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Ethology

Ethology is a branch of zoology that studies the behaviour of non-human animals. It has its scientific roots in the work of Charles Darwin and of American and German ornithologists of the late 19th and early 20th century, including Charles O. Whitman, Oskar Heinroth, and Wallace Craig. The modern discipline of ethology is generally considered to have begun during the 1930s with the work of the Dutch biologist Nikolaas Tinbergen and the Austrian biologists Konrad Lorenz and Karl von Frisch, the three winners of the 1973 Nobel Prize in Physiology or Medicine. Ethology combines laboratory and field science, with a strong relation to neuroanatomy, ecology, and evolutionary biology.

Etymology
The modern term ethology derives from the Greek language: ἦθος, ethos meaning "character" and -λογία, -logia meaning "the study of". The term was first popularized by the American entomologist William Morton Wheeler in 1902.

The beginnings of ethology

Ethologists have been concerned particularly with the evolution of behaviour and its understanding in terms of natural selection. In one sense, the first modern ethologist was Charles Darwin, whose 1872 book The Expression of the Emotions in Man and Animals influenced many ethologists. He pursued his interest in behaviour by encouraging his protégé George Romanes, who investigated animal learning and intelligence using an anthropomorphic method, anecdotal cognitivism, that did not gain scientific support.

Other early ethologists, such as Eugène Marais, Charles O. Whitman, Oskar Heinroth, Wallace Craig and Julian Huxley, instead concentrated on behaviours that can be called instinctive in that they occur in all members of a species under specified circumstances. Their starting point for studying the behaviour of a new species was to construct an ethogram, a description of the main types of behaviour with their frequencies of occurrence. This provided an objective, cumulative database of behaviour.

Growth of the field
Due to the work of Konrad Lorenz and Niko Tinbergen, ethology developed strongly in continental Europe during the years prior to World War II. After the war, Tinbergen moved to the University of Oxford, and ethology became stronger in the UK, with the additional influence of William Thorpe, Robert Hinde, and Patrick Bateson at the University of Cambridge.

Lorenz, Tinbergen, and von Frisch were jointly awarded the Nobel Prize in Physiology or Medicine in 1973 for their work of developing ethology.

Ethology is now a well-recognized scientific discipline, with its own journals such as Animal Behaviour, Applied Animal Behaviour Science, Animal Cognition, Behaviour, Behavioral Ecology and Ethology. In 1972, the International Society for Human Ethology was founded along with its journal, Human Ethology.

Social ethology
In 1972, the English ethologist John H. Crook distinguished comparative ethology from social ethology, and argued that much of the ethology that had existed so far was really comparative ethology—examining animals as individuals—whereas, in the future, ethologists would need to concentrate on the behaviour of social groups of animals and the social structure within them.

E. O. Wilson's book Sociobiology: The New Synthesis appeared in 1975, and since that time, the study of behaviour has been much more concerned with social aspects. It has been driven by the Darwinism associated with Wilson, Robert Trivers, and W. D. Hamilton. The related development of behavioural ecology has helped transform ethology. Furthermore, a substantial rapprochement with comparative psychology has occurred, so the modern scientific study of behaviour offers a spectrum of approaches. In 2020, Tobias Starzak and Albert Newen from the Institute of Philosophy II at the Ruhr University Bochum postulated that animals may have beliefs.

Determinants of behaviour
Behaviour is determined by three major factors, namely inborn instincts, learning, and environmental factors. The latter include abiotic and biotic factors. Abiotic factors such as temperature or light conditions have dramatic effects on animals, especially if they are ectothermic or nocturnal. Biotic factors include members of the same species (e.g. sexual behavior), predators (fight or flight), or parasites and diseases.

Instinct

Webster's Dictionary defines instinct as "A largely inheritable and unalterable tendency of an organism to make a complex and specific response to environmental stimuli without involving reason".

Fixed action patterns
An important development, associated with the name of Konrad Lorenz though probably due more to his teacher, Oskar Heinroth, was the identification of fixed action patterns. Lorenz popularized these as instinctive responses that would occur reliably in the presence of identifiable stimuli called sign stimuli or "releasing stimuli". Fixed action patterns are now considered to be instinctive behavioural sequences that are relatively invariant within the species and that almost inevitably run to completion.

One example of a releaser is the beak movements of many bird species performed by newly hatched chicks, which stimulates the mother to regurgitate food for her offspring. Other examples are the classic studies by Tinbergen on the egg-retrieval behaviour and the effects of a "supernormal stimulus" on the behaviour of graylag geese.

One investigation of this kind was the study of the waggle dance ("dance language") in bee communication by Karl von Frisch.

Habituation
Habituation is a simple form of learning and occurs in many animal taxa. It is the process whereby an animal ceases responding to a stimulus. Often, the response is an innate behavior. Essentially, the animal learns not to respond to irrelevant stimuli. For example, prairie dogs (Cynomys ludovicianus) give alarm calls when predators approach, causing all individuals in the group to quickly scramble down burrows. When prairie dog towns are located near trails used by humans, giving alarm calls every time a person walks by is expensive in terms of time and energy. Habituation to humans is therefore an important behavior in this context.

Associative learning
Associative learning in animal behaviour is any learning process in which a new response becomes associated with a particular stimulus. The first studies of associative learning were made by the Russian physiologist Ivan Pavlov, who observed that dogs trained to associate food with the ringing of a bell would salivate on hearing the bell.

Imprinting

Imprinting enables the young to discriminate the members of their own species, vital for reproductive success. This important type of learning only takes place in a very limited period of time. Konrad Lorenz observed that the young of birds such as geese and chickens followed their mothers spontaneously from almost the first day after they were hatched, and he discovered that this response could be imitated by an arbitrary stimulus if the eggs were incubated artificially and the stimulus were presented during a critical period that continued for a few days after hatching.

Imitation
Imitation is an advanced behavior whereby an animal observes and exactly replicates the behavior of another. The National Institutes of Health reported that capuchin monkeys preferred the company of researchers who imitated them to that of researchers who did not. The monkeys not only spent more time with their imitators but also preferred to engage in a simple task with them even when provided with the option of performing the same task with a non-imitator. Imitation has been observed in recent research on chimpanzees; not only did these chimps copy the actions of another individual, when given a choice, the chimps preferred to imitate the actions of the higher-ranking elder chimpanzee as opposed to the lower-ranking young chimpanzee.

