Quantum Mechanics



Quantum mechanics is a fundamental branch of theoretical physics that replaces Newtonian mechanics and classical electromagnetism at the atomic and subatomic levels. It is the underlying mathematical framework of many fields of physics and chemistry, including condensed matter physics, atomic physics, molecular physics, computational chemistry, quantum chemistry, particle physics, and nuclear physics. Along with general relativity, quantum mechanics is one of the pillars of modern physics.




Introduction

The term quantum (Latin, "how much") refers to discrete units that the theory assigns to certain physical quantities, such as the energy of an atom at rest (see Figure 1, at right). The discovery that waves could be measured in particle-like small packets of energy called quanta led to the branch of physics that deals with atomic and subatomic systems which we today call Quantum Mechanics.

The foundations of quantum mechanics were established during the first half of the 20th century by Max Planck, Albert Einstein, Niels Bohr, Werner Heisenberg, Erwin Schrodinger, Max Born, John von Neumann, Paul Dirac, Wolfgang Pauli and others. Some fundamental aspects of the theory are still actively studied.

Quantum mechanics is a more fundamental theory than Newtonian mechanics and classical electromagnetism, in the sense that it provides accurate and precise descriptions for many phenomena 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 atomic length scales and smaller. For example, if Newtonian mechanics governed the workings of an atom, electrons would rapidly travel towards and collide with the nucleus. However, in the natural world the electron normally remains in a stable orbit around a nucleus -- seemingly defying classical electromagnetism.

Quantum mechanics was initially developed to explain the atom, especially the spectra of light emitted by different atomic species. The quantum theory of the atom developed as an explanation for the electron's staying in its orbital, which could not be explained by Newton's laws of motion and by classical electromagnetism.

Quantum mechanics uses complex number wave functions (sometimes referred to as orbitals in the case of atomic electrons), and more generally, elements of a complex vector space to explain such effects. These are related to classical physics largely through probability.

Probability in the context of quantum mechanics has to do with the likelihood of finding a system in a particular state at a certain time, for example, finding an electron, in a particular region around the nucleus at a particular time. Therefore, electrons cannot be pictured as localized particles in space but rather should be thought of as "clouds" of negative charge spread out over the entire orbit.

These clouds represent the regions around the nucleus where the probability of "finding" an electron is the largest. This probability cloud obeys a quantum mechanical principle called Heisenberg's Uncertainty Principle, which states that there is an uncertainty in the classical position of any subatomic particle, including the electron; so instead of describing where an electron or other particle is, the entire range of possible values is used, describing a probability distribution.

So in normal atoms with electrons in stationary states, the probability of the electron being within the nucleus (or somewhere else in atom within similarly small volume) is nearly zero according to the Uncertainty Principle (it is nearly zero as the nucleus has a volume and is not a point). Therefore, quantum mechanics, translated to Newton's equally deterministic description, leads to a probabilistic description of nature.

The other exemplar that led to quantum mechanics was the study of electromagnetic waves such as 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 exploited this idea to show that an electromagnetic wave such as light could be described by a particle called the photon with a discrete energy dependent on its frequency.

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 describes the world of the very small, it also is needed to explain certain "macroscopic quantum systems" such as superconductors and superfluids.

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

Each of these phenomena will be described in greater detail in subsequent sections.

Most physicists believe that quantum mechanics provides a correct description for the physical world under almost all circumstances. However, the effects of quantum mechanics are generally not significant when considering the observable Universe as a whole. This is because although atoms and subatomic particles are the building blocks of matter, when analyzing the universe on large scales one finds that the dominant force becomes gravity -- which is described using Einstein's general theory of relativity. In some cases, both general relativity and quantum mechanics converge. As an example, general relativity is unable to explain what will happen if a subatomic particle hits the singularity of a black hole which is a phenomenon predicted by general relativity and involves gravity in the macro world. Only quantum mechanics can provide the answer: the particle's position will have an uncertainty that follows the Heisenberg Uncertainty Principle, such that it might not really reach the singularity and thus escape the possible collapse to infinite density.

