Quantum mechanics (QM - also known as quantum physics, or quantum theory) is a branch of physics dealing with physical phenomena where the action is on the order of the Planck constant. Quantum mechanics departs from classical mechanics primarily at the quantum realm of atomic and subatomic length scales. QM provides a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter.

In advanced topics of quantum mechanics, some of these behaviors are macroscopic and only emerge at extreme (i.e., very low or very high) energies or temperatures. The name quantum mechanics derives from the observation that some physical quantities can change only in discrete amounts (Latin quanta), and not in a continuous (cf. analog) way. For example, the angular momentum of an electron bound to an atom or molecule is quantized.^[1] In the context of quantum mechanics, the wave–particle duality of energy and matter and the uncertainty principle provide a unified view of the behavior of photons, electrons, and other atomic-scale objects.

The mathematical formulations of quantum mechanics are abstract. A mathematical function called the wavefunction provides information about the probability amplitude of position, momentum, and other physical properties of a particle. Mathematical manipulations of the wavefunction usually involve the bra-ket notation, which requires an understanding of complex numbers and linear functionals. The wavefunction treats the object as a quantum harmonic oscillator, and the mathematics is akin to that describing acoustic resonance. Many of the results of quantum mechanics are not easily visualized in terms of classical mechanics - for instance, the ground state in a quantum mechanical model is a non-zero energy state that is the lowest permitted energy state of a system, as opposed a more "traditional" system that is thought of as simply being at rest, with zero kinetic energy. Instead of a traditional static, unchanging zero state, quantum mechanics allows for far more dynamic, chaotic possibilities, according to John Wheeler.

The earliest versions of quantum mechanics were formulated in the first decade of the 20th century. At around the same time, the atomic theory and the corpuscular theory of light (as updated by Einstein) first came to be widely accepted as scientific fact; these latter theories can be viewed as quantum theories of matter and electromagnetic radiation, respectively. Early quantum theory was significantly reformulated in the mid-1920s by Werner Heisenberg, Max Born, Wolfgang Pauli and their collaborators, and the Copenhagen interpretation of Niels Bohr became widely accepted. By 1930, quantum mechanics had been further unified and formalized by the work of Paul Dirac and John von Neumann, with a greater emphasis placed on measurement in quantum mechanics, the statistical nature of our knowledge of reality, and philosophical speculation about the role of the observer. Quantum mechanics has since branched out into almost every aspect of 20th century physics and other disciplines, such as quantum chemistry, quantum electronics, quantum optics, and quantum information science. Much 19th century physics has been re-evaluated as the "classical limit" of quantum mechanics, and its more advanced developments in terms of quantum field theory, string theory, and speculative quantum gravity theories.

History[link]

The history of quantum mechanics dates back to the 1838 discovery of cathode rays by Michael Faraday. This was followed by the 1859 statement of the black body radiation problem by Gustav Kirchhoff, the 1877 suggestion by Ludwig Boltzmann that the energy states of a physical system can be discrete, and the 1900 quantum hypothesis of Max Planck.^[2] Planck's hypothesis that energy is radiated and absorbed in discrete "quanta" (or "energy elements") precisely matched the observed patterns of blackbody radiation. According to Planck, each energy element E is proportional to its frequency ν:

Failed to parse (Missing texvc executable; please see math/README to configure.): E = h \nu\

where h is Planck's constant. Planck (cautiously) insisted that this was simply an aspect of the processes of absorption and emission of radiation and had nothing to do with the physical reality of the radiation itself.^[3] However, in 1905 Albert Einstein interpreted Planck's quantum hypothesis realistically and used it to explain the photoelectric effect, in which shining light on certain materials can eject electrons from the material.

The 1927 Solvay Conference in Brussels.

The foundations of quantum mechanics were established during the first half of the 20th century by Niels Bohr, Werner Heisenberg, Max Planck, Louis de Broglie, Albert Einstein, Erwin Schrödinger, Max Born, John von Neumann, Paul Dirac, Wolfgang Pauli, David Hilbert, and others. In the mid-1920s, developments in quantum mechanics led to its becoming the standard formulation for atomic physics. In the summer of 1925, Bohr and Heisenberg published results that closed the "Old Quantum Theory". Out of deference to their particle-like behavior in certain processes and measurements, light quanta came to be called photons (1926). From Einstein's simple postulation was born a flurry of debating, theorizing, and testing. Thus the entire field of quantum physics emerged, leading to its wider acceptance at the Fifth Solvay Conference in 1927.

The other exemplar that led to quantum mechanics was the study of electromagnetic waves, such as visible light. When it was found in 1900 by Max Planck that the energy of waves could be described as consisting of small packets or "quanta", Albert Einstein further developed this idea to show that an electromagnetic wave such as light could be described as a particle (later called the photon) with a discrete quantum of energy that was dependent on its frequency.^[4] This led to a theory of unity between subatomic particles and electromagnetic waves, called wave–particle duality, in which particles and waves were neither one nor the other, but had certain properties of both.

While quantum mechanics traditionally described the world of the very small, it is also needed to explain certain recently investigated macroscopic systems such as superconductors and superfluids.

The word quantum derives from the Latin, meaning "how great" or "how much".^[5] In quantum mechanics, it refers to a discrete unit that quantum theory assigns to certain physical quantities, such as the energy of an atom at rest (see Figure 1). The discovery that particles are discrete packets of energy with wave-like properties led to the branch of physics dealing with atomic and sub-atomic systems which is today called quantum mechanics. It is the underlying mathematical framework of many fields of physics and chemistry, including condensed matter physics, solid-state physics, atomic physics, molecular physics, computational physics, computational chemistry, quantum chemistry, particle physics, nuclear chemistry, and nuclear physics.^[6] Some fundamental aspects of the theory are still actively studied^[7]

Quantum mechanics is essential to understanding the behavior of systems at atomic length scales and smaller. For example, if classical mechanics truly governed the workings of an atom, electrons would rapidly travel toward, and collide with, the nucleus, making stable atoms impossible. However, in the natural world electrons normally remain in an uncertain, non-deterministic, "smeared", probabilistic wave–particle wavefunction orbital path around (or through) the nucleus, defying classical electromagnetism.^[8]

Quantum mechanics was initially developed to provide a better explanation of the atom, especially the differences in the spectra of light emitted by different isotopes of the same element. The quantum theory of the atom was developed as an explanation for the electron remaining in its orbit, which could not be explained by Newton's laws of motion and Maxwell's laws of (classical) electromagnetism.

Broadly speaking, quantum mechanics incorporates four classes of phenomena for which classical physics cannot account:

• The quantization of certain physical properties
• Wave–particle duality
• The Uncertainty principle
• Quantum entanglement.

