineering, such as engines, phase transitions, chemical reactions, transport phenomena, and even black holes. The results of thermodynamics are essential for other fields of physics and for chemistry, chemical engineering, aerospace engineering, mechanical engineering, cell biology, biomedical engineering, and materials science to name a few.[6][7]

The laws of thermodynamics

In thermodynamics, there are four laws of very general validity, and as such they do not depend on the details of the interactions or the systems being studied. Hence, they can be applied to systems about which one knows nothing other than the balance of energy and matter transfer. Examples of this include Einstein’s prediction of spontaneous emission around the turn of the 20th century and current research into the thermodynamics of black holes.

The four laws are:

Zeroth law of thermodynamics, stating that thermodynamic equilibrium is an equivalence relation.
If two thermodynamic systems are separately in thermal equilibrium with a third, they are also in thermal equilibrium with each other.
First law of thermodynamics, about the conservation of energy
The change in the internal energy of a closed thermodynamic system is equal to the sum of the amount of heat energy supplied to the system and the work done on the system.
Second law of thermodynamics, about entropy
The total entropy of any isolated thermodynamic system tends to increase over time, approaching a maximum value.
Third law of thermodynamics, about absolute zero temperature
As a system asymptotically approaches absolute zero of temperature all processes virtually cease and the entropy of the system asymptotically approaches a minimum value; also stated as: “the entropy of all systems and of all states of a system is zero at absolute zero” or equivalently “it is impossible to reach the absolute zero of temperature by any finite number of processes”.
See also: Bose–Einstein condensate and negative temperature.

The laws of thermodynamics, in principle, describe the specifics for the transport of heat and work in thermodynamic processes. Since their conception, however, these laws have become some of the most important in all of physics and other branches of science connected to thermodynamics. They are often associated with concepts far beyond what is directly stated in the wording.

http://en.wikipedia.org/wiki/Laws_of_thermodynamics

Electromagnetism

Electromagnetism is the physics of the electromagnetic field: a field which exerts a force on particles that possess the property of electric charge, and is in turn affected by the presence and motion of those particles.

The magnetic field is produced by the motion of electric charges, i.e. electric current. The magnetic field causes the magnetic force associated with magnets.

A changing magnetic field produces an electric field (this is the phenomenon of electromagnetic induction, which provides for the operation of electrical generators, induction motors, and transformers). Similarly, a changing electric field generates a magnetic field. Because of this interdependence of the electric and magnetic fields, it makes sense to consider them as a single coherent entity—the electromagnetic field.

This unification, which was completed by James Clerk Maxwell, and formulated by Oliver Heaviside, is one of the triumphs of 19th century physics. It had far-reaching consequences, one of which was the understanding of the nature of light. As it turns out, what is thought of as “light” is actually a propagating oscillatory disturbance in the electromagnetic field, i.e., an electromagnetic wave. Different frequencies of oscillation give rise to the different forms of electromagnetic radiation, from radio waves at the lowest frequencies, to visible light at intermediate frequencies, to gamma rays at the highest frequencies.

The theoretical implications of electromagnetism led to the development of special relativity by Albert Einstein in 1905.

The electromagnetic force

Main article: electromagnetic force
The force that the electromagnetic field exerts on electrically charged particles, called the electromagnetic force, is one of the four fundamental forces. The other fundamental forces are the strong nuclear force (which holds atomic nuclei together), the weak nuclear force (which causes certain forms of radioactive decay), and the gravitational force. All other forces are ultimately derived from these fundamental forces.

As it turns out, the electromagnetic force is the one responsible for practically all the phenomena encountered in daily life, with the exception of gravity. Roughly speaking, all the forces involved in interactions between atoms can be traced to the electromagnetic force acting on the electrically charged protons and electrons inside the atoms. This includes the forces we experience in “pushing” or “pulling” ordinary material objects, which come from the intermolecular forces between the individual molecules in our bodies and those in the objects. It also includes all forms of chemical phenomena, which arise from interactions between electron orbitals.

