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Quantum mechanics is the science of the very small: the body of scientific principles that explains the behaviour of matter and its interactions with energy on the scale of atoms and subatomic particles.
Classical physics explains matter and energy on a scale familiar to human experience, including the behaviour of astronomical bodies. It remains the key to measurement for much of modern science and technology. However, toward the end of the 19th century, scientists discovered phenomena in both the large (macro) and the small (micro) worlds that classical physics could not explain.[1] As Thomas Kuhn explains in his analysis of the philosophy of science, The Structure of Scientific Revolutions, coming to terms with these limitations led to two major revolutions in physics which created a shift in the original scientific paradigm: the theory of relativity and the development of quantum mechanics.[2] This article describes how physicists discovered the limitations of classical physics and developed the main concepts of the quantum theory that replaced it in the early decades of the 20th century. These concepts are described in roughly the order in which they were first discovered. For a more complete history of the subject, see History of quantum mechanics.
In this sense, the word quantum means the minimum amount of any physical entity involved in an interaction. Certain characteristics of matter can take only discrete values.
Light behaves in some respects like particles and in other respects like waves. Matter—particles such as electrons and atoms—exhibits wavelike behaviour too. Some light sources, including neon lights, give off only certain discrete frequencies of light. Quantum mechanics shows that light, along with all other forms of electromagnetic radiation, comes in discrete units, called photons, and predicts its energies, colours, and spectral intensities.
Some aspects of quantum mechanics can seem counterintuitive or even paradoxical, because they describe behaviour quite different from that seen at larger length scales. In the words of Richard Feynman, quantum mechanics deals with "nature as She is – absurd".[3] For example, the uncertainty principle of quantum mechanics means that the more closely one pins down one measurement (such as the position of a particle), the less precise another measurement pertaining to the same particle (such as its momentum) must become.
Thermal radiation is electromagnetic radiation emitted from the surface of an object due to the object's temperature. If an object is heated sufficiently, it starts to emit light at the red end of the spectrum, as it becomes red hot.
Heating it further causes the colour to change from red to yellow, white, and blue, as light at shorter wavelengths (higher frequencies) begins to be emitted. A perfect emitter is also a perfect absorber: When it is cold, such an object looks perfectly black, because it absorbs all the light that falls on it and emits none. Consequently, an ideal thermal emitter is known as a black body, and the radiation it emits is called black-body radiation.
In the late 19th century, thermal radiation had been fairly well characterized experimentally.[note 1] However, classical physics was unable to explain the relationship between temperatures and predominant frequencies of radiation. Physicists searched for a single theory that explained all the experimental results.
The first model that was able to explain the full spectrum of thermal radiation was put forward by Max Planck in 1900.[4] He proposed a mathematical model in which the thermal radiation was in equilibrium with a set of harmonic oscillators. To reproduce the experimental results, he had to assume that each oscillator produced an integer number of units of energy at its single characteristic frequency, rather than being able to emit any arbitrary amount of energy. In other words, the energy of each oscillator was quantized.[note 2] The quantum of energy for each oscillator, according to Planck, was proportional to the frequency of the oscillator; the constant of proportionality is now known as the Planck constant. The Planck constant, usually written as h, has the value of 6.63×10−34 J s. So, the energy E of an oscillator of frequency f is given by
Planck's law was the first quantum theory in physics, and Planck won the Nobel Prize in 1918 "in recognition of the services he rendered to the advancement of Physics by his discovery of energy quanta".[6] At the time, however, Planck's view was that quantization was purely a mathematical construct, rather than (as is now believed) a fundamental change in our understanding of the world.[7]
In 1905, Albert Einstein took an extra step. He suggested that quantisation was not just a mathematical construct, but that the energy in a beam of light actually occurs in individual packets, which are now called photons.[8] The energy of a single photon is given by its frequency multiplied by Planck's constant:
In 1887, Heinrich Hertz observed that, when light with sufficient frequency hits a metallic surface, it emits electrons.[9] In 1902, Philipp Lenard discovered that the maximum possible energy of an ejected electron is related to the frequency of the light, not to its intensity: if the frequency is too low, no electrons are ejected regardless of the intensity. Strong beams of light toward the red end of the spectrum might produce no electrical potential at all, while weak beams of light toward the violet end of the spectrum would produce higher and higher voltages. The lowest frequency of light that can cause electrons to be emitted, called the threshold frequency, is different for different metals. This observation is at odds with classical electromagnetism, which predicts that the electron's energy should be proportional to the intensity of the radiation.[10]:24 So when physicists first discovered devices exhibiting the photoelectric effect, they initially expected that a higher intensity of light would produce a higher voltage from the photoelectric device.
Einstein explained the effect by postulating that a beam of light is a stream of particles ("photons") and that, if the beam is of frequency f, then each photon has an energy equal to hf.[9] An electron is likely to be struck only by a single photon, which imparts at most an energy hf to the electron.[9] Therefore, the intensity of the beam has no effect[note 3] and only its frequency determines the maximum energy that can be imparted to the electron.[9]
To explain the threshold effect, Einstein argued that it takes a certain amount of energy, called the work function, denoted by φ, to remove an electron from the metal.[9] This amount of energy is different for each metal. If the energy of the photon is less than the work function, then it does not carry sufficient energy to remove the electron from the metal. The threshold frequency, f0, is the frequency of a photon whose energy is equal to the work function:
All photons of the same frequency have identical energy, and all photons of different frequencies have proportionally different energies.
Although the energy imparted by photons is invariant at any given frequency, the initial energy state of the electrons in a photoelectric device prior to absorption of light is not necessarily uniform. Anomalous results may occur in the case of individual electrons. For instance, an electron that was already excited above the equilibrium level of the photoelectric device might be ejected when it absorbed uncharacteristically low frequency illumination. Statistically, however, the characteristic behaviour of a photoelectric device will reflect the behaviour of the vast majority of its electrons, which will be at their equilibrium level. This point is helpful in comprehending the distinction between the study of individual particles in quantum dynamics and the study of massed particles in classical physics.
A second, related, puzzle was the emission spectrum of atoms. When a gas is heated, it gives off light only at discrete frequencies. For example, the visible light given off by hydrogen consists of four different colours, as shown in the picture below. The intensity of the light at different frequencies is also different. By contrast, white light consists of a continuous emission across the whole range of visible frequencies. By the end of the nineteenth century, a simple rule had been found which showed how the frequencies of the different lines were related to each other, though without explaining why this was, or making any prediction about the intensities. The formula also predicted some additional spectral lines in ultraviolet and infrared light which had not been observed at the time. These lines were later observed experimentally, raising confidence in the value of the formula.