Stimulus and local enhancement
Animals can learn using observational learning but without the process of imitation. One way is stimulus enhancement in which individuals become interested in an object as the result of observing others interacting with the object. Increased interest in an object can result in object manipulation which allows for new object-related behaviours by trial-and-error learning. Haggerty (1909) devised an experiment in which a monkey climbed up the side of a cage, placed its arm into a wooden chute, and pulled a rope in the chute to release food. Another monkey was provided an opportunity to obtain the food after watching a monkey go through this process on four occasions. The monkey performed a different method and finally succeeded after trial-and-error. In local enhancement, a demonstrator attracts an observer's attention to a particular location. Local enhancement has been observed to transmit foraging information among birds, rats and pigs. The stingless bee (Trigona corvina) uses local enhancement to locate other members of their colony and food resources.

Social transmission
A well-documented example of social transmission of a behaviour occurred in a group of macaques on Hachijojima Island, Japan. The macaques lived in the inland forest until the 1960s, when a group of researchers started giving them potatoes on the beach: soon, they started venturing onto the beach, picking the potatoes from the sand, and cleaning and eating them. About one year later, an individual was observed bringing a potato to the sea, putting it into the water with one hand, and cleaning it with the other. This behaviour was soon expressed by the individuals living in contact with her; when they gave birth, this behaviour was also expressed by their young—a form of social transmission.

Teaching
Teaching is a highly specialized aspect of learning in which the "teacher" (demonstrator) adjusts their behaviour to increase the probability of the "pupil" (observer) achieving the desired end-result of the behaviour. For example, orcas are known to intentionally beach themselves to catch pinniped prey. Mother orcas teach their young to catch pinnipeds by pushing them onto the shore and encouraging them to attack the prey. Because the mother orca is altering her behaviour to help her offspring learn to catch prey, this is evidence of teaching. Teaching is not limited to mammals. Many insects, for example, have been observed demonstrating various forms of teaching to obtain food. Ants, for example, will guide each other to food sources through a process called "tandem running," in which an ant will guide a companion ant to a source of food. It has been suggested that the pupil ant is able to learn this route to obtain food in the future or teach the route to other ants. This behaviour of teaching is also exemplified by crows, specifically New Caledonian crows. The adults (whether individual or in families) teach their young adolescent offspring how to construct and utilize tools. For example, Pandanus branches are used to extract insects and other larvae from holes within trees.

Mating and the fight for supremacy

Individual reproduction is the most important phase in the proliferation of individuals or genes within a species: for this reason, there exist complex mating rituals, which can be very complex even if they are often regarded as fixed action patterns. The stickleback's complex mating ritual, studied by Tinbergen, is regarded as a notable example.

Often in social life, animals fight for the right to reproduce, as well as social supremacy. A common example of fighting for social and sexual supremacy is the so-called pecking order among poultry. Every time a group of poultry cohabitate for a certain time length, they establish a pecking order. In these groups, one chicken dominates the others and can peck without being pecked. A second chicken can peck all the others except the first, and so on. Chickens higher in the pecking order may at times be distinguished by their healthier appearance when compared to lower level chickens. While the pecking order is establishing, frequent and violent fights can happen, but once established, it is broken only when other individuals enter the group, in which case the pecking order re-establishes from scratch.

Social behaviour
Several animal species, including humans, tend to live in groups. Group size is a major aspect of their social environment. Social life is probably a complex and effective survival strategy. It may be regarded as a sort of symbiosis among individuals of the same species: a society is composed of a group of individuals belonging to the same species living within well-defined rules on food management, role assignments and reciprocal dependence.

When biologists interested in evolution theory first started examining social behaviour, some apparently unanswerable questions arose, such as how the birth of sterile castes, like in bees, could be explained through an evolving mechanism that emphasizes the reproductive success of as many individuals as possible, or why, amongst animals living in small groups like squirrels, an individual would risk its own life to save the rest of the group. These behaviours may be examples of altruism. Not all behaviours are altruistic, as indicated by the table below. For example, revengeful behaviour was at one point claimed to have been observed exclusively in Homo sapiens. However, other species have been reported to be vengeful including chimpanzees, as well as anecdotal reports of vengeful camels.

Altruistic behaviour has been explained by the gene-centred view of evolution.

Benefits and costs of group living
One advantage of group living is decreased predation. If the number of predator attacks stays the same despite increasing prey group size, each prey has a reduced risk of predator attacks through the dilution effect. Further, according to the selfish herd theory, the fitness benefits associated with group living vary depending on the location of an individual within the group. The theory suggests that conspecifics positioned at the centre of a group will reduce the likelihood predations while those at the periphery will become more vulnerable to attack. In groups, prey can also actively reduce their predation risk through more effective defence tactics, or through earlier detection of predators through increased vigilance.

Another advantage of group living is an increased ability to forage for food. Group members may exchange information about food sources, facilitating the process of resource location. Honeybees are a notable example of this, using the waggle dance to communicate the location of flowers to the rest of their hive. Predators also receive benefits from hunting in groups, through using better strategies and being able to take down larger prey.

Some disadvantages accompany living in groups. Living in close proximity to other animals can facilitate the transmission of parasites and disease, and groups that are too large may also experience greater competition for resources and mates.

Group size
Theoretically, social animals should have optimal group sizes that maximize the benefits and minimize the costs of group living. However, in nature, most groups are stable at slightly larger than optimal sizes. Because it generally benefits an individual to join an optimally-sized group, despite slightly decreasing the advantage for all members, groups may continue to increase in size until it is more advantageous to remain alone than to join an overly full group.

Tinbergen's four questions for ethologists
Tinbergen argued that ethology needed to include four kinds of explanation in any instance of behaviour:
 * Function – How does the behaviour affect the animal's chances of survival and reproduction? Why does the animal respond that way instead of some other way?
 * Causation – What are the stimuli that elicit the response, and how has it been modified by recent learning?
 * Development – How does the behaviour change with age, and what early experiences are necessary for the animal to display the behaviour?
 * Evolutionary history – How does the behaviour compare with similar behaviour in related species, and how might it have begun through the process of phylogeny?

These explanations are complementary rather than mutually exclusive—all instances of behaviour require an explanation at each of these four levels. For example, the function of eating is to acquire nutrients (which ultimately aids survival and reproduction), but the immediate cause of eating is hunger (causation). Hunger and eating are evolutionarily ancient and are found in many species (evolutionary history), and develop early within an organism's lifespan (development). It is easy to confuse such questions—for example, to argue that people eat because they are hungry and not to acquire nutrients—without realizing that the reason people experience hunger is because it causes them to acquire nutrients.

title: Ethology


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Electromagnetic radiation

In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy.

