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Introduction to quantum mechanics – Wikipedia

This article is a non-technical introduction to the subject. For the main encyclopedia article, see Quantum mechanics.

Quantum mechanics is the science of the very small. It explains the behavior of matter and its interactions with energy on the scale of atoms and subatomic particles. By contrast, classical physics only explains matter and energy on a scale familiar to human experience, including the behavior of astronomical bodies such as the Moon. Classical physics is still used in much of modern science and technology. However, towards 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] The desire to resolve inconsistencies between observed phenomena and classical theory led to two major revolutions in physics that 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. It describes these concepts in roughly the order in which they were first discovered. For a more complete history of the subject, see History of quantum mechanics.

Light behaves in some aspects like particles and in other aspects like waves. Matterthe “stuff” of the universe consisting of particles such as electrons and atomsexhibits wavelike behavior too. Some light sources, such as neon lights, give off only certain 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, colors, and spectral intensities. A single photon is a quantum, or smallest observable amount, of the electromagnetic field because a partial photon has never been observed. More broadly, quantum mechanics shows that many quantities, such as angular momentum, that appeared continuous in the zoomed-out view of classical mechanics, turn out to be (at the small, zoomed-in scale of quantum mechanics) quantized. Angular momentum is required to take on one of a set of discrete allowable values, and since the gap between these values is so minute, the discontinuity is only apparent at the atomic level.

Many aspects of quantum mechanics are counterintuitive[3] and can seem paradoxical, because they describe behavior quite different from that seen at larger length scales. In the words of quantum physicist Richard Feynman, quantum mechanics deals with “nature as She is absurd”.[4] 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 accurate 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 internal energy. 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 it emits light at increasingly shorter wavelengths (higher frequencies). 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 led to the Rayleigh-Jeans law, which, as shown in the figure, agrees with experimental results well at low frequencies, but strongly disagrees at high frequencies. 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.[5] 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 emitted 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 emitted by an 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 69666629999999999996.631034J s. So, the energy E of an oscillator of frequency f is given by

To change the color of such a radiating body, it is necessary to change its temperature. Planck’s law explains why: increasing the temperature of a body allows it to emit more energy overall, and means that a larger proportion of the energy is towards the violet end of the spectrum.

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”.[7] At the time, however, Planck’s view was that quantization was purely a heuristic mathematical construct, rather than (as is now believed) a fundamental change in our understanding of the world.[8]

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.[9] The energy of a single photon is given by its frequency multiplied by Planck’s constant:

For centuries, scientists had debated between two possible theories of light: was it a wave or did it instead comprise a stream of tiny particles? By the 19th century, the debate was generally considered to have been settled in favor of the wave theory, as it was able to explain observed effects such as refraction, diffraction, interference and polarization. James Clerk Maxwell had shown that electricity, magnetism and light are all manifestations of the same phenomenon: the electromagnetic field. Maxwell’s equations, which are the complete set of laws of classical electromagnetism, describe light as waves: a combination of oscillating electric and magnetic fields. Because of the preponderance of evidence in favor of the wave theory, Einstein’s ideas were met initially with great skepticism. Eventually, however, the photon model became favored. One of the most significant pieces of evidence in its favor was its ability to explain several puzzling properties of the photoelectric effect, described in the following section. Nonetheless, the wave analogy remained indispensable for helping to understand other characteristics of light: diffraction, refraction and interference.

In 1887, Heinrich Hertz observed that when light with sufficient frequency hits a metallic surface, it emits electrons.[10] 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.[11]: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.[10] An electron is likely to be struck only by a single photon, which imparts at most an energy hf to the electron.[10] 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.[10]

To explain the threshold effect, Einstein argued that it takes a certain amount of energy, called the work function and denoted by , to remove an electron from the metal.[10] 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:

If f is greater than f0, the energy hf is enough to remove an electron. The ejected electron has a kinetic energy, EK, which is, at most, equal to the photon’s energy minus the energy needed to dislodge the electron from the metal:

Einstein’s description of light as being composed of particles extended Planck’s notion of quantised energy, which is that a single photon of a given frequency, f, delivers an invariant amount of energy, hf. In other words, individual photons can deliver more or less energy, but only depending on their frequencies. In nature, single photons are rarely encountered. The Sun and emission sources available in the 19th century emit vast numbers of photons every second, and so the importance of the energy carried by each individual photon was not obvious. Einstein’s idea that the energy contained in individual units of light depends on their frequency made it possible to explain experimental results that had hitherto seemed quite counterintuitive. However, although the photon is a particle, it was still being described as having the wave-like property of frequency. Effectively, the account of light as a particle is insufficient, and its wave-like nature is still required.[12][note 4]

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 delivers a high amount of energyenough to contribute to cellular damage such as occurs in a sunburn. A photon of infrared light delivers less energyonly 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.[14]

All photons of the same frequency have identical energy, and all photons of different frequencies have proportionally (order 1, Ephoton = hf ) different energies.[15] However, 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 behavior of a photoelectric device reflects the behavior of the vast majority of its electrons, which are 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.[citation needed]

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 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 colors, 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 known as Balmer’s formula showed how the frequencies of the different lines 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 that had not been observed at the time. These lines were later observed experimentally, raising confidence in the value of the formula.

The mathematical formula describing hydrogen’s emission spectrum.

In 1885 the Swiss mathematician Johann Balmer discovered that each wavelength (lambda) in the visible spectrum of hydrogen is related to some integer n by the equation

where B is a constant Balmer determined is equal to 364.56nm.

In 1888 Johannes Rydberg generalized and greatly increased the explanatory utility of Balmer’s formula. He predicted that is related to two integers n and m according to what is now known as the Rydberg formula:[16]

where R is the Rydberg constant, equal to 0.0110nm1, and n must be greater than m.

Rydberg’s formula accounts for the four visible wavelengths of hydrogen by setting m = 2 and n = 3, 4, 5, 6. It also predicts additional wavelengths in the emission spectrum: for m = 1 and for n > 1, the emission spectrum should contain certain ultraviolet wavelengths, and for m = 3 and n > 3, it should also contain certain infrared wavelengths. Experimental observation of these wavelengths came two decades later: in 1908 Louis Paschen found some of the predicted infrared wavelengths, and in 1914 Theodore Lyman found some of the predicted ultraviolet wavelengths.[16]

Note that both Balmer and Rydberg’s formulas involve integers: in modern terms, they imply that some property of the atom is quantised. Understanding exactly what this property was, and why it was quantised, was a major part in the development of quantum mechanics, as shown in the rest of this article.

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.[17] 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.[18] 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.[19]

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, nor was it able to make accurate predictions for atoms with more than one electron, or to explain why some spectral lines are brighter than others.

Some fundamental assumptions of the Bohr model were soon proven wrongbut 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.

A more detailed explanation of the Bohr model.

Bohr theorised that the angular momentum, L, of an electron is quantised:

where n is an integer and h is the Planck constant. Starting from this assumption, Coulomb’s law and the equations of circular motion show that an electron with n units of angular momentum orbit a proton at a distance r given by

where ke is the Coulomb constant, m is the mass of an electron, and e is the charge on an electron.For simplicity this is written as

where a0, called the Bohr radius, is equal to 0.0529nm.The Bohr radius is the radius of the smallest allowed orbit.

The energy of the electron[note 6] can also be calculated, and is given by

Thus Bohr’s assumption that angular momentum is quantised means that an electron can only inhabit certain orbits around the nucleus, and that it can have only certain energies. A consequence of these constraints is that the electron does not crash into the nucleus: it cannot continuously emit energy, and it cannot come closer to the nucleus than a0 (the Bohr radius).

An electron loses energy by jumping instantaneously from its original orbit to a lower orbit; the extra energy is emitted in the form of a photon. Conversely, an electron that absorbs a photon gains energy, hence it jumps to an orbit that is farther from the nucleus.

Each photon from glowing atomic hydrogen is due to an electron moving from a higher orbit, with radius rn, to a lower orbit, rm. The energy E of this photon is the difference in the energies En and Em of the electron:

Since Planck’s equation shows that the photon’s energy is related to its wavelength by E = hc/, the wavelengths of light that can be emitted are given by

This equation has the same form as the Rydberg formula, and predicts that the constant R should be given by

Therefore, the Bohr model of the atom can predict the emission spectrum of hydrogen in terms of fundamental constants.[note 7] However, it was not able to make accurate predictions for multi-electron atoms, or to explain why some spectral lines are brighter than others.