In 1913 Niels Bohr proposed a new model of the atom that included quantized electron orbits: electrons still orbit the nucleus much as planets orbit around the sun, but they are only permitted to inhabit certain orbits, not to orbit at any distance.[14] When an atom emitted (or absorbed) energy, the electron did not move in a continuous trajectory from one orbit around the nucleus to another, as might be expected classically. Instead, the electron would jump instantaneously from one orbit to another, giving off the emitted light in the form of a photon.[15] The possible energies of photons given off by each element were determined by the differences in energy between the orbits, and so the emission spectrum for each element would contain a number of lines.[16]
Starting from only one simple assumption about the rule that the orbits must obey, the Bohr model was able to relate the observed spectral lines in the emission spectrum of hydrogen to previously-known constants. In Bohr's model the electron simply wasn't allowed to emit energy continuously and crash into the nucleus: once it was in the closest permitted orbit, it was stable forever. Bohr's model didn't explain why the orbits should be quantised in that way, and it was also unable to make accurate predictions for atoms with more than one electron, or to explain why some spectral lines are brighter than others.
Although some of the fundamental assumptions of the Bohr model were soon found to be wrong, the key result that the discrete lines in emission spectra are due to some property of the electrons in atoms being quantised is correct. The way that the electrons actually behave is strikingly different from Bohr's atom, and from what we see in the world of our everyday experience; this modern quantum mechanical model of the atom is discussed below.
Just as light has both wave-like and particle-like properties, matter also has wave-like properties.[17]
Matter behaving as a wave was first demonstrated experimentally for electrons: A beam of electrons can exhibit diffraction, just like a beam of light or a water wave.[note 8] Similar wave-like phenomena were later shown for atoms and even small molecules.
The wavelength, λ, associated with any object is related to its momentum, p, through the Planck constant, h:[18][19]
The concept of wave–particle duality says that neither the classical concept of "particle" nor of "wave" can fully describe the behaviour of quantum-scale objects, either photons or matter. Wave–particle duality is an example of the principle of complementarity in quantum physics. An elegant example of wave–particle duality, the double slit experiment, is discussed in the section below.
In the double-slit experiment, as originally performed by Thomas Young and Augustin Fresnel in 1827, a beam of light is directed through two narrow, closely spaced slits, producing an interference pattern of light and dark bands on a screen. If one of the slits is covered up, one might naively expect that the intensity of the fringes due to interference would be halved everywhere. In fact, a much simpler pattern is seen, a simple diffraction pattern. Closing one slit results in a much simpler pattern diametrically opposite the open slit. Exactly the same behaviour can be demonstrated in water waves, and so the double-slit experiment was seen as a demonstration of the wave nature of light.
The double-slit experiment has also been performed using electrons, atoms, and even molecules, and the same type of interference pattern is seen. Thus it has been demonstrated that all matter possesses both particle and wave characteristics.
Even if the source intensity is turned down, so that only one particle (e.g. photon or electron) is passing through the apparatus at a time, the same interference pattern develops over time. The quantum particle acts as a wave when passing through the double slits, but as a particle when it is detected. This is a typical feature of quantum complementarity: a quantum particle will act as a wave in an experiment to measure its wave-like properties, and like a particle in an experiment to measure its particle-like properties. The point on the detector screen where any individual particle shows up will be the result of a random process. However, the distribution pattern of many individual particles will mimic the diffraction pattern produced by waves.
De Broglie's treatment of quantum events served as a starting point for Schrödinger when he set out to construct a wave equation to describe quantum theoretical events.
Ralph Kronig originated the idea that particles such as atoms or electrons behave as if they rotate, or "spin", about an axis. Spin would account for the missing magnetic moment[clarification needed], and allow two electrons in the same orbital to occupy distinct quantum states if they "spun" in opposite directions, thus satisfying the exclusion principle. The quantum number represented the sense (positive or negative) of spin.
The choice of orientation of the magnetic field used in the Stern-Gerlach experiment is arbitrary. In the animation shown here, the field is vertical and so the atoms are deflected either up or down. If the magnet is rotated a quarter turn, the atoms will be deflected either left or right. Using a vertical field shows that the spin along the vertical axis is quantised, and using a horizontal field shows that the spin along the horizontal axis is quantised.
If, instead of hitting a detector screen, one of the beams of atoms coming out of the Stern-Gerlach apparatus is passed into another (inhomogeneous) magnetic field oriented in the same direction, all of the atoms will be deflected the same way in this second field. However, if the second field is oriented at 90° to the first, then half of the atoms will be deflected one way and half the other, so that the atom's spin about the horizontal and vertical axes are independent of each other. However, if one of these beams (e.g. the atoms that were deflected up then left) is passed into a third magnetic field, oriented the same way as the first, half of the atoms will go one way and half the other. The action of measuring the atoms' spin with respect to a horizontal field has changed their spin with respect to a vertical field.
The Stern-Gerlach experiment demonstrates a number of important features of quantum mechanics:
In 1925, Werner Heisenberg attempted to solve one of the problems that the Bohr model left unanswered, explaining the intensities of the different lines in the hydrogen emission spectrum. Through a series of mathematical analogies, he wrote out the quantum mechanical analogue for the classical computation of intensities.[21] Shortly afterwards, Heisenberg's colleague Max Born realised that Heisenberg's method of calculating the probabilities for transitions between the different energy levels could best be expressed by using the mathematical concept of matrices.[note 9]
In the same year, building on de Broglie's hypothesis, Erwin Schrödinger developed the equation that describes the behaviour of a quantum mechanical wave.[22] The mathematical model, called the Schrödinger equation after its creator, is central to quantum mechanics, defines the permitted stationary states of a quantum system, and describes how the quantum state of a physical system changes in time.[23] The wave itself is described by a mathematical function known as a "wave function". Schrödinger said that the wave function provides the "means for predicting probability of measurement results".[24]
Schrödinger was able to calculate the energy levels of hydrogen by treating a hydrogen atom's electron as a classical wave, moving in a well of electrical potential created by the proton. This calculation accurately reproduced the energy levels of the Bohr model.
In May 1926, Schrödinger proved that Heisenberg's matrix mechanics and his own wave mechanics made the same predictions about the properties and behaviour of the electron; mathematically, the two theories were identical. Yet the two men disagreed on the interpretation of their mutual theory. For instance, Heisenberg saw no problem in the theoretical prediction of instantaneous transitions of electrons between orbits in an atom, but Schrödinger hoped that a theory based on continuous wave-like properties could avoid what he called (as paraphrased by Wilhelm Wien) "this nonsense about quantum jumps."[25]
Bohr, Heisenberg and others tried to explain what these experimental results and mathematical models really mean. Their description, known as the Copenhagen interpretation of quantum mechanics, aimed to describe the nature of reality that was being probed by the measurements and described by the mathematical formulations of quantum mechanics.
The main principles of the Copenhagen interpretation are:
Suppose it is desired to measure the position and speed of an object – for example a car going through a radar speed trap. It can be assumed that the car has a definite position and speed at a particular moment in time. How accurately these values can be measured depends on the quality of the measuring equipment – if the precision of the measuring equipment is improved, it will provide a result that is closer to the true value. In particular, it would be assumed that the precision of measuring the speed of the car does not affect its position, and vice versa.
