Myswizard

Consciousness

Consciousness is a quality of the mind generally regarded to comprise qualities such as subjectivity, self-awareness, sentience, sapience, and the ability to perceive the relationship between oneself and one’s environment. It is a subject of much research in philosophy of mind, psychology, neurology, and cognitive science.

Some philosophers divide consciousness into phenomenal consciousness which is experience itself and access consciousness which is the processing of the things in experience (Block 2004), while others consider this distinction to be mistaken (Dennett 1991). Many cultures and religious traditions place the seat of consciousness in a soul separate from the body. Conversely, many scientists and philosophers consider consciousness to be intimately linked to the neural functioning of the brain dictating the way in which the world is experienced.

Humans (and often other animals as well) are variously said to possess consciousness, self- awareness, and a mind, that contains our sensations, perceptions, dreams, lucid dreams, inner speech and imagination etc.. Each of us has a subjective view. There are many debates about the extent to which the mind constructs or experiences the outer world, the passage of time, and free will.

An understanding of necessary preconditions for consciousness in the human brain may allow us to address important ethical questions. For instance, to what extent are non-human animals conscious? At what point in fetal development does consciousness begin? Can machines ever achieve conscious states? These issues are of great interest to those concerned with the ethical treatment of other beings, be they animals, fetuses, or in the future, machines.

In common parlance, consciousness denotes being awake and responsive to one’s environment; this contrasts with being asleep or being in a coma. The term ‘level of consciousness’ denotes how consciousness seems to vary during anesthesia and during various states of mind such as day dreaming, lucid dreaming, imagining etc. Nonconsciousness exists when consciousness is not present. There is speculation, especially amongst religious groups, that consciousness may exist after death or before birth.

Etymology
“Consciousness” derives from Latin “conscientia”, which primarily means moral conscience. Literally, “conscientia” means knowledge-with, that is, shared knowledge. The word first appears in Latin juridic texts by writers such as Cicero. Here, conscientia is the knowledge that a witness has of the deed of someone else. In Christian theology, conscience stands for the moral conscience in which our actions and intentions are registered and which is only fully known to god. Medieval writers such as Thomas Aquinas describe the conscientia as the act by which we apply practical and moral knowledge to our own actions (Aquinas, De Veritate 17,1 c.a.). René Descartes was the first to use “conscientia” in a way that does not seem to fit this traditional meaning, and consequently, the translators of his writings in other languages like French and English coined new words in order to denote merely psychological consciousness. These are, for instance, “conscience psychologique”, “consciousness”, and “Bewusstsein”. See Catherine G. Davies, Conscience as Consciousness, Oxford 1990, and Hennig, Cartesian Conscientia.

Consciousness and language
Because humans express their conscious states using language, it is tempting to equate language abilities and consciousness. There are, however, speechless humans (infants, feral children, aphasics), to whom consciousness is attributed despite language lost or not yet acquired. Moreover, the study of brain states of non-linguistic primates, in particular the macaques, has been used extensively by scientists and philosophers in their quest for the neural correlates of the contents of consciousness.

Cognitive neuroscience approaches
Modern investigations into and discoveries about consciousness are based on psychological statistical studies and case studies of consciousness states and the deficits caused by lesions, stroke, injury, or surgery that disrupt the normal functioning of human senses and cognition. These discoveries suggest that the mind is a complex structure derived from various localized functions that are bound together with a unitary awareness.

Several studies point to common mechanisms in different clinical conditions that lead to loss of consciousness. Persistent vegetative state (PVS) is a condition in which an individual loses the higher cerebral powers of the brain, but maintains sleep-wake cycles with full or partial autonomic functions. Studies comparing PVS with healthy, awake subjects consistently demonstrate an impaired connectivity between the deeper (brainstem and thalamic) and the upper (cortical) areas of the brain. In addition, it is agreed that the general brain activity in the cortex is lower in the PVS state. Some electroneurobiological interpretations of consciousness characterize this loss of consciousness as a loss of the ability to resolve time (similar to playing an old phonographic record at very slow or very rapid speed), along a continuum that starts with inattention, continues on sleep and arrives to coma and death.