Classically, electromagnetic radiation consists of electromagnetic waves, which are synchronized oscillations of electric and magnetic fields. In a vacuum, electromagnetic waves travel at the speed of light, commonly denoted c. There, depending on the frequency of oscillation, different wavelengths of electromagnetic spectrum are produced. In homogeneous, isotropic media, the oscillations of the two fields are on average perpendicular to each other and perpendicular to the direction of energy and wave propagation, forming a transverse wave.

The position of an electromagnetic wave within the electromagnetic spectrum can be characterized by either its frequency of oscillation or its wavelength. Electromagnetic waves of different frequency are called by different names since they have different sources and effects on matter. In order of increasing frequency and decreasing wavelength, the electromagnetic spectrum includes: radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays.

Electromagnetic waves are emitted by electrically charged particles undergoing acceleration, and these waves can subsequently interact with other charged particles, exerting force on them. EM waves carry energy, momentum, and angular momentum away from their source particle and can impart those quantities to matter with which they interact. Electromagnetic radiation is associated with those EM waves that are free to propagate themselves ("radiate") without the continuing influence of the moving charges that produced them, because they have achieved sufficient distance from those charges. Thus, EMR is sometimes referred to as the far field, while the near field refers to EM fields near the charges and current that directly produced them, specifically electromagnetic induction and electrostatic induction phenomena.

In quantum mechanics, an alternate way of viewing EMR is that it consists of photons, uncharged elementary particles with zero rest mass which are the quanta of the electromagnetic field, responsible for all electromagnetic interactions. Quantum electrodynamics is the theory of how EMR interacts with matter on an atomic level. Quantum effects provide additional sources of EMR, such as the transition of electrons to lower energy levels in an atom and black-body radiation. The energy of an individual photon is quantized and proportional to frequency according to Planck's equation E = hf, where E is the energy per photon, f is the frequency of the photon, and h is the Planck constant. Thus, higher frequency photons have more energy. For example, a $Hz$ gamma ray photon has $$ times the energy of a $Hz$ extremely low frequency radio wave photon.

The effects of EMR upon chemical compounds and biological organisms depend both upon the radiation's power and its frequency. EMR of lower energy ultraviolet or lower frequencies (i.e., near ultraviolet, visible light, infrared, microwaves, and radio waves) is non-ionizing because its photons do not individually have enough energy to ionize atoms or molecules or to break chemical bonds. The effect of non-ionizing radiation on chemical systems and living tissue is primarily simply heating, through the combined energy transfer of many photons. In contrast, high frequency ultraviolet, X-rays and gamma rays are ionizing – individual photons of such high frequency have enough energy to ionize molecules or break chemical bonds. Ionizing radiation can cause chemical reactions and damage living cells beyond simply heating, and can be a health hazard and dangerous.

Maxwell's equations
James Clerk Maxwell derived a wave form of the electric and magnetic equations, thus uncovering the wave-like nature of electric and magnetic fields and their symmetry. Because the speed of EM waves predicted by the wave equation coincided with the measured speed of light, Maxwell concluded that light itself is an EM wave. Maxwell's equations were confirmed by Heinrich Hertz through experiments with radio waves.

Near and far fields
Maxwell's equations established that some charges and currents (sources) produce local electromagnetic fields near them that do not radiate. Currents directly produce magnetic fields, but such fields of a magnetic-dipole–type that dies out with distance from the current. In a similar manner, moving charges pushed apart in a conductor by a changing electrical potential (such as in an antenna) produce an electric-dipole–type electrical field, but this also declines with distance. These fields make up the near field. Neither of these behaviours is responsible for EM radiation. Instead, they only efficiently transfer energy to a receiver very close to the source, such as inside a transformer. The near field has strong effects its source, with any energy withdrawn by a receiver causing increased load (decreased electrical reactance) on the source. The near field does not propagate freely into space, carrying energy away without a distance limit, but rather oscillates, returning its energy to the transmitter if it is not absorbed by a receiver.

By contrast, the far field is composed of radiation that is free of the transmitter, in the sense that the transmitter requires the same power to send changes in the field out regardless of whether anything absorbs the signal, e.g. a radio station does not need to increase its power when more receivers use the signal. This far part of the electromagnetic field is electromagnetic radiation. The far fields propagate (radiate) without allowing the transmitter to affect them. This causes them to be independent in the sense that their existence and their energy, after they have left the transmitter, is completely independent of both transmitter and receiver. Due to conservation of energy, the amount of power passing through any spherical surface drawn around the source is the same. Because such a surface has an area proportional to the square of its distance from the source, the power density of EM radiation from an isotropic source decreases with the inverse square of the distance from the source; this is called the inverse-square law. This is in contrast to dipole parts of the EM field, the near field, which varies in intensity according to an inverse cube power law, and thus does not transport a conserved amount of energy over distances but instead fades with distance, with its energy (as noted) rapidly returning to the transmitter or absorbed by a nearby receiver (such as a transformer secondary coil).

In the Liénard–Wiechert potential formulation of the electric and magnetic fields due to motion of a single particle (according to Maxwell's equations), the terms associated with acceleration of the particle are those that are responsible for the part of the field that is regarded as electromagnetic radiation. By contrast, the term associated with the changing static electric field of the particle and the magnetic term that results from the particle's uniform velocity are both associated with the near field, and do not comprise electromagnetic radiation.

Properties

Electric and magnetic fields obey the properties of superposition. Thus, a field due to any particular particle or time-varying electric or magnetic field contributes to the fields present in the same space due to other causes. Further, as they are vector fields, all magnetic and electric field vectors add together according to vector addition. For example, in optics two or more coherent light waves may interact and by constructive or destructive interference yield a resultant irradiance deviating from the sum of the component irradiances of the individual light waves.

The electromagnetic fields of light are not affected by traveling through static electric or magnetic fields in a linear medium such as a vacuum. However, in nonlinear media, such as some crystals, interactions can occur between light and static electric and magnetic fields—these interactions include the Faraday effect and the Kerr effect.

In refraction, a wave crossing from one medium to another of different density alters its speed and direction upon entering the new medium. The ratio of the refractive indices of the media determines the degree of refraction, and is summarized by Snell's law. Light of composite wavelengths (natural sunlight) disperses into a visible spectrum passing through a prism, because of the wavelength-dependent refractive index of the prism material (dispersion); that is, each component wave within the composite light is bent a different amount.