In 1927, Heisenberg proved that these assumptions are not correct.[27] Quantum mechanics shows that certain pairs of physical properties, like position and speed, cannot both be known to arbitrary precision: the more precisely one property is known, the less precisely the other can be known. This statement is known as the uncertainty principle. The uncertainty principle isn't a statement about the accuracy of our measuring equipment, but about the nature of the system itself – our assumption that the car had a definite position and speed was incorrect. On a scale of cars and people, these uncertainties are too small to notice, but when dealing with atoms and electrons they become critical.[28]
Heisenberg gave, as an illustration, the measurement of the position and momentum of an electron using a photon of light. In measuring the electron's position, the higher the frequency of the photon the more accurate is the measurement of the position of the impact, but the greater is the disturbance of the electron, which absorbs a random amount of energy, rendering the measurement obtained of its momentum increasingly uncertain (momentum is velocity multiplied by mass), for one is necessarily measuring its post-impact disturbed momentum, from the collision products, not its original momentum. With a photon of lower frequency the disturbance – hence uncertainty – in the momentum is less, but so is the accuracy of the measurement of the position of the impact.[29]
The uncertainty principle shows mathematically that the product of the uncertainty in the position and momentum of a particle (momentum is velocity multiplied by mass) could never be less than a certain value, and that this value is related to Planck's constant.
In the Stern-Gerlach experiment discussed above, the spin of the atom about the vertical axis has two eigenstates: up and down. Before measuring it, we can only say that any individual atom has equal probability of being found to have spin up or spin down. The measurement process causes the wavefunction to collapse into one of the two states.
The eigenstates of spin about the vertical axis are not simultaneously eigenstates of spin about the horizontal axis, so this atom has equal probability of being found to having either value of spin about the horizontal axis. As described in the section above, measuring the spin about the horizontal axis can allow an atom which was spin up to become spin down: measuring its spin about the horizontal axis collapses its wave function into one of the eigenstates of this measurement, which means it is no longer in an eignenstate of spin about the vertical axis, so can take either value.
In 1924, Wolfgang Pauli proposed a new quantum degree of freedom (or quantum number), with two possible values, to resolve inconsistencies between observed molecular spectra and the predictions of quantum mechanics. In particular, the spectrum of atomic hydrogen had a doublet, or pair of lines differing by a small amount, where only one line was expected. Pauli formulated his exclusion principle, stating that "There cannot exist an atom in such a quantum state that two electrons within [it] have the same set of quantum numbers."[30]
A year later, Uhlenbeck and Goudsmit identified Pauli's new degree of freedom with the property called spin whose effects were observed in the Stern–Gerlach experiment.
Schrödinger was able to calculate the energy levels of hydrogen by treating a hydrogen atom's electron as a wave, represented by the "wave function" Ψ, in an electric potential well, V, created by the proton. The solutions to Schrödinger's equation are distributions of probabilities for electron positions and locations. Orbitals have a range of different shapes in three dimensions. The energies of the different orbitals can be calculated, and they accurately match the energy levels of the Bohr model.
Within Schrödinger's picture, each electron has four properties:
The first property describing the orbital is the principal quantum number, n, which is the same as in Bohr's model. n denotes the energy level of each orbital. The possible values for n are integers:
The third quantum number, the magnetic quantum number, describes the magnetic moment of the electron, and is denoted by ml (or simply m). The possible values for ml are integers from −l to l:
The fourth quantum number, the spin quantum number (pertaining to the "orientation" of the electron's spin) is denoted ms, with values +1⁄2 or −1⁄2.
The chemist Linus Pauling wrote, by way of example:
In 1928, Paul Dirac extended the Pauli equation, which described spinning electrons, to account for special relativity. The result was a theory that dealt properly with events, such as the speed at which an electron orbits the nucleus, occurring at a substantial fraction of the speed of light. By using the simplest electromagnetic interaction, Dirac was able to predict the value of the magnetic moment associated with the electron's spin, and found the experimentally observed value, which was too large to be that of a spinning charged sphere governed by classical physics. He was able to solve for the spectral lines of the hydrogen atom, and to reproduce from physical first principles Sommerfeld's successful formula for the fine structure of the hydrogen spectrum.
Dirac's equations sometimes yielded a negative value for energy, for which he proposed a novel solution: he posited the existence of an antielectron and of a dynamical vacuum. This led to the many-particle quantum field theory.
The Pauli exclusion principle says that two electrons in one system cannot be in the same state. Nature leaves open the possibility, however, that two electrons can have both states "superimposed" over each of them. Recall that the wave functions that emerge simultaneously from the double slits arrive at the detection screen in a state of superposition. Nothing is certain until the superimposed waveforms "collapse", At that instant an electron shows up somewhere in accordance with the probability that is the square of the absolute value of the sum of the complex-valued amplitudes of the two superimposed waveforms. The situation there is already very abstract. A concrete way of thinking about entangled photons, photons in which two contrary states are superimposed on each of them in the same event, is as follows:
Imagine that the superposition of a state that can be mentally labeled as blue and another state that can be mentally labeled as red will then appear (in imagination, of course) as a purple state. Two photons are produced as the result of the same atomic event. Perhaps they are produced by the excitation of a crystal that characteristically absorbs a photon of a certain frequency and emits two photons of half the original frequency. So the two photons come out "purple." If the experimenter now performs some experiment that will determine whether one of the photons is either blue or red, then that experiment changes the photon involved from one having a superposition of "blue" and "red" characteristics to a photon that has only one of those characteristics. The problem that Einstein had with such an imagined situation was that if one of these photons had been kept bouncing between mirrors in a laboratory on earth, and the other one had traveled halfway to the nearest star, when its twin was made to reveal itself as either blue or red, that meant that the distant photon now had to lose its "purple" status too. So whenever it might be investigated after its twin had been measured, it would necessarily show up in the opposite state to whatever its twin had revealed.
In trying to show that quantum mechanics was not a complete theory, Einstein started with the theory's prediction that two or more particles that have interacted in the past can appear strongly correlated when their various properties are later measured. He sought to explain this seeming interaction in a classical way, through their common past, and preferably not by some "spooky action at a distance." The argument is worked out in a famous paper, Einstein, Podolsky, and Rosen (1935; abbreviated EPR), setting out what is now called the EPR paradox. Assuming what is now usually called local realism, EPR attempted to show from quantum theory that a particle has both position and momentum simultaneously, while according to the Copenhagen interpretation, only one of those two properties actually exists and only at the moment that it is being measured. EPR concluded that quantum theory is incomplete in that it refuses to consider physical properties which objectively exist in nature. (Einstein, Podolsky, & Rosen 1935 is currently Einstein's most cited publication in physics journals.) In the same year, Erwin Schrödinger used the word "entanglement" and declared: "I would not call that one but rather the characteristic trait of quantum mechanics."[32] The question of whether entanglement is a real condition is still in dispute.[33] The Bell inequalities are the most powerful challenge to Einstein's claims.