Just as light has both wave-like and particle-like properties, matter also has wave-like properties.[20]

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 molecules.

The wavelength, , associated with any object is related to its momentum, p, through the Planck constant, h:[21][22]

The relationship, called the de Broglie hypothesis, holds for all types of matter: all matter exhibits properties of both particles and waves.

The concept of waveparticle duality says that neither the classical concept of “particle” nor of “wave” can fully describe the behavior of quantum-scale objects, either photons or matter. Waveparticle duality is an example of the principle of complementarity in quantum physics.[23][24][25][26][27] An elegant example of waveparticle 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 behavior can be demonstrated in water waves, and so the double-slit experiment was seen as a demonstration of the wave nature of light.

Variations of the double-slit experiment have been performed using electrons, atoms, and even large molecules,[28][29] 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 acts 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 is the result of a random process. However, the distribution pattern of many individual particles mimics the diffraction pattern produced by waves.

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 is 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 2 l n {displaystyle {frac {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.[30]

De Broglie’s treatment of quantum events served as a starting point for Schrdinger when he set out to construct a wave equation to describe quantum theoretical events.

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 that 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 theory 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 are 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 are 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 are 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 go one way and half the other, even though they all went in the same direction originally. 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.[31] 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 Schrdinger developed the equation that describes the behavior of a quantum mechanical wave.[32] The mathematical model, called the Schrdinger 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.[33] The wave itself is described by a mathematical function known as a “wave function”. Schrdinger said that the wave function provides the “means for predicting probability of measurement results”.[34]

Schrdinger 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, Schrdinger proved that Heisenberg’s matrix mechanics and his own wave mechanics made the same predictions about the properties and behavior of the electron; mathematically, the two theories had an underlying common form. Yet the two men disagreed on the interpretation of their mutual theory. For instance, Heisenberg accepted the theoretical prediction of jumps of electrons between orbitals in an atom,[35] but Schrdinger 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.”[36]

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:

Various consequences of these principles are discussed in more detail in the following subsections.

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 provides a result closer to the true value. It might be assumed that the speed of the car and its position could be operationally defined and measured simultaneously, as precisely as might be desired.

In 1927, Heisenberg proved that this last assumption is not correct.[39] Quantum mechanics shows that certain pairs of physical properties, such as for example position and speed, cannot be simultaneously measured, nor defined in operational terms, to arbitrary precision: the more precisely one property is measured, or defined in operational terms, the less precisely can the other. This statement is known as the uncertainty principle. The uncertainty principle isn’t only a statement about the accuracy of our measuring equipment, but, more deeply, is about the conceptual nature of the measured quantities the assumption that the car had simultaneously defined position and speed does not work in quantum mechanics. On a scale of cars and people, these uncertainties are negligible, but when dealing with atoms and electrons they become critical.[40]

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 of the photon with the electron, but the greater is the disturbance of the electron. This is because from the impact with the photon, the electron 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 and not its original momentum. With a photon of lower frequency, the disturbance (and hence uncertainty) in the momentum is less, but so is the accuracy of the measurement of the position of the impact.[41]

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 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.

Because of the uncertainty principle, statements about both the position and momentum of particles can only assign a probability that the position or momentum has 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 have 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 that was spun up to 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 eigenstate 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.”[42]

A year later, Uhlenbeck and Goudsmit identified Pauli’s new degree of freedom with the property called spin whose effects were observed in the SternGerlach experiment.

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.[42] 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.[43]

Schrdinger was able to calculate the energy levels of hydrogen by treating a hydrogen atom’s electron as a wave, represented by the “wave function” , in an electric potential well, V, created by the proton. The solutions to Schrdinger’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 Schrdinger’s picture, each electron has four properties:

The collective name for these properties is the quantum state of the electron. The quantum state can be described by giving a number to each of these properties; these are known as the electron’s quantum numbers. The quantum state of the electron is described by its wave function. The Pauli exclusion principle demands that no two electrons within an atom may have the same values of all four numbers.

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 next quantum number, the azimuthal quantum number, denoted l, describes the shape of the orbital. The shape is a consequence of the angular momentum of the orbital. The angular momentum represents the resistance of a spinning object to speeding up or slowing down under the influence of external force. The azimuthal quantum number represents the orbital angular momentum of an electron around its nucleus. The possible values for l are integers from 0 to n 1 (where n is the principal quantum number of the electron):

The shape of each orbital is usually referred to by a letter, rather than by its azimuthal quantum number. The first shape (l=0) is denoted by the letter s (a mnemonic being “sphere”). The next shape is denoted by the letter p and has the form of a dumbbell. The other orbitals have more complicated shapes (see atomic orbital), and are denoted by the letters d, f, g, etc.

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 (where l is the azimuthal quantum number of the electron):

The magnetic quantum number measures the component of the angular momentum in a particular direction. The choice of direction is arbitrary, conventionally the z-direction is chosen.

The fourth quantum number, the spin quantum number (pertaining to the “orientation” of the electron’s spin) is denoted ms, with values +12 or 12.

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 +12 for one electron and 12 for the other.”[42]

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.

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 labeled blue, and another state labeled red then appear (in imagination) 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 determines 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 that objectively exist in nature. (Einstein, Podolsky, & Rosen 1935 is currently Einstein’s most cited publication in physics journals.) In the same year, Erwin Schrdinger used the word “entanglement” and declared: “I would not call that one but rather the characteristic trait of quantum mechanics.”[44] The question of whether entanglement is a real condition is still in dispute.[45] 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.”[46] Other effects that manifest themselves as fields are gravitation and static electricity.[47] 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.”[48]:108

In 1931, Dirac proposed the existence of particles that later became known as antimatter.[49] Dirac shared the Nobel Prize in Physics for 1933 with Schrdinger, “for the discovery of new productive forms of atomic theory.”[50]

On its face, quantum field theory allows infinite numbers of particles, and leaves it up to the theory itself to predict how many and with which probabilities or numbers they should exist. When developed further, the theory often contradicts observation, so that its creation and annihilation operators can be empirically tied down.[clarification needed] Furthermore, empirical conservation laws like that of mass-energy suggest certain constraints on the mathematical form of the theory, which are mathematically speaking finicky. The latter fact both serves to make quantum field theories difficult to handle, but has also lead to further restrictions on admissible forms of the theory; the complications are mentioned below under the rubrik of renormalization.

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.

See the article here:

Introduction to quantum mechanics – Wikipedia

Physics4Kids.com: Modern Physics: Quantum Mechanics

If you apply this idea to the structure of an atom, in the older, Bohr model, there is a nucleus and there are rings (levels) of energy around the nucleus. The length of each orbit was related to a wavelength. No two electrons can have all the same wave characteristics. Scientists now say that electrons behave like waves, and fill areas of the atom like sound waves might fill a room. The electrons, then, exist in something scientists call “electron clouds”. The size of the shells now relates to the size of the cloud. This is where the spdf stuff comes in, as these describe the shape of the clouds.

Look at the Heisenberg uncertainty principle in a more general way using the observer effect. While Heisenberg looks at measurements, you can see parallels in larger observations. You can not observe something naturally without affecting it in some way. The light and photons used to watch an electron would move the electron. When you go out in a field in Africa and the animals see you, they will act differently. If you are a psychiatrist asking a patient some questions, you are affecting him, so the answers may be changed by the way the questions are worded. Field scientists work very hard to try and observe while interfering as little as possible.

See more here:

Physics4Kids.com: Modern Physics: Quantum Mechanics

Physics4Kids.com: Modern Physics: Quantum Mechanics

If you apply this idea to the structure of an atom, in the older, Bohr model, there is a nucleus and there are rings (levels) of energy around the nucleus. The length of each orbit was related to a wavelength. No two electrons can have all the same wave characteristics. Scientists now say that electrons behave like waves, and fill areas of the atom like sound waves might fill a room. The electrons, then, exist in something scientists call “electron clouds”. The size of the shells now relates to the size of the cloud. This is where the spdf stuff comes in, as these describe the shape of the clouds.