Mathematical formulations[link]

In the mathematically rigorous formulation of quantum mechanics developed by Paul Dirac^[9] and John von Neumann,^[10] the possible states of a quantum mechanical system are represented by unit vectors (called "state vectors"). Formally, these reside in a complex separable Hilbert space - variously called the "state space" or the "associated Hilbert space" of the system - that is well defined up to a complex number of norm 1 (the phase factor). In other words, the possible states are points in the projective space of a Hilbert space, usually called the complex projective space. The exact nature of this Hilbert space is dependent on the system - for example, the state space for position and momentum states is the space of square-integrable functions, while the state space for the spin of a single proton is just the product of two complex planes. Each observable is represented by a maximally Hermitian (precisely: by a self-adjoint) linear operator acting on the state space. Each eigenstate of an observable corresponds to an eigenvector of the operator, and the associated eigenvalue corresponds to the value of the observable in that eigenstate. If the operator's spectrum is discrete, the observable can only attain those discrete eigenvalues.

In the formalism of quantum mechanics, the state of a system at a given time is described by a complex wave function, also referred to as state vector in a complex vector space.^[11] This abstract mathematical object allows for the calculation of probabilities of outcomes of concrete experiments. For example, it allows one to compute the probability of finding an electron in a particular region around the nucleus at a particular time. Contrary to classical mechanics, one can never make simultaneous predictions of conjugate variables, such as position and momentum, with accuracy. For instance, electrons may be considered (to a certain probability) to be located somewhere within a given region of space, but with their exact positions unknown. Contours of constant probability, often referred to as "clouds", may be drawn around the nucleus of an atom to conceptualize where the electron might be located with the most probability. Heisenberg's uncertainty principle quantifies the inability to precisely locate the particle given its conjugate momentum.^[12]

According to one interpretation, as the result of a measurement the wave function containing the probability information for a system collapses from a given initial state to a particular eigenstate. The possible results of a measurement are the eigenvalues of the operator representing the observable — which explains the choice of Hermitian operators, for which all the eigenvalues are real. The probability distribution of an observable in a given state can be found by computing the spectral decomposition of the corresponding operator. Heisenberg's uncertainty principle is represented by the statement that the operators corresponding to certain observables do not commute.

The probabilistic nature of quantum mechanics thus stems from the act of measurement. This is one of the most difficult aspects of quantum systems to understand. It was the central topic in the famous Bohr-Einstein debates, in which the two scientists attempted to clarify these fundamental principles by way of thought experiments. In the decades after the formulation of quantum mechanics, the question of what constitutes a "measurement" has been extensively studied. Newer interpretations of quantum mechanics have been formulated that do away with the concept of "wavefunction collapse" (see, for example, the relative state interpretation). The basic idea is that when a quantum system interacts with a measuring apparatus, their respective wavefunctions become entangled, so that the original quantum system ceases to exist as an independent entity. For details, see the article on measurement in quantum mechanics.^[13]

Generally, quantum mechanics does not assign definite values. Instead, it makes a prediction using a probability distribution; that is, it describes the probability of obtaining the possible outcomes from measuring an observable. Often these results are skewed by many causes, such as dense probability clouds. Probability clouds are approximate, but better than the Bohr model, whereby electron location is given by a probability function, the wave function eigenvalue, such that the probability is the squared modulus of the complex amplitude, or quantum state nuclear attraction.^[14][15] Naturally, these probabilities will depend on the quantum state at the "instant" of the measurement. Hence, uncertainty is involved in the value. There are, however, certain states that are associated with a definite value of a particular observable. These are known as eigenstates of the observable ("eigen" can be translated from German as meaning "inherent" or "characteristic").^[16]

In the everyday world, it is natural and intuitive to think of everything (every observable) as being in an eigenstate. Everything appears to have a definite position, a definite momentum, a definite energy, and a definite time of occurrence. However, quantum mechanics does not pinpoint the exact values of a particle's position and momentum (since they are conjugate pairs) or its energy and time (since they too are conjugate pairs); rather, it only provides a range of probabilities of where that particle might be given its momentum and momentum probability. Therefore, it is helpful to use different words to describe states having uncertain values and states having definite values (eigenstates). Usually, a system will not be in an eigenstate of the observable (particle) we are interested in. However, if one measures the observable, the wavefunction will instantaneously be an eigenstate (or "generalized" eigenstate) of that observable. This process is known as wavefunction collapse, a controversial and much-debated process^[17] that involves expanding the system under study to include the measurement device. If one knows the corresponding wave function at the instant before the measurement, one will be able to compute the probability of the wavefunction collapsing into each of the possible eigenstates. For example, the free particle in the previous example will usually have a wavefunction that is a wave packet centered around some mean position x₀ (neither an eigenstate of position nor of momentum). When one measures the position of the particle, it is impossible to predict with certainty the result.^[13] It is probable, but not certain, that it will be near x₀, where the amplitude of the wave function is large. After the measurement is performed, having obtained some result x, the wave function collapses into a position eigenstate centered at x.^[18]

The time evolution of a quantum state is described by the Schrödinger equation, in which the Hamiltonian (the operator corresponding to the total energy of the system) generates the time evolution. The time evolution of wave functions is deterministic in the sense that - given a wavefunction at an initial time - it makes a definite prediction of what the wavefunction will be at any later time.^[19]

During a measurement, on the other hand, the change of the initial wavefunction into another, later wavefunction is not deterministic, it is unpredictable (i.e. random). A time-evolution simulation can be seen here.^[20][21]

Wave functions change as time progresses. The Schrödinger equation describes how wavefunctions change in time, playing a role similar to Newton's second law in classical mechanics. The Schrödinger equation, applied to the aforementioned example of the free particle, predicts that the center of a wave packet will move through space at a constant velocity (like a classical particle with no forces acting on it). However, the wave packet will also spread out as time progresses, which means that the position becomes more uncertain with time. This also has the effect of turning a position eigenstate (which can be thought of as an infinitely sharp wave packet) into a broadened wave packet that no longer represents a (definite, certain) position eigenstate.^[22]

Fig. 1: Probability densities corresponding to the wavefunctions of an electron in a hydrogen atom possessing definite energy levels (increasing from the top of the image to the bottom: n = 1, 2, 3, ...) and angular momenta (increasing across from left to right: s, p, d, ...). Brighter areas correspond to higher probability density in a position measurement. Wavefunctions like these are directly comparable to Chladni's figures of acoustic modes of vibration in classical physics, and are indeed modes of oscillation as well, possessing a sharp energy and, thus, a definite frequency. The angular momentum and energy are quantized, and take only discrete values like those shown (as is the case for resonant frequencies in acoustics)

Some wave functions produce probability distributions that are constant, or independent of time - such as when in a stationary state of constant energy, time vanishes in the absolute square of the wave function. Many systems that are treated dynamically in classical mechanics are described by such "static" wave functions. For example, a single electron in an unexcited atom is pictured classically as a particle moving in a circular trajectory around the atomic nucleus, whereas in quantum mechanics it is described by a static, spherically symmetric wavefunction surrounding the nucleus (Fig. 1) (note, however, that only the lowest angular momentum states, labeled s, are spherically symmetric).^[23]

The Schrödinger equation acts on the entire probability amplitude, not merely its absolute value. Whereas the absolute value of the probability amplitude encodes information about probabilities, its phase encodes information about the interference between quantum states. This gives rise to the "wave-like" behavior of quantum states. As it turns out, analytic solutions of the Schrödinger equation are only available for a very small number of relatively simple model Hamiltonians, of which the quantum harmonic oscillator, the particle in a box, the hydrogen molecular ion, and the hydrogen atom are the most important representatives. Even the helium atom - which contains just one more electron than does the hydrogen atom - has defied all attempts at a fully analytic treatment.