EM radiation exhibits both wave properties and particle properties at the same time (see wave-particle duality). Both wave and particle characteristics have been confirmed in many experiments. Wave characteristics are more apparent when EM radiation is measured over relatively large timescales and over large distances while particle characteristics are more evident when measuring small timescales and distances. For example, when electromagnetic radiation is absorbed by matter, particle-like properties will be more obvious when the average number of photons in the cube of the relevant wavelength is much smaller than 1. It is not so difficult to experimentally observe non-uniform deposition of energy when light is absorbed, however this alone is not evidence of "particulate" behavior. Rather, it reflects the quantum nature of matter. Demonstrating that the light itself is quantized, not merely its interaction with matter, is a more subtle affair.

Some experiments display both the wave and particle natures of electromagnetic waves, such as the self-interference of a single photon. When a single photon is sent through an interferometer, it passes through both paths, interfering with itself, as waves do, yet is detected by a photomultiplier or other sensitive detector only once.

A quantum theory of the interaction between electromagnetic radiation and matter such as electrons is described by the theory of quantum electrodynamics.

Electromagnetic waves can be polarized, reflected, refracted, or diffracted, and can interfere with each other.

Wave model
In homogeneous, isotropic media, electromagnetic radiation is a transverse wave, meaning that its oscillations are perpendicular to the direction of energy transfer and travel. It comes from the following equations:$$\begin{align} \nabla \cdot \mathbf{E} &= 0\\ \nabla \cdot \mathbf{B} &= 0 \end{align}$$These equations predicate that any electromagnetic wave must be a transverse wave, where the electric field $E$ and the magnetic field $B$ are both perpendicular to the direction of wave propagation.

The electric and magnetic parts of the field in an electromagnetic wave stand in a fixed ratio of strengths to satisfy the two Maxwell equations that specify how one is produced from the other. In dissipation-less (lossless) media, these E and B fields are also in phase, with both reaching maxima and minima at the same points in space (see illustrations). In the far-field EM radiation which is described by the two source-free Maxwell curl operator equations, a time-change in one type of field is proportional to the curl of the other. These derivatives require that the E and B fields in EMR are in-phase (see mathematics section below).

An important aspect of light's nature is its frequency. The frequency of a wave is its rate of oscillation and is measured in hertz, the SI unit of frequency, where one hertz is equal to one oscillation per second. Light usually has multiple frequencies that sum to form the resultant wave. Different frequencies undergo different angles of refraction, a phenomenon known as dispersion.

A monochromatic wave (a wave of a single frequency) consists of successive troughs and crests, and the distance between two adjacent crests or troughs is called the wavelength. Waves of the electromagnetic spectrum vary in size, from very long radio waves longer than a continent to very short gamma rays smaller than atom nuclei. Frequency is inversely proportional to wavelength, according to the equation:
 * $$\displaystyle v=f\lambda$$

where v is the speed of the wave (c in a vacuum or less in other media), f is the frequency and λ is the wavelength. As waves cross boundaries between different media, their speeds change but their frequencies remain constant.

Electromagnetic waves in free space must be solutions of Maxwell's electromagnetic wave equation. Two main classes of solutions are known, namely plane waves and spherical waves. The plane waves may be viewed as the limiting case of spherical waves at a very large (ideally infinite) distance from the source. Both types of waves can have a waveform which is an arbitrary time function (so long as it is sufficiently differentiable to conform to the wave equation). As with any time function, this can be decomposed by means of Fourier analysis into its frequency spectrum, or individual sinusoidal components, each of which contains a single frequency, amplitude and phase. Such a component wave is said to be monochromatic. A monochromatic electromagnetic wave can be characterized by its frequency or wavelength, its peak amplitude, its phase relative to some reference phase, its direction of propagation, and its polarization.

Interference is the superposition of two or more waves resulting in a new wave pattern. If the fields have components in the same direction, they constructively interfere, while opposite directions cause destructive interference. Additionally, multiple polarization signals can be combined (i.e. interfered) to form new states of polarization, which is known as parallel polarization state generation.

The energy in electromagnetic waves is sometimes called radiant energy.

Particle model and quantum theory
An anomaly arose in the late 19th century involving a contradiction between the wave theory of light and measurements of the electromagnetic spectra that were being emitted by thermal radiators known as black bodies. Physicists struggled with this problem unsuccessfully for many years, and it later became known as the ultraviolet catastrophe. In 1900, Max Planck developed a new theory of black-body radiation that explained the observed spectrum. Planck's theory was based on the idea that black bodies emit light (and other electromagnetic radiation) only as discrete bundles or packets of energy. These packets were called quanta. In 1905, Albert Einstein proposed that light quanta be regarded as real particles. Later the particle of light was given the name photon, to correspond with other particles being described around this time, such as the electron and proton. A photon has an energy, E, proportional to its frequency, f, by
 * $$E = hf = \frac{hc}{\lambda} \,\! $$

where h is the Planck constant, $$\lambda$$ is the wavelength and c is the speed of light. This is sometimes known as the Planck–Einstein equation. In quantum theory (see first quantization) the energy of the photons is thus directly proportional to the frequency of the EMR wave.

Likewise, the momentum p of a photon is also proportional to its frequency and inversely proportional to its wavelength:
 * $$p = { E \over c } = { hf \over c } = { h \over \lambda }. $$

The source of Einstein's proposal that light was composed of particles (or could act as particles in some circumstances) was an experimental anomaly not explained by the wave theory: the photoelectric effect, in which light striking a metal surface ejected electrons from the surface, causing an electric current to flow across an applied voltage. Experimental measurements demonstrated that the energy of individual ejected electrons was proportional to the frequency, rather than the intensity, of the light. Furthermore, below a certain minimum frequency, which depended on the particular metal, no current would flow regardless of the intensity. These observations appeared to contradict the wave theory, and for years physicists tried in vain to find an explanation. In 1905, Einstein explained this puzzle by resurrecting the particle theory of light to explain the observed effect. Because of the preponderance of evidence in favor of the wave theory, however, Einstein's ideas were met initially with great skepticism among established physicists. Eventually Einstein's explanation was accepted as new particle-like behavior of light was observed, such as the Compton effect.

