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PowerPedia:Quantum mechanics

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Quantum mechanics is a There was an error working with the wiki: Code[6] There was an error working with the wiki: Code[7] levels. It is a fundamental branch of Physics that provides the underlying There was an error working with the wiki: Code[87] framework for many fields of physics and Chemistry, including There was an error working with the wiki: Code[88], atomic physics, There was an error working with the wiki: Code[89], There was an error working with the wiki: Code[90], There was an error working with the wiki: Code[91], There was an error working with the wiki: Code[92], and There was an error working with the wiki: Code[93]. Quantum mechanics is sometimes used in a more general sense, to mean quantum physics.

Terminology and theories

The term quantum (There was an error working with the wiki: Code[8], There was an error working with the wiki: Code[9]. Some fundamental aspects of the theory are still actively studied.

A quantum theory is a theory of physics that uses Planck's constant. In contrast to classical physics, where variables are often continuous, many of the variables in a quantum theory take on discrete values. The quantum was concept that grew out of the realisation that electromagnetic radiation came in discrete packets, called quanta. The process of converting a classical theory into a quantum theory is called quantisation and is divided into stages: first quantisation, second quantisation, etc depending on the extent to which the theory is quantised. Quantum physics is the set of quantum theories. There are several of them:

quantum mechanics -- a first quantised or semi-classical theory in which particle properties are quantised, but not particle numbers, fields and fundamental interactions.

quantum field theory or QFT -- a second or canonically quantized theory in which all aspects of particles, fields and interactions are quantised, with the exception of gravitation. Quantum electrodynamics, quantum chromodynamics and electroweak theory are examples of relativistic fundamental QFTs which taken together form the Standard Model. Solid state physics is a non-fundamental QFT.

quantum gravity -- a third quantised theory in which general relativity (i.e. gravity) is also quantised. This theory is incomplete, and is hoped to be finalised within the framework of a theory of everything, such as string theory or M-theory.

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History of Quantum mechanics

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In There was an error working with the wiki: Code[10] put forward his theory of matter waves by stating that particles can exhibit wave characteristics and vice versa.

These theories, though successful, were strictly There was an error working with the wiki: Code[11]: there was no rigorous justification for quantization (aside, perhaps, for There was an error working with the wiki: Code[12] developed There was an error working with the wiki: Code[13] invented There was an error working with the wiki: Code[94] and the non-relativistic Schrödinger equation. Schrödinger subsequently showed that the two approaches were equivalent.

Heisenberg formulated his There was an error working with the wiki: Code[95] in There was an error working with the wiki: Code[96], and the Copenhagen interpretation took shape at about the same time. Starting around There was an error working with the wiki: Code[96], There was an error working with the wiki: Code[98] began the process of unifying quantum mechanics with There was an error working with the wiki: Code[99] by discovering the There was an error working with the wiki: Code[100] for the Electron. He also pioneered the use of operator theory, including the influential There was an error working with the wiki: Code[101], as described in his famous 1930 textbook. During the same period, Hungarian polymath There was an error working with the wiki: Code[102] formulated the rigorous mathematical basis for quantum mechanics as the theory of linear operators on Hilbert spaces, as described in his likewise famous 1932 textbook. These, like many other works from the founding period still stand, and remain widely used. The field of There was an error working with the wiki: Code[103] was pioneered by physicists There was an error working with the wiki: Code[104] and There was an error working with the wiki: Code[105], who published a study of the There was an error working with the wiki: Code[106] of the There was an error working with the wiki: Code[107] in There was an error working with the wiki: Code[96]. Quantum chemistry was subsequently developed by a large number of workers, including the American theoretical chemist There was an error working with the wiki: Code[109] at Cal Tech, and John Slater into various theories such as Molecular Orbital Theory or Valence Theory.

Beginning in There was an error working with the wiki: Code[14]. Early workers in this area included There was an error working with the wiki: Code[15], There was an error working with the wiki: Code[16], There was an error working with the wiki: Code[17], and There was an error working with the wiki: Code[18]. This area of research culminated in the formulation of There was an error working with the wiki: Code[19], There was an error working with the wiki: Code[20], There was an error working with the wiki: Code[21], and There was an error working with the wiki: Code[22] during the There was an error working with the wiki: Code[110]. Quantum electrodynamics is a quantum theory of Electrons, There was an error working with the wiki: Code[111]s, and the Electromagnetic field, and served as a role model for subsequent quantum field theories.