It is believed that the theories of general relativity and quantum mechanics, the two great achievements of physics in the 20th century, contradict one another for two main reasons.

One is that the former is an essentially deterministic theory and the latter is essentially indeterministic.

Secondly, general relativity relies mainly on the force of gravity while quantum mechanics relies mainly on the other three fundamental forces, those being the strong, the weak, and the electromagnetic.

The question of how to resolve this contradiction remains an area of active research (see, for example, quantum gravity).In certain situations, the laws of classical physics approximate the laws of quantum mechanics to a high degree of precision.

This is often expressed by saying that in case of large quantum numbers quantum mechanics "reduces" to classical mechanics and classical electromagnetism . This situation is called the correspondence, or classical limit.

Quantum mechanics can be formulated in either a relativistic or non-relativistic manner. Relativistic quantum mechanics (quantum field theory) provides the framework for some of the most accurate physical theories known.

Still, non-relativistic quantum mechanics is also used due to its simplicity and when relativistic effects are relatively small. We will use the terms quantum mechanics, quantum physics, and quantum theory synonymously, to refer to both relativistic and non-relativistic quantum mechanics.

It should be noted, however, that certain authors refer to "quantum mechanics" in the more restricted sense of non-relativistic quantum mechanics. Also, in quantum mechanics, the use of the term particle refers to an elementary or subatomic particle.




Description of the Theory

There are a number of mathematically equivalent formulations of quantum mechanics. One of the oldest and most commonly used formulations is the transformation theory invented by Cambridge theoretical physicist Paul Dirac FRS, which unifies and generalizes the two earliest formulations of quantum mechanics, matrix mechanics (invented by Werner Heisenberg) and wave mechanics (invented by Erwin Schršdinger).

In this 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).

Generally, quantum mechanics does not assign definite values to observables. Instead, it makes predictions about probability distributions; that is, the probability of obtaining each of the possible outcomes from measuring an observable.

Naturally, these probabilities will depend on the quantum state at the instant of the measurement. 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" meaning "own" in German). 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 free particle.

In quantum mechanics, there is wave-particle duality so the properties of the particle can be described as a wave. Therefore, its quantum state can be represented as a wave, of arbitrary shape and extending over all of space, called a wavefunction.

The position and momentum of the particle are observables. The Uncertainty Principle 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 plane wave. 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.

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 wavefunction collapse. 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 wave packet 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 Schršdinger equation describes how wave functions change in time, a role similar to Newton's second law in classical mechanics.

The Schršdinger equation, applied to our 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. This also has the effect of turning position eigenstates (which can be thought of as infinitely sharp wave packets) into broadened wave packets that are no longer position eigenstates.

Some wave functions produce probability distributions that are constant in time. 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.

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. During a measurement, the change of the wavefunction into another one is not deterministic, but rather unpredictable, i.e., random.

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. Interpretations of quantum mechanics have been formulated to 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.




Quantum Mechanical 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 quantization 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.

Examples of quantized observables include angular momentum, the total energy of a bound system, and the energy contained in an electromagnetic wave of a given frequency. Particle in a Box

Another quantum effect is the uncertainty principle, which is the phenomenon that consecutive measurements of two or more observables may possess a fundamental limitation on accuracy. In our free particle example, it turns out that it is impossible to find a wavefunction that is an eigenstate of both position and momentum. This implies that position and momentum can never be simultaneously measured with arbitrary precision, even in principle: as the precision of the position measurement improves, the maximum precision of the momentum measurement decreases, and vice versa. Those variables for which it holds (e.g., momentum and position, or energy and time) are canonically conjugate variables in classical physics.