As a photon is absorbed by an atom, it excites the atom, elevating an electron to a higher energy level (one that is on average farther from the nucleus). When an electron in an excited molecule or atom descends to a lower energy level, it emits a photon of light at a frequency corresponding to the energy difference. Since the energy levels of electrons in atoms are discrete, each element and each molecule emits and absorbs its own characteristic frequencies. Immediate photon emission is called fluorescence, a type of photoluminescence. An example is visible light emitted from fluorescent paints, in response to ultraviolet (blacklight). Many other fluorescent emissions are known in spectral bands other than visible light. Delayed emission is called phosphorescence.

Wave–particle duality
The modern theory that explains the nature of light includes the notion of wave–particle duality.

Wave and particle effects of electromagnetic radiation
Together, wave and particle effects fully explain the emission and absorption spectra of EM radiation. The matter-composition of the medium through which the light travels determines the nature of the absorption and emission spectrum. These bands correspond to the allowed energy levels in the atoms. Dark bands in the absorption spectrum are due to the atoms in an intervening medium between source and observer. The atoms absorb certain frequencies of the light between emitter and detector/eye, then emit them in all directions. A dark band appears to the detector, due to the radiation scattered out of the light beam. For instance, dark bands in the light emitted by a distant star are due to the atoms in the star's atmosphere. A similar phenomenon occurs for emission, which is seen when an emitting gas glows due to excitation of the atoms from any mechanism, including heat. As electrons descend to lower energy levels, a spectrum is emitted that represents the jumps between the energy levels of the electrons, but lines are seen because again emission happens only at particular energies after excitation. An example is the emission spectrum of nebulae. Rapidly moving electrons are most sharply accelerated when they encounter a region of force, so they are responsible for producing much of the highest frequency electromagnetic radiation observed in nature.

These phenomena can aid various chemical determinations for the composition of gases lit from behind (absorption spectra) and for glowing gases (emission spectra). Spectroscopy (for example) determines what chemical elements comprise a particular star. Spectroscopy is also used in the determination of the distance of a star, using the red shift.

Propagation speed
When any wire (or other conducting object such as an antenna) conducts alternating current, electromagnetic radiation is propagated at the same frequency as the current.

As a wave, light is characterized by a velocity (the speed of light), wavelength, and frequency. As particles, light is a stream of photons. Each has an energy related to the frequency of the wave given by Planck's relation E = hf, where E is the energy of the photon, h is the Planck constant, 6.626 × 10−34 J·s, and f is the frequency of the wave.

In a medium (other than vacuum), velocity factor or refractive index are considered, depending on frequency and application. Both of these are ratios of the speed in a medium to speed in a vacuum.

History of discovery
Electromagnetic radiation of wavelengths other than those of visible light were discovered in the early 19th century. The discovery of infrared radiation is ascribed to astronomer William Herschel, who published his results in 1800 before the Royal Society of London. Herschel used a glass prism to refract light from the Sun and detected invisible rays that caused heating beyond the red part of the spectrum, through an increase in the temperature recorded with a thermometer. These "calorific rays" were later termed infrared.

In 1801, German physicist Johann Wilhelm Ritter discovered ultraviolet in an experiment similar to Herschel's, using sunlight and a glass prism. Ritter noted that invisible rays near the violet edge of a solar spectrum dispersed by a triangular prism darkened silver chloride preparations more quickly than did the nearby violet light. Ritter's experiments were an early precursor to what would become photography. Ritter noted that the ultraviolet rays (which at first were called "chemical rays") were capable of causing chemical reactions.

In 1862–64 James Clerk Maxwell developed equations for the electromagnetic field which suggested that waves in the field would travel with a speed that was very close to the known speed of light. Maxwell therefore suggested that visible light (as well as invisible infrared and ultraviolet rays by inference) all consisted of propagating disturbances (or radiation) in the electromagnetic field. Radio waves were first produced deliberately by Heinrich Hertz in 1887, using electrical circuits calculated to produce oscillations at a much lower frequency than that of visible light, following recipes for producing oscillating charges and currents suggested by Maxwell's equations. Hertz also developed ways to detect these waves, and produced and characterized what were later termed radio waves and microwaves.

Wilhelm Röntgen discovered and named X-rays. After experimenting with high voltages applied to an evacuated tube on 8 November 1895, he noticed a fluorescence on a nearby plate of coated glass. In one month, he discovered X-rays' main properties.

The last portion of the EM spectrum to be discovered was associated with radioactivity. Henri Becquerel found that uranium salts caused fogging of an unexposed photographic plate through a covering paper in a manner similar to X-rays, and Marie Curie discovered that only certain elements gave off these rays of energy, soon discovering the intense radiation of radium. The radiation from pitchblende was differentiated into alpha rays (alpha particles) and beta rays (beta particles) by Ernest Rutherford through simple experimentation in 1899, but these proved to be charged particulate types of radiation. However, in 1900 the French scientist Paul Villard discovered a third neutrally charged and especially penetrating type of radiation from radium, and after he described it, Rutherford realized it must be yet a third type of radiation, which in 1903 Rutherford named gamma rays. In 1910 British physicist William Henry Bragg demonstrated that gamma rays are electromagnetic radiation, not particles, and in 1914 Rutherford and Edward Andrade measured their wavelengths, finding that they were similar to X-rays but with shorter wavelengths and higher frequency, although a 'cross-over' between X and gamma rays makes it possible to have X-rays with a higher energy (and hence shorter wavelength) than gamma rays and vice versa. The origin of the ray differentiates them, gamma rays tend to be natural phenomena originating from the unstable nucleus of an atom and X-rays are electrically generated (and hence man-made) unless they are as a result of bremsstrahlung X-radiation caused by the interaction of fast moving particles (such as beta particles) colliding with certain materials, usually of higher atomic numbers.

Electromagnetic spectrum
[[File:Light spectrum.svg|right|frame|Legend:

γ = Gamma rays

HX = Hard X-rays

SX = Soft X-Rays

EUV = Extreme-ultraviolet

NUV = Near-ultraviolet

Visible light (colored bands)

NIR = Near-infrared

MIR = Mid-infrared

FIR = Far-infrared

EHF = Extremely high frequency (microwaves)

SHF = Super-high frequency (microwaves)

UHF = Ultrahigh frequency (radio waves)

VHF = Very high frequency (radio)

HF = High frequency (radio)

MF = Medium frequency (radio)

LF = Low frequency (radio)

VLF = Very low frequency (radio)

VF = Voice frequency

ULF = Ultra-low frequency (radio)

SLF = Super-low frequency (radio)

ELF = Extremely low frequency (radio)]]

EM radiation (the designation 'radiation' excludes static electric and magnetic and near fields) is classified by wavelength into radio, microwave, infrared, visible, ultraviolet, X-rays and gamma rays. Arbitrary electromagnetic waves can be expressed by Fourier analysis in terms of sinusoidal waves (monochromatic radiation), which in turn can each be classified into these regions of the EMR spectrum.