Look at the Heisenberg uncertainty principle in a more general way using the observer effect. While Heisenberg looks at measurements, you can see parallels in larger observations. You can not observe something naturally without affecting it in some way. The light and photons used to watch an electron would move the electron. When you go out in a field in Africa and the animals see you, they will act differently. If you are a psychiatrist asking a patient some questions, you are affecting him, so the answers may be changed by the way the questions are worded. Field scientists work very hard to try and observe while interfering as little as possible.

Originally posted here:

Physics4Kids.com: Modern Physics: Quantum Mechanics

Quantum mind – Wikipedia

The quantum mind or quantum consciousness[1] group of hypotheses propose that classical mechanics cannot explain consciousness. It posits that quantum mechanical phenomena, such as quantum entanglement and superposition, may play an important part in the brain’s function and could contribute to form the basis of an explanation of consciousness.

Hypotheses have been proposed about ways for quantum effects to be involved in the process of consciousness, but even those who advocate them admit that the hypotheses remain unproven, and possibly unprovable. Some of the proponents propose experiments that could demonstrate quantum consciousness, but the experiments have not yet been possible to perform.

Terms used in the theory of quantum mechanics can be misinterpreted by laymen in ways that are not valid but that sound mystical or religious, and therefore may seem to be related to consciousness. These misinterpretations of the terms are not justified in the theory of quantum mechanics. According to Sean Carroll, “No theory in the history of science has been more misused and abused by cranks and charlatansand misunderstood by people struggling in good faith with difficult ideasthan quantum mechanics.”[2] Lawrence Krauss says, “No area of physics stimulates more nonsense in the public arena than quantum mechanics.”[3] Some proponents of pseudoscience use quantum mechanical terms in an effort to justify their statements, but this effort is misleading, and it is a false interpretation of the physical theory. Quantum mind theories of consciousness that are based on this kind of misinterpretations of terms are not valid by scientific methods or from empirical experiments.

Eugene Wigner developed the idea that quantum mechanics has something to do with the workings of the mind. He proposed that the wave function collapses due to its interaction with consciousness. Freeman Dyson argued that “mind, as manifested by the capacity to make choices, is to some extent inherent in every electron.”[4]

Other contemporary physicists and philosophers considered these arguments to be unconvincing.[5] Victor Stenger characterized quantum consciousness as a “myth” having “no scientific basis” that “should take its place along with gods, unicorns and dragons.”[6]

David Chalmers argued against quantum consciousness. He instead discussed how quantum mechanics may relate to dualistic consciousness.[7] Chalmers is skeptical of the ability of any new physics to resolve the hard problem of consciousness.[8][9]

David Bohm viewed quantum theory and relativity as contradictory, which implied a more fundamental level in the universe.[10] He claimed both quantum theory and relativity pointed towards this deeper theory, which he formulated as a quantum field theory. This more fundamental level was proposed to represent an undivided wholeness and an implicate order, from which arises the explicate order of the universe as we experience it.

Bohm’s proposed implicate order applies both to matter and consciousness. He suggested that it could explain the relationship between them. He saw mind and matter as projections into our explicate order from the underlying implicate order. Bohm claimed that when we look at matter, we see nothing that helps us to understand consciousness.

Bohm discussed the experience of listening to music. He believed the feeling of movement and change that make up our experience of music derive from holding the immediate past and the present in the brain together. The musical notes from the past are transformations rather than memories. The notes that were implicate in the immediate past become explicate in the present. Bohm viewed this as consciousness emerging from the implicate order.

Bohm saw the movement, change or flow, and the coherence of experiences, such as listening to music, as a manifestation of the implicate order. He claimed to derive evidence for this from Jean Piaget’s[11] work on infants. He held these studies to show that young children learn about time and space because they have a “hard-wired” understanding of movement as part of the implicate order. He compared this “hard-wiring” to Chomsky’s theory that grammar is “hard-wired” into human brains.

Bohm never proposed a specific means by which his proposal could be falsified, nor a neural mechanism through which his “implicate order” could emerge in a way relevant to consciousness.[10] Bohm later collaborated on Karl Pribram’s holonomic brain theory as a model of quantum consciousness.[12]

According to philosopher Paavo Pylkknen, Bohm’s suggestion “leads naturally to the assumption that the physical correlate of the logical thinking process is at the classically describable level of the brain, while the basic thinking process is at the quantum-theoretically describable level.”[13]

Theoretical physicist Roger Penrose and anaesthesiologist Stuart Hameroff collaborated to produce the theory known as Orchestrated Objective Reduction (Orch-OR). Penrose and Hameroff initially developed their ideas separately and later collaborated to produce Orch-OR in the early 1990s. The theory was reviewed and updated by the authors in late 2013.[14][15]

Penrose’s argument stemmed from Gdel’s incompleteness theorems. In Penrose’s first book on consciousness, The Emperor’s New Mind (1989),[16] he argued that while a formal system cannot prove its own consistency, Gdels unprovable results are provable by human mathematicians.[17] He took this disparity to mean that human mathematicians are not formal proof systems and are not running a computable algorithm. According to Bringsjorg and Xiao, this line of reasoning is based on fallacious equivocation on the meaning of computation.[18] In the same book, Penrose wrote, “One might speculate, however, that somewhere deep in the brain, cells are to be found of single quantum sensitivity. If this proves to be the case, then quantum mechanics will be significantly involved in brain activity.”[16]:p.400

Penrose determined wave function collapse was the only possible physical basis for a non-computable process. Dissatisfied with its randomness, Penrose proposed a new form of wave function collapse that occurred in isolation and called it objective reduction. He suggested each quantum superposition has its own piece of spacetime curvature and that when these become separated by more than one Planck length they become unstable and collapse.[19] Penrose suggested that objective reduction represented neither randomness nor algorithmic processing but instead a non-computable influence in spacetime geometry from which mathematical understanding and, by later extension, consciousness derived.[19]

Hameroff provided a hypothesis that microtubules would be suitable hosts for quantum behavior.[20] Microtubules are composed of tubulin protein dimer subunits. The dimers each have hydrophobic pockets that are 8nm apart and that may contain delocalized pi electrons. Tubulins have other smaller non-polar regions that contain pi electron-rich indole rings separated by only about 2nm. Hameroff proposed that these electrons are close enough to become entangled.[21] Hameroff originally suggested the tubulin-subunit electrons would form a BoseEinstein condensate, but this was discredited.[22] He then proposed a Frohlich condensate, a hypothetical coherent oscillation of dipolar molecules. However, this too was experimentally discredited.[23]

However, Orch-OR made numerous false biological predictions, and is not an accepted model of brain physiology.[24] In other words, there is a missing link between physics and neuroscience,[25] for instance, the proposed predominance of ‘A’ lattice microtubules, more suitable for information processing, was falsified by Kikkawa et al.,[26][27] who showed all in vivo microtubules have a ‘B’ lattice and a seam. The proposed existence of gap junctions between neurons and glial cells was also falsified.[28] Orch-OR predicted that microtubule coherence reaches the synapses via dendritic lamellar bodies (DLBs), however De Zeeuw et al. proved this impossible,[29] by showing that DLBs are located micrometers away from gap junctions.[30]

In January 2014, Hameroff and Penrose claimed that the discovery of quantum vibrations in microtubules by Anirban Bandyopadhyay of the National Institute for Materials Science in Japan in March 2013[31] corroborates the Orch-OR theory.[15][32]

Although these theories are stated in a scientific framework, it is difficult to separate them from the personal opinions of the scientist. The opinions are often based on intuition or subjective ideas about the nature of consciousness. For example, Penrose wrote,

my own point of view asserts that you can’t even simulate conscious activity. What’s going on in conscious thinking is something you couldn’t properly imitate at all by computer…. If something behaves as though it’s conscious, do you say it is conscious? People argue endlessly about that. Some people would say, ‘Well, you’ve got to take the operational viewpoint; we don’t know what consciousness is. How do you judge whether a person is conscious or not? Only by the way they act. You apply the same criterion to a computer or a computer-controlled robot.’ Other people would say, ‘No, you can’t say it feels something merely because it behaves as though it feels something.’ My view is different from both those views. The robot wouldn’t even behave convincingly as though it was conscious unless it really was which I say it couldn’t be, if it’s entirely computationally controlled.[33]