Loss of consciousness also occurs in other conditions, such as general (tonic-clonic) epileptic seizures, in general anaesthesia, maybe even in deep (slow wave) sleep. The currently best supported hypotheses about such cases of loss of consciousness (or loss of time resolution) focus on the need for 1) a widespread cortical network, including particularly the frontal, parietal and temporal cortices, and 2) cooperation between the deep layers of the brain, especially the thalamus, and the upper layers; the cortex. Such hypotheses go under the common term “globalist theories” of consciousness, due to the claim for a widespread, global network necessary for consciousness to interact with non-mental reality in the first place.

Brain chemistry affects human consciousness. Sleeping drugs (such as Midazolam = Dormicum) can bring the brain from the awake condition (conscious) to the sleep (unconscious). Wake-up drugs such as Anexate reverse this process. Many other drugs (such as heroin, cocaine, LSD, MDMA) have a consciousness-changing effect.

There is a neural link between the left and right hemispheres of the brain, known as the corpus callosum. This link is sometimes surgically severed to control severe seizures in epilepsy patients. This procedure was first performed by Roger Sperry in the 1960’s. Tests of these patients have shown that after the link is completely severed, the hemispheres are no longer able to communicate, leading to certain problems which usually arise only in test conditions. For example, while the left side of the brain can verbally describe what is going on in the right visual field, the right hemisphere is esentially mute, instead relying on its spatial abilities to interact with the world on the left visual field. Some say it is as if two separate minds now share the same skull, but both still represent themselves as a single “I” to the outside world.

The bilateral removal of the Centromedian nucleus (part of the Intra-laminar nucleus of the Thalamus) appears to abolish consciousness, causing coma, PVS, severe mutism and other features that mimic brain death. The centromedian nucleus is also one of the principal sites of action of general anaesthetics and anti-psychotic drugs.

Neurophysiological studies in awake, behaving monkeys performed by neuroscientists (e.g., Steven Wise, Mikhail Lebedev, Nikos Logothetis) point to advanced cortical areas in prefrontal cortex and temporallobes as carriers of neuronal correlate of consciousness.

Philosophical approaches
Some philosophers suggest that consciousness resists or even defies definition. Others believe it can be usefully distinguished between phenomenal consciousness and access or psychological consciousness, while still others disagree. There are many philosophical stances on consciousness, including: behaviorism, dualism, idealism, functionalism, phenomenalism, physicalism, emergentism, and mysticism.

Phenomenal and access consciousness
Philosophers call our current experience phenomenal consciousness. Phenomenal consciousness is simply experience, it is moving, coloured forms, sounds, sensations, emotions and feelings with our bodies and responses at the centre. These experiences, considered independently of any impact on behavior, are called qualia. The hard problem of consciousness was formulated by Chalmers in 1996, dealing with the issue of “how to explain a state of phenomenal consciousness in terms of its neurological basis” (Block 2004). Daniel Dennett(1988) identifies qualia with the results of judgements and consequent behaviour, he extends this analysis (Dennett (1996)) by arguing that phenomenal consciousness can be explained in terms of access consciousness, and hence denies the existence of both qualia and the “hard problem”.

Access consciousness is the phenomenon whereby information in our minds is accessible for verbal report, reasoning, and the control of behavior. So when we perceive, information about what we perceive is often access conscious; when we introspect, information about our thoughts is access conscious; when we remember, information about the past (e.g. something that we learned) is often access conscious; and so on. Chalmers thinks that access consciousness is less mysterious than phenomenal consciousness, so that it is held to pose one of the easy problems of consciousness. Dennett disagrees, asserting that the totality of consciousness can be understood in terms of impact on behavior, as studied through heterophenomenology.

Events that occur in the mind or brain that are not within phenomenal or access consciousness are known as subconscious events.