For certain classes of EM waves, the waveform is most usefully treated as random, and then spectral analysis must be done by slightly different mathematical techniques appropriate to random or stochastic processes. In such cases, the individual frequency components are represented in terms of their power content, and the phase information is not preserved. Such a representation is called the power spectral density of the random process. Random electromagnetic radiation requiring this kind of analysis is, for example, encountered in the interior of stars, and in certain other very wideband forms of radiation such as the Zero point wave field of the electromagnetic vacuum.

The behavior of EM radiation and its interaction with matter depends on its frequency, and changes qualitatively as the frequency changes. Lower frequencies have longer wavelengths, and higher frequencies have shorter wavelengths, and are associated with photons of higher energy. There is no fundamental limit known to these wavelengths or energies, at either end of the spectrum, although photons with energies near the Planck energy or exceeding it (far too high to have ever been observed) will require new physical theories to describe.

Radio and microwave
When radio waves impinge upon a conductor, they couple to the conductor, travel along it and induce an electric current on the conductor surface by moving the electrons of the conducting material in correlated bunches of charge.

Electromagnetic radiation phenomena with wavelengths ranging from as long as one meter to as short as one millimeter are called microwaves; with frequencies between 300 MHz (0.3 GHz) and 300 GHz.

At radio and microwave frequencies, EMR interacts with matter largely as a bulk collection of charges which are spread out over large numbers of affected atoms. In electrical conductors, such induced bulk movement of charges (electric currents) results in absorption of the EMR, or else separations of charges that cause generation of new EMR (effective reflection of the EMR). An example is absorption or emission of radio waves by antennas, or absorption of microwaves by water or other molecules with an electric dipole moment, as for example inside a microwave oven. These interactions produce either electric currents or heat, or both.

Infrared
Like radio and microwave, infrared (IR) also is reflected by metals (and also most EMR, well into the ultraviolet range). However, unlike lower-frequency radio and microwave radiation, Infrared EMR commonly interacts with dipoles present in single molecules, which change as atoms vibrate at the ends of a single chemical bond. It is consequently absorbed by a wide range of substances, causing them to increase in temperature as the vibrations dissipate as heat. The same process, run in reverse, causes bulk substances to radiate in the infrared spontaneously (see thermal radiation section below).

Infrared radiation is divided into spectral subregions. While different subdivision schemes exist, the spectrum is commonly divided as near-infrared (0.75–1.4 μm), short-wavelength infrared (1.4–3 μm), mid-wavelength infrared (3–8 μm), long-wavelength infrared (8–15 μm) and far infrared (15–1000 μm).

Visible light
Natural sources produce EM radiation across the spectrum. EM radiation with a wavelength between approximately 400 nm and 700 nm is directly detected by the human eye and perceived as visible light. Other wavelengths, especially nearby infrared (longer than 700 nm) and ultraviolet (shorter than 400 nm) are also sometimes referred to as light.

As frequency increases into the visible range, photons have enough energy to change the bond structure of some individual molecules. It is not a coincidence that this happens in the visible range, as the mechanism of vision involves the change in bonding of a single molecule, retinal, which absorbs a single photon. The change in retinal causes a change in the shape of the rhodopsin protein it is contained in, which starts the biochemical process that causes the retina of the human eye to sense the light.

Photosynthesis becomes possible in this range as well, for the same reason. A single molecule of chlorophyll is excited by a single photon. In plant tissues that conduct photosynthesis, carotenoids act to quench electronically excited chlorophyll produced by visible light in a process called non-photochemical quenching, to prevent reactions that would otherwise interfere with photosynthesis at high light levels.

Animals that detect infrared make use of small packets of water that change temperature, in an essentially thermal process that involves many photons.

Infrared, microwaves and radio waves are known to damage molecules and biological tissue only by bulk heating, not excitation from single photons of the radiation.

Visible light is able to affect only a tiny percentage of all molecules. Usually not in a permanent or damaging way, rather the photon excites an electron which then emits another photon when returning to its original position. This is the source of color produced by most dyes. Retinal is an exception. When a photon is absorbed, the retinal permanently changes structure from cis to trans, and requires a protein to convert it back, i.e. reset it to be able to function as a light detector again.

Limited evidence indicate that some reactive oxygen species are created by visible light in skin, and that these may have some role in photoaging, in the same manner as ultraviolet A.

Ultraviolet
As frequency increases into the ultraviolet, photons now carry enough energy (about three electron volts or more) to excite certain doubly bonded molecules into permanent chemical rearrangement. In DNA, this causes lasting damage. DNA is also indirectly damaged by reactive oxygen species produced by ultraviolet A (UVA), which has energy too low to damage DNA directly. This is why ultraviolet at all wavelengths can damage DNA, and is capable of causing cancer, and (for UVB) skin burns (sunburn) that are far worse than would be produced by simple heating (temperature increase) effects.

At the higher end of the ultraviolet range, the energy of photons becomes large enough to impart enough energy to electrons to cause them to be liberated from the atom, in a process called photoionisation. The energy required for this is always larger than about 10 electron volt (eV) corresponding with wavelengths smaller than 124 nm (some sources suggest a more realistic cutoff of 33 eV, which is the energy required to ionize water). This high end of the ultraviolet spectrum with energies in the approximate ionization range, is sometimes called "extreme UV." Ionizing UV is strongly filtered by the Earth's atmosphere.

X-rays and gamma rays
Electromagnetic radiation composed of photons that carry minimum-ionization energy, or more, (which includes the entire spectrum with shorter wavelengths), is therefore termed ionizing radiation. (Many other kinds of ionizing radiation are made of non-EM particles). Electromagnetic-type ionizing radiation extends from the extreme ultraviolet to all higher frequencies and shorter wavelengths, which means that all X-rays and gamma rays qualify. These are capable of the most severe types of molecular damage, which can happen in biology to any type of biomolecule, including mutation and cancer, and often at great depths below the skin, since the higher end of the X-ray spectrum, and all of the gamma ray spectrum, penetrate matter.