Penrose continues,

A lot of what the brain does you could do on a computer. I’m not saying that all the brain’s action is completely different from what you do on a computer. I am claiming that the actions of consciousness are something different. I’m not saying that consciousness is beyond physics, either although I’m saying that it’s beyond the physics we know now…. My claim is that there has to be something in physics that we don’t yet understand, which is very important, and which is of a noncomputational character. It’s not specific to our brains; it’s out there, in the physical world. But it usually plays a totally insignificant role. It would have to be in the bridge between quantum and classical levels of behavior that is, where quantum measurement comes in.[34]

In response, W. Daniel Hillis replied, “Penrose has committed the classical mistake of putting humans at the center of the universe. His argument is essentially that he can’t imagine how the mind could be as complicated as it is without having some magic elixir brought in from some new principle of physics, so therefore it must involve that. It’s a failure of Penrose’s imagination…. It’s true that there are unexplainable, uncomputable things, but there’s no reason whatsoever to believe that the complex behavior we see in humans is in any way related to uncomputable, unexplainable things.”[34]

Lawrence Krauss is also blunt in criticizing Penrose’s ideas. He said, “Well, Roger Penrose has given lots of new-age crackpots ammunition by suggesting that at some fundamental scale, quantum mechanics might be relevant for consciousness. When you hear the term ‘quantum consciousness,’ you should be suspicious…. Many people are dubious that Penrose’s suggestions are reasonable, because the brain is not an isolated quantum-mechanical system.”[3]

Hiroomi Umezawa and collaborators proposed a quantum field theory of memory storage.[35][36] Giuseppe Vitiello and Walter Freeman proposed a dialog model of the mind. This dialog takes place between the classical and the quantum parts of the brain.[37][38][39] Their quantum field theory models of brain dynamics are fundamentally different from the Penrose-Hameroff theory.

Karl Pribram’s holonomic brain theory (quantum holography) invoked quantum mechanics to explain higher order processing by the mind.[40][41] He argued that his holonomic model solved the binding problem.[42] Pribram collaborated with Bohm in his work on the quantum approaches to mind and he provided evidence on how much of the processing in the brain was done in wholes.[43] He proposed that ordered water at dendritic membrane surfaces might operate by structuring Bose-Einstein condensation supporting quantum dynamics.[44]

Although Subhash Kak’s work is not directly related to that of Pribram, he likewise proposed that the physical substrate to neural networks has a quantum basis,[45][46] but asserted that the quantum mind has machine-like limitations.[47] He points to a role for quantum theory in the distinction between machine intelligence and biological intelligence, but that in itself cannot explain all aspects of consciousness.[48][49] He has proposed that the mind remains oblivious of its quantum nature due to the principle of veiled nonlocality.[50][51]

Henry Stapp proposed that quantum waves are reduced only when they interact with consciousness. He argues from the Orthodox Quantum Mechanics of John von Neumann that the quantum state collapses when the observer selects one among the alternative quantum possibilities as a basis for future action. The collapse, therefore, takes place in the expectation that the observer associated with the state. Stapp’s work drew criticism from scientists such as David Bourget and Danko Georgiev.[52] Georgiev[53][54][55] criticized Stapp’s model in two respects:

Stapp has responded to both of Georgiev’s objections.[56][57]

British philosopher David Pearce defends what he calls physicalistic idealism (“”Physicalistic idealism” is the non-materialist physicalist claim that reality is fundamentally experiential and that the natural world is exhaustively described by the equations of physics and their solutions […],” and has conjectured that unitary conscious minds are physical states of quantum coherence (neuronal superpositions).[58][59][60][61] This conjecture is, according to Pearce, amenable to falsification unlike most theories of consciousness, and Pearce has outlined an experimental protocol describing how the hypothesis could be tested using matter-wave interferometry to detect nonclassical interference patterns of neuronal superpositions at the onset of thermal decoherence.[62] Pearce admits that his ideas are “highly speculative,” “counterintuitive,” and “incredible.”[60]

These hypotheses of the quantum mind remain hypothetical speculation, as Penrose and Pearce admitted in their discussion. Until they make a prediction that is tested by experiment, the hypotheses aren’t based in empirical evidence. According to Lawrence Krauss, “It is true that quantum mechanics is extremely strange, and on extremely small scales for short times, all sorts of weird things happen. And in fact we can make weird quantum phenomena happen. But what quantum mechanics doesn’t change about the universe is, if you want to change things, you still have to do something. You can’t change the world by thinking about it.”[3]

The process of testing the hypotheses with experiments is fraught with problems, including conceptual/theoretical, practical, and ethical issues.

The idea that a quantum effect is necessary for consciousness to function is still in the realm of philosophy. Penrose proposes that it is necessary. But other theories of consciousness do not indicate that it is needed. For example, Daniel Dennett proposed a theory called multiple drafts model that doesn’t indicate that quantum effects are needed. The theory is described in Dennett’s book, Consciousness Explained, published in 1991.[63] A philosophical argument on either side isn’t scientific proof, although the philosophical analysis can indicate key differences in the types of models, and they can show what type of experimental differences might be observed. But since there isn’t a clear consensus among philosophers, it isn’t conceptual support that a quantum mind theory is needed.

There are computers that are specifically designed to compute using quantum mechanical effects. Quantum computing is computing using quantum-mechanical phenomena, such as superposition and entanglement.[64] They are different from binary digital electronic computers based on transistors. Whereas common digital computing requires that the data be encoded into binary digits (bits), each of which is always in one of two definite states (0 or 1), quantum computation uses quantum bits, which can be in superpositions of states. One of the greatest challenges is controlling or removing quantum decoherence. This usually means isolating the system from its environment as interactions with the external world cause the system to decohere. Currently, some quantum computers require their qubits to be cooled to 20 millikelvins in order to prevent significant decoherence.[65] As a result, time consuming tasks may render some quantum algorithms inoperable, as maintaining the state of qubits for a long enough duration will eventually corrupt the superpositions.[66] There aren’t any obvious analogies between the functioning of quantum computers and the human brain. Some of the hypothetical models of quantum mind have proposed mechanisms for maintaining quantum coherence in the brain, but they have not been shown to operate.

Quantum entanglement is a physical phenomenon often invoked for quantum mind models. This effect occurs when pairs or groups of particles interact so that the quantum state of each particle cannot be described independently of the other(s), even when the particles are separated by a large distance. Instead, a quantum state has to be described for the whole system. Measurements of physical properties such as position, momentum, spin, and polarization, performed on entangled particles are found to be correlated. If one of the particles is measured, the same property of the other particle immediately adjusts to maintain the conservation of the physical phenomenon. According to the formalism of quantum theory, the effect of measurement happens instantly, no matter how far apart the particles are.[67][68] It is not possible to use this effect to transmit classical information at faster-than-light speeds[69] (see Faster-than-light Quantum mechanics). Entanglement is broken when the entangled particles decohere through interaction with the environment; for example, when a measurement is made[70] or the particles undergo random collisions or interactions. According to David Pearce, “In neuronal networks, ion-ion scattering, ion-water collisions, and long-range Coulomb interactions from nearby ions all contribute to rapid decoherence times; but thermally-induced decoherence is even harder experimentally to control than collisional decoherence.” He anticipated that quantum effects would have to be measured in femtoseconds, a trillion times faster than the rate at which neurons function (milliseconds).[62]

Another possible conceptual approach is to use quantum mechanics as an analogy to understand a different field of study like consciousness, without expecting that the laws of quantum physics will apply. An example of this approach is the idea of Schrdinger’s cat. Erwin Schrdinger described how one could, in principle, create entanglement of a large-scale system by making it dependent on an elementary particle in a superposition. He proposed a scenario with a cat in a locked steel chamber, wherein the cat’s life or death depended on the state of a radioactive atom, whether it had decayed and emitted radiation or not. According to Schrdinger, the Copenhagen interpretation implies that the cat remains both alive and dead until the state has been observed. Schrdinger did not wish to promote the idea of dead-and-alive cats as a serious possibility; on the contrary, he intended the example to illustrate the absurdity of the existing view of quantum mechanics.[71] However, since Schrdinger’s time, other interpretations of the mathematics of quantum mechanics have been advanced by physicists, some of which regard the “alive and dead” cat superposition as quite real.[72][73] Schrdinger’s famous thought experiment poses the question, “when does a quantum system stop existing as a superposition of states and become one or the other?” In the same way, it is possible to ask whether the brain’s act of making a decision is analogous to having a superposition of states of two decision outcomes, so that making a decision means “opening the box” to reduce the brain from a combination of states to one state. But even Schrdinger didn’t think this really happened to the cat; he didn’t think the cat was literally alive and dead at the same time. This analogy about making a decision uses a formalism that is derived from quantum mechanics, but it doesn’t indicate the actual mechanism by which the decision is made. In this way, the idea is similar to quantum cognition. This field clearly distinguishes itself from the quantum mind as it is not reliant on the hypothesis that there is something micro-physical quantum mechanical about the brain. Quantum cognition is based on the quantum-like paradigm,[74][75] generalized quantum paradigm,[76] or quantum structure paradigm[77] that information processing by complex systems such as the brain can be mathematically described in the framework of quantum information and quantum probability theory. This model uses quantum mechanics only as an analogy, but doesn’t propose that quantum mechanics is the physical mechanism by which it operates. For example, quantum cognition proposes that some decisions can be analyzed as if there are interference between two alternatives, but it is not a physical quantum interference effect.