The theory of There was an error working with the wiki: Code[23], There was an error working with the wiki: Code[24] and There was an error working with the wiki: Code[25] in There was an error working with the wiki: Code[26], There was an error working with the wiki: Code[27], There was an error working with the wiki: Code[28], There was an error working with the wiki: Code[29], There was an error working with the wiki: Code[30] and There was an error working with the wiki: Code[31] independently showed how the weak nuclear force and quantum electrodynamics could be merged into a single There was an error working with the wiki: Code[112].

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Quantum mechanics formalism

Quantum mechanics is a more fundamental theory than There was an error working with the wiki: Code[32] and classical There was an error working with the wiki: Code[33] descriptions for many There was an error working with the wiki: Code[34] that these "classical" theories simply cannot explain on the atomic and subatomic level. It is necessary to use quantum mechanics to understand the behavior of systems at There was an error working with the wiki: Code[35] of light emitted by different atomic species. The quantum theory of the atom developed as an explanation for the electron's staying in its There was an error working with the wiki: Code[36], which could not be explained by Newton's laws of motion and by classical electromagnetism.

In the formalism of quantum mechanics, the state of a system at a given time is described by a There was an error working with the wiki: Code[37] between subatomic particles and electromagnetic waves called There was an error working with the wiki: Code[38] and There was an error working with the wiki: Code[113]s.

Broadly speaking, quantum mechanics incorporates four classes of phenomena that classical physics cannot account for: (i) the There was an error working with the wiki: Code[39] (discretization) of There was an error working with the wiki: Code[40], (ii) There was an error working with the wiki: Code[41].

Theory

There are numerous mathematically equivalent formulations of quantum mechanics. One of the oldest and most commonly used formulations is the There was an error working with the wiki: Code[42] invented by Cambridge theoretical physicist There was an error working with the wiki: Code[43] encodes the probabilities of its measurable properties, or "There was an error working with the wiki: Code[44] (e.g., the position of a particle) or There was an error working with the wiki: Code[45] (e.g., the energy of an electron bound to a hydrogen atom).

Generally, quantum mechanics does not assign definite values to observables. Instead, it makes predictions about There was an error working with the wiki: Code[46]). In the everyday world, it is natural and intuitive to think of everything being in an eigenstate of every observable. Everything appears to have a definite position, a definite momentum, and a definite time of occurrence. However, Quantum Mechanics does not pinpoint the exact values for the position or momentum of a certain particle in a given space in a finite time, but, rather, it only provides a range of probabilities of where that particle might be. Therefore, it became necessary to use different words for a) the state of something having an uncertainty relation and b) a state that has a definite value. The latter is called the "eigenstate" of the property being measured.

A concrete example will be useful here. Let us consider a There was an error working with the wiki: Code[47]. The position and momentum of the particle are observables. The There was an error working with the wiki: Code[114] of quantum mechanics states that both the position and the momentum cannot simultaneously be known with infinite precision at the same time. However, we can measure just the position alone of a moving free particle creating an eigenstate of position with a wavefunction that is very large at a particular position x, and zero everywhere else. If we perform a position measurement on such a wavefunction, we will obtain the result x with 100% probability. In other words, we will know the position of the free particle. This is called an eigenstate of position. If the particle is in an eigenstate of position then its momentum is completely unknown. An eigenstate of momentum, on the other hand, has the form of a There was an error working with the wiki: Code[115]. It can be shown that the There was an error working with the wiki: Code[116] is equal to h/p, where h is There was an error working with the wiki: Code[117] and p is the momentum of the There was an error working with the wiki: Code[118]. If the particle is in an eigenstate of momentum then its position is completely blurred out.