There exist several techniques for generating approximate solutions, however. In the important method known as perturbation theory, one uses the analytic result for a simple quantum mechanical model to generate a result for a more complicated model that is related to the simpler model by (for one 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 only weak (small) deviations from classical behavior. These deviations can then be computed based on the classical motion. This approach is particularly important in the field of quantum chaos.

Mathematically equivalent formulations of quantum mechanics[link]

There are numerous mathematically equivalent formulations of quantum mechanics. One of the oldest and most commonly used formulations is the "transformation theory" proposed by the late Cambridge theoretical physicist Paul Dirac, which unifies and generalizes the two earliest formulations of quantum mechanics - matrix mechanics (invented by Werner Heisenberg)^[24] and wave mechanics (invented by Erwin Schrödinger).^[25]

Especially since Werner Heisenberg was awarded the Nobel Prize in Physics in 1932 for the creation of quantum mechanics, the role of Max Born in the development of QM has become somewhat confused and overlooked. A 2005 biography of Born details his role as the creator of the matrix formulation of quantum mechanics. This fact was recognized in a paper that Heisenberg himself published in 1940 honoring Max Planck.^[26] and In the matrix formulation, the instantaneous state of a quantum system encodes the probabilities of its measurable properties, or "observables". Examples of observables include energy, position, momentum, and angular momentum. Observables can be either continuous (e.g., the position of a particle) or discrete (e.g., the energy of an electron bound to a hydrogen atom).^[27] An alternative formulation of quantum mechanics is Feynman's path integral formulation, in which a quantum-mechanical amplitude is considered as a sum over all possible histories between the initial and final states. This is the quantum-mechanical counterpart of the action principle in classical mechanics.

Interactions with other scientific theories[link]

The rules of quantum mechanics are fundamental. They assert that the state space of a system is a Hilbert space, and that observables of that system are Hermitian operators acting on that space - although they do not tell us which Hilbert space or which operators. These can be chosen appropriately in order to obtain a quantitative description of a quantum system. An important guide for making these choices is the correspondence principle, which states that the predictions of quantum mechanics reduce to those of classical mechanics when a system moves to higher energies or - equivalently - larger quantum numbers, i.e. whereas a single particle exhibits a degree of randomness, in systems incorporating millions of particles averaging takes over and, at the high energy limit, the statistical probability of random behaviour approaches zero. In other words, classical mechanics is simply a quantum mechanics of large systems. This "high energy" limit is known as the classical or correspondence limit. One can even start from an established classical model of a particular system, then attempt to guess the underlying quantum model that would give rise to the classical model in the correspondence limit.

When quantum mechanics was originally formulated, it was applied to models whose correspondence limit was non-relativistic classical mechanics. For instance, the well-known model of the quantum harmonic oscillator uses an explicitly non-relativistic expression for the kinetic energy of the oscillator, and is thus a quantum version of the classical harmonic oscillator.

Early attempts to merge quantum mechanics with special relativity involved the replacement of the Schrödinger equation with a covariant equation such as the Klein-Gordon equation or the Dirac equation. While these theories were successful in explaining many experimental results, they had certain unsatisfactory qualities stemming from their neglect of the relativistic creation and annihilation of particles. A fully relativistic quantum theory required the development of quantum field theory, which applies quantization to a field (rather than a fixed set of particles). The first complete quantum field theory, quantum electrodynamics, provides a fully quantum description of the electromagnetic interaction. The full apparatus of quantum field theory is often unnecessary for describing electrodynamic systems. A simpler approach, one that has been employed since the inception of quantum mechanics, is to treat charged particles as quantum mechanical objects being acted on by a classical electromagnetic field. For example, the elementary quantum model of the hydrogen atom describes the electric field of the hydrogen atom using a classical Failed to parse (Missing texvc executable; please see math/README to configure.): \scriptstyle -e^2/(4 \pi\ \epsilon_{_0}\ 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 photons by charged particles.

Quantum field theories for the strong nuclear force and the weak nuclear force have also been developed. The quantum field theory of the strong nuclear force is called quantum chromodynamics, and describes the interactions of subnuclear particles such as quarks and gluons. The weak nuclear force and the electromagnetic force were unified, in their quantized forms, into a single quantum field theory (known as electroweak theory), by the physicists Abdus Salam, Sheldon Glashow and Steven Weinberg. These three men shared the Nobel Prize in Physics in 1979 for this work.^[28]

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

Classical mechanics has also been extended into the complex domain, with complex classical mechanics exhibiting behaviors similar to quantum mechanics.^[29]

Quantum mechanics and classical physics[link]

Predictions of quantum mechanics have been verified experimentally to an extremely high degree of accuracy. According to the correspondence principle between classical and quantum mechanics, all objects obey the laws of quantum mechanics, and classical mechanics is just an approximation for large systems of objects (or a statistical quantum mechanics of a large collection of particles). The laws of classical mechanics thus follow from the laws of quantum mechanics as a statistical average at the limit of large systems or large quantum numbers.^[30] However, chaotic systems do not have good quantum numbers, and quantum chaos studies the relationship between classical and quantum descriptions in these systems.

Quantum coherence is an essential difference between classical and quantum theories, and is illustrated by the Einstein-Podolsky-Rosen paradox. Quantum interference involves adding together probability amplitudes, whereas classical "waves" infer that there is an adding together of intensities. For microscopic bodies, the extension of the system is much smaller than the coherence length, which gives rise to long-range entanglement and other nonlocal phenomena that are characteristic of quantum systems.^[31] Quantum coherence is not typically evident at macroscopic scales - although an exception to this rule can occur at extremely low temperatures (i.e. approaching absolute zero), when quantum behavior can manifest itself on more macroscopic scales (see macroscopic quantum phenomena, Bose-Einstein condensate, and Quantum machine). This is in accordance with the following observations:

• Many macroscopic properties of a classical system are a direct consequence of the quantum behavior of its parts. For example, the stability of bulk matter (which consists of atoms and molecules which would quickly collapse under electric forces alone), the rigidity of solids, and the mechanical, thermal, chemical, optical and magnetic properties of matter are all results of the interaction of electric charges under the rules of quantum mechanics.^[32]
• While the seemingly "exotic" behavior of matter posited by quantum mechanics and relativity theory become more apparent when dealing with particles of extremely small size or velocities approaching the speed of light, the laws of classical Newtonian physics remain accurate in predicting the behavior of the vast majority of "large" objects (on the order of the size of large molecules or bigger) at velocities much smaller than the velocity of light.^[33]