The description and location of phenomenal consciousness
Although it is the conventional wisdom that consciousness cannot be defined, philosophers have been describing phenomenal consciousness for centuries. Rene Descartes wrote Meditations on First Philosophy in the seventeenth century, and this contains extensive descriptions of what it is to be conscious. Descartes described conscious experience as imaginings and perceptions laid out in space and time that are viewed from a point. Each thing appears as a result of some quality (qualia) such as colour, smell etc. Other philosophers, such as Nicholas Malebranche, John Locke, David Hume and Immanuel Kant, also agreed with much of this description, although some avoid mentioning the viewing point. The extension of things in time was considered in more detail by Kant and James. Kant wrote that “only on the presupposition of time can we represent to ourselves a number of things as existing at one and the same time (simultaneously) or at different times (successively)”. William James stressed the extension of experience in time and said that time is “the short duration of which we are immediately and incessantly sensible”. These philosophers also go on to describe dreams, thoughts, emotions etc.

When we look around a room or have a dream, things are laid out in space and time and viewed as if from a point. However, when philosophers and scientists consider the location of the form and contents of this phenomenal consciousness there are fierce disagreements. As an example, Descartes proposed that the contents were brain activity seen by a non-physical place without extension (the Res Cogitans) which he identified as the soul. This idea is known as ‘Cartesian Dualism’. Another example is found in the work of Thomas Reid who thought the contents of consciousness are the world itself which becomes conscious experience in some way. This concept is a type of Direct realism. The precise physical substrate of conscious experience in the world, such as photons, quantum fields etc. is usually not specified. Other philosophers, such as George Berkeley, have proposed that the contents of consciousness are an aspect of minds and do not involve matter at all. This is a type of Idealism. Yet others, such as Leibniz, have considered that each point in the universe is endowed with conscious content. This is a form of Panpsychism. The concept of the things in conscious experience being impressions in the brain is a type of representationalism and representationalism can be a form of indirect realism.

Some philosophers, such as David Armstrong and Daniel Dennett, believe that conscious experiences exist in terms of judgements or beliefs about things in the world, and is therefore meaningless except when separated from behavior, while other philosophers insist that experience constitute qualia which cannot be understood in terms of belief.

It is sometimes held that consciousness emerges from the complexity of brain processing (see for instance the Multiple Drafts Model of consciousness). The general label ‘emergence’ applies to new phenomena that emerge from a physical basis without the connection between the two explicitly specified. Some theorists hold that phenomenal consciousness poses an explanatory gap, and have proposed scientific theories such as Quantum mind, space-time theories of consciousness and Electromagnetic theories of consciousness, to explain the correspondence between brain activity and experience. As yet there is little evidence from brain studies to support these theories. Evidence from parapsychology of psychokinesis or telepathy, if substantiatied, might support the theory that the location of consciousness is not confined to the brain.

Access consciousness
There have been numerous approaches to the processes that act on conscious experience from instant to instant. Philosophers who have explored this problem include Gerald Edelman, G. Spencer-Brown, Edmund Husserl and Daniel Dennett.

Some philosophers have concentrated on reflexive processes to link one instant to the next, some on discriminations, differerences and differentiation between things in conscious experience and and others on the overall behaviour of the organism.

G. Spencer-Brown provides an example of the analysis of consciousness as a process, the process in this case being differentiating one thing from another.G. Spencer-Brown proposes in Laws of Form that the root of cognition is the ability to perceive dualism, i.e., in its most simple construct, the capability of differentiating a “this” from a “that.” A mathematician, he captured this concept of elementary content-in-context in an abstraction: an algebraic and tautological symbol he referred to as the “Mark,” also referred to as a “distinction.” Francisco Varela, a co-founder of the Integral Institute, and Humberto Maturana also identify “distinction” as the elementary act of cognition. By definition, this concept extends the notion of “consciousness” well beyond that solely evidenced by humans and lends itself to the idea of a “scale” of consciousness.

Physical approaches
Even at the dawn of Newtonian science, Leibniz and many others were suggesting physical theories of consciousness. Modern physical theories of consciousness can be divided into three types: theories to explain behaviour and access consciousness, theories to explain phenomenal consciousness and theories to explain the quantum mechanical (QM) Quantum mind. Theories that seek to explain behaviour are an everyday part of neuroscience, some of these theories of access consciousness, such as Edelman’s theory, contentiously identify phenomenal consciousness with reflex events in the brain. Theories that seek to explain phenomenal consciousness directly, such as Space-time theories of consciousness and Electromagnetic theories of consciousness, have been available for almost a century but have not as yet been confirmed by experiment. Theories that attempt to explain the QM measurement problem include Pribram and Bohm’s Holonomic brain theory, Hameroff and Penrose’s Orch-OR theory, Spin-Mediated Consciousness Theory and the Many-minds interpretation. Some of these QM theories offer descriptions of phenomenal consciousness as well as QM interpretations of access consciousness. None of the quantum mechanical theories has been confirmed by experiment, and there are philosopher who are that QM has no bearing on consciousness.