Usually, a system will not be in an eigenstate of whatever observable we are interested in. However, if we measure the observable, the wavefunction will immediately become an eigenstate of that observable. This process is known as There was an error working with the wiki: Code[119]. If we know the wavefunction at the instant before the measurement, we will be able to compute the probability of collapsing into each of the possible eigenstates. For example, the free particle in our previous example will usually have a wavefunction that is a There was an error working with the wiki: Code[120] centered around some mean position x0, neither an eigenstate of position nor of momentum. When we measure the position of the particle, it is impossible for us to predict with certainty the result that we will obtain. It is probable, but not certain, that it will be near x0, where the amplitude of the wavefunction is large. After we perform the measurement, obtaining some result x, the wavefunction collapses into a position eigenstate centered at x.

Wave functions can change as time progresses. An equation known as the There was an error working with the wiki: Code[48] wavefunction surrounding the nucleus. (Note that only the lowest angular momentum states, labeled s, are spherically symmetric).

The time evolution of wave functions is There was an error working with the wiki: Code[49] in the sense that, given a wavefunction at an initial time, it makes a definite prediction of what the wavefunction will be at any later time. During a There was an error working with the wiki: Code[50], the change of the wavefunction into another one is not deterministic, but rather unpredictable, i.e., There was an error working with the wiki: Code[51] nature of quantum mechanics thus stems from the act of measurement. This is one of the most difficult aspects of quantum systems to understand. It was the central topic in the famous There was an error working with the wiki: Code[52] of quantum mechanics have been formulated to do away with the concept of "wavefunction collapse" see, for example, the There was an error working with the wiki: Code[121]. The basic idea is that when a quantum system interacts with a measuring apparatus, their respective wavefunctions become There was an error working with the wiki: Code[122], so that the original quantum system ceases to exist as an independent entity. For details, see the article on There was an error working with the wiki: Code[123].

Effects

As mentioned in the introduction, there are several classes of phenomena that appear under quantum mechanics which have no analogue in classical physics. These are sometimes referred to as "quantum effects". The first type of quantum effect is the There was an error working with the wiki: Code[53] of certain physical quantities. Quantization first arose in the mathematical formulae of Max Planck in 1900 as discussed in the introduction. Max Planck was analyzing how the radiation emitted from a body was related to its temperature, in other words, he was analyzing the energy of a wave. The energy of a wave could not be infinite, so Planck used the property of the wave we designate as the frequency to define energy. Max Planck discovered a constant that when multiplied by the frequency of any wave gives the energy of the wave. This constant is referred to by the letter h in mathematical formulae. It is a cornerstone of physics. By measuring the energy in a discrete non-continuous portion of the wave, the wave took on the appearance of chunks or packets of energy. These chunks of energy resembled particles. So energy is said to be quantized because it only comes in discrete chunks instead of a continuous range of energies.

In the example we have given, of a free particle in empty space, both the position and the momentum are continuous observables. However, if we restrict the particle to a region of space (the so-called "There was an error working with the wiki: Code[54], and they play an important role in many physical systems. Examples of quantized observables include There was an error working with the wiki: Code[55] in classical physics.

Another quantum effect is the There was an error working with the wiki: Code[56] behavior, such as There was an error working with the wiki: Code[57]. We can observe only one type of property at a time, never both at the same time. Another quantum effect is There was an error working with the wiki: Code[124]. In some cases, the wave function of a system composed of many particles cannot be separated into independent wave functions, one for each particle. In that case, the particles are said to be "entangled". If quantum mechanics is correct, entangled particles can display remarkable and counter-intuitive properties. For example, a measurement made on one particle can produce, through the collapse of the total wavefunction, an instantaneous effect on other particles with which it is entangled, even if they are far apart. (This does not conflict with There was an error working with the wiki: Code[125] because There was an error working with the wiki: Code[126] cannot be transmitted in this way.)

Mathematical formulation

In the mathematically rigorous formulation of quantum mechanics, developed by There was an error working with the wiki: Code[58] There was an error working with the wiki: Code[59] There was an error working with the wiki: Code[60] of a Hilbert space. The exact nature of this Hilbert space is dependent on the system for example, the state space for position and momentum states is the space of There was an error working with the wiki: Code[61]) linear There was an error working with the wiki: Code[127] acting on the state space. Each eigenstate of an observable corresponds to an There was an error working with the wiki: Code[128] of the operator, and the associated There was an error working with the wiki: Code[129] corresponds to the value of the observable in that eigenstate. If the operator's spectrum is discrete, the observable can only attain those discrete eigenvalues.