Relativity and quantum mechanics[link]

Main articles: Quantum gravity and Theory of everything

Even with the defining postulates of both Einstein's theory of general relativity and quantum theory being indisputably supported by rigorous and repeated empirical evidence and while they do not directly contradict each other theoretically (at least with regard to their primary claims), they have proven extremely difficult to being incorporated within one consistent, cohesive model.^[34]

Einstein himself is well known for rejecting some of the claims of quantum mechanics. While clearly contributing to the field, he did not accept many of the more "philosophical consequences and interpretations" of quantum mechanics, such as the lack of deterministic causality. He is famously quoted as saying, in response to this aspect, "My God does not play with dice". He also had difficulty with the assertion that a single subatomic particle can occupy numerous areas of space at one time. However, he was also the first to notice some of the apparently exotic consequences of entanglement, and used them to formulate the Einstein-Podolsky-Rosen paradox in the hope of showing that quantum mechanics had unacceptable implications. This was 1935, but in 1964 it was shown by John Bell (see Bell inequality) that - although Einstein was correct in identifying seemingly paradoxical implications of quantum mechanical nonlocality - these implications could be experimentally tested. Alain Aspect's initial experiments in 1982, and many subsequent experiments since, have definitively verified quantum entanglement.

According to the paper of J. Bell and the Copenhagen interpretation - the common interpretation of quantum mechanics by physicists since 1927 - and contrary to Einstein's ideas, quantum mechanics was not, at the same time:

• a "realistic" theory

and

• a local theory.

The Einstein-Podolsky-Rosen paradox shows in any case that there exist experiments by which one can measure the state of one particle and instantaneously change the state of its entangled partner - although the two particles can be an arbitrary distance apart. However, this effect does not violate causality, since no transfer of information happens. Quantum entanglement forms the basis of quantum cryptography, which is used in high-security commercial applications in banking and government.

Gravity is negligible in many areas of particle physics, so that unification between general relativity and quantum mechanics is not an urgent issue in those particular applications. However, the lack of a correct theory of quantum gravity is an important issue in cosmology and the search by physicists for an elegant "Theory of Everything" (TOE). Consequently, resolving the inconsistencies between both theories has been a major goal of 20th and 21st century physics. Many prominent physicists, including Stephen Hawking, have labored for many years in the attempt to discover a theory underlying everything. This TOE would combine not only the different models of subatomic physics, but also derive the four fundamental forces of nature - the strong force, electromagnetism, the weak force, and gravity - from a single force or phenomenon. While Stephen Hawking was initially a believer in the Theory of Everything, after considering Gödel's Incompleteness Theorem, he has concluded that one is not obtainable, and has stated so publicly in his lecture "Gödel and the End of Physics" (2002).^[35] One of the leading authorities continuing the search for a coherent TOE is Edward Witten, a theoretical physicist who formulated the groundbreaking M-theory, which is an attempt at describing the supersymmetrical based string theory. M-theory posits that our apparent 4-dimensional spacetime is, in reality, actually an 11-dimensional spacetime containing 10 spatial dimensions and 1 time dimension, although 7 of the spatial dimensions are - at lower energies - completely "compactified" (or infinitely curved) and not readily amenable to measurement or probing.

Attempts at a unified field theory[link]

The quest to unify the fundamental forces through quantum mechanics is still ongoing. Quantum electrodynamics (or "quantum electromagnetism"), which is currently (in the perturbative regime at least) the most accurately tested physical theory,^{[36][unreliable source](blog)} has been successfully merged with the weak nuclear force into the electroweak force and work is currently being done to merge the electroweak and strong force into the electrostrong force. Current predictions state that at around 10¹⁴ GeV the three aforementioned forces are fused into a single unified field,^[37] Beyond this "grand unification," it is speculated that it may be possible to merge gravity with the other three gauge symmetries, expected to occur at roughly 10¹⁹ GeV. However — and while special relativity is parsimoniously incorporated into quantum electrodynamics — the expanded general relativity, currently the best theory describing the gravitation force, has not been fully incorporated into quantum theory.

Philosophical implications[link]

Since its inception, the many counter-intuitive aspects and results of quantum mechanics have provoked strong philosophical debates and many interpretations. Even fundamental issues, such as Max Born's basic rules concerning probability amplitudes and probability distributions took decades to be appreciated by society and many leading scientists. Indeed, the renown physicist Richard Feynman once said, "I think I can safely say that nobody understands quantum mechanics."^[38]

The Copenhagen interpretation - due largely to the Danish theoretical physicist Niels Bohr - remains the quantum mechanical formalism that is currently most widely accepted amongst physicists, some 75 years after its enunciation. According to this interpretation, the probabilistic nature of quantum mechanics is not a temporary feature which will eventually be replaced by a deterministic theory, but instead must be considered a final renunciation of the classical idea of "causality". It is also believed therein that any well-defined application of the quantum mechanical formalism must always make reference to the experimental arrangement, due to the complementarity nature of evidence obtained under different experimental situations.

Albert Einstein, himself one of the founders of quantum theory, disliked this loss of determinism in measurement. Einstein held that there should be a local hidden variable theory underlying quantum mechanics and, consequently, that the present theory was incomplete. He produced a series of objections to the theory, the most famous of which has become known as the Einstein-Podolsky-Rosen paradox. John Bell showed that this "EPR" paradox led to experimentally testable differences between quantum mechanics and local realistic theories. Experiments have been performed confirming the accuracy of quantum mechanics, thereby demonstrating that the physical world cannot be described by any local realistic theory.^[39] The Bohr-Einstein debates provide a vibrant critique of the Copenhagen Interpretation from an epistemological point of view.

The Everett many-worlds interpretation, formulated in 1956, holds that all the possibilities described by quantum theory simultaneously occur in a multiverse composed of mostly independent parallel universes.^[40] 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 of 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 - quantum superposition. Such a superposition of consistent state combinations of different systems is called an entangled state. While the multiverse is deterministic, we perceive non-deterministic behavior governed by probabilities, because we can observe only the universe (i.e., the consistent state contribution to the aforementioned superposition) that we, as observers, inhabit. Everett's interpretation is perfectly consistent with John Bell's experiments and makes them intuitively understandable. However, according to the theory of quantum decoherence, these "parallel universes" will never be accessible to us. The inaccessibility can be understood as follows: once a measurement is done, the measured system becomes entangled with both the physicist who measured it and a huge number of other particles, some of which are photons flying away at the speed of light 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 originally measured. Not only is this completely impractical, but even if one could theoretically do this, it would destroy any evidence that the original measurement took place (to include the physicist's memory).^{[citation needed]}

Applications[link]

Quantum mechanics had enormous^[41] success in explaining many of the features of our world. The individual behaviors of the subatomic particles that make up all forms of matter (elections, protons, neutrons, photons, and others) can often only be satisfactorily described using quantum mechanics. Quantum mechanics has strongly influenced string theories, candidates for a Theory of Everything (see reductionism), and the multiverse hypotheses.