Atmosphere and magnetosphere
Most UV and X-rays are blocked by absorption first from molecular nitrogen, and then (for wavelengths in the upper UV) from the electronic excitation of dioxygen and finally ozone at the mid-range of UV. Only 30% of the Sun's ultraviolet light reaches the ground, and almost all of this is well transmitted.

Visible light is well transmitted in air, a property known as an atmospheric window, as it is not energetic enough to excite nitrogen, oxygen, or ozone, but too energetic to excite molecular vibrational frequencies of water vapor and CO2.

Absorption bands in the infrared are due to modes of vibrational excitation in water vapor. However, at energies too low to excite water vapor, the atmosphere becomes transparent again, allowing free transmission of most microwave and radio waves.

Finally, at radio wavelengths longer than 10 m or so (about 30 MHz), the air in the lower atmosphere remains transparent to radio, but plasma in certain layers of the ionosphere begins to interact with radio waves (see skywave). This property allows some longer wavelengths (100 m or 3 MHz) to be reflected and results in shortwave radio beyond line-of-sight. However, certain ionospheric effects begin to block incoming radiowaves from space, when their frequency is less than about 10 MHz (wavelength longer than about 30 m).

Thermal and electromagnetic radiation as a form of heat
The basic structure of matter involves charged particles bound together. When electromagnetic radiation impinges on matter, it causes the charged particles to oscillate and gain energy. The ultimate fate of this energy depends on the context. It could be immediately re-radiated and appear as scattered, reflected, or transmitted radiation. It may get dissipated into other microscopic motions within the matter, coming to thermal equilibrium and manifesting itself as thermal energy, or even kinetic energy, in the material. With a few exceptions related to high-energy photons (such as fluorescence, harmonic generation, photochemical reactions, the photovoltaic effect for ionizing radiations at far ultraviolet, X-ray and gamma radiation), absorbed electromagnetic radiation simply deposits its energy by heating the material. This happens for infrared, microwave and radio wave radiation. Intense radio waves can thermally burn living tissue and can cook food. In addition to infrared lasers, sufficiently intense visible and ultraviolet lasers can easily set paper afire.

Ionizing radiation creates high-speed electrons in a material and breaks chemical bonds, but after these electrons collide many times with other atoms eventually most of the energy becomes thermal energy all in a tiny fraction of a second. This process makes ionizing radiation far more dangerous per unit of energy than non-ionizing radiation. This caveat also applies to UV, even though almost all of it is not ionizing, because UV can damage molecules due to electronic excitation, which is far greater per unit energy than heating effects.

Infrared radiation in the spectral distribution of a black body is usually considered a form of heat, since it has an equivalent temperature and is associated with an entropy change per unit of thermal energy. However, "heat" is a technical term in physics and thermodynamics and is often confused with thermal energy. Any type of electromagnetic energy can be transformed into thermal energy in interaction with matter. Thus, any electromagnetic radiation can "heat" (in the sense of increase the thermal energy temperature of) a material, when it is absorbed.

The inverse or time-reversed process of absorption is thermal radiation. Much of the thermal energy in matter consists of random motion of charged particles, and this energy can be radiated away from the matter. The resulting radiation may subsequently be absorbed by another piece of matter, with the deposited energy heating the material.

The electromagnetic radiation in an opaque cavity at thermal equilibrium is effectively a form of thermal energy, having maximum radiation entropy.

Biological effects
Bioelectromagnetics is the study of the interactions and effects of EM radiation on living organisms. The effects of electromagnetic radiation upon living cells, including those in humans, depends upon the radiation's power and frequency. For low-frequency radiation (radio waves to near ultraviolet) the best-understood effects are those due to radiation power alone, acting through heating when radiation is absorbed. For these thermal effects, frequency is important as it affects the intensity of the radiation and penetration into the organism (for example, microwaves penetrate better than infrared). It is widely accepted that low frequency fields that are too weak to cause significant heating could not possibly have any biological effect.

Some research suggests that weaker non-thermal electromagnetic fields (including weak ELF magnetic fields, although the latter does not strictly qualify as EM radiation ) and modulated RF and microwave fields can have biological effects, though the significance of this is unclear.

The World Health Organization has classified radio frequency electromagnetic radiation as Group 2B – possibly carcinogenic. This group contains possible carcinogens such as lead, DDT, and styrene.

At higher frequencies (some of visible and beyond), the effects of individual photons begin to become important, as these now have enough energy individually to directly or indirectly damage biological molecules. All UV frequencies have been classed as Group 1 carcinogens by the World Health Organization. Ultraviolet radiation from sun exposure is the primary cause of skin cancer.

Thus, at UV frequencies and higher, electromagnetic radiation does more damage to biological systems than simple heating predicts. This is most obvious in the "far" (or "extreme") ultraviolet. UV, with X-ray and gamma radiation, are referred to as ionizing radiation due to the ability of photons of this radiation to produce ions and free radicals in materials (including living tissue). Since such radiation can severely damage life at energy levels that produce little heating, it is considered far more dangerous (in terms of damage-produced per unit of energy, or power) than the rest of the electromagnetic spectrum.

Use as a weapon
The heat ray is an application of EMR that makes use of microwave frequencies to create an unpleasant heating effect in the upper layer of the skin. A publicly known heat ray weapon called the Active Denial System was developed by the US military as an experimental weapon to deny the enemy access to an area. A death ray is a theoretical weapon that delivers heat ray based on electromagnetic energy at levels that are capable of injuring human tissue. An inventor of a death ray, Harry Grindell Matthews, claimed to have lost sight in his left eye while working on his death ray weapon based on a microwave magnetron from the 1920s (a normal microwave oven creates a tissue damaging cooking effect inside the oven at around 2 kV/m).