The demonstration of a quantum mind effect by experiment is necessary. Is there a way to show that consciousness is impossible without a quantum effect? Can a sufficiently complex digital, non-quantum computer be shown to be incapable of consciousness? Perhaps a quantum computer will show that quantum effects are needed. In any case, complex computers that are either digital or quantum computers may be built. These could demonstrate which type of computer is capable of conscious, intentional thought. But they don’t exist yet, and no experimental test has been demonstrated.

Quantum mechanics is a mathematical model that can provide some extremely accurate numerical predictions. Richard Feynman called quantum electrodynamics, based on the quantum mechanics formalism, “the jewel of physics” for its extremely accurate predictions of quantities like the anomalous magnetic moment of the electron and the Lamb shift of the energy levels of hydrogen.[78]:Ch1 So it is not impossible that the model could provide an accurate prediction about consciousness that would confirm that a quantum effect is involved. If the mind depends on quantum mechanical effects, the true proof is to find an experiment that provides a calculation that can be compared to an experimental measurement. It has to show a measurable difference between a classical computation result in a brain and one that involves quantum effects.

The main theoretical argument against the quantum mind hypothesis is the assertion that quantum states in the brain would lose coherency before they reached a scale where they could be useful for neural processing. This supposition was elaborated by Tegmark. His calculations indicate that quantum systems in the brain decohere at sub-picosecond timescales.[79][80] No response by a brain has shows computation results or reactions on this fast of a timescale. Typical reactions are on the order of milliseconds, trillions of times longer than sub-picosecond time scales.[81]

Daniel Dennett uses an experimental result in support of his Multiple Drafts Model of an optical illusion that happens on a time scale of less than a second or so. In this experiment, two different colored lights, with an angular separation of a few degrees at the eye, are flashed in succession. If the interval between the flashes is less than a second or so, the first light that is flashed appears to move across to the position of the second light. Furthermore, the light seems to change color as it moves across the visual field. A green light will appear to turn red as it seems to move across to the position of a red light. Dennett asks how we could see the light change color before the second light is observed.[63] Velmans argues that the cutaneous rabbit illusion, another illusion that happens in about a second, demonstrates that there is a delay while modelling occurs in the brain and that this delay was discovered by Libet.[82] These slow illusions that happen at times of less than a second don’t support a proposal that the brain functions on the picosecond time scale.

According to David Pearce, a demonstration of picosecond effects is “the fiendishly hard part feasible in principle, but an experimental challenge still beyond the reach of contemporary molecular matter-wave interferometry. …The conjecture predicts that we’ll discover the interference signature of sub-femtosecond macro-superpositions.”[62]

Penrose says,

The problem with trying to use quantum mechanics in the action of the brain is that if it were a matter of quantum nerve signals, these nerve signals would disturb the rest of the material in the brain, to the extent that the quantum coherence would get lost very quickly. You couldn’t even attempt to build a quantum computer out of ordinary nerve signals, because they’re just too big and in an environment that’s too disorganized. Ordinary nerve signals have to be treated classically. But if you go down to the level of the microtubules, then there’s an extremely good chance that you can get quantum-level activity inside them.

For my picture, I need this quantum-level activity in the microtubules; the activity has to be a large scale thing that goes not just from one microtubule to the next but from one nerve cell to the next, across large areas of the brain. We need some kind of coherent activity of a quantum nature which is weakly coupled to the computational activity that Hameroff argues is taking place along the microtubules.

A demonstration of a quantum effect in the brain has to explain this problem or explain why it is not relevant, or that the brain somehow circumvents the problem of the loss of quantum coherency at body temperature. As Penrose proposes, it may require a new type of physical theory.

Can self-awareness, or understanding of a self in the surrounding environment, be done by a classical parallel processor, or are quantum effects needed to have a sense of “oneness”? According to Lawrence Krauss, “You should be wary whenever you hear something like, ‘Quantum mechanics connects you with the universe’ … or ‘quantum mechanics unifies you with everything else.’ You can begin to be skeptical that the speaker is somehow trying to use quantum mechanics to argue fundamentally that you can change the world by thinking about it.”[3] A subjective feeling is not sufficient to make this determination. Humans don’t have a reliable subjective feeling for how we do a lot of functions. According to Daniel Dennett, “On this topic, Everybody’s an expert… but they think that they have a particular personal authority about the nature of their own conscious experiences that can trump any hypothesis they find unacceptable.”[83]

Since humans are the only animals known to be conscious, then performing experiments to demonstrate quantum effects in consciousness requires experimentation on a living human brain. This is not automatically excluded or impossible, but it seriously limits the kinds of experiments that can be done. Studies of the ethics of brain studies are being actively solicited[84] by the BRAIN Initiative, a U.S. Federal Government funded effort to document the connections of neurons in the brain.

An ethically objectionable practice by proponents of quantum mind theories involves the practice of using quantum mechanical terms in an effort to make the argument sound more impressive, even when they know that those terms are irrelevant. Dale DeBakcsy notes that “trendy parapsychologists, academic relativists, and even the Dalai Lama have all taken their turn at robbing modern physics of a few well-sounding phrases and stretching them far beyond their original scope in order to add scientific weight to various pet theories.”[85] At the very least, these proponents must make a clear statement about whether quantum formalism is being used as an analogy or as an actual physical mechanism, and what evidence they are using for support. An ethical statement by a researcher should specify what kind of relationship their hypothesis has to the physical laws.

Misleading statements of this type have been given by, for example, Deepak Chopra. Chopra has commonly referred to topics such as quantum healing or quantum effects of consciousness. Seeing the human body as being undergirded by a “quantum mechanical body” composed not of matter but of energy and information, he believes that “human aging is fluid and changeable; it can speed up, slow down, stop for a time, and even reverse itself,” as determined by one’s state of mind.[86] Robert Carroll states Chopra attempts to integrate Ayurveda with quantum mechanics to justify his teachings.[87] Chopra argues that what he calls “quantum healing” cures any manner of ailments, including cancer, through effects that he claims are literally based on the same principles as quantum mechanics.[88] This has led physicists to object to his use of the term quantum in reference to medical conditions and the human body.[88] Chopra said, “I think quantum theory has a lot of things to say about the observer effect, about non-locality, about correlations. So I think theres a school of physicists who believe that consciousness has to be equated, or at least brought into the equation, in understanding quantum mechanics.”[89] On the other hand, he also claims “[Quantum effects are] just a metaphor. Just like an electron or a photon is an indivisible unit of information and energy, a thought is an indivisible unit of consciousness.”[89] In his book Quantum Healing, Chopra stated the conclusion that quantum entanglement links everything in the Universe, and therefore it must create consciousness.[90] In either case, the references to the word “quantum” don’t mean what a physicist would claim, and arguments that use the word “quantum” shouldn’t be taken as scientifically proven.

Chris Carter includes statements in his book, Science and Psychic Phenomena,[91] of quotes from quantum physicists in support of psychic phenomena. In a review of the book, Benjamin Radford wrote that Carter used such references to “quantum physics, which he knows nothing about and which he (and people like Deepak Chopra) love to cite and reference because it sounds mysterious and paranormal…. Real, actual physicists I’ve spoken to break out laughing at this crap…. If Carter wishes to posit that quantum physics provides a plausible mechanism for psi, then it is his responsibility to show that, and he clearly fails to do so.”[92] Sharon Hill has studied amateur paranormal research groups, and these groups like to use “vague and confusing language: ghosts ‘use energy,’ are made up of ‘magnetic fields’, or are associated with a ‘quantum state.'”[93][94]

Statements like these about quantum mechanics indicate a temptation to misinterpret technical, mathematical terms like entanglement in terms of mystical feelings. This approach can be interpreted as a kind of Scientism, using the language and authority of science when the scientific concepts don’t apply.