Another quantum effect is the wave-particle duality. It has been shown that, under certain experimental conditions, microscopic objects like atoms or electrons exhibit particle-like behavior, such as scattering. ("Particle-like" in the sense of an object that can be localized to a particular region of space.) Under other conditions, the same type of objects exhibit wave-like behavior, such as interference. We can observe only one type of property at a time, never both at the same time.

Another quantum effect is quantum entanglement. 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 special relativity because information cannot be transmitted in this way.)

Mathematical formulation of quantum mechanics

In the mathematically rigorous formulation of quantum mechanics, developed by Paul Dirac and John von Neumann, the possible states of a quantum mechanical system are represented by unit vectors (called "state vectors") residing in a complex separable Hilbert space (variously called the "state space" or the "associated Hilbert space" of the system).

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 densely defined Hermitian (or 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.

The time evolution of a quantum state is described by the Schršdinger equation, in which the Hamiltonian, the operator corresponding to the total energy of the system, generates time evolution.

The inner product between two state vectors is a complex number known as a probability amplitude. During a measurement, the probability that a system collapses from a given initial state to a particular eigenstate is given by the square of the absolute value of the probability amplitudes between the initial and final states. The possible results of a measurement are the eigenvalues of the operator - which explains the choice of Hermitian operators, for which all the eigenvalues are real.

We can find the probability distribution of an observable in a given state 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 Schršdinger 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.It turns out that analytic solutions of Schršdinger's equation are only available for a small number of 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 hydrogen, defies all attempts at a fully analytic treatment. There exist several techniques for generating approximate solutions. For instance, in the method known as perturbation theory 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. A

nother 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 quantum chaos.

An alternative formulation of quantum mechanics is Feynman's path integral formulation, 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 action principles 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 correspondence principle, which states that the predictions of quantum mechanics reduce to those of classical physics when a system becomes large. This "large system" limit is known as the classical or correspondence limit. One can therefore start from an established classical model of a particular system, and attempt to guess the underlying quantum model that gives 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 Schršdinger 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 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 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 photons by charged particles.

Quantum field theories for the strong nuclear force and the weak nuclear force have been developed. The quantum field theory of the strong nuclear force is called quantum chromodynamics, and describes the interactions of the subnuclear particles: 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.

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.




Applications of quantum theory

Quantum mechanics has had enormous success in explaining many of the features of our world. The individual behavior of the subatomic particles that make up all forms of matter - electrons, protons, neutrons, and so forth - can often only be satisfactorily described using quantum mechanics.Quantum mechanics has strongly influenced string theory, a candidate for a theory of everything (see Reductionism. It is also related to statistical mechanics.

Quantum mechanics is important for understanding how individual atoms combine covalently to form chemicals or 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 provide quantitative insight into ionic and covalent bonding processes by explicitly showing which molecules are energetically favorable to which others, and by approximately how much. Most of the calculations performed in computational chemistry rely on quantum mechanics.

Much of modern technology operates at a scale where quantum effects are significant. Examples include the laser, the transistor, the electron microscope, and magnetic resonance imaging. The study of semiconductors led to the invention of the diode and the transistor, which are indispensable for modern electronics.

Researchers are currently seeking robust methods of directly manipulating quantum states. Efforts are being made to develop quantum cryptography, which will 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 states over arbitrary distances.




Philosophical Consequences

Since its inception, the many counter-intuitive results of quantum mechanics have provoked strong philosophical debate and many interpretations. Even fundamental issues such as Max Born's basic rules concerning probability amplitudes and probability distributions took decades to be appreciated.

The Copenhagen interpretation, due largely to the Danish theoretical physicist Niels Bohr, is the interpretation of quantum mechanics most widely accepted amongst physicists. According to it, the probabilistic nature of quantum mechanics predictions cannot be explained in terms of some other deterministic theory, and does not simply reflect our limited knowledge.

Quantum mechanics provides probabilistic results because the physical universe is itself probabilistic rather than deterministic.