The idea of quantum field theory began in the late 1920s with British physicist Paul Dirac, when he attempted to quantise the electromagnetic field – a procedure for constructing a quantum theory starting from a classical theory.
A field in physics is "a region or space in which a given effect (such as magnetism) exists."[34] Other effects that manifest themselves as fields are gravitation and static electricity.[35] In 2008, physicist Richard Hammond wrote that
In 1931, Dirac proposed the existence of particles that later became known as anti-matter.[37] Dirac shared the Nobel Prize in Physics for 1933 with Schrödinger, "for the discovery of new productive forms of atomic theory."[38]
Electric charges are the sources of, and create, electric fields. An electric field is a field which exerts a force on any particles that carry electric charges, at any point in space. This includes the electron, proton, and even quarks, among others. As a force is exerted, electric charges move, a current flows and a magnetic field is produced. The magnetic field, in turn causes electric current (moving electrons). The interacting electric and magnetic field is called an electromagnetic field.
The physical description of interacting charged particles, electrical currents, electrical fields, and magnetic fields is called electromagnetism.
In 1928 Paul Dirac produced a relativistic quantum theory of electromagnetism. This was the progenitor to modern quantum electrodynamics, in that it had essential ingredients of the modern theory. However, the problem of unsolvable infinities developed in this relativistic quantum theory. Years later, renormalization solved this problem. Initially viewed as a suspect, provisional procedure by some of its originators, renormalization eventually was embraced as an important and self-consistent tool in QED and other fields of physics. Also, in the late 1940s Feynman's diagrams depicted all possible interactions pertaining to a given event. The diagrams showed that the electromagnetic force is the interactions of photons between interacting particles.
An example of a prediction of quantum electrodynamics which has been verified experimentally is the Lamb shift. This refers to an effect whereby the quantum nature of the electromagnetic field causes the energy levels in an atom or ion to deviate slightly from what they would otherwise be. As a result, spectral lines may shift or split.
In the 1960s physicists realized that QED broke down at extremely high energies. From this inconsistency the Standard Model of particle physics was discovered, which remedied the higher energy breakdown in theory. The Standard Model unifies the electromagnetic and weak interactions into one theory. This is called the electroweak theory.
In even the simple light switch, quantum tunnelling is absolutely vital, as otherwise the electrons in the electric current could not penetrate the potential barrier made up of a layer of oxide. Flash memory chips found in USB drives also use quantum tunnelling, to erase their memory cells.[39]
Classical physics explains matter and energy on a scale familiar to human experience, including the behaviour of astronomical bodies. It remains the key to measurement for much of modern science and technology. However, toward the end of the 19th century, scientists discovered phenomena in both the large (macro) and the small (micro) worlds that classical physics could not explain.[1] As Thomas Kuhn explains in his analysis of the philosophy of science, The Structure of Scientific Revolutions, coming to terms with these limitations led to two major revolutions in physics which created a shift in the original scientific paradigm: the theory of relativity and the development of quantum mechanics.[2] This article describes how physicists discovered the limitations of classical physics and developed the main concepts of the quantum theory that replaced it in the early decades of the 20th century. These concepts are described in roughly the order in which they were first discovered. For a more complete history of the subject, see History of quantum mechanics.
In this sense, the word quantum means the minimum amount of any physical entity involved in an interaction. Certain characteristics of matter can take only discrete values.
Light behaves in some respects like particles and in other respects like waves. Matter—particles such as electrons and atoms—exhibits wavelike behaviour too. Some light sources, including neon lights, give off only certain discrete frequencies of light. Quantum mechanics shows that light, along with all other forms of electromagnetic radiation, comes in discrete units, called photons, and predicts its energies, colours, and spectral intensities.
Some aspects of quantum mechanics can seem counterintuitive or even paradoxical, because they describe behaviour quite different from that seen at larger length scales. In the words of Richard Feynman, quantum mechanics deals with "nature as She is – absurd".[3] For example, the uncertainty principle of quantum mechanics means that the more closely one pins down one measurement (such as the position of a particle), the less precise another measurement pertaining to the same particle (such as its momentum) must become.
The first quantum theory: Max Planck and black-body radiation
Hot metalwork. The yellow-orange glow is the visible part of the thermal radiation emitted due to the high temperature. Everything else in the picture is glowing with thermal radiation as well, but less brightly and at longer wavelengths than the human eye can detect. A far-infrared camera can observe this radiation.
Thermal radiation is electromagnetic radiation emitted from the surface of an object due to the object's temperature. If an object is heated sufficiently, it starts to emit light at the red end of the spectrum, as it becomes red hot.
Heating it further causes the colour to change from red to yellow, white, and blue, as light at shorter wavelengths (higher frequencies) begins to be emitted. A perfect emitter is also a perfect absorber: When it is cold, such an object looks perfectly black, because it absorbs all the light that falls on it and emits none. Consequently, an ideal thermal emitter is known as a black body, and the radiation it emits is called black-body radiation.
In the late 19th century, thermal radiation had been fairly well characterized experimentally.[note 1] However, classical physics was unable to explain the relationship between temperatures and predominant frequencies of radiation. Physicists searched for a single theory that explained all the experimental results.
Predictions of the amount of thermal radiation of different frequencies emitted by a body. Correct values predicted by Planck's law (green) contrasted against the classical values of Rayleigh-Jeans law (red) and Wien approximation (blue).
The first model that was able to explain the full spectrum of thermal radiation was put forward by Max Planck in 1900.[4] He proposed a mathematical model in which the thermal radiation was in equilibrium with a set of harmonic oscillators. To reproduce the experimental results, he had to assume that each oscillator produced an integer number of units of energy at its single characteristic frequency, rather than being able to emit any arbitrary amount of energy. In other words, the energy of each oscillator was quantized.[note 2] The quantum of energy for each oscillator, according to Planck, was proportional to the frequency of the oscillator; the constant of proportionality is now known as the Planck constant. The Planck constant, usually written as h, has the value of 6.63×10−34 J s. So, the energy E of an oscillator of frequency f is given by
E=nhf,wheren=1,2,3,… [5]
Planck's law was the first quantum theory in physics, and Planck won the Nobel Prize in 1918 "in recognition of the services he rendered to the advancement of Physics by his discovery of energy quanta".[6] At the time, however, Planck's view was that quantization was purely a mathematical construct, rather than (as is now believed) a fundamental change in our understanding of the world.[7]
Photons: the quantisation of light
In 1905, Albert Einstein took an extra step. He suggested that quantisation was not just a mathematical construct, but that the energy in a beam of light actually occurs in individual packets, which are now called photons.[8] The energy of a single photon is given by its frequency multiplied by Planck's constant:
E=hf
The photoelectric effect
Einstein explained the effect by postulating that a beam of light is a stream of particles ("photons") and that, if the beam is of frequency f, then each photon has an energy equal to hf.[9] An electron is likely to be struck only by a single photon, which imparts at most an energy hf to the electron.[9] Therefore, the intensity of the beam has no effect[note 3] and only its frequency determines the maximum energy that can be imparted to the electron.[9]
To explain the threshold effect, Einstein argued that it takes a certain amount of energy, called the work function, denoted by φ, to remove an electron from the metal.[9] This amount of energy is different for each metal. If the energy of the photon is less than the work function, then it does not carry sufficient energy to remove the electron from the metal. The threshold frequency, f0, is the frequency of a photon whose energy is equal to the work function:
φ=hf0.