A larger problem in the popular press with the quantum mind hypotheses is that they are extracted without scientific support or justification and used to support areas of pseudoscience. In brief, for example, the property of quantum entanglement refers to the connection between two particles that share a property such as angular momentum. If the particles collide, then they are no longer entangled. Extrapolating this property from the entanglement of two elementary particles to the functioning of neurons in the brain to be used in a computation is not simple. It is a long chain to prove a connection between entangled elementary particles and a macroscopic effect that affects human consciousness. It is also necessary to show how sensory inputs affect the coupled particles and then computation is accomplished.

Perhaps the final question is, what difference does it make if quantum effects are involved in computations in the brain? It is already known that quantum mechanics plays a role in the brain, since quantum mechanics determines the shapes and properties of molecules like neurotransmitters and proteins, and these molecules affect how the brain works. This is the reason that drugs such as morphine affect consciousness. As Daniel Dennett said, “quantum effects are there in your car, your watch, and your computer. But most things most macroscopic objects are, as it were, oblivious to quantum effects. They don’t amplify them; they don’t hinge on them.”[34] Lawrence Krauss said, “We’re also connected to the universe by gravity, and we’re connected to the planets by gravity. But that doesn’t mean that astrology is true…. Often, people who are trying to sell whatever it is they’re trying to sell try to justify it on the basis of science. Everyone knows quantum mechanics is weird, so why not use that to justify it? … I don’t know how many times I’ve heard people say, ‘Oh, I love quantum mechanics because I’m really into meditation, or I love the spiritual benefits that it brings me.’ But quantum mechanics, for better or worse, doesn’t bring any more spiritual benefits than gravity does.”[3]

But it appears that these molecular quantum effects are not what the proponents of the quantum mind are interested in. Proponents seem to want to use the nonlocal, nonclassical aspects of quantum mechanics to connect the human consciousness to a kind of universal consciousness or to long-range supernatural abilities. Although it isn’t impossible that these effects may be observed, they have not been found at present, and the burden of proof is on those who claim that these effects exist. The ability of humans to transfer information at a distance without a known classical physical mechanism has not been shown.

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Quantum – Wikipedia

In physics, a quantum (plural: quanta) is the minimum amount of any physical entity (physical property) involved in an interaction. The fundamental notion that a physical property may be “quantized” is referred to as “the hypothesis of quantization”.[1] This means that the magnitude of the physical property can take on only discrete values consisting of integer multiples of one quantum.

For example, a photon is a single quantum of light (or of any other form of electromagnetic radiation), and can be referred to as a “light quantum”, or as a light particle. Similarly, the energy of an electron bound within an atom is quantized and can exist only in certain discrete values. (Indeed, atoms and matter in general are stable because electrons can exist only at discrete energy levels within an atom.) Quantization is one of the foundations of the much broader physics of quantum mechanics. Quantization of energy and its influence on how energy and matter interact (quantum electrodynamics) is part of the fundamental framework for understanding and describing nature.

The word quantum comes from the Latin quantus, meaning “how great”. “Quanta”, short for “quanta of electricity” (electrons), was used in a 1902 article on the photoelectric effect by Philipp Lenard, who credited Hermann von Helmholtz for using the word in the area of electricity. However, the word quantum in general was well known before 1900.[2] It was often used by physicians, such as in the term quantum satis. Both Helmholtz and Julius von Mayer were physicians as well as physicists. Helmholtz used quantum with reference to heat in his article[3] on Mayer’s work, and the word quantum can be found in the formulation of the first law of thermodynamics by Mayer in his letter[4] dated July 24, 1841.

In 1901, Max Planck used quanta to mean “quanta of matter and electricity”,[5] gas, and heat.[6] In 1905, in response to Planck’s work and the experimental work of Lenard (who explained his results by using the term quanta of electricity), Albert Einstein suggested that radiation existed in spatially localized packets which he called “quanta of light” (“Lichtquanta”).[7]

The concept of quantization of radiation was discovered in 1900 by Max Planck, who had been trying to understand the emission of radiation from heated objects, known as black-body radiation. By assuming that energy can be absorbed or released only in tiny, differential, discrete packets (which he called “bundles”, or “energy elements”),[8] Planck accounted for certain objects changing colour when heated.[9] On December 14, 1900, Planck reported his findings to the German Physical Society, and introduced the idea of quantization for the first time as a part of his research on black-body radiation.[10] As a result of his experiments, Planck deduced the numerical value of h, known as the Planck constant, and reported more precise values for the unit of electrical charge and the AvogadroLoschmidt number, the number of real molecules in a mole, to the German Physical Society. After his theory was validated, Planck was awarded the Nobel Prize in Physics for his discovery in 1918.

While quantization was first discovered in electromagnetic radiation, it describes a fundamental aspect of energy not just restricted to photons.[11] In the attempt to bring theory into agreement with experiment, Max Planck postulated that electromagnetic energy is absorbed or emitted in discrete packets, or quanta.[12]

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If you apply this idea to the structure of an atom, in the older, Bohr model, there is a nucleus and there are rings (levels) of energy around the nucleus. The length of each orbit was related to a wavelength. No two electrons can have all the same wave characteristics. Scientists now say that electrons behave like waves, and fill areas of the atom like sound waves might fill a room. The electrons, then, exist in something scientists call “electron clouds”. The size of the shells now relates to the size of the cloud. This is where the spdf stuff comes in, as these describe the shape of the clouds.

Look at the Heisenberg uncertainty principle in a more general way using the observer effect. While Heisenberg looks at measurements, you can see parallels in larger observations. You can not observe something naturally without affecting it in some way. The light and photons used to watch an electron would move the electron. When you go out in a field in Africa and the animals see you, they will act differently. If you are a psychiatrist asking a patient some questions, you are affecting him, so the answers may be changed by the way the questions are worded. Field scientists work very hard to try and observe while interfering as little as possible.

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Introduction to quantum mechanics – Wikipedia

This article is a non-technical introduction to the subject. For the main encyclopedia article, see Quantum mechanics.

Quantum mechanics is the science of the very small. It explains the behavior of matter and its interactions with energy on the scale of atoms and subatomic particles.

By contrast, classical physics only explains matter and energy on a scale familiar to human experience, including the behavior of astronomical bodies such as the Moon. Classical physics is still used in much of modern science and technology. However, towards 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] The desire to resolve inconsistencies between observed phenomena and classical theory led to two major revolutions in physics that 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. It describes these concepts in roughly the order in which they were first discovered. For a more complete history of the subject, see History of quantum mechanics.

Light behaves in some aspects like particles and in other aspects like waves. Matterthe “stuff” of the universe consisting of particles such as electrons and atomsexhibits wavelike behavior too. Some light sources, such as neon lights, give off only certain 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, colors, and spectral intensities. A single photon is a quantum, or smallest observable amount, of the electromagnetic field because a partial photon has never been observed. More broadly, quantum mechanics shows that many quantities, such as angular momentum, that appeared continuous in the zoomed-out view of classical mechanics, turn out to be (at the small, zoomed-in scale of quantum mechanics) quantized. Angular momentum is required to take on one of a set of discrete allowable values, and since the gap between these values is so minute, the discontinuity is only apparent at the atomic level.

Many aspects of quantum mechanics are counterintuitive[3] and can seem paradoxical, because they describe behavior quite different from that seen at larger length scales. In the words of quantum physicist Richard Feynman, quantum mechanics deals with “nature as She is absurd”.[4] 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 accurate 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 internal energy. 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 it emits light at increasingly shorter wavelengths (higher frequencies). 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 led to the Rayleigh-Jeans law, which, as shown in the figure, agrees with experimental results well at low frequencies, but strongly disagrees at high frequencies. 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.[5] 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 emitted 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 emitted by an 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 69666629999999999996.631034J s. So, the energy E of an oscillator of frequency f is given by

To change the color of such a radiating body, it is necessary to change its temperature. Planck’s law explains why: increasing the temperature of a body allows it to emit more energy overall, and means that a larger proportion of the energy is towards the violet end of the spectrum.