Albert Einstein, himself one of the founders of quantum theory, disliked this loss of determinism in measurement. He held that there should be a local hidden variable theory underlying quantum mechanics and consequently the present theory was incomplete. He produced a series of objections to the theory, the most famous of which has become known as the EPR paradox.

John Bell 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. "Loopholes" in the experiments, however, mean that the question is still not quite settled.


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.

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) 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 mentioned superposition, we 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, the parallel universes will never be accessible for us, making them physically meaningless. This inaccessiblity 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 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).




History

In 1900 the German physicist Max Planck introduced the idea that energy is quantized, in order to derive a formula for the observed frequency dependence of the energy emitted by a black body.

In 1905, Einstein explained the photoelectric effect by postulating that light energy comes in quanta called photons. The idea that each photon had to consist of energy in terms of quanta was a remarkable achievement as it effectively removed the possibility of black body radiation attaining infinite energy if it were to be explained in terms of wave forms only.

In 1913, Bohr explained the spectral lines of the hydrogen atom, again by using quantization, in his paper of July 1913 'On the Constitution of Atoms and Molecules'.

In 1924, the French physicist Louis de Broglie put forward his theory of matter waves by stating that particles can exhibit wave characteristics and vice versa.

These theories, though successful, were strictly phenomenological: there was no rigorous justification for quantization (aside, perhaps, for Henri PoincarŽ's discussion of Planck's theory in his 1912 paper "Sur la thŽorie des quanta"). They are collectively known as the old quantum theory.

The phrase "quantum physics" was first used in Johnston's Planck's Universe in Light of Modern Physics.

Modern quantum mechanics was born in 1925, when the German physicist Heisenberg developed matrix mechanics and the Austrian physicist Schršdinger invented wave mechanics and the non-relativistic Schršdinger equation. Schršdinger subsequently showed that the two approaches were equivalent.

Heisenberg formulated his uncertainty principle in 1927, and the Copenhagen interpretation took shape at about the same time. Starting around 1927, Paul Dirac began the process of unifying quantum mechanics with special relativity by discovering the Dirac equation for the electron. He also pioneered the use of operator theory, including the influential bra-ket notation, as described in his famous 1930 textbook. During the same period, Hungarian polymath John von Neumann 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 quantum chemistry was pioneered by physicists Walter Heitler and Fritz London, who published a study of the covalent bond of the hydrogen molecule in 1927. Quantum chemistry was subsequently developed by a large number of workers, including the American theoretical chemist Linus Pauling at Cal Tech, and John Slater into various theories such as Molecular Orbital Theory or Valence Theory.

Beginning in 1927, attempts were made to apply quantum mechanics to fields rather than single particles, resulting in what are known as quantum field theories. Early workers in this area included Dirac, Pauli, Weisskopf, and Jordan. This area of research culminated in the formulation of quantum electrodynamics by Feynman, Dyson, Schwinger, and Tomonaga during the 1940s.

Quantum electrodynamics is a quantum theory of electrons, positrons, and the electromagnetic field, and served as a role model for subsequent quantum field theories.

The theory of quantum chromodynamics was formulated beginning in the early 1960s. The theory as we know it today was formulated by Politzer, Gross and Wilzcek in 1975.

Building on pioneering work by Schwinger, Higgs, Goldstone, Glashow, Weinberg and Salam independently showed how the weak nuclear force and quantum electrodynamics could be merged into a single electroweak force.


Quantum Mechanics Wikipedia




In the News ...



The beginning of everything: A new paradigm shift for the infant universe   PhysOrg - November 29, 2012
A new paradigm for understanding the earliest eras in the history of the universe has been developed by scientists at Penn State University. Using techniques from an area of modern physics called loop quantum cosmology, the scientists now have extended analyses that include quantum physics farther back in time than ever before - all the way to the beginning. The new paradigm of loop quantum origins shows, for the first time, that the large-scale structures we now see in the universe evolved from fundamental fluctuations in the essential quantum nature of "space-time," which existed even at the very beginning of the universe over 14 billion years ago. The achievement also provides new opportunities for testing competing theories of modern cosmology against breakthrough observations expected from next-generation telescopes.