EK=hf−φ=h(f−f0).
Consequences of the light being quantised
The relationship between the frequency of electromagnetic radiation and the energy of each individual photon is why ultraviolet light can cause sunburn, but visible or infrared light cannot. A photon of ultraviolet light will deliver a high amount of energy – enough to contribute to cellular damage such as occurs in a sunburn. A photon of infrared light will deliver a lower amount of energy – only enough to warm one's skin. So, an infrared lamp can warm a large surface, perhaps large enough to keep people comfortable in a cold room, but it cannot give anyone a sunburn.All photons of the same frequency have identical energy, and all photons of different frequencies have proportionally different energies.
Although the energy imparted by photons is invariant at any given frequency, the initial energy state of the electrons in a photoelectric device prior to absorption of light is not necessarily uniform. Anomalous results may occur in the case of individual electrons. For instance, an electron that was already excited above the equilibrium level of the photoelectric device might be ejected when it absorbed uncharacteristically low frequency illumination. Statistically, however, the characteristic behaviour of a photoelectric device will reflect the behaviour of the vast majority of its electrons, which will be at their equilibrium level. This point is helpful in comprehending the distinction between the study of individual particles in quantum dynamics and the study of massed particles in classical physics.
The quantisation of matter: the Bohr model of the atom
By the dawn of the 20th century, evidence required a model of the atom with a diffuse cloud of negatively-charged electrons surrounding a small, dense, positively-charged nucleus. These properties suggested a model in which the electrons circle around the nucleus like planets orbiting a sun.[note 5] However, it was also known that the atom in this model would be unstable: according to classical theory orbiting electrons are undergoing centripetal acceleration, and should therefore give off electromagnetic radiation, the loss of energy also causing them to spiral toward the nucleus, colliding with it in a fraction of a second.A second, related, puzzle was the emission spectrum of atoms. When a gas is heated, it gives off light only at discrete frequencies. For example, the visible light given off by hydrogen consists of four different colours, as shown in the picture below. The intensity of the light at different frequencies is also different. By contrast, white light consists of a continuous emission across the whole range of visible frequencies. By the end of the nineteenth century, a simple rule had been found which showed how the frequencies of the different lines were related to each other, though without explaining why this was, or making any prediction about the intensities. The formula also predicted some additional spectral lines in ultraviolet and infrared light which had not been observed at the time. These lines were later observed experimentally, raising confidence in the value of the formula.
Emission spectrum of hydrogen. When excited, hydrogen gas gives off light in four distinct colours (spectral lines) in the visible spectrum, as well as a number of lines in the infrared and ultraviolet.
The Bohr model of the atom, showing an electron transitioning from one orbit to another by emitting a photon.
In 1913 Niels Bohr proposed a new model of the atom that included quantized electron orbits: electrons still orbit the nucleus much as planets orbit around the sun, but they are only permitted to inhabit certain orbits, not to orbit at any distance.[14] When an atom emitted (or absorbed) energy, the electron did not move in a continuous trajectory from one orbit around the nucleus to another, as might be expected classically. Instead, the electron would jump instantaneously from one orbit to another, giving off the emitted light in the form of a photon.[15] The possible energies of photons given off by each element were determined by the differences in energy between the orbits, and so the emission spectrum for each element would contain a number of lines.[16]
Starting from only one simple assumption about the rule that the orbits must obey, the Bohr model was able to relate the observed spectral lines in the emission spectrum of hydrogen to previously-known constants. In Bohr's model the electron simply wasn't allowed to emit energy continuously and crash into the nucleus: once it was in the closest permitted orbit, it was stable forever. Bohr's model didn't explain why the orbits should be quantised in that way, and it was also unable to make accurate predictions for atoms with more than one electron, or to explain why some spectral lines are brighter than others.
Although some of the fundamental assumptions of the Bohr model were soon found to be wrong, the key result that the discrete lines in emission spectra are due to some property of the electrons in atoms being quantised is correct. The way that the electrons actually behave is strikingly different from Bohr's atom, and from what we see in the world of our everyday experience; this modern quantum mechanical model of the atom is discussed below.
Wave-particle duality
Louis de Broglie in 1929. De Broglie won the Nobel Prize in Physics for his prediction that matter acts as a wave, made in his 1924 PhD thesis.
Just as light has both wave-like and particle-like properties, matter also has wave-like properties.[17]
Matter behaving as a wave was first demonstrated experimentally for electrons: A beam of electrons can exhibit diffraction, just like a beam of light or a water wave.[note 8] Similar wave-like phenomena were later shown for atoms and even small molecules.
The wavelength, λ, associated with any object is related to its momentum, p, through the Planck constant, h:[18][19]
p=hλ.
The concept of wave–particle duality says that neither the classical concept of "particle" nor of "wave" can fully describe the behaviour of quantum-scale objects, either photons or matter. Wave–particle duality is an example of the principle of complementarity in quantum physics. An elegant example of wave–particle duality, the double slit experiment, is discussed in the section below.
The double-slit experiment
In the double-slit experiment, as originally performed by Thomas Young and Augustin Fresnel in 1827, a beam of light is directed through two narrow, closely spaced slits, producing an interference pattern of light and dark bands on a screen. If one of the slits is covered up, one might naively expect that the intensity of the fringes due to interference would be halved everywhere. In fact, a much simpler pattern is seen, a simple diffraction pattern. Closing one slit results in a much simpler pattern diametrically opposite the open slit. Exactly the same behaviour can be demonstrated in water waves, and so the double-slit experiment was seen as a demonstration of the wave nature of light.
The double-slit experiment has also been performed using electrons, atoms, and even molecules, and the same type of interference pattern is seen. Thus it has been demonstrated that all matter possesses both particle and wave characteristics.
Even if the source intensity is turned down, so that only one particle (e.g. photon or electron) is passing through the apparatus at a time, the same interference pattern develops over time. The quantum particle acts as a wave when passing through the double slits, but as a particle when it is detected. This is a typical feature of quantum complementarity: a quantum particle will act as a wave in an experiment to measure its wave-like properties, and like a particle in an experiment to measure its particle-like properties. The point on the detector screen where any individual particle shows up will be the result of a random process. However, the distribution pattern of many individual particles will mimic the diffraction pattern produced by waves.