There is also a concerted effort in the field of Artificial Intelligence to create digital computer programs that can simulate consciousness.

Spiritual approaches
Spiritual approaches to consciousness involve the idea of altered states of consciousness or religious experience. Changes in the state of consciousness or a religious experience can occur spontaneously or as a result of religious observance. It is also maintained by some religions and religious factions that the universe itself is consciousness.

In shamanic practice the change in state of consciousness is induced by mind altering drugs or as a result of activities that induce trance. The experience that occurs is interpreted as entering a real, but parallel, world. In many polytheistic religions a change in emotional state is often attributed to the action of a god, for instance love was ruled by Aphrodite and Eros in Ancient Greek polytheism. In Hinduism the change in state is induced by the practice of yoga. Yoga means “joining” and is intended to produce a state of oneness between the practitioner and the divine. In Islam and Christianity the change of state can occur as a result of prayer or as a religious experience.

The change in state of consciousness in Hinduism, Buddhism, Christianity and Islam is reported to be quite similar. The pursuit of yoga and the Buddhist Jhanas involve feelings of oneness with the world that give rise to a state of rapture. This is also reported by those undergoing some forms of Christian (or Islamic) religious experience, for instance James (1902) provides the following report:

I cannot express it in any other way than to say that I did “lie down in the stream of life and let it flow over me.” I gave up all fear of any impending disease; I was perfectly willing and obedient. There was no intellectual effort, or train of thought. My dominant idea was: “Behold the handmaid of the Lord: be it unto me even as thou wilt,” and a perfect confidence that all would be well, that all was well. The creative life was flowing into me every instant, and I felt myself allied with the Infinite, in harmony, and full of the peace that passeth understanding. There was no place in my mind for a jarring body. I had no consciousness of time or space or persons; but only of love and happiness and faith.
Meditation is used in some forms of yoga such as Raja Yoga, Hatha Yoga, Transcendental meditation, the Buddhist Jhanas, the Buddhist Immaterial Jhanas (there are several versions of the jhanas in different types of Buddhism), in the practices of Christian monks and Islamic scholars such as Sufis. Meditation can have a calming influence on practitioners as well as changing the state of consciousness. Therevada Buddhism views the Jhanas and some yogic practices view the early stages of meditation as a preliminary “serenity meditation” in which it is demonstrated that states such as rapture are delusions, products of mind rather than the soul. In most types of Buddhism serenity meditation is followed by a philosophical “insight meditation” that focusses on the idea that the universe is consciousness only, one that is perhaps indistinguishable from Monism.

Functions of consciousness
We generally agree that our fellow human beings are conscious and that much simpler life forms, such as bacteria, are not. Many of us attribute consciousness to higher-order animals such as dolphins and primates; academic research is investigating the extent to which animals are conscious. This suggests the hypothesis that consciousness has co-evolved with life, which would require it to have some sort of added value. People have therefore looked for specific functions of consciousness. Bernard Baars (1997) for instance states that “consciousness is a supremely functional adaptation” and suggests a variety of functions in which consciousness plays a role: prioritization of alternatives, problem solving, decision making, brain processes recruiting, action control, error detection, planning, learning, adaptation, context creation, and access to information. Antonio Damasio (1999) regards consciousness as part of an organism’s survival kit, allowing planned rather than instinctual responses. He also points out that awareness of self allows a concern for one’s own survival, which increases the drive to survive, although how far consciousness is involved in behaviour is an actively debated issue. Many psychologists, such as radical behaviourists, and many philosophers, such as those who support Ryle’s approach, would maintain that behaviour can be explained by non-conscious processes akin to artificial intelligence and might consider consciousness to be epiphenomenal or only weakly related to function.