According to quantum electrodynamics, electromagnetic force is the mathematical by-product of interaction of real charged particles with virtual photons. In 3-dimensional space such interaction (with spin-1 virtual particles) results in inverse square law.

Classical electrodynamics

The scientist William Gilbert proposed, in his De Magnete (1600), that electricity and magnetism, while both capable of causing attraction and repulsion of objects, were distinct effects. Mariners had noticed that lightning strikes had the ability to disturb a compass needle, but the link between lightning and electricity was not confirmed until Benjamin Franklin’s proposed experiments in 1752. One of the first to discover and publish a link between man-made electric current and magnetism was Romagnosi, who in 1802 noticed that connecting a wire across a Voltaic pile deflected a nearby compass needle. However, the effect did not become widely known until 1820, when Ørsted performed a similar experiment. Ørsted’s work influenced Ampère to produce a theory of electromagnetism that set the subject on a mathematical foundation.

An accurate theory of electromagnetism, known as classical electromagnetism, was developed by various physicists over the course of the 19th century, culminating in the work of James Clerk Maxwell, who unified the preceding developments into a single theory and discovered the electromagnetic nature of light. In classical electromagnetism, the electromagnetic field obeys a set of equations known as Maxwell’s equations, and the electromagnetic force is given by the Lorentz force law.

One of the peculiarities of classical electromagnetism is that it is difficult to reconcile with classical mechanics, but it is compatible with special relativity. According to Maxwell’s equations, the speed of light is a universal constant, dependent only on the electrical permittivity and magnetic permeability of the vacuum. This violates Galilean invariance, a long-standing cornerstone of classical mechanics. One way to reconcile the two theories is to assume the existence of a luminiferous aether through which the light propagates. However, subsequent experimental efforts failed to detect the presence of the aether. In 1905, Albert Einstein solved the problem with the introduction of special relativity, which replaces classical kinematics with a new theory of kinematics that is compatible with classical electromagnetism.

In addition, relativity theory shows that in moving frames of reference a magnetic field transforms to a field with a nonzero electric component and vice versa; thus firmly showing that they are two sides of the same coin, and thus the term “electromagnetism”.

The photoelectric effect

In another paper published in that same year, Einstein undermined the very foundations of classical electromagnetism. His theory of the photoelectric effect (for which he won the Nobel prize for physics) posited that light could exist in discrete particle-like quantities, which later came to be known as photons. Einstein’s theory of the photoelectric effect extended the insights that appeared in the solution of the ultraviolet catastrophe presented by Max Planck in 1900. In his work, Planck showed that hot objects emit electromagnetic radiation in discrete packets, which leads to a finite total energy emitted as black body radiation. Both of these results were in direct contradiction with the classical view of light as a continuous wave. Planck’s and Einstein’s theories were progenitors of quantum mechanics, which, when formulated in 1925, necessitated the invention of a quantum theory of electromagnetism. This theory, completed in the 1940s, is known as quantum electrodynamics (or “QED”), and is one of the most accurate theories known to physics.

http://en.wikipedia.org/wiki/Electromagnetism

Phase (matter)

In the physical sciences, a phase is a set of states of a macroscopic physical system that have relatively uniform chemical composition and physical properties (i.e. density, crystal structure, index of refraction, and so forth).

Phases are sometimes confused with states of matter, but there are significant differences. States of matter refers to the differences between gases, liquids, solids, etc. If there are two regions in a chemical system that are in different states of matter, then they must be different phases. However, the reverse is not true — a system can have multiple phases which are in equilibrium with each other and also in the same state of matter. For example, diamond and graphite are both solids but they are different phases, even though their composition may be identical. A system with oil and water at room temperature will be two different phases of differing composition, but both will be the liquid state of matter. This difference is especially important when considering the Gibbs’ phase rule, which governs the number of allowed phases.

In general, two different states of a system are in different phases if there is an abrupt change in their physical properties while transforming from one state to the other. Conversely, two states are in the same phase if they can be transformed into one another without any abrupt changes. There are, however, exceptions to this statement — for example the liquid-gas critical point discussed below in the Phase Diagrams section.