Quantum mechanics is also critically important for understanding how individual atoms combine covalently to form molecules. The application of quantum mechanics to chemistry is known as quantum chemistry. Relativistic quantum mechanics can, in principle, mathematically describe most of chemistry. Quantum mechanics can also provide quantitative insight into ionic and covalent bonding processes by explicitly showing which molecules are energetically favorable to which others, and the magnitudes of the energies involved.^[42] Furthermore, most of the calculations performed in modern computational chemistry rely on quantum mechanics.^[43]

A working mechanism of a resonant tunneling diode device, based on the phenomenon of quantum tunneling through potential barriers

A great deal of modern technological inventions operate at a scale where quantum effects are significant. Examples include the laser, the transistor (and thus the microchip), the electron microscope, and magnetic resonance imaging (MRI). The study of semiconductors led to the invention of the diode and the transistor, which are indispensable parts of modern electronics systems and devices.

Researchers are currently seeking robust methods of directly manipulating quantum states. Efforts are being made to more fully develop quantum cryptography, which will theoretically allow guaranteed secure transmission of information. A more distant goal is the development of quantum computers, which are expected to perform certain computational tasks exponentially faster than classical computers. Another active research topic is quantum teleportation, which deals with techniques to transmit quantum information over arbitrary distances.

Quantum tunneling is vital to the operation of many devices - even in the simple light switch, as otherwise the electrons in the electric current could not penetrate the potential barrier made up of a layer of oxide. Flash memory chips found in USB drives use quantum tunneling to erase their memory cells.

While quantum mechanics primarily applies to the atomic regimes of matter and energy, some systems exhibit quantum mechanical effects on a large scale - superfluidity, the frictionless flow of a liquid at temperatures near absolute zero, is one well-known example. Quantum theory also provides accurate descriptions for many previously unexplained phenomena, such as black body radiation and the stability of the orbitals of electrons in atoms. It has also given insight into the workings of many different biological systems, including smell receptors and protein structures.^[44] Recent work on photosynthesis has provided evidence that quantum correlations play an essential role in this basic fundamental process of the plant kingdom.^[45] Even so, classical physics can often provide good approximations to results otherwise obtained by quantum physics, typically in circumstances with large numbers of particles or large quantum numbers.

Examples[link]

Free particle[link]

For example, consider a free particle. In quantum mechanics, there is wave-particle duality, so the properties of the particle can be described as the properties of a wave. Therefore, its quantum state can be represented as a wave of arbitrary shape and extending over space as a wave function. The position and momentum of the particle are observables. The Uncertainty Principle states that both the position and the momentum cannot simultaneously be measured with complete precision. However, one can measure the position (alone) of a moving free particle, creating an eigenstate of position with a wavefunction that is very large (a Dirac delta) at a particular position x, and zero everywhere else. If one performs a position measurement on such a wavefunction, the resultant x will be obtained with 100% probability (i.e., with full certainty, or complete precision). This is called an eigenstate of position - or, stated in mathematical terms, a generalized position eigenstate (eigendistribution). If the particle is in an eigenstate of position, then its momentum is completely unknown. On the other hand, if the particle is in an eigenstate of momentum, then its position is completely unknown.^[46] In an eigenstate of momentum having a plane wave form, it can be shown that the wavelength is equal to h/p, where h is Planck's constant and p is the momentum of the eigenstate.^[47]

3D confined electron wave functions for each eigenstate in a Quantum Dot. Here, rectangular and triangular-shaped quantum dots are shown. Energy states in rectangular dots are more ‘s-type’ and ‘p-type’. However, in a triangular dot, the wave functions are mixed due to confinement symmetry.

Step potential[link]

Scattering at a finite potential step of height V₀, shown in green. The amplitudes and direction of left- and right-moving waves are indicated. Yellow is the incident wave, blue are reflected and transmitted waves, red does not occur. E > V₀ for this figure.

The potential in this case is given by:

Failed to parse (Missing texvc executable; please see math/README to configure.): V(x)= \begin{cases} 0, & x < 0, \\ V_0, & x \ge 0. \end{cases}

The solutions are superpositions of left- and right-moving waves:

Failed to parse (Missing texvc executable; please see math/README to configure.): \psi_1(x)= \frac{1}{\sqrt{k_1}} \left(A_\rightarrow e^{i k_1 x} + A_\leftarrow e^{-ik_1x}\right)\quad x<0

,

Failed to parse (Missing texvc executable; please see math/README to configure.): \psi_2(x)= \frac{1}{\sqrt{k_2}} \left(B_\rightarrow e^{i k_2 x} + B_\leftarrow e^{-ik_2x}\right)\quad x>0

where the wave vectors are related to the energy via

Failed to parse (Missing texvc executable; please see math/README to configure.): k_1=\sqrt{2m E/\hbar^2}

, and

Failed to parse (Missing texvc executable; please see math/README to configure.): k_2=\sqrt{2m (E-V_0)/\hbar^2}

and the coefficients A and B are determined from the boundary conditions and by imposing a continuous derivative on the solution.

Each term of the solution can be interpreted as an incident, reflected, or transmitted component of the wave, allowing the calculation of transmission and reflection coefficients. In contrast to classical mechanics, incident particles with energies higher than the size of the potential step are still partially reflected.

Rectangular potential barrier[link]

This is a model for the quantum tunneling effect, which has important applications to modern devices such as flash memory and the scanning tunneling microscope.

Particle in a box[link]

1-dimensional potential energy box (or infinite potential well)

The particle in a one-dimensional potential energy box is the most simple example where restraints lead to the quantization of energy levels. The box is defined as having zero potential energy everywhere inside a certain region, and infinite potential energy everywhere outside' that region. For the one-dimensional case in the Failed to parse (Missing texvc executable; please see math/README to configure.): x

direction, the time-independent Schrödinger equation can be written as:[48]

Failed to parse (Missing texvc executable; please see math/README to configure.): - \frac {\hbar ^2}{2m} \frac {d ^2 \psi}{dx^2} = E \psi.

Writing the differential operator

Failed to parse (Missing texvc executable; please see math/README to configure.): \hat{p}_x = -i\hbar\frac{d}{dx}

the previous equation can be seen to be evocative of the classic kinetic energy analogue

Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{1}{2m} \hat{p}_x^2 = E

with Failed to parse (Missing texvc executable; please see math/README to configure.): E

as the energy for the state Failed to parse (Missing texvc executable; please see math/README to configure.): \psi

, whioch in this case coincides with the kinetic energy of the particle.

