Quantum mechanics

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Quantum Mechanics

Quantum mechanics is the underlying framework of many fields of physics and chemistry, including condensed matter physics, quantum chemistry, and particle physics.

It describes with great accuracy and precision many phenomena where classical mechanics drastically fails, including the behavior of systems at atomic length scales and below (for instance, classical mechanics is unable to account for the existence of stable atoms), as well as special macroscopic systems such as superconductors and superfluids.

However, quantum mechanics is also compatible with classical mechanics, in the sense that it reduces to classical mechanics in physical situations where classical mechanics agrees with experiment. This property of quantum mechanics was highlighted by Niels Bohr, and is known as the correspondence principle.

Most physicists now believe that quantum mechanics is an essentially correct theory of the physical world, in situations where the effects of general relativity are negligible (which is almost always the case, but not near black holes or when considering the observable Universe as a whole.) The question of compatibility between quantum mechanics and general relativity remains an area of active research.

Description

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.

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. In the example we have given, of a free particle in empty space, both the position and the momentum are continuous observables. However, if we restrict the particle to a region of space (the so-called "particle in a box" problem), the momentum observable will become discrete; it will only take on the values h/L, where L is the length of the box. Such observables are said to be quantized, and they play an important role in many physical systems. 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.

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.

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 a particle can produce, through the collapse of the total wavefunction, an instantaneous effect on the other particles with which it is entangled, even if they are far apart.

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 Borns basic rules concerning probability amplitudes and probability distributions took decades to be appreciated. Quantum Physics is often regarded as the black magic of science.

Another difficulty with quantum mechanics is that the nature of an object isnt known, in the sense that an objects position, or the shape of the spatial distribution of the probability of presence, is only known by the properties (charge for example) and the environment (presence of an electric potential).

The Copenhagen interpretation, due largely to Niels Bohr, was the standard interpretation of quantum mechanics when it was first formulated. According to it, the probabilistic nature of quantum mechanics predictions cannot be explained in terms of some other deterministic theory, and do 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 the question is still not quite settled.

See the Bohr-Einstein debates

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. While the multiverse is deterministic, we perceive non-deterministic behavior governed by probabilities because we can observe only the universe we inhabit.

The Bohm interpretation, formulated by David Bohm, postulates the existence of a non-local, universal wavefunction (Schrödinger equation) which allows distant particles to interact instantaneously. Based on this interpretation, Bohm has speculated that the _ultimate nature of physical reality is not a collection of separate objects (as it appears to us), but rather an undivided whole that is in perpetual dynamic flux_. However, the Bohm interpretation is not popular among physicists, largely because it is considered very inelegant.

Reference: http://en.wikipedia.org/wiki/Quantum_mechanics

-- Main.Geir_thomas_andersen - 13 Mar 2005

Quantum mechanics

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