An important point is that different types of phases are associated with different physical qualities. When discussing the solid, liquid, and gaseous phases, we talked about rigidity and compressibility, and the effects of varying the pressure and volume, because those are the relevant properties that distinguish a solid, a liquid, and a gas. On the other hand, when discussing paramagnetism and ferromagnetism, we look at the magnetization, because that is what distinguishes the ferromagnetic phase from the paramagnetic phase. Several more examples of phases will be given in the following section.

In more technical language, a phase is a region in the parameter space of thermodynamic variables in which the free energy is analytic; between such regions there are abrupt changes in the properties of the system, which correspond to discontinuities in the derivatives of the free energy function. As long as the free energy is analytic, all thermodynamic properties (such as entropy, heat capacity, magnetization, and compressibility) will be well-behaved, because they can be expressed in terms of the free energy and its derivatives. For example, the entropy is the first derivative of the free energy with temperature.

When a system goes from one phase to another, there will generally be a stage where the free energy is non-analytic. This is a phase transition. Due to this non-analyticity, the free energies on either side of the transition are two different functions, so one or more thermodynamic properties will behave very differently after the transition. The property most commonly examined in this context is the heat capacity. During a transition, the heat capacity may become infinite, jump abruptly to a different value, or exhibit a “kink” or discontinuity in its derivative. See also differential scanning calorimetry.

The distribution of kinetic energy among molecules is not uniform, and it changes randomly. This means that at, say, the surface of a liquid, there may be an individual molecule with enough kinetic energy to jump into the gas phase. Likewise, individual gas molecules may have low enough kinetic energy to join other molecules in the liquid phase. This phenomenon means that at any given temperature and pressure, multiple phases may co-exist.

For example, under standard conditions for temperature and pressure, a bowl of liquid water in dry air will evaporate until the partial pressure of gaseous water equals the vapor pressure of water. At this point, the rate of molecules leaving and entering the liquid phase becomes the same (due to the increased number of gaseous water molecules available to re-condense). The fact that liquid molecules with above-average kinetic energy have been removed from the bowl results in evaporative cooling. Similar processes may occur on other types of phase boundaries.

Gibbs’ phase rule relates the number of possible phases, variables such as temperature and pressure, and whether or not an equilibrium will be reached.

States of matter

States of matter refers to the differences between gases, liquids, solids, etc

In addition to the specific chemical properties that distinguish different chemical classifications chemicals can exist in several phases. For the most part, the chemical classifications are independent of these bulk phase classifications; however, some more exotic phases are incompatible with certain chemical properties. A phase is a set of states of a chemical system that have similar bulk structural properties, over a range of conditions, such as pressure or temperature. Physical properties, such as density and refractive index tend to fall within values characteristic of the phase. The phase of matter is defined by the phase transition, which is when energy put into or taken out of the system goes into rearranging the structure of the system, instead of changing the bulk conditions.

Sometimes the distinction between phases can be continuous instead of having a discrete boundary, in this case the matter is considered to be in a supercritical state. When three states meet based on the conditions, it is known as a triple point and since this is invariant, it is a convenient way to define a set of conditions.

The most familiar examples of phases are solids, liquids, and gases. Many substances exhibit multiple solid phases. For example, there are three phases of solid iron (alpha, gamma, and delta) that vary based on temperature and pressure. A principle difference between solid phases is the crystal structure, or arrangement, of the atoms. Less familiar phases include plasmas, Bose-Einstein condensates and fermionic condensates and the paramagnetic and ferromagnetic phases of magnetic materials. While most familiar phases deal with three-dimensional systems, it is also possible to define analogs in two-dimensional systems, which has received attention for its relevance to systems in biology.

Elements

A chemical element, or element for short, is a type of atom that is defined by its atomic number; that is, by the number of protons in its nucleus. The term is also used to refer to a pure chemical substance composed of atoms with the same number of protons.[1]

Common examples of elements are hydrogen, nitrogen, and carbon. In total, 117 elements have been observed as of 2007, of which 94 occur naturally on Earth. Elements with atomic numbers greater than 82 (i.e,. bismuth and those above), are inherently unstable and undergo radioactive decay. In addition, elements 43 and 61 (technetium and promethium) have no stable isotopes, and also decay. However, the unstable elements up to atomic number 94 with no stable nuclei are found in nature as a result of the natural decay processes of uranium and thorium.[2]

All chemical matter consists of these elements. New elements are discovered from time to time through artificial nuclear reactions.