Derivation from electromagnetic theory
Electromagnetic waves are predicted by the classical laws of electricity and magnetism, known as Maxwell's equations. There are nontrivial solutions of the homogeneous Maxwell's equations (without charges or currents), describing waves of changing electric and magnetic fields. Beginning with Maxwell's equations in free space:

where
 * $$\mathbf{E}$$ and $$\mathbf{B}$$ are the electric field (measured in V/m or N/C) and the magnetic field (measured in T or Wb/m2), respectively;
 * $$\nabla \cdot \mathbf X $$ yields the divergence and $$\nabla \times \mathbf X $$ the curl of a vector field $$\mathbf X;$$
 * $$\frac{\partial \mathbf{B}}{\partial t}$$ and $$\frac{\partial \mathbf{E}}{\partial t}$$ are partial derivatives (rate of change in time, with location fixed) of the magnetic and electric field;
 * $$\mu_0$$ is the permeability of a vacuum (4$\pi$ × 10−7 H/m), and $$\varepsilon_0$$ is the permittivity of a vacuum (8.85 × 10−12 F/m);

Besides the trivial solution $$\mathbf{E} = \mathbf{B} = \mathbf{0},$$ useful solutions can be derived with the following vector identity, valid for all vectors $$\mathbf{A}$$ in some vector field: $$\nabla \times \left( \nabla \times \mathbf{A} \right) = \nabla \left( \nabla \cdot \mathbf{A} \right) - \nabla^2 \mathbf{A}.$$

Taking the curl of the second Maxwell equation ($$) yields:

Evaluating the left hand side of ($$) with the above identity and simplifying using ($$), yields:

Evaluating the right hand side of ($$) by exchanging the sequence of derivatives and inserting the fourth Maxwell equation ($$), yields:

Combining ($$) and ($$) again, gives a vector-valued differential equation for the electric field, solving the homogeneous Maxwell equations:

$$

Taking the curl of the fourth Maxwell equation ($$) results in a similar differential equation for a magnetic field solving the homogeneous Maxwell equations:

$$

Both differential equations have the form of the general wave equation for waves propagating with speed $$c_0,$$ where $$f$$ is a function of time and location, which gives the amplitude of the wave at some time at a certain location: $$\nabla^2 f = \frac{1}{{c_0}^2} \frac{\partial^2 f}{\partial t^2}$$ This is also written as: $$\Box f = 0$$ where $$\Box$$ denotes the so-called d'Alembert operator, which in Cartesian coordinates is given as: $$\Box = \nabla^2 - \frac{1}{{c_0}^2} \frac{\partial^2}{\partial t^2} = \frac{\partial^2}{\partial x^2} + \frac{\partial^2}{\partial y^2} + \frac{\partial^2}{\partial z^2} - \frac{1}{{c_0}^2} \frac{\partial^2}{\partial t^2} \ $$

Comparing the terms for the speed of propagation, yields in the case of the electric and magnetic fields: $$c_0 = \frac{1}{\sqrt{\mu_0 \varepsilon_0}}.$$

This is the speed of light in vacuum. Thus Maxwell's equations connect the vacuum permittivity $$\varepsilon_0$$, the vacuum permeability $$\mu_0$$, and the speed of light, c0, via the above equation. This relationship had been discovered by Wilhelm Eduard Weber and Rudolf Kohlrausch prior to the development of Maxwell's electrodynamics, however Maxwell was the first to produce a field theory consistent with waves traveling at the speed of light.

These are only two equations versus the original four, so more information pertains to these waves hidden within Maxwell's equations. A generic vector wave for the electric field has the form $$\mathbf{E} = \mathbf{E}_0 f{\left( \hat{\mathbf{k}} \cdot \mathbf{x} - c_0 t \right)}$$

Here, $$\mathbf{E}_0$$ is a constant vector, $$f$$ is any second differentiable function, $$ \hat{\mathbf{k}}$$ is a unit vector in the direction of propagation, and $$ {\mathbf{x}} $$ is a position vector. $$f{\left( \hat{\mathbf{k}} \cdot \mathbf{x} - c_0 t \right)}$$ is a generic solution to the wave equation. In other words, $$\nabla^2 f{\left( \hat{\mathbf{k}} \cdot \mathbf{x} - c_0 t \right)} = \frac{1}{{c_0}^2} \frac{\partial^2}{\partial t^2} f{\left( \hat{\mathbf{k}} \cdot \mathbf{x} - c_0 t \right)},$$ for a generic wave traveling in the $$\hat{\mathbf{k}}$$ direction.

From the first of Maxwell's equations, we get $$\nabla \cdot \mathbf{E} = \hat{\mathbf{k}} \cdot \mathbf{E}_0 f'{\left( \hat{\mathbf{k}} \cdot \mathbf{x} - c_0 t \right)} = 0$$

Thus, $$\mathbf{E} \cdot \hat{\mathbf{k}} = 0$$ which implies that the electric field is orthogonal to the direction the wave propagates. The second of Maxwell's equations yields the magnetic field, namely, $$\nabla \times \mathbf{E} = \hat{\mathbf{k}} \times \mathbf{E}_0 f'{\left( \hat{\mathbf{k}} \cdot \mathbf{x} - c_0 t \right)} = -\frac{\partial \mathbf{B}}{\partial t}$$

Thus, $$\mathbf{B} = \frac{1}{c_0} \hat{\mathbf{k}} \times \mathbf{E}$$

The remaining equations will be satisfied by this choice of $$\mathbf{E},\mathbf{B}$$.

The electric and magnetic field waves in the far-field travel at the speed of light. They have a special restricted orientation and proportional magnitudes, $$E_0 = c_0 B_0$$, which can be seen immediately from the Poynting vector. The electric field, magnetic field, and direction of wave propagation are all orthogonal, and the wave propagates in the same direction as $$\mathbf{E} \times \mathbf{B}$$. Also, E and B far-fields in free space, which as wave solutions depend primarily on these two Maxwell equations, are in-phase with each other. This is guaranteed since the generic wave solution is first order in both space and time, and the curl operator on one side of these equations results in first-order spatial derivatives of the wave solution, while the time-derivative on the other side of the equations, which gives the other field, is first-order in time, resulting in the same phase shift for both fields in each mathematical operation.

From the viewpoint of an electromagnetic wave traveling forward, the electric field might be oscillating up and down, while the magnetic field oscillates right and left. This picture can be rotated with the electric field oscillating right and left and the magnetic field oscillating down and up. This is a different solution that is traveling in the same direction. This arbitrariness in the orientation with respect to propagation direction is known as polarization. On a quantum level, it is described as photon polarization. The direction of the polarization is defined as the direction of the electric field.

More general forms of the second-order wave equations given above are available, allowing for both non-vacuum propagation media and sources. Many competing derivations exist, all with varying levels of approximation and intended applications. One very general example is a form of the electric field equation, which was factorized into a pair of explicitly directional wave equations, and then efficiently reduced into a single uni-directional wave equation by means of a simple slow-evolution approximation.

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title: Electromagnetic radiation