Tests of consciousness
As there is still not a clear definition of consciousness, no empirical tests currently exist to test consciousness as a whole. Some have even argued that empirical tests of consciousness are intrinsically impossible. However, some researchers have devised tests to detect what they feel are certain aspects of consciousness. A test similar to this was used in the novel “Do Androids Dream of Electric Sheep” by Philip K. Dick to see if a person was a robot or an actual human. In the Ridley Scott movie, Blade Runner, which was inspired by that book, it is known as the “Voigt-Kampf” test and tests the subject for empathy.

Turing Test
Alan Turing proposed what is now known as the Turing test to determine if a computer could simulate human conversation undetectably. This test is commonly cited in discussion of artificial intelligence. The application to consciousness is that, according to some philosophers, anything capable of passing the Turing test as well as a person is necessarily conscious. Other philosophers say that a philosophical zombie could pass the test yet fail to be conscious. This matter is heavily disputed. Still others take it for granted that computers can think since this is what they were designed to do; Edsger Dijkstra’s commented that “The question of whether a computer can think is no more interesting than the question of whether a submarine can swim”.

A thought experiment which is intended to show problems with the Turing Test is as follows. Imagine a computer in which are stored a very large number of questions and a very large number of actual human responses to these questions. If the number of questions and answers was large enough, then the computer would be able to mimic consciousness by a purely mechanical procedure. Of course, this is a purely hypothetical example, because any attempt to create a lookup table for all possible responses would entail a device of truly gigantic proportions. For this reasons, some consider this thought experiment to be misleading. See Chinese room.

Mirror test
With the mirror test, devised by Gordon Gallup in the 1970s, one is interested in whether animals are able to recognize themselves in a mirror. Such self-recognition is said to be an indicator of consciousness. Humans (older than 18 months), great apes (except for gorillas), and bottlenose dolphins have all been observed to pass this test.

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article “Consciousness”.

I have this definition of Quantum Mechanics (Physics), because the Heisenberg Theory, Schrödinger equations, wave collapse, etc. are scientifially as close as you can get to the spiritual realm. When an intention goes out into the universe (as well as prayer), you are collapsing the wave function, which in turn, creates change. By providing this science, you can get an idea of how this relates to creation and the non-linear, I often refer to on my site. I hope this adds some clarity to ( Spirituality), which is difficult to explain in scientific terms…Myswizard

Quantum mechanics is a fundamental physical theory that extends, corrects and unifies Newtonian mechanics and Maxwellian electromagnetism, at the atomic and subatomic levels. It is the underlying framework of many fields of physics and chemistry, including condensed matter physics, quantum chemistry, and particle physics. The term quantum (Latin, “how much”) refers to the discrete units that the theory assigns to certain physical quantities, such as the energy of an atom at rest (see Figure 1, at right). Fig. 1: The wavefunctions of an electron in a hydrogen atom possessing definite energy (increasing downward: n=1,2,3,…) and angular momentum (increasing across: s, p, d,…). Brighter areas correspond to higher probability density for a position measurement. The angular momentum and energy are quantized, and only take on discrete values like those shown.

Quantum mechanics is a theory of mechanics, a branch of physics that deals with the motion of bodies and associated physical quantities such as energy and momentum. It is a more fundamental theory than Newtonian mechanics, in the sense that it provides accurate and precise descriptions for many phenomena where Newtonian mechanics drastically fails. Such phenomena include the behavior of systems at atomic length scales and below (in fact, Newtonian mechanics is unable to account for the existence of stable atoms), as well as special macroscopic systems such as superconductors and superfluids. The predictions of quantum mechanics have never been disproven after a century’s worth of experiments. Quantum mechanics incorporates at least three classes of phenomena that classical physics cannot account for: (i) the quantization (discretization) of certain physical quantities, (ii) wave-particle duality, and (iii) quantum entanglement. However, in certain situations, the laws of quantum mechanics approximate the laws of classical mechanics to a high degree of precision; this is often expressed by saying that quantum mechanics “reduces” to classical mechanics, and is known as the correspondence principle.