Quantum test pricks uncertainty   BBC - September 8, 2012

Pioneering experiments have cast doubt on a founding idea of the branch of physics called quantum mechanics. The Heisenberg uncertainty principle is in part an embodiment of the idea that in the quantum world, the mere act of observing an event changes it. But the idea had never been put to the test, and a team writing in Physical Review Letters says "weak measurements" prove the rule was never quite right. That could play havoc with "uncrackable codes" of quantum cryptography. Quantum mechanics has since its very inception raised a great many philosophical and metaphysical debates about the nature of nature itself.


Quantum Entanglement Holds DNA Together, Say Physicists   Technology Review - January 11, 2012

A new theoretical model suggests that quantum entanglement helps prevent the molecules of life from breaking apart. There was a time, not so long ago, when biologists swore black and blue that quantum mechanics could play no role in the hot, wet systems of life. Since then, the discipline of quantum biology has emerged as one of the most exciting new fields in science


Vibration rocks for entangled diamonds   PhysOrg - December 16, 2011

You can take two diamonds - not quite everyday objects, but at least simple and recognizable - and put them in such a state: in particular a superposition of a state of one diamond vibrating and the other not, and vice versa.


Two Diamonds Linked by Strange Quantum Entanglement   Live Science - December 1, 2011
Scientists have linked two diamonds in a mysterious process called entanglement that is normally only seen on the quantum scale. Entanglement is so weird that Einstein dubbed it "spooky action at a distance." It's a strange effect where one object gets connected to another so that even if they are separated by large distances, an action performed on one will affect the other. Entanglement usually occurs with subatomic particles, and was predicted by the theory of quantum mechanics, which governs the realm of the very small. But now physicists have succeeded in entangling two macroscopic diamonds, demonstrating that quantum mechanical effects are not limited to the microscopic scale.


One clock with two times: When quantum mechanics meets general relativity   PhysOrg - October 20, 2011

According to general relativity, time flows differently at different positions due to the distortion of space-time by a nearby massive object. A single clock being in a superposition of two locations allows probing quantum interference effects in combination with general relativity.


Near-Perfect Particle Measurement Achieved   Live Science - July 14, 2011

The mind-bending laws of quantum mechanics say we can't observe the smallest particles without affecting them. Physicists have now caused the smallest-ever disturbance while making a quantum measurement - in fact, almost the minimum thought to be possible. This disturbance is called back-action, and it is one of the hallmarks of quantum mechanics, which governs the actions of the very small. It arises from the supposition that before a measurement is made, particles exist in a sort of limbo state, being neither here nor there while retaining the possibility of either.


Bridging the gap to quantum world   BBC - June 3, 2009
Scientists have "entangled" the motions of pairs of atoms for the first time. Entanglement is an effect in quantum mechanics, a relatively new branch of physics that is based more in probability than in classical laws. It describes how properties of two or more objects can be inextricably linked over "vast" distances. The results, published in Nature, further bridge the gap between the world of quantum mechanics and the laws of everyday experience. This is the first time entanglement has been seen in a so-called "mechanical system". The phenomenon suggests that a measurement performed on one object can affect the measurement on another object some distance away.


Einstein's 'Spooky Physics' Gets More Entangled   Live Science - June 3, 2009
Quantum entanglement is just spooky - even Einstein thought so. As if particles (as in particle physics) have telepathic empathy. The theory of quantum mechanics predicts that two or more particles can become "entangled" so that even after they are separated in space, when an action is performed on one particle, the other particle responds immediately. Scientists still don't know how the particles send these instantaneous messages to each other, but somehow, once they are entwined, they retain a fundamental connection. This bizarre idea riled Einstein so much he called it "spooky action at a distance."




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