The general solutions of the Schrödinger equation for the particle in a box are:

Failed to parse (Missing texvc executable; please see math/README to configure.): \psi(x) = A e^{ikx} + B e ^{-ikx} \qquad\qquad E = \frac{\hbar^2 k^2}{2m}

or, from Euler's formula,

Failed to parse (Missing texvc executable; please see math/README to configure.): \psi(x) = C \sin kx + D \cos kx.\!

The presence of the walls of the box determines the values of C, D, and k. At each wall (x = 0 and x = L), ψ = 0. Thus when x = 0,

Failed to parse (Missing texvc executable; please see math/README to configure.): \psi(0) = 0 = C\sin 0 + D\cos 0 = D\!

and so D = 0. When x = L,

Failed to parse (Missing texvc executable; please see math/README to configure.): \psi(L) = 0 = C\sin kL.\!

C cannot be zero, since this would conflict with the Born interpretation. Therefore, sin kL = 0, and so it must be that kL is an integer multiple of π. And additionally,

Failed to parse (Missing texvc executable; please see math/README to configure.): k = \frac{n\pi}{L}\qquad\qquad n=1,2,3,\ldots.

The quantization of energy levels follows from this constraint on k, since

Failed to parse (Missing texvc executable; please see math/README to configure.): E = \frac{\hbar^2 \pi^2 n^2}{2mL^2} = \frac{n^2h^2}{8mL^2}.

Finite potential well[link]

This is the generalization of the infinite potential well problem to potential wells of finite depth.

Harmonic oscillator[link]

Some trajectories of a harmonic oscillator (i.e. a ball attached to a spring) in classical mechanics (A-B) and quantum mechanics (C-H). In quantum mechanics, the position of the ball is represented by a wave (called the wavefunction), with the real part shown in blue and the imaginary part shown in red. Some of the trajectories (such as C,D,E,and F) are standing waves (or "stationary states"). Each standing-wave frequency is proportional to a possible energy level of the oscillator. This "energy quantization" does not occur in classical physics, where the oscillator can have any energy.

As in the classical case, the potential for the quantum harmonic oscillator is given by:

Failed to parse (Missing texvc executable; please see math/README to configure.): V(x)=\frac{1}{2}m\omega^2x^2

This problem can be solved either by solving the Schrödinger equation directly, which is not trivial, or by using the more elegant "ladder method", first proposed by Paul Dirac. The eigenstates are given by:

Failed to parse (Missing texvc executable; please see math/README to configure.): \psi_n(x) = \sqrt{\frac{1}{2^n\,n!}} \cdot \left(\frac{m\omega}{\pi \hbar}\right)^{1/4} \cdot e^{ - \frac{m\omega x^2}{2 \hbar}} \cdot H_n\left(\sqrt{\frac{m\omega}{\hbar}} x \right), \qquad n = 0,1,2,\ldots.

where H_n are the Hermite polynomials:

Failed to parse (Missing texvc executable; please see math/README to configure.): H_n(x)=(-1)^n e^{x^2}\frac{d^n}{dx^n}\left(e^{-x^2}\right)

and the corresponding energy levels are

Failed to parse (Missing texvc executable; please see math/README to configure.): E_n = \hbar \omega \left(n + {1\over 2}\right)

.

This is another example which illustrates the quantization of energy for bound states.

Notes[link]

See also[link]

Physics portal

• EPR paradox
• Macroscopic quantum phenomena

References[link]

Further reading[link]

• Bernstein, Jeremy (2009). Quantum Leaps. Cambridge, Massachusetts: Belknap Press of Harvard University Press. ISBN 978-0-674-03541-6. http://books.google.com/books?id=j0Me3brYOL0C&printsec=frontcover. 
• Bohm, David (1989). Quantum Theory. Dover Publications. ISBN 0-486-65969-0. 
• Eisberg, Robert; Resnick, Robert (1985). Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles (2nd ed.). Wiley. ISBN 0-471-87373-X. 
• Liboff, Richard L. (2002). Introductory Quantum Mechanics. Addison-Wesley. ISBN 0-8053-8714-5. 
• Merzbacher, Eugen (1998). Quantum Mechanics. Wiley, John & Sons, Inc. ISBN 0-471-88702-1. 
• Sakurai, J. J. (1994). Modern Quantum Mechanics. Addison Wesley. ISBN 0-201-53929-2. 
• Shankar, R. (1994). Principles of Quantum Mechanics. Springer. ISBN 0-306-44790-8. 
• Cox, Brian; Forshaw, Jeff (2011). The Quantum Universe: Everything That Can Happen Does Happen. Allen Lane. ISBN 1-84614-432-9. 

External links[link]

Find more about Quantum mechanics on Wikipedia's sister projects:
	Definitions and translations from Wiktionary
	Images and media from Commons
	Learning resources from Wikiversity
	News stories from Wikinews
	Quotations from Wikiquote
	Source texts from Wikisource
	Textbooks from Wikibooks

• Quantum Cook Book by R. Shankar, Open Yale PHYS 201 material (4pp)
• A foundation approach to quantum Theory that does not rely on wave-particle duality.
• The Modern Revolution in Physics - an online textbook.
• J. O'Connor and E. F. Robertson: A history of quantum mechanics.
• Introduction to Quantum Theory at Quantiki.
• Quantum Physics Made Relatively Simple: three video lectures by Hans Bethe
• H is for h-bar.
• Quantum Mechanics Books Collection: Collection of free books

Course material

• Doron Cohen: Lecture notes in Quantum Mechanics (comprehensive, with advanced topics).
• MIT OpenCourseWare: Chemistry.
• MIT OpenCourseWare: Physics. See 8.04
• Stanford Continuing Education PHY 25: Quantum Mechanics by Leonard Susskind, see course description Fall 2007
• 5½ Examples in Quantum Mechanics
• Imperial College Quantum Mechanics Course.
• Spark Notes - Quantum Physics.
• Quantum Physics Online : interactive introduction to quantum mechanics (RS applets).
• Experiments to the foundations of quantum physics with single photons.
• AQME : Advancing Quantum Mechanics for Engineers — by T.Barzso, D.Vasileska and G.Klimeck online learning resource with simulation tools on nanohub
• Quantum Mechanics by Martin Plenio
• Quantum Mechanics by Richard Fitzpatrick
• Online course on Quantum Transport

FAQs

• Many-worlds or relative-state interpretation.
• Measurement in Quantum mechanics.

Media

• PHYS 201: Fundamentals of Physics II by Ramamurti Shankar, Open Yale Course
• Lectures on Quantum Mechanics by Leonard Susskind
• Everything you wanted to know about the quantum world — archive of articles from New Scientist.
• Quantum Physics Research from Science Daily
• Overbye, Dennis (December 27, 2005). "Quantum Trickery: Testing Einstein's Strangest Theory". The New York Times. http://www.nytimes.com/2005/12/27/science/27eins.html?scp=1&sq=quantum%20trickery&st=cse. Retrieved April 12, 2010. 
• Audio: Astronomy Cast Quantum Mechanics — June 2009. Fraser Cain interviews Pamela L. Gay.