The time evolution of a quantum state is described by the There was an error working with the wiki: Code[62], the There was an error working with the wiki: Code[63] corresponding to the total energy of the system, generates time evolution. The There was an error working with the wiki: Code[64] of the corresponding operator. Heisenberg's There was an error working with the wiki: Code[65].

The Schrödinger equation acts on the entire probability amplitude, not merely its absolute value. Whereas the absolute value of the probability amplitude encodes information about probabilities, its There was an error working with the wiki: Code[66] encodes information about the There was an error working with the wiki: Code[67] one uses the analytic results for a simple quantum mechanical model to generate results for a more complicated model related to the simple model by, for example, the addition of a weak Potential energy. Another method is the "semi-classical equation of motion" approach, which applies to systems for which quantum mechanics produces weak deviations from classical behavior. The deviations can be calculated based on the classical motion. This approach is important for the field of There was an error working with the wiki: Code[130]. An alternative formulation of quantum mechanics is There was an error working with the wiki: Code[131]'s There was an error working with the wiki: Code[132], in which a quantum-mechanical amplitude is considered as a sum over histories between initial and final states this is the quantum-mechanical counterpart of There was an error working with the wiki: Code[133]s in classical mechanics.

Interactions with other scientific theories

The fundamental rules of quantum mechanics are very broad. They state that the state space of a system is a Hilbert space and the observables are Hermitian operators acting on that space, but do not tell us which Hilbert space or which operators. These must be chosen appropriately in order to obtain a quantitative description of a quantum system. An important guide for making these choices is the There was an error working with the wiki: Code[68] There was an error working with the wiki: Code[69].

Early attempts to merge quantum mechanics with There was an error working with the wiki: Code[70]. The full apparatus of quantum field theory is often unnecessary for describing electrodynamic systems. A simpler approach, one employed since the inception of quantum mechanics, is to treat Electric charge particles as quantum mechanical objects being acted on by a classical electromagnetic field. For example, the elementary quantum model of the There was an error working with the wiki: Code[134] describes the electric field of the hydrogen atom using a classical -\frac{e^2}{4 \pi\ \epsilon_0\ } \frac{1}{r} Coulomb potential. This "semi-classical" approach fails if quantum fluctuations in the electromagnetic field play an important role, such as in the emission of There was an error working with the wiki: Code[135]s by charged particles.

Quantum field theories for the There was an error working with the wiki: Code[71]. It has proven difficult to construct quantum models of Gravity, the remaining There was an error working with the wiki: Code[136]. Semi-classical approximations are workable, and have led to predictions such as There was an error working with the wiki: Code[137]. However, the formulation of a complete theory of There was an error working with the wiki: Code[138] is hindered by apparent incompatibilities between There was an error working with the wiki: Code[139], the most accurate theory of gravity currently known, and some of the fundamental assumptions of quantum theory. The resolution of these incompatibilities is an area of active research, and theories such as There was an error working with the wiki: Code[140] are among the possible candidates for a future theory of quantum gravity.

Applications

Quantum mechanics has had enormous success in explaining many of the features of our world. The individual behaviour of the subatomic particles that make up all forms of There was an error working with the wiki: Code[72]. The study of semiconductors led to the invention of the There was an error working with the wiki: Code[141] and the There was an error working with the wiki: Code[142], which are indispensable for modern There was an error working with the wiki: Code[143]. Researchers are currently seeking robust methods of directly manipulating quantum states. Efforts are being made to develop There was an error working with the wiki: Code[144], which will allow guaranteed secure transmission of There was an error working with the wiki: Code[145]. A more distant goal is the development of There was an error working with the wiki: Code[146]s, which are expected to perform certain computational tasks exponentially faster than classical There was an error working with the wiki: Code[147]s. Another active research topic is There was an error working with the wiki: Code[148], which deals with techniques to transmit quantum states over arbitrary distances.

Philosophical consequences

An interpretation of quantum mechanics is an attempt to answer the question, What exactly is quantum mechanics talking about? The question has its historical roots in the nature of quantum mechanics itself which was considered as a radical departure from previous physical theories. However, quantum mechanics has been described as "the most precisely tested and most successful theory in the history of science" (c.f. Jackiw and Kleppner, 2000.)