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”.[7] At the time, however, Planck’s view was that quantization was purely a heuristic mathematical construct, rather than (as is now believed) a fundamental change in our understanding of the world.[8]

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.[9] The energy of a single photon is given by its frequency multiplied by Planck’s constant:

For centuries, scientists had debated between two possible theories of light: was it a wave or did it instead comprise a stream of tiny particles? By the 19th century, the debate was generally considered to have been settled in favor of the wave theory, as it was able to explain observed effects such as refraction, diffraction, interference and polarization. James Clerk Maxwell had shown that electricity, magnetism and light are all manifestations of the same phenomenon: the electromagnetic field. Maxwell’s equations, which are the complete set of laws of classical electromagnetism, describe light as waves: a combination of oscillating electric and magnetic fields. Because of the preponderance of evidence in favor of the wave theory, Einstein’s ideas were met initially with great skepticism. Eventually, however, the photon model became favored. One of the most significant pieces of evidence in its favor was its ability to explain several puzzling properties of the photoelectric effect, described in the following section. Nonetheless, the wave analogy remained indispensable for helping to understand other characteristics of light: diffraction, refraction and interference.

In 1887, Heinrich Hertz observed that when light with sufficient frequency hits a metallic surface, it emits electrons.[10] 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.[11]: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.[10] An electron is likely to be struck only by a single photon, which imparts at most an energy hf to the electron.[10] 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.[10]

To explain the threshold effect, Einstein argued that it takes a certain amount of energy, called the work function and denoted by , to remove an electron from the metal.[10] 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:

If f is greater than f0, the energy hf is enough to remove an electron. The ejected electron has a kinetic energy, EK, which is, at most, equal to the photon’s energy minus the energy needed to dislodge the electron from the metal:

Einstein’s description of light as being composed of particles extended Planck’s notion of quantised energy, which is that a single photon of a given frequency, f, delivers an invariant amount of energy, hf. In other words, individual photons can deliver more or less energy, but only depending on their frequencies. In nature, single photons are rarely encountered. The Sun and emission sources available in the 19th century emit vast numbers of photons every second, and so the importance of the energy carried by each individual photon was not obvious. Einstein’s idea that the energy contained in individual units of light depends on their frequency made it possible to explain experimental results that had hitherto seemed quite counterintuitive. However, although the photon is a particle, it was still being described as having the wave-like property of frequency. Effectively, the account of light as a particle is insufficient, and its wave-like nature is still required.[12][note 4]

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 delivers a high amount of energyenough to contribute to cellular damage such as occurs in a sunburn. A photon of infrared light delivers less energyonly 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.[14]

All photons of the same frequency have identical energy, and all photons of different frequencies have proportionally (order 1, Ephoton = hf ) different energies.[15] However, 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 behavior of a photoelectric device reflects the behavior of the vast majority of its electrons, which are 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.[citation needed]

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 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 colors, 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 known as Balmer’s formula showed how the frequencies of the different lines 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 that had not been observed at the time. These lines were later observed experimentally, raising confidence in the value of the formula.

The mathematical formula describing hydrogen’s emission spectrum.

In 1885 the Swiss mathematician Johann Balmer discovered that each wavelength (lambda) in the visible spectrum of hydrogen is related to some integer n by the equation

where B is a constant Balmer determined is equal to 364.56nm.

In 1888 Johannes Rydberg generalized and greatly increased the explanatory utility of Balmer’s formula. He predicted that is related to two integers n and m according to what is now known as the Rydberg formula:[16]

where R is the Rydberg constant, equal to 0.0110nm1, and n must be greater than m.

Rydberg’s formula accounts for the four visible wavelengths of hydrogen by setting m = 2 and n = 3, 4, 5, 6. It also predicts additional wavelengths in the emission spectrum: for m = 1 and for n > 1, the emission spectrum should contain certain ultraviolet wavelengths, and for m = 3 and n > 3, it should also contain certain infrared wavelengths. Experimental observation of these wavelengths came two decades later: in 1908 Louis Paschen found some of the predicted infrared wavelengths, and in 1914 Theodore Lyman found some of the predicted ultraviolet wavelengths.[16]

Note that both Balmer and Rydberg’s formulas involve integers: in modern terms, they imply that some property of the atom is quantised. Understanding exactly what this property was, and why it was quantised, was a major part in the development of quantum mechanics, as shown in the rest of this article.

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.[17] 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.[18] 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.[19]

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, nor was it able to make accurate predictions for atoms with more than one electron, or to explain why some spectral lines are brighter than others.

Some fundamental assumptions of the Bohr model were soon proven wrongbut 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.

A more detailed explanation of the Bohr model.

Bohr theorised that the angular momentum, L, of an electron is quantised:

where n is an integer and h is the Planck constant. Starting from this assumption, Coulomb’s law and the equations of circular motion show that an electron with n units of angular momentum orbit a proton at a distance r given by

where ke is the Coulomb constant, m is the mass of an electron, and e is the charge on an electron. For simplicity this is written as

where a0, called the Bohr radius, is equal to 0.0529nm. The Bohr radius is the radius of the smallest allowed orbit.

The energy of the electron[note 6] can also be calculated, and is given by

Thus Bohr’s assumption that angular momentum is quantised means that an electron can only inhabit certain orbits around the nucleus, and that it can have only certain energies. A consequence of these constraints is that the electron does not crash into the nucleus: it cannot continuously emit energy, and it cannot come closer to the nucleus than a0 (the Bohr radius).

An electron loses energy by jumping instantaneously from its original orbit to a lower orbit; the extra energy is emitted in the form of a photon. Conversely, an electron that absorbs a photon gains energy, hence it jumps to an orbit that is farther from the nucleus.

Each photon from glowing atomic hydrogen is due to an electron moving from a higher orbit, with radius rn, to a lower orbit, rm. The energy E of this photon is the difference in the energies En and Em of the electron:

Since Planck’s equation shows that the photon’s energy is related to its wavelength by E = hc/, the wavelengths of light that can be emitted are given by

This equation has the same form as the Rydberg formula, and predicts that the constant R should be given by

Therefore, the Bohr model of the atom can predict the emission spectrum of hydrogen in terms of fundamental constants.[note 7] However, it was not able to make accurate predictions for multi-electron atoms, or to explain why some spectral lines are brighter than others.

Just as light has both wave-like and particle-like properties, matter also has wave-like properties.[20]

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 molecules.

The wavelength, , associated with any object is related to its momentum, p, through the Planck constant, h:[21][22]

The relationship, called the de Broglie hypothesis, holds for all types of matter: all matter exhibits properties of both particles and waves.

The concept of waveparticle duality says that neither the classical concept of “particle” nor of “wave” can fully describe the behavior of quantum-scale objects, either photons or matter. Waveparticle duality is an example of the principle of complementarity in quantum physics.[23][24][25][26][27] An elegant example of waveparticle 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 behavior can be demonstrated in water waves, and so the double-slit experiment was seen as a demonstration of the wave nature of light.

Variations of the double-slit experiment have been performed using electrons, atoms, and even large molecules,[28][29] 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 acts 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 is the result of a random process. However, the distribution pattern of many individual particles mimics the diffraction pattern produced by waves.

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 is 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 2 l n {displaystyle {frac {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.[30]

De Broglie’s treatment of quantum events served as a starting point for Schrdinger when he set out to construct a wave equation to describe quantum theoretical events.

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 that 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 theory 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 are 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 are 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 are 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 go one way and half the other, even though they all went in the same direction originally. 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.[31] 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 Schrdinger developed the equation that describes the behavior of a quantum mechanical wave.[32] The mathematical model, called the Schrdinger 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.[33] The wave itself is described by a mathematical function known as a “wave function”. Schrdinger said that the wave function provides the “means for predicting probability of measurement results”.[34]

Schrdinger 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, Schrdinger proved that Heisenberg’s matrix mechanics and his own wave mechanics made the same predictions about the properties and behavior of the electron; mathematically, the two theories had an underlying common form. Yet the two men disagreed on the interpretation of their mutual theory. For instance, Heisenberg accepted the theoretical prediction of jumps of electrons between orbitals in an atom,[35] but Schrdinger 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.”[36]

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:

Various consequences of these principles are discussed in more detail in the following subsections.