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, though non-relativistic quantum mechanics is also frequently used for reasons of convenience. We will use the term “quantum mechanics” to refer to both relativistic and non-relativistic quantum mechanics; the terms quantum physics and quantum theory are synonymous. It should be noted, however, that certain authors refer to “quantum mechanics” in the more restricted sense of non-relativistic quantum mechanics.

Most physicists believe that quantum mechanics provides a correct description for the physical world under almost all circumstances. It seems likely that quantum mechanics fails in the vicinity of black holes, or when considering the observable Universe as a whole. In these regimes, quantum mechanics conflicts with the predictions of general relativity, the dominant theory of gravity. The question of compatibility between quantum mechanics and general relativity remains an area of active research.

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 Schrödinger, Max Born, John von Neumann, Paul Dirac, Wolfgang Pauli and others. Some fundamental aspects of the theory are still actively studied.

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 Paul Dirac, which unifies and generalizes the two earliest formulations of quantum mechanics, matrix mechanics (invented by Werner Heisenberg) and wave mechanics (invented by Erwin Schrödinger).

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).

A concrete example will be useful here. Let us consider a free particle. 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. An eigenstate of position is 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. 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.

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 Schrödinger equation describes how wave functions change in time, a role similar to Newton’s second law in classical mechanics. The Schrödinger 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 (Fig. 1). (Note that only the lowest angular momentum states, labelled s, are spherically symmetric).

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. 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 nℏπ/L, where L is the length of the box and ℏ is Planck’s constant divided by 2 π. 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.

Unsolved problems in physics: In the correspondence limit of quantum mechanics: Is there a preferred interpretation of quantum mechanics? How does the quantum description of reality, which includes elements such as the superposition of states and wavefunction collapse, give rise to the reality we perceive?

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
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 electron 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 Schrödinger 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 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.

It turns out that analytic solutions of Schrödinger’s equation are only available for a small number of model Hamiltonians, of which the quantum harmonic oscillator 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.

Another method is the “semi-classical equation of motion” approach, which applies to systems for which quantum mechanics produces weak deviations from classical behavior. The deviations can be calculated based on the classical motion. This approach is important for the field of 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 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 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 microscopic 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 is important for understanding how individual atoms combine to form chemicals. The application of quantum mechanics to chemistry is known as quantum chemistry. Quantum mechanics can provide quantitative insight into chemical 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 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 that 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.
Fritjof Capra has drawn the parallels between Taoist thought and quantum physics in his book, ‘The Tao of Physics’.

History
In 1900, 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. In 1913, Bohr explained the spectral lines of the hydrogen atom, again by using quantization. In 1924, Louis de Broglie put forward his theory of matter waves.

These theories, though successful, were strictly phenomenological: there was no rigorous justification for quantization. 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 Heisenberg developed matrix mechanics and Schrödinger invented wave mechanics and the Schrödinger equation. Schrödinger 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 unified quantum mechanics with special relativity. 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, 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 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 chemist Linus Pauling.

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 many worlds interpretation was formulated by Everett in 1956.

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 and others, Glashow, Weinberg and Salam independently showed how the weak nuclear force and quantum electrodynamics could be merged into a single electroweak force.

Founding experiments
• Thomas Young’s double-slit experiment proving the wave nature of light (c1805)
• Henri Becquerel discovers radioactivity (1896)
• Joseph John Thomson’s cathode ray tube experiments (discovers the electron and its negative charge) (1897)
• The study of black body radiation between 1850 and 1900, which could not be explained without quantum concepts.
• The photoelectric effect: Einstein explained this in 1905 (and later received a Nobel prize for it) using the concept of photons, particles of light with quantized energy
• Robert Millikan’s oil-drop experiment, which showed that electric charge occurs as quanta (whole units), (1909)
• Ernest Rutherford’s gold foil experiment disproved the plum pudding model of the atom which suggested that the positive charge and mass of the atom are almost uniformly distributed. (1911)
• Otto Stern and Walter Gerlach conduct the Stern-Gerlach experiment, which demonstrates the quantized nature of particle spin (1920)
• Clinton Davisson and Lester Germer demonstrate the wave nature of the electron 1 (1927)

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article “quantum mechanics”.