Since its inception, the many counter-intuitive results of quantum mechanics have provoked strong There was an error working with the wiki: Code[73] debate and many There was an error working with the wiki: Code[74]. Even fundamental issues such as There was an error working with the wiki: Code[75].

An interpretation can be characterized by whether it satisfies certain properties, such as:

Realism

Completeness

Local realism

Determinism

To explain these properties, we need to be more explicit about the kind of picture an interpretation provides. To that end we will regard an interpretation as a correspondence between the elements of the mathematical formalism M and the elements of an interpreting structure I, where:

The mathematical formalism consists of the Hilbert space machinery of ket-vectors, self-adjoint operators acting on the space of ket-vectors, unitary time dependence of ket-vectors and measurement operations. In this context a measurement operation can be regarded as a transformation which carries a ket-vector into a probability distribution on ket-vectors. See also quantum operations for a formalization of this concept.

The interpreting structure includes states, transitions between states, measurement operations and possibly information about spatial extension of these elements. A measurement operation here refers to an operation which returns a value and results in a possible system state change. Spatial information, for instance would be exhibited by states represented as functions on configuration space. The transitions may be non-deterministic or probabilistic or there may be infinitely many states. However, the critical assumption of an interpretation is that the elements of I are regarded as physically real.

In this sense, an interpretation can be regarded as a semantics for the mathematical formalism.

In particular, the bare instrumentalist view of quantum mechanics outlined in the previous section is not an interpretation at all since it makes no claims about elements of physical reality. The current use in physics of "completeness" and "realism" is often considered to have originated in the paper (Einstein et al., 1935) which proposed the EPR paradox. In that paper the authors proposed the concept "element of reality" and "completeness" of a physical theory. Though they did not define "element of reality", they did provide a sufficient characterization for it, namely a quantity whose value can be predicted with certainty before measuring it or disturbing it in any way. EPR define a "complete physical theory" as one in which every element of physical reality is accounted for by the theory. In the semantic view of interpretation, an interpretation of a theory is complete if every element of the interpreting structure is accounted for by the mathematical formalism. Realism is a property of each one of the elements of the mathematical formalism any such element is real if it corresponds to something in the interpreting structure. For instance, in some interpretations of quantum mechanics (such as the many-worlds interpretation) the ket vector associated to the system state is assumed to correspond to an element of physical reality, while in others it does not.

Determinism is a property characterizing state changes due to the passage of time, namely that the state at an instant of time in the future is a function of the state at the present (see time evolution). It may not always be clear whether a particular interpreting structure is deterministic or not, precisely because there may not be a clear choice for a time parameter. Moreover, a given theory may have two interpretations, one of which is deterministic, and the other not.

Local realism has two parts:

The value returned by a measurement corresponds to the value of some function on the state space. Stated in another way, this value is an element of reality

The effects of measurement have a propagation speed not exceeding some universal bound (e.g., the speed of light). In order for this to make sense, measurement operations must be spatially localized in the interpreting structure.

A precise formulation of local realism in terms of a local hidden variable theory was proposed by John Bell. Bell's theorem and its experimental verification restrict the kinds of properties a quantum theory can have. For instance, Bell's theorem implies quantum mechanics cannot satisfy local realism.

There was an error working with the wiki: Code[76] showed that the EPR paradox led to experimentally testable differences between quantum mechanics and local hidden variable theories. Experiments have been taken as confirming that quantum mechanics is correct and the real world cannot be described in terms of such hidden variables. "There was an error working with the wiki: Code[77]" in the experiments, however, mean that the question is still not quite settled.

The There was an error working with the wiki: Code[78]" composed of mostly independent parallel universes. This is not accomplished by introducing some new axiom to quantum mechanics, but on the contrary by removing the axiom of the collapse of the wave packet: All the possible consistent states of the measured system and the measuring apparatus (including the observer) are present in a real physical (not just formally mathematical, as in other interpretations) There was an error working with the wiki: Code[79]'s experiments and makes them intuitively understandable. However, according to the theory of There was an error working with the wiki: Code[80] with both the physicist who measured it and a huge number of other particles, some of which are There was an error working with the wiki: Code[149]s flying away towards the other end of the universe in order to prove that the wave function did not collapse one would have to bring all these particles back and measure them again, together with the system that was measured originally. This is completely impractical, but even if one can theoretically do this, it would destroy any evidence that the original measurement took place (including the physicist's memory).