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 provides a result closer to the true value. It might be assumed that the speed of the car and its position could be operationally defined and measured simultaneously, as precisely as might be desired.

In 1927, Heisenberg proved that this last assumption is not correct.[39] Quantum mechanics shows that certain pairs of physical properties, such as for example position and speed, cannot be simultaneously measured, nor defined in operational terms, to arbitrary precision: the more precisely one property is measured, or defined in operational terms, the less precisely can the other. This statement is known as the uncertainty principle. The uncertainty principle isn’t only a statement about the accuracy of our measuring equipment, but, more deeply, is about the conceptual nature of the measured quantities the assumption that the car had simultaneously defined position and speed does not work in quantum mechanics. On a scale of cars and people, these uncertainties are negligible, but when dealing with atoms and electrons they become critical.[40]

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 of the photon with the electron, but the greater is the disturbance of the electron. This is because from the impact with the photon, the electron 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 and not its original momentum. With a photon of lower frequency, the disturbance (and hence uncertainty) in the momentum is less, but so is the accuracy of the measurement of the position of the impact.[41]

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 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.

Because of the uncertainty principle, statements about both the position and momentum of particles can only assign a probability that the position or momentum has 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 have 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 that was spun up to 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 eigenstate 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.”[42]

A year later, Uhlenbeck and Goudsmit identified Pauli’s new degree of freedom with the property called spin whose effects were observed in the SternGerlach experiment.

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.[42] 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.[43]

Schrdinger was able to calculate the energy levels of hydrogen by treating a hydrogen atom’s electron as a wave, represented by the “wave function” , in an electric potential well, V, created by the proton. The solutions to Schrdinger’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 Schrdinger’s picture, each electron has four properties:

The collective name for these properties is the quantum state of the electron. The quantum state can be described by giving a number to each of these properties; these are known as the electron’s quantum numbers. The quantum state of the electron is described by its wave function. The Pauli exclusion principle demands that no two electrons within an atom may have the same values of all four numbers.

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 next quantum number, the azimuthal quantum number, denoted l, describes the shape of the orbital. The shape is a consequence of the angular momentum of the orbital. The angular momentum represents the resistance of a spinning object to speeding up or slowing down under the influence of external force. The azimuthal quantum number represents the orbital angular momentum of an electron around its nucleus. The possible values for l are integers from 0 to n 1 (where n is the principal quantum number of the electron):

The shape of each orbital is usually referred to by a letter, rather than by its azimuthal quantum number. The first shape (l=0) is denoted by the letter s (a mnemonic being “sphere”). The next shape is denoted by the letter p and has the form of a dumbbell. The other orbitals have more complicated shapes (see atomic orbital), and are denoted by the letters d, f, g, etc.

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 (where l is the azimuthal quantum number of the electron):

The magnetic quantum number measures the component of the angular momentum in a particular direction. The choice of direction is arbitrary, conventionally the z-direction is chosen.

The fourth quantum number, the spin quantum number (pertaining to the “orientation” of the electron’s spin) is denoted ms, with values +12 or 12.

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 +12 for one electron and 12 for the other.”[42]

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.

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 labeled blue, and another state labeled red then appear (in imagination) 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 determines 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 that objectively exist in nature. (Einstein, Podolsky, & Rosen 1935 is currently Einstein’s most cited publication in physics journals.) In the same year, Erwin Schrdinger used the word “entanglement” and declared: “I would not call that one but rather the characteristic trait of quantum mechanics.”[44] The question of whether entanglement is a real condition is still in dispute.[45] 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.”[46] Other effects that manifest themselves as fields are gravitation and static electricity.[47] 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.”[48]:108

In 1931, Dirac proposed the existence of particles that later became known as antimatter.[49] Dirac shared the Nobel Prize in Physics for 1933 with Schrdinger, “for the discovery of new productive forms of atomic theory.”[50]

On its face, quantum field theory allows infinite numbers of particles, and leaves it up to the theory itself to predict how many and with which probabilities or numbers they should exist. When developed further, the theory often contradicts observation, so that its creation and annihilation operators can be empirically tied down.[clarification needed] Furthermore, empirical conservation laws like that of mass-energy suggest certain constraints on the mathematical form of the theory, which are mathematically speaking finicky. The latter fact both serves to make quantum field theories difficult to handle, but has also lead to further restrictions on admissible forms of the theory; the complications are mentioned below under the rubrik of renormalization.

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Quantum – Wikipedia

In physics, a quantum (plural: quanta) is the minimum amount of any physical entity (physical property) involved in an interaction. The fundamental notion that a physical property may be “quantized” is referred to as “the hypothesis of quantization”.[1] This means that the magnitude of the physical property can take on only discrete values consisting of integer multiples of one quantum.

For example, a photon is a single quantum of light (or of any other form of electromagnetic radiation), and can be referred to as a “light quantum”, or as a light particle. Similarly, the energy of an electron bound within an atom is quantized and can exist only in certain discrete values. (Indeed, atoms and matter in general are stable because electrons can exist only at discrete energy levels within an atom.) Quantization is one of the foundations of the much broader physics of quantum mechanics. Quantization of energy and its influence on how energy and matter interact (quantum electrodynamics) is part of the fundamental framework for understanding and describing nature.

The word quantum comes from the Latin quantus, meaning “how great”. “Quanta”, short for “quanta of electricity” (electrons), was used in a 1902 article on the photoelectric effect by Philipp Lenard, who credited Hermann von Helmholtz for using the word in the area of electricity. However, the word quantum in general was well known before 1900.[2] It was often used by physicians, such as in the term quantum satis. Both Helmholtz and Julius von Mayer were physicians as well as physicists. Helmholtz used quantum with reference to heat in his article[3] on Mayer’s work, and the word quantum can be found in the formulation of the first law of thermodynamics by Mayer in his letter[4] dated July 24, 1841.

In 1901, Max Planck used quanta to mean “quanta of matter and electricity”,[5] gas, and heat.[6] In 1905, in response to Planck’s work and the experimental work of Lenard (who explained his results by using the term quanta of electricity), Albert Einstein suggested that radiation existed in spatially localized packets which he called “quanta of light” (“Lichtquanta”).[7]

The concept of quantization of radiation was discovered in 1900 by Max Planck, who had been trying to understand the emission of radiation from heated objects, known as black-body radiation. By assuming that energy can be absorbed or released only in tiny, differential, discrete packets (which he called “bundles”, or “energy elements”),[8] Planck accounted for certain objects changing colour when heated.[9] On December 14, 1900, Planck reported his findings to the German Physical Society, and introduced the idea of quantization for the first time as a part of his research on black-body radiation.[10] As a result of his experiments, Planck deduced the numerical value of h, known as the Planck constant, and reported more precise values for the unit of electrical charge and the AvogadroLoschmidt number, the number of real molecules in a mole, to the German Physical Society. After his theory was validated, Planck was awarded the Nobel Prize in Physics for his discovery in 1918.

While quantization was first discovered in electromagnetic radiation, it describes a fundamental aspect of energy not just restricted to photons.[11] In the attempt to bring theory into agreement with experiment, Max Planck postulated that electromagnetic energy is absorbed or emitted in discrete packets, or quanta.[12]

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Physics4Kids.com: Modern Physics: Quantum Mechanics

If you apply this idea to the structure of an atom, in the older, Bohr model, there is a nucleus and there are rings (levels) of energy around the nucleus. The length of each orbit was related to a wavelength. No two electrons can have all the same wave characteristics. Scientists now say that electrons behave like waves, and fill areas of the atom like sound waves might fill a room. The electrons, then, exist in something scientists call “electron clouds”. The size of the shells now relates to the size of the cloud. This is where the spdf stuff comes in, as these describe the shape of the clouds.

Look at the Heisenberg uncertainty principle in a more general way using the observer effect. While Heisenberg looks at measurements, you can see parallels in larger observations. You can not observe something naturally without affecting it in some way. The light and photons used to watch an electron would move the electron. When you go out in a field in Africa and the animals see you, they will act differently. If you are a psychiatrist asking a patient some questions, you are affecting him, so the answers may be changed by the way the questions are worded. Field scientists work very hard to try and observe while interfering as little as possible.

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Quantum Physics I | Physics | MIT OpenCourseWare

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