Philosophy

• "Quantum Mechanics" entry by Jenann Ismael in the Stanford Encyclopedia of Philosophy
• "Measurement in Quantum Theory" entry by Henry Krips in the Stanford Encyclopedia of Philosophy

Seth Lloyd is a professor of mechanical engineering at the Massachusetts Institute of Technology. He refers to himself as a "quantum mechanic".

Lloyd was born on August 2, 1960. He graduated from Phillips Academy in 1978 and received a bachelor of arts degree from Harvard College in 1982. He earned a certificate of advanced study in mathematics and a master of philosophy degree from Cambridge University in 1983 and 1984, while on a Marshall Scholarship. Lloyd was awarded a doctorate by Rockefeller University in 1988 (advisor Heinz Pagels) after submitting a thesis on Black Holes, Demons, and the Loss of Coherence: How Complex Systems Get Information, and What They Do With It. From 1988 to 1991, Lloyd was a postdoctoral fellow in the High Energy Physics Department at the California Institute of Technology, where he worked with Murray Gell-Mann on applications of information to quantum-mechanical systems. From 1991 to 1994, he was a postdoctoral fellow at Los Alamos National Laboratory, where he worked at the Center for Nonlinear Systems on quantum computation. In 1994, he joined the faculty of the Department of Mechanical Engineering at MIT. Since 1988, Lloyd has also been an adjunct faculty member at the Santa Fe Institute. He is married to Eve Zimmerman, a professor of Japanese studies at Wellesley College.

His research area is the interplay of information with complex systems, especially quantum systems. He has performed seminal work in the fields of quantum computation and quantum communication, including proposing the first technologically feasible design for a quantum computer, demonstrating the viability of quantum analog computation, proving quantum analogs of Shannon's noisy channel theorem, and designing novel methods for quantum error correction and noise reduction.

In his book, Programming the Universe, Lloyd contends that the universe itself is one big quantum computer producing what we see around us, and ourselves, as it runs a cosmic program. According to Lloyd, once we understand the laws of physics completely, we will be able to use small-scale quantum computing to understand the universe completely as well.

Lloyd states that we could have the whole universe simulated in a computer in 600 years provided that computational power increases according to Moore's Law. However, Lloyd shows that there are limits to rapid exponential growth in a finite universe, and that it is very unlikely that Moore's Law will be maintained indefinitely.

Lloyd is principal investigator at the MIT Research Laboratory of Electronics, and directs the Center for Extreme Quantum Information Theory (xQIT) at MIT.

Honors[link]

• 2007 Fellow of the American Physical Society^[1]

Works[link]

• Lloyd, Seth (1988). Black Holes, Demons and the Loss of Coherence: How complex systems get information, and what they do with it. (Ph.D. thesis). The Rockefeller University. http://meche.mit.edu/documents/slloyd_thesis.pdf. 

• Lloyd, S. (2000-08-31). "Ultimate physical limits to computation". Nature 406 (6799): 1047–1054. arXiv:quant-ph/9908043v3. DOI:10.1038/35023282. PMID 10984064. 
• Lloyd, S., Programming the Universe: A Quantum Computer Scientist Takes On the Cosmos, Knopf, March 14, 2006, 240 p., ISBN 1-4000-4092-2
• Interview: The Computational Universe: Seth Lloyd (video), Edge Foundation

See also[link]

• Digital physics
• Quantum Aspects of Life
• Simulated reality

Notes[link]

External links[link]

Wikiquote has a collection of quotations related to: Seth Lloyd

• Personal web page
• "Crazy Molecules: Pulse Berlin Interview"
• Programming the Universe
• Radio Interview from This Week in Science September 26, 2006 Broadcast
• Seth Lloyd at the Mathematics Genealogy Project

This article contains Japanese text. Without proper rendering support, you may see question marks, boxes, or other symbols instead of kanji and kana.

Michio Kaku (加来 道雄, Kaku Michio^?, born January 24, 1947) is an American theoretical physicist, the Henry Semat Professor of Theoretical Physics in the City College of New York of City University of New York, a co-founder of string field theory,^[1] a futurist, and a "communicator" and "popularizer" of science. He has written several books about physics and related topics; he has made frequent appearances on radio, television, and film; and he writes extensive online blogs and articles. He has written two New York Times best sellers, Physics of the Impossible (2008) and Physics of the Future (2011). He has hosted several TV specials for BBC-TV, the Discovery Channel, and the Science Channel.

Early life and education[link]

Kaku was born in San Jose, California to Japanese immigrant parents. His grandfather came to the United States to take part in the clean-up operation after the 1906 San Francisco Earthquake^{[citation needed]}. His father was born in California but was educated in Japan and spoke little English. Both his parents were put in the Tule Lake War Relocation Center, where they met and where his two brothers were born.

At Cubberley High School in Palo Alto, Kaku assembled an atom smasher in his parents' garage for a science fair project.^[2] At the National Science Fair in Albuquerque, New Mexico, he attracted the attention of physicist Edward Teller, who took Kaku as a protégé, awarding him the Hertz Engineering Scholarship. Kaku graduated summa cum laude from Harvard University in 1968 and was first in his physics class. He attended the Berkeley Radiation Laboratory at the University of California, Berkeley and received a Ph.D. in 1972, and in 1972 he held a lectureship at Princeton University.

During the Vietnam War, Kaku completed his U.S. Army basic training at Fort Benning, Georgia and his advanced individual training at Fort Lewis, Washington.^[3] However, the Vietnam War ended before he was deployed as an infantryman.

Academic career[link]

Kaku became a visiting professor at the Institute for Advanced Study in Princeton,^[4] and New York University.^[5] He currently holds the Henry Semat Chair and Professorship in theoretical physics at the City College of New York.^[6]

Kaku has had over 70 articles published in physics journals such as Physical Review, covering topics such as superstring theory, supergravity, supersymmetry, and hadronic physics.^[7] In 1974, along with Prof. Keiji Kikkawa of Osaka University, he authored the first papers describing string theory in a field form.^[8][9]

Kaku is the author of several textbooks on string theory and quantum field theory.

Popular science[link]

Kaku is most widely known as a popularizer of science.^[10] He has written books and appeared on many television programs as well as film. He also hosts a weekly radio program.

Books[link]

Kaku is the author of various popular science books.

• Hyperspace (1994)
• Beyond Einstein (with Jennifer Thompson) (1995)
• Visions: How Science Will Revolutionize the 21st Century^[11] (1998)
• Einstein's Cosmos (2004)
• Parallel Worlds (2004)
• Physics of the Impossible (2008)
• Physics of the Future (2011)

Hyperspace was a best-seller and was voted one of the best science books of the year by both The New York Times^[10] and The Washington Post. Parallel Worlds was a finalist for the Samuel Johnson Prize for non-fiction in the UK.^[12]

Radio[link]

Kaku is the host of the weekly, one-hour radio program Explorations, produced by the Pacifica Foundation's WBAI in New York. "Explorations" is syndicated to community and independent radio stations and makes previous broadcasts available on the program's website. Kaku defines the show as dealing with the general topics of science, war, peace, and the environment.