An element is a class of atoms which have the same number of protons in the nucleus. This number is known as the atomic number of the element. For example, all atoms with 6 protons in their nuclei are atoms of the chemical element carbon, and all atoms with 92 protons in their nuclei are atoms of the element uranium.

The most convenient presentation of the chemical elements is in the periodic table of the chemical elements, which groups elements by atomic number. Due to its ingenious arrangement, groups, or columns, and periods, or rows, of elements in the table either share several chemical properties, or follow a certain trend in characteristics such as atomic radius, electronegativity, etc. Lists of the elements by name, by symbol, and by atomic number are also available. In addition, several isotopes of an element may exist.

Atoms

In chemistry and physics, an atom (Greek ἄτομος or átomos meaning “indivisible”) is still characterized as a chemical element.[2] (átomos is usually translated as “indivisible” or “uncuttable.” Until the advent of quantum mechanics, dividing a material object was invariably equated with cutting it.) Whereas the word atom originally denoted a particle that cannot be cut into smaller particles, the atoms of modern parlance are composed of subatomic particles:

electrons, which have a negative charge, a size which is so small as to be currently unmeasurable, and which are the least heavy (i.e., massive) of the three;
protons, which have a positive charge, and are about 1836 times more massive than electrons; and
neutrons, which have no charge, and are the same size as protons.
Protons and neutrons make up a dense, massive atomic nucleus, and are collectively called nucleons. The electrons form the much larger electron cloud surrounding the nucleus.

Atoms can differ in the number of each of the subatomic particles they contain. Atoms of the same element have the same number of protons (called the atomic number). Within a single element, the number of neutrons may vary, determining the isotope of that element. The number of electrons associated with an atom is most easily changed, due to the lower energy of binding of electrons. The number of protons (and neutrons) in the atomic nucleus may also change, via nuclear fusion, nuclear fission, bombardment by high energy subatomic particles or photons, or certain (but not all) types of radioactive decay. In such processes which change the number of protons in a nucleus, the atom becomes an atom of a different chemical element.

Atoms are electrically neutral if they have an equal number of protons and electrons. Atoms which have either a deficit or a surplus of electrons are called ions. Electrons that are furthest from the nucleus may be transferred to other nearby atoms or shared between atoms. By this mechanism atoms are able to bond into molecules and other types of chemical compounds like ionic and covalent network crystals.

Atoms are the fundamental building blocks of chemistry, and are conserved in chemical reactions.

http://en.wikipedia.org/wiki/Atom

Quantum mechanics

Quantum mechanics is the branch of mathematical physics treating atomic and subatomic systems and their interaction with radiation in terms of observable quantities. It is based on the observation that all forms of energy are released in discrete units or bundles called quanta. Quantum mechanics provides a physical theory of matter that is based on the concept of the possession of wave properties by elementary particles, affords a mathematical interpretation of the structure and interactions of matter on the basis of these properties, and incorporates within it quantum theory and the uncertainty principle — called also wave mechanics. Remarkably, quantum theory typically permits only probable or statistical calculation of the observed features of subatomic particles, understood in terms of wavefunctions. The discovery of quantum mechanics in the early 20th century revolutionized physics, and quantum mechanics is fundamental to most areas of current research.

theory of relativity

The theory of relativity is:

• a physical theory which is based on the two postulates: (1) that the speed of light in a vacuum is constant and independent of the source or observer and (2) that the mathematical forms of the laws of physics are invariant in all inertial systems– called also special relativity, special theory of relativity. It leads to the assertion of the equivalence of mass and energy and of change in mass,dimension, and time with increased velocity.
• an extension of special relativity to include transformations between non-inertial frames– also called general relativity or the general theory of relativity. It is formulated using differential geometry and interprets gravity as a distortion of spacetime caused by the presence of mass or energy.