Consistent histories

The There was an error working with the wiki: Code[150] generalizes the conventional Copenhagen interpretation and attempts to provide a natural interpretation of There was an error working with the wiki: Code[151]. The theory is based on a consistency criterion that then allows the history of a system to be described so that the probabilities for each history obey the additive rules of classical probability while being consistent with the There was an error working with the wiki: Code[152]. According to this interpretation, the purpose of a quantum-mechanical theory is to predict probabilities of various alternative histories.

Many worlds

The There was an error working with the wiki: Code[81].

The Copenhagen Interpretation

The There was an error working with the wiki: Code[153] is an interpretation of quantum mechanics formulated by Niels Bohr and Werner Heisenberg while collaborating in Copenhagen around 1927. Bohr and Heisenberg extended the probabilistic interpretation of the wavefunction, proposed by Max Born. The Copenhagen interpretation rejects questions like "where was the particle before I measured its position" as meaningless. The act of measurement causes an instantaneous "collapse of the wave function". This means that the measurement process randomly picks out exactly one of the many possibilities allowed for by the state's wave function, and the wave function instantaneously changes to reflect that pick.

Quantum Logic

There was an error working with the wiki: Code[154] can be regarded as a kind of propositional logic suitable for understanding the apparent anomalies regarding quantum measurement, most notably those concerning composition of measurement operations of complementary variables. This research area and its name originated in the 1936 paper by There was an error working with the wiki: Code[155] and There was an error working with the wiki: Code[156], who attempted to reconcile some of the apparent inconsistencies of classical boolean logic with the facts related to measurement and observation in quantum mechanics.

The Bohm interpretation

The There was an error working with the wiki: Code[157] of quantum mechanics is an interpretation postulated by There was an error working with the wiki: Code[158] in which the existence of a non-local universal wavefunction allows distant particles to interact instantaneously. The interpretation generalizes There was an error working with the wiki: Code[159]'s pilot wave theory from 1927, which posits that both wave and particle are real. The wave function 'guides' the motion of the particle, and evolves according to the Schrödinger equation. The interpretation assumes a single, nonsplitting universe (unlike the Everett many-worlds interpretation) and is deterministic (unlike the Copenhagen interpretation). It says the state of the universe evolves smoothly through time, without the collapsing of wavefunctions when a measurement occurs, as in the Copenhagen interpretation. However, it does this by assuming a number of hidden variables, namely the positions of all the particles in the universe, which, like probability amplitudes in other interpretations, can never be measured directly.

Transactional interpretation

The There was an error working with the wiki: Code[160] of quantum mechanics (TIQM) by There was an error working with the wiki: Code[161] is an unusual interpretation of quantum mechanics that describes quantum interactions in terms of a standing wave formed by retarded (forward-in-time) and advanced (backward-in-time) waves. The author argues that it avoids the philosophical problems with the Copenhagen interpretation and the role of the observer, and resolves various quantum paradoxes.

Consciousness causes collapse

There was an error working with the wiki: Code[162] is the speculative theory that observation by a conscious observer is responsible for the wavefunction collapse. It is an attempt to solve the There was an error working with the wiki: Code[163] paradox by simply stating that collapse occurs at the first "conscious" observer. Supporters claim this is not a revival of substance dualism, since (in a ramification of this view) consciousness and objects are entangled and cannot be considered as distinct. The consciousness causes collapse theory can be considered as a speculative appendage to almost any interpretation of quantum mechanics and most physicists reject it as unverifiable and introducing unnecessary elements into physics.