In April 2006, Kaku began broadcasting Science Fantastic on 90 commercial radio stations, the only nationally syndicated science program on commercial radio in the United States. It is syndicated by Talk Radio Network and now reaches 130 radio stations and America's Talk on XM. The program is formatted as a live listener call-in show, focusing on "futurology," which he defines as the future of science.^{[citation needed]} Featured guests include Nobel laureates and top researchers on the topics of string theory, time travel, black holes, gene therapy, aging, space travel, artificial intelligence, and SETI. When Kaku is busy filming for television, Science Fantastic goes on hiatus, sometimes for several months. Kaku is also a frequent guest on many programs, where he is outspoken in all areas and issues he considers of importance, such as the program Coast to Coast AM, where on 30 November 2007, he reaffirmed his belief that there is a 100% probability of extraterrestrial life in the universe.^[13]

Kaku has appeared on The Opie and Anthony Show a number of times, discussing popular fiction such as Back to The Future, Lost, and the theories behind time-travel that these and other fictional entertainment focus on.

Television and film[link]

Kaku has appeared in many forms of media and on many programs and networks, including Good Morning America, The Screen Savers, Larry King Live, 60 Minutes, Nightline, 20/20, Naked Science, CNN, ABC News, CBS News, NBC News, Al Jazeera English, Fox News Channel, The History Channel, Conan, The Science Channel, The Discovery Channel, TLC, Countdown with Keith Olbermann, The Colbert Report, The Art Bell Show and its successor, Coast To Coast AM, BBC World News America, The Opie & Anthony Show, The Covino & Rich Show, Head Rush, The Late Show with David Letterman, and Real Time with Bill Maher.

In 1999, Kaku was one of the scientists profiled in the feature-length film Me and Isaac Newton, directed by Michael Apted. It played theatrically in the United States, was later broadcast on national TV, and won several film awards.^{[citation needed]}

In 2005, Kaku appeared in the short documentary Obsessed & Scientific. The film is about the possibility of time travel and the people who dream about it. It screened at the Montreal World Film Festival and a feature film expansion is in development talks. Kaku also appeared in the ABC documentary UFOs: Seeing Is Believing, in which he suggested that while he believes it is extremely unlikely that extraterrestrials have ever actually visited Earth, we must keep our minds open to the possible existence of civilizations a million years ahead of us in technology, where entirely new avenues of physics open up. He also discussed the future of interstellar exploration and alien life in the Discovery Channel special Alien Planet as one of the multiple speakers who co-hosted the show, and Einstein's Theory of Relativity on The History Channel.

In February 2006, Kaku appeared as presenter in the BBC-TV four-part documentary Time which seeks to explore the mysterious nature of time. Part one of the series concerns personal time, and how we perceive and measure the passing of time. The second in the series deals with cheating time, exploring possibilities of extending the lifespan of organisms. The geological time covered in part three explores the ages of the earth and the sun. Part four covers the topics of cosmological time, the beginning of time and the events that occurred at the instant of the big bang.

On January 28, 2007, Kaku hosted the Discovery Channel series 2057. This three-hour program discussed how medicine, the city, and energy could change over the next 50 years.

In 2008, Kaku hosted the three-hour BBC-TV documentary Visions of the Future, on the future of computers, medicine, and quantum physics, and he appeared in several episodes of the History Channel's Universe series.

On December 1, 2009, he began hosting a 12-episode weekly TV series for the Science Channel at 10 pm, called Sci Fi Science: Physics of the Impossible, based on his best-selling book. Each 30-minute episode discusses the scientific basis behind imaginative schemes, such as time travel, parallel universes, warp drive, star ships, light sabers, force fields, teleportation, invisibility, death stars, and even superpowers and flying saucers. Each episode includes interviews with the world's top scientists working on prototypes of these technologies, interviews with science fiction fans, clips from science fiction movies, and special effects and computer graphics. Although these inventions are impossible today, the series discusses when these technologies might become feasible in the future.^[14]

In 2010, he began to appear in a series on the website Gametrailers.com called Science of Games, discussing the scientific aspects of various popular video games such as Mass Effect 2 and Star Wars: The Force Unleashed.

Kaku is popular in mainstream media because of his knowledge and his accessible approach to presenting complex subjects in science. While his technical writings are confined to theoretical physics, his public speaking and media appearances cover a broad range of topics, from the Kardashev scale to more esoteric subjects such as wormholes and time travel. In January 2007, Kaku visited Oman. While there, he talked at length to select members of that country's decision makers. In an interview with local media, Dr Kaku elaborated on his vision of mankind's future. Kaku considers climate change and terrorism as serious threats in man's evolution from a Type 0 civilization to Type 1.^[15]

He is pictured in Symphony of Science's newest song (as of September 6, 2011), 'The Quantum World.'

On October 11, 2010, Michio Kaku appeared in the BBC program "What Happened Before the Big Bang" (along with Laura Mersini-Houghton, Andrei Linde, Roger Penrose, Lee Smolin, Neil Turok, and other notable cosmologists and physicists), where he propounded his theory of the universe created out of nothing.^[16]

Social policy advocacy[link]

Kaku has publicly stated his concerns over matters including the anthropogenic cause of global warming, nuclear armament, nuclear power and the general misuse of science.^[17] He was critical of the Cassini–Huygens space probe because of the 72 pounds (33 kg) of plutonium contained in the craft for use by its radioisotope thermoelectric generator. Conscious of the possibility of casualties if the probe's fuel were dispersed into the environment during a malfunction and crash as the probe was making a 'sling-shot' maneuver around earth, Kaku publicly criticized NASA's risk assessment.^[18] He has also spoken on the dangers of space junk and called for more and better monitoring. Kaku is generally a vigorous supporter of the exploration of outer space, believing that the ultimate destiny of the human race may lie in extrasolar planets; but he is critical of some of the cost-ineffective missions and methods of NASA.

Kaku credits his anti-nuclear war position to programs he heard on the Pacifica Radio network, during his student years in California. It was during this period that he made the decision to turn away from a career developing the next generation of nuclear weapons in association with Edward Teller and focused on research, teaching, writing and media.^{[citation needed]} Kaku joined with others such as Helen Caldicott, Jonathan Schell, Peace Action and was instrumental in building a global anti-nuclear weapons movement that arose in the 1980s, during the administration of U.S. President Ronald Reagan.

Kaku was a board member of Peace Action and on the board of radio station WBAI-FM in New York City where he originated his long running program, Explorations, that focused on the issues of science, war, peace and the environment.

His remark from an interview in support of SETI, "We could be in the middle of an intergalactic conversation...and we wouldn't even know.", is used in the third Symphony of Science installment "Our Place in the Cosmos".

Personal life[link]