Application to the Bohr model
De Broglie expanded the Bohr model of the atom by showing that an electron in orbit around a nucleus could be thought of as having wave-like properties. In particular, an electron will be observed only in situations that permit a standing wave around a nucleus. An example of a standing wave is a violin string, which is fixed at both ends and can be made to vibrate. The waves created by a stringed instrument appear to oscillate in place, moving from crest to trough in an up-and-down motion. The wavelength of a standing wave is related to the length of the vibrating object and the boundary conditions. For example, because the violin string is fixed at both ends, it can carry standing waves of wavelengths 2l/n, where l is the length and n is a positive integer. De Broglie suggested that the allowed electron orbits were those for which the circumference of the orbit would be an integer number of wavelengths. The electron's wavelength therefore determines that only Bohr orbits of certain distances from the nucleus are possible. In turn, at any distance from the nucleus smaller than a certain value it would be impossible to establish an orbit. The minimum possible distance from the nucleus is called the Bohr radius.[20]De Broglie's treatment of quantum events served as a starting point for Schrödinger when he set out to construct a wave equation to describe quantum theoretical events.
Spin
Main article: Spin (physics)
In 1922, Otto Stern and Walther Gerlach shot silver atoms through an (inhomogeneous) magnetic field. In classical mechanics, a magnet thrown through a magnetic field may be, depending on its orientation (if it is pointing with its northern pole upwards or down, or somewhere in between), deflected a small or large distance upwards or downwards. The atoms that Stern and Gerlach shot through the magnetic field acted in a similar way. However, while the magnets could be deflected variable distances, the atoms would always be deflected a constant distance either up or down. This implied that the property of the atom which corresponds to the magnet's orientation must be quantised, taking one of two values (either up or down), as opposed to being chosen freely from any angle.Ralph Kronig originated the idea that particles such as atoms or electrons behave as if they rotate, or "spin", about an axis. Spin would account for the missing magnetic moment[clarification needed], and allow two electrons in the same orbital to occupy distinct quantum states if they "spun" in opposite directions, thus satisfying the exclusion principle. The quantum number represented the sense (positive or negative) of spin.
The choice of orientation of the magnetic field used in the Stern-Gerlach experiment is arbitrary. In the animation shown here, the field is vertical and so the atoms are deflected either up or down. If the magnet is rotated a quarter turn, the atoms will be deflected either left or right. Using a vertical field shows that the spin along the vertical axis is quantised, and using a horizontal field shows that the spin along the horizontal axis is quantised.
If, instead of hitting a detector screen, one of the beams of atoms coming out of the Stern-Gerlach apparatus is passed into another (inhomogeneous) magnetic field oriented in the same direction, all of the atoms will be deflected the same way in this second field. However, if the second field is oriented at 90° to the first, then half of the atoms will be deflected one way and half the other, so that the atom's spin about the horizontal and vertical axes are independent of each other. However, if one of these beams (e.g. the atoms that were deflected up then left) is passed into a third magnetic field, oriented the same way as the first, half of the atoms will go one way and half the other. The action of measuring the atoms' spin with respect to a horizontal field has changed their spin with respect to a vertical field.
The Stern-Gerlach experiment demonstrates a number of important features of quantum mechanics:
- a feature of the natural world has been demonstrated to be quantised, and only able to take certain discrete values
- particles possess an intrinsic angular momentum that is closely analogous to the angular momentum of a classically spinning object
- measurement changes the system being measured in quantum mechanics. Only the spin of an object in one direction can be known, and observing the spin in another direction will destroy the original information about the spin.
- quantum mechanics is probabilistic: whether the spin of any individual atom sent into the apparatus is positive or negative is random.
Development of modern quantum mechanics
In 1925, Werner Heisenberg attempted to solve one of the problems that the Bohr model left unanswered, explaining the intensities of the different lines in the hydrogen emission spectrum. Through a series of mathematical analogies, he wrote out the quantum mechanical analogue for the classical computation of intensities.[21] Shortly afterwards, Heisenberg's colleague Max Born realised that Heisenberg's method of calculating the probabilities for transitions between the different energy levels could best be expressed by using the mathematical concept of matrices.[note 9]
In the same year, building on de Broglie's hypothesis, Erwin Schrödinger developed the equation that describes the behaviour of a quantum mechanical wave.[22] The mathematical model, called the Schrödinger equation after its creator, is central to quantum mechanics, defines the permitted stationary states of a quantum system, and describes how the quantum state of a physical system changes in time.[23] The wave itself is described by a mathematical function known as a "wave function". Schrödinger said that the wave function provides the "means for predicting probability of measurement results".[24]
Schrödinger was able to calculate the energy levels of hydrogen by treating a hydrogen atom's electron as a classical wave, moving in a well of electrical potential created by the proton. This calculation accurately reproduced the energy levels of the Bohr model.
In May 1926, Schrödinger proved that Heisenberg's matrix mechanics and his own wave mechanics made the same predictions about the properties and behaviour of the electron; mathematically, the two theories were identical. Yet the two men disagreed on the interpretation of their mutual theory. For instance, Heisenberg saw no problem in the theoretical prediction of instantaneous transitions of electrons between orbits in an atom, but Schrödinger hoped that a theory based on continuous wave-like properties could avoid what he called (as paraphrased by Wilhelm Wien) "this nonsense about quantum jumps."[25]
Copenhagen interpretation
The Niels Bohr Institute in Copenhagen, which was a focal point for researchers in quantum mechanics and related subjects in the 1920s and 1930s. Most of the world's best known theoretical physicists spent time there.
Bohr, Heisenberg and others tried to explain what these experimental results and mathematical models really mean. Their description, known as the Copenhagen interpretation of quantum mechanics, aimed to describe the nature of reality that was being probed by the measurements and described by the mathematical formulations of quantum mechanics.
The main principles of the Copenhagen interpretation are:
- A system is completely described by a wave function, usually represented by the Greek letter
ψ ("psi"). (Heisenberg) - How
ψ changes over time is given by the Schrödinger equation. - The description of nature is essentially probabilistic. The probability of an event – for example, where on the screen a particle will show up in the two slit experiment – is related to the square of the absolute value of the amplitude of its wave function. (Born rule, due to Max Born, which gives a physical meaning to the wave function in the Copenhagen interpretation: the probability amplitude)
- It is not possible to know the values of all of the properties of the system at the same time; those properties that are not known with precision must be described by probabilities. (Heisenberg's uncertainty principle)
- Matter, like energy, exhibits a wave–particle duality. An experiment can demonstrate the particle-like properties of matter, or its wave-like properties; but not both at the same time. (Complementarity principle due to Bohr)
- Measuring devices are essentially classical devices, and measure classical properties such as position and momentum.