Relational Quantum Mechanics

The essential idea behind Relational Quantum Mechanics, following the precedent of There was an error working with the wiki: Code[164], is that different observers may give different accounts of the same series of events: for example, to one observer at a given point in time, a system may be in a single, "collapsed" eigenstate, while to another observer at the same time, it may be in a superposition of two or more states. Consequently, if quantum mechanics is to be a complete theory, Relational Quantum Mechanics argues that the notion of "state" describes not the observed system itself, but the relationship, or correlation, between the system and its observer(s). The There was an error working with the wiki: Code[165] of conventional quantum mechanics becomes a description of the correlation of some degrees of freedom in the observer, with respect to the observed system. However, it is held by Relational Quantum Mechanics that this applies to all physical objects, whether or not they are conscious or macroscopic. Any "measurement event" is seen simply as an ordinary physical interaction, an establishment of the sort of correlation discussed above. Thus the physical content of the theory is to do not with objects themselves, but the relations between them There was an error working with the wiki: Code[1]. For more information, see Rovelli (1996).

Modal Interpretations of Quantum Theory

Modal interpretations of Quantum mechanics were first conceived of in 1972 by B. van Fraassen, in his paper “A formal approach to the philosophy of science". However, this term now is used to describe a larger set of models that grew out of this approach. The There was an error working with the wiki: Code[166] describes several versions:

The Copenhagen Variant

Kochen-Dieks-Healey Interpretations

Motivating Early Modal Interpretations, based on the work of R. Clifton, M. Dickson and J. Bub.

Explanation of quantum mechanics enigmas

The Spacetime Model can be considered as the continuation of Eintein's works. Instead of limiting spacetime to General Relativity (mass and gravity), the author has extended it to all elements of the universe. The result is that spacetime explains with logic and consistency 53 enigmas of Quantum Mechanics: wave-particle duality, elementary particles (quarks and leptons), mass, gravity, charge, antimatter, Standard Model.... It unifies the three basic forces (electroweak, stong nuclear and gravity) in two generic forces. Contrary to other theories, the Spacetime Model requires only four dimensions: x, y, z and t. To get additional information concerning this new theory, please download the free 220 pages document at www.spacetime-model.com.

Founding experiments

There was an error working with the wiki: Code[82]'s There was an error working with the wiki: Code[167] demonstrating the wave nature of light (cThere was an error working with the wiki: Code[168])

There was an error working with the wiki: Code[169] discovers There was an error working with the wiki: Code[170] (There was an error working with the wiki: Code[171])

There was an error working with the wiki: Code[172]'s cathode ray tube experiments (discovers the Electron and its negative charge) (There was an error working with the wiki: Code[173])

The study of There was an error working with the wiki: Code[174] between 1850 and 1900, which could not be explained without quantum concepts.

The There was an error working with the wiki: Code[83] explained this in 1905 (and later received a Nobel prize for it) using the concept of photons, particles of light with quantized energy

There was an error working with the wiki: Code[84] (whole units), (There was an error working with the wiki: Code[175])

There was an error working with the wiki: Code[85] disproved the plum pudding model of the Atom which suggested that the mass and positive charge of the atom are almost uniformly distributed. (There was an error working with the wiki: Code[176])

There was an error working with the wiki: Code[177]'s There was an error working with the wiki: Code[178] disproved the There was an error working with the wiki: Code[179] model and temporarily cast doubt on the distribution of protons throughout an atom.

There was an error working with the wiki: Code[86] (There was an error working with the wiki: Code[180])

There was an error working with the wiki: Code[181] and There was an error working with the wiki: Code[182] demonstrate the wave nature of the Electron There was an error working with the wiki: Code[2] in the There was an error working with the wiki: Code[183] experiment (There was an error working with the wiki: Code[184])

There was an error working with the wiki: Code[185] and There was an error working with the wiki: Code[186] confirm the existence of the Neutrino in the There was an error working with the wiki: Code[187] (There was an error working with the wiki: Code[188])

There was an error working with the wiki: Code[189]s There was an error working with the wiki: Code[190] with electrons (There was an error working with the wiki: Code[191])

Research and Development

Marine Algae Using Quantum Mechanics Principles for Light Harvesting - Experimental results suggest that the energy of absorbed light resides in two places at once — a quantum superposition state, or coherence – and such a state lies at the heart of quantum mechanical theory. (The Green Optimistic Feb. 4, 2010)

One small step for a man, one giant leap for teleportation - According to LiveScience, the university's Joint Quantum Institute for the first time was able to teleport information between two separate atoms across a distance of a meter - about one step for an adult, using "entanglement". (CNet News Jan. 26, 2009)