- The quantum mechanical description of large systems should closely approximate the classical description. (Correspondence principle of Bohr and Heisenberg)
Uncertainty principle[edit]
Main article: Uncertainty principle
Werner Heisenberg at the age of 26. Heisenberg won the Nobel Prize in Physics in 1932 for the work that he did at around this time.[26]
Suppose it is desired to measure the position and speed of an object – for example a car going through a radar speed trap. It can be assumed that the car has a definite position and speed at a particular moment in time. How accurately these values can be measured depends on the quality of the measuring equipment – if the precision of the measuring equipment is improved, it will provide a result that is closer to the true value. In particular, it would be assumed that the precision of measuring the speed of the car does not affect its position, and vice versa.
In 1927, Heisenberg proved that these assumptions are not correct.[27] Quantum mechanics shows that certain pairs of physical properties, like position and speed, cannot both be known to arbitrary precision: the more precisely one property is known, the less precisely the other can be known. This statement is known as the uncertainty principle. The uncertainty principle isn't a statement about the accuracy of our measuring equipment, but about the nature of the system itself – our assumption that the car had a definite position and speed was incorrect. On a scale of cars and people, these uncertainties are too small to notice, but when dealing with atoms and electrons they become critical.[28]
Heisenberg gave, as an illustration, the measurement of the position and momentum of an electron using a photon of light. In measuring the electron's position, the higher the frequency of the photon the more accurate is the measurement of the position of the impact, but the greater is the disturbance of the electron, which absorbs a random amount of energy, rendering the measurement obtained of its momentum increasingly uncertain (momentum is velocity multiplied by mass), for one is necessarily measuring its post-impact disturbed momentum, from the collision products, not its original momentum. With a photon of lower frequency the disturbance – hence uncertainty – in the momentum is less, but so is the accuracy of the measurement of the position of the impact.[29]
The uncertainty principle shows mathematically that the product of the uncertainty in the position and momentum of a particle (momentum is velocity multiplied by mass) could never be less than a certain value, and that this value is related to Planck's constant.
Wave function collapse
Wave function collapse is a forced expression for whatever just happened when it becomes appropriate to replace the description of an uncertain state of a system by a description of the system in a definite state. Explanations for the nature of the process of becoming certain are controversial. At any time before a photon "shows up" on a detection screen it can only be described by a set of probabilities for where it might show up. When it does show up, for instance in the CCD of an electronic camera, the time and the space where it interacted with the device are known within very tight limits. However, the photon has disappeared, and the wave function has disappeared with it. In its place some physical change in the detection screen has appeared, e.g., an exposed spot in a sheet of photographic film, or a change in electric potential in some cell of a CCD.Eigenstates and eigenvalues
Because of the uncertainty principle, statements about both the position and momentum of particles can only assign a probability that the position or momentum will have some numerical value. Therefore it is necessary to formulate clearly the difference between the state of something that is indeterminate, such as an electron in a probability cloud, and the state of something having a definite value. When an object can definitely be "pinned-down" in some respect, it is said to possess an eigenstate.In the Stern-Gerlach experiment discussed above, the spin of the atom about the vertical axis has two eigenstates: up and down. Before measuring it, we can only say that any individual atom has equal probability of being found to have spin up or spin down. The measurement process causes the wavefunction to collapse into one of the two states.
The eigenstates of spin about the vertical axis are not simultaneously eigenstates of spin about the horizontal axis, so this atom has equal probability of being found to having either value of spin about the horizontal axis. As described in the section above, measuring the spin about the horizontal axis can allow an atom which was spin up to become spin down: measuring its spin about the horizontal axis collapses its wave function into one of the eigenstates of this measurement, which means it is no longer in an eignenstate of spin about the vertical axis, so can take either value.
The Pauli exclusion principle
Main article: Pauli exclusion principle
In 1924, Wolfgang Pauli proposed a new quantum degree of freedom (or quantum number), with two possible values, to resolve inconsistencies between observed molecular spectra and the predictions of quantum mechanics. In particular, the spectrum of atomic hydrogen had a doublet, or pair of lines differing by a small amount, where only one line was expected. Pauli formulated his exclusion principle, stating that "There cannot exist an atom in such a quantum state that two electrons within [it] have the same set of quantum numbers."[30]
A year later, Uhlenbeck and Goudsmit identified Pauli's new degree of freedom with the property called spin whose effects were observed in the Stern–Gerlach experiment.
Application to the hydrogen atom
Bohr's model of the atom was essentially a planetary one, with the electrons orbiting around the nuclear "sun." However, the uncertainty principle states that an electron cannot simultaneously have an exact location and velocity in the way that a planet does. Instead of classical orbits, electrons are said to inhabit atomic orbitals. An orbital is the "cloud" of possible locations in which an electron might be found, a distribution of probabilities rather than a precise location.[30] Each orbital is three dimensional, rather than the two dimensional orbit, and is often depicted as a three-dimensional region within which there is a 95 percent probability of finding the electron.[31]Schrödinger was able to calculate the energy levels of hydrogen by treating a hydrogen atom's electron as a wave, represented by the "wave function" Ψ, in an electric potential well, V, created by the proton. The solutions to Schrödinger's equation are distributions of probabilities for electron positions and locations. Orbitals have a range of different shapes in three dimensions. The energies of the different orbitals can be calculated, and they accurately match the energy levels of the Bohr model.
Within Schrödinger's picture, each electron has four properties:
- An "orbital" designation, indicating whether the particle wave is one that is closer to the nucleus with less energy or one that is farther from the nucleus with more energy;
- The "shape" of the orbital, spherical or otherwise;
- The "inclination" of the orbital, determining the magnetic moment of the orbital around the z-axis.
- The "spin" of the electron.
The first property describing the orbital is the principal quantum number, n, which is the same as in Bohr's model. n denotes the energy level of each orbital. The possible values for n are integers:
n=1,2,3…
l=0,1,…,n−1.
The third quantum number, the magnetic quantum number, describes the magnetic moment of the electron, and is denoted by ml (or simply m). The possible values for ml are integers from −l to l:
ml=−l,−(l−1),…,0,1,…,l.
The fourth quantum number, the spin quantum number (pertaining to the "orientation" of the electron's spin) is denoted ms, with values +1⁄2 or −1⁄2.
The chemist Linus Pauling wrote, by way of example:
In the case of a helium atom with two electrons in the 1s orbital, the Pauli Exclusion Principle requires that the two electrons differ in the value of one quantum number. Their values of n, l, and ml are the same. Accordingly they must differ in the value of ms, which can have the value of +1⁄2 for one electron and −1⁄2 for the other."[30]It is the underlying structure and symmetry of atomic orbitals, and the way that electrons fill them, that leads to the organisation of the periodic table. The way the atomic orbitals on different atoms combine to form molecular orbitals determines the structure and strength of chemical bonds between atoms.