External articles and references

citations

There was an error working with the wiki: Code[3]The Davisson-Germer experiment, which demonstrates the wave nature of the electron

There was an error working with the wiki: Code[4] http://plato.stanford.edu/entries/qm-relational/

Books:

P. A. M. Dirac, The Principles of Quantum Mechanics (1930) -- the beginning chapters provide a very clear and comprehensible introduction

David Griffiths, Introduction to Quantum Mechanics, Prentice Hall, 1995. ISBN 0-13-111892-7

Richard P. Feynman, Robert B. Leighton and Matthew Sands (1965). The Feynman Lectures on Physics, Addison-Wesley. Richard Feynman's original lectures (given at CALTECH in early 1962) can also be downloaded as an MP3 file from www.audible.com[1]

Hugh Everett, Relative State Formulation of Quantum Mechanics, Reviews of Modern Physics vol 29, (1957) pp 454-462.

Bryce DeWitt, R. Neill Graham, eds, The Many-Worlds Interpretation of Quantum Mechanics, Princeton Series in Physics, Princeton University Press (1973), ISBN 0-691-08131-X

Albert Messiah, Quantum Mechanics, English translation by G. M. Temmer of Mécanique Quantique, 1966, John Wiley and Sons, vol. I, chapter IV, section III.

Richard P. Feynman, QED: The Strange Theory of Light and Matter -- a popular science book about quantum mechanics and quantum field theory that contains many enlightening insights that are interesting for the expert as well

Marvin Chester, Primer of Quantum Mechanics, 1987, John Wiley, N.Y. ISBN 0-486-42878-8

Hagen Kleinert, Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets, 3th edition, World Scientific (Singapore, 2004)(also available online here)

George Mackey (2004). The mathematical foundations of quantum mechanics. Dover Publications. ISBN 0-486-43517-2.

Griffiths, David J. (2004). Introduction to Quantum Mechanics (2nd ed.). Prentice Hall. ISBN 0-13-805326-X.

Omnes, Roland (1999). Understanding Quantum Mechanics. Princeton University Press. ISBN 0-691-00435-8.

J. von Neumann, Mathematical Foundations of Quantum Mechanics, Princeton University Press, 1955.

H. Weyl, The Theory of Groups and Quantum Mechanics, Dover Publications 1950.

Max Jammer, "The Conceptual Development of Quantum Mechanics" (McGraw Hill Book Co., 1966)

Gunther Ludwig, "Wave Mechanics" (Pergamon Press, 1968) ISBN 08-203204-1

General:

J J O'Connor and E F Robertson, A history of quantum mechanics www-history.mcs.st-andrews.ac.uk

James Higgo A Lazy Layman's Guide to Quantum Physics higgo.com 1999

Introduction to Quantum Theory at Quantiki, cam.qubit.org. Content is available under GNU Free Documentation License.

There was an error working with the wiki: Code[1], Wikipedia: The Free Encyclopedia. Wikimedia Foundation.

Quantum Physics Made Relatively Simple: three video lectures by There was an error working with the wiki: Code[192]

Decoherence by Erich Joos

Course material:

There was an error working with the wiki: Code[193]: Chemistry. See 5.61, 5.73, and 5.74

MIT OpenCourseWare: Physics. See 8.04, 8.05, and 8.06.

Spark Notes - Quantum Physics

FAQs:

Many-worlds or relative-state interpretation

Measurement in Quantum mechanics

A short FAQ on quantum resonances

Media:

Everything you wanted to know about the quantum world &mdash archive of articles from There was an error working with the wiki: Code[194] magazine.

Quantum Physics Research From ScienceDaily

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The mystery of the wave-particle duality

Explanation of 53 enigmas of Quantum Physics. The PDF document available on this link is also edited by AC42 ISBN 97829531234-0-1.

Philosophy:

Quantum Mechanics (Stanford Encyclopedia of Philosophy)

David Mermin on the future directions of physics

Quantum Physics Quackery by Victor Stenger, Skeptical Inquirer (January/February 1997).

Crank Dot Net's quantum physics page &mdash "cranks, crackpots, kooks & loons on the net"

Hinduism & Quantum Physics