Dirac wave equation
Paul Dirac (1902–1984)
In 1928, Paul Dirac extended the Pauli equation, which described spinning electrons, to account for special relativity. The result was a theory that dealt properly with events, such as the speed at which an electron orbits the nucleus, occurring at a substantial fraction of the speed of light. By using the simplest electromagnetic interaction, Dirac was able to predict the value of the magnetic moment associated with the electron's spin, and found the experimentally observed value, which was too large to be that of a spinning charged sphere governed by classical physics. He was able to solve for the spectral lines of the hydrogen atom, and to reproduce from physical first principles Sommerfeld's successful formula for the fine structure of the hydrogen spectrum.
Dirac's equations sometimes yielded a negative value for energy, for which he proposed a novel solution: he posited the existence of an antielectron and of a dynamical vacuum. This led to the many-particle quantum field theory.
Quantum entanglement
The Pauli exclusion principle says that two electrons in one system cannot be in the same state. Nature leaves open the possibility, however, that two electrons can have both states "superimposed" over each of them. Recall that the wave functions that emerge simultaneously from the double slits arrive at the detection screen in a state of superposition. Nothing is certain until the superimposed waveforms "collapse", At that instant an electron shows up somewhere in accordance with the probability that is the square of the absolute value of the sum of the complex-valued amplitudes of the two superimposed waveforms. The situation there is already very abstract. A concrete way of thinking about entangled photons, photons in which two contrary states are superimposed on each of them in the same event, is as follows:
Imagine that the superposition of a state that can be mentally labeled as blue and another state that can be mentally labeled as red will then appear (in imagination, of course) as a purple state. Two photons are produced as the result of the same atomic event. Perhaps they are produced by the excitation of a crystal that characteristically absorbs a photon of a certain frequency and emits two photons of half the original frequency. So the two photons come out "purple." If the experimenter now performs some experiment that will determine whether one of the photons is either blue or red, then that experiment changes the photon involved from one having a superposition of "blue" and "red" characteristics to a photon that has only one of those characteristics. The problem that Einstein had with such an imagined situation was that if one of these photons had been kept bouncing between mirrors in a laboratory on earth, and the other one had traveled halfway to the nearest star, when its twin was made to reveal itself as either blue or red, that meant that the distant photon now had to lose its "purple" status too. So whenever it might be investigated after its twin had been measured, it would necessarily show up in the opposite state to whatever its twin had revealed.
In trying to show that quantum mechanics was not a complete theory, Einstein started with the theory's prediction that two or more particles that have interacted in the past can appear strongly correlated when their various properties are later measured. He sought to explain this seeming interaction in a classical way, through their common past, and preferably not by some "spooky action at a distance." The argument is worked out in a famous paper, Einstein, Podolsky, and Rosen (1935; abbreviated EPR), setting out what is now called the EPR paradox. Assuming what is now usually called local realism, EPR attempted to show from quantum theory that a particle has both position and momentum simultaneously, while according to the Copenhagen interpretation, only one of those two properties actually exists and only at the moment that it is being measured. EPR concluded that quantum theory is incomplete in that it refuses to consider physical properties which objectively exist in nature. (Einstein, Podolsky, & Rosen 1935 is currently Einstein's most cited publication in physics journals.) In the same year, Erwin Schrödinger used the word "entanglement" and declared: "I would not call that one but rather the characteristic trait of quantum mechanics."[32] The question of whether entanglement is a real condition is still in dispute.[33] The Bell inequalities are the most powerful challenge to Einstein's claims.
Quantum field theory
A field in physics is "a region or space in which a given effect (such as magnetism) exists."[34] Other effects that manifest themselves as fields are gravitation and static electricity.[35] In 2008, physicist Richard Hammond wrote that
Sometimes we distinguish between quantum mechanics (QM) and quantum field theory (QFT). QM refers to a system in which the number of particles is fixed, and the fields (such as the electromechanical field) are continuous classical entities. QFT ... goes a step further and allows for the creation and annihilation of particles . . . .He added, however, that quantum mechanics is often used to refer to "the entire notion of quantum view."[36]:108
In 1931, Dirac proposed the existence of particles that later became known as anti-matter.[37] Dirac shared the Nobel Prize in Physics for 1933 with Schrödinger, "for the discovery of new productive forms of atomic theory."[38]
Quantum electrodynamics
Quantum electrodynamics (QED) is the name of the quantum theory of the electromagnetic force. Understanding QED begins with understanding electromagnetism. Electromagnetism can be called "electrodynamics" because it is a dynamic interaction between electrical and magnetic forces. Electromagnetism begins with the electric charge.Electric charges are the sources of, and create, electric fields. An electric field is a field which exerts a force on any particles that carry electric charges, at any point in space. This includes the electron, proton, and even quarks, among others. As a force is exerted, electric charges move, a current flows and a magnetic field is produced. The magnetic field, in turn causes electric current (moving electrons). The interacting electric and magnetic field is called an electromagnetic field.
The physical description of interacting charged particles, electrical currents, electrical fields, and magnetic fields is called electromagnetism.
In 1928 Paul Dirac produced a relativistic quantum theory of electromagnetism. This was the progenitor to modern quantum electrodynamics, in that it had essential ingredients of the modern theory. However, the problem of unsolvable infinities developed in this relativistic quantum theory. Years later, renormalization solved this problem. Initially viewed as a suspect, provisional procedure by some of its originators, renormalization eventually was embraced as an important and self-consistent tool in QED and other fields of physics. Also, in the late 1940s Feynman's diagrams depicted all possible interactions pertaining to a given event. The diagrams showed that the electromagnetic force is the interactions of photons between interacting particles.
An example of a prediction of quantum electrodynamics which has been verified experimentally is the Lamb shift. This refers to an effect whereby the quantum nature of the electromagnetic field causes the energy levels in an atom or ion to deviate slightly from what they would otherwise be. As a result, spectral lines may shift or split.
In the 1960s physicists realized that QED broke down at extremely high energies. From this inconsistency the Standard Model of particle physics was discovered, which remedied the higher energy breakdown in theory. The Standard Model unifies the electromagnetic and weak interactions into one theory. This is called the electroweak theory.
Interpretations
The physical measurements, equations, and predictions pertinent to quantum mechanics are all consistent and hold a very high level of confirmation. However, the question of what these abstract models say about the underlying nature of the real world has received competing answers.Applications
Applications of quantum mechanics include the laser, the transistor, the electron microscope, and magnetic resonance imaging. A special class of quantum mechanical applications is related to macroscopic quantum phenomena such as superfluid helium and superconductors. The study of semiconductors led to the invention of the diode and the transistor, which are indispensable for modern electronics.In even the simple light switch, quantum tunnelling is absolutely vital, as otherwise the electrons in the electric current could not penetrate the potential barrier made up of a layer of oxide. Flash memory chips found in USB drives also use quantum tunnelling, to erase their memory cells.[39]
