Myswizard

There is no clock; “time” is an illusion
• Time has no indivisible unit.
• There is no “now,” only sequences of events.
Peter Lynds
Time, Classical Mechanics, Quantum Mechanics, Indeterminacy, Discontinuity, Relativity, Cosmology, Imaginary Time, Chronons, Zeno’s Paradoxes.
It is postulated there is not a precise static instant in time underlying a dynamical physical process at which the relative position of a body in relative motion or a specific physical magnitude would theoretically be precisely determined. It is concluded it is exactly because of this that time (relative interval as indicated by a clock) and the continuity of a physical process is possible, with there being a necessary trade off of all precisely determined physical values at a time, for their continuity through time. This explanation is also shown to be the correct solution to the motion and infinity paradoxes, excluding the Stadium, originally
conceived by the ancient Greek mathematician Zeno of Elea. Quantum Cosmology, Imaginary Time and Chronons are also then discussed, with the latter two appearing to be superseded on a theoretical basis.
Peter Lynds___Time and Classical and Quantum Mechanics: Indeterminacy vs. Discontinuity
Ground-breaking work in understanding of time
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In quantum mechanics, the EPR paradox (Einstein-Podolsky-Rosen) is a thought experiment which demonstrates that the result of a measurement performed on one part of a quantum system can have an instantaneous effect on the result of a measurement performed on another part, regardless of the distance separating the two parts. Although this may seem incompatible with special relativity, which states that information cannot be transmitted faster than the speed of light, this is not the case. “EPR” stands for Albert Einstein, Boris Podolsky, and Nathan Rosen, who introduced the thought experiment in a 1935 paper to argue that quantum mechanics is not a complete physical theory. It is sometimes referred to as the EPRB paradox for David Bohm, who converted the original thought experiment into something closer to being experimentally testable.

Although originally devised as a thought experiment that should expose quantum mechanics’ incompleteness, actual experimental results, carried out when technology later became available, do demonstrate the non-local effect, effectively retorting against the EPR trio’s original purpose. The “spooky action at a distance” that so disturbed EPR consistently occurs in numerous and widely replicated experiments. Einstein never really accepted quantum mechanics as a “real” and complete theory, struggling to the end of his career (and life) for an interpretation that could comply with his Relativity without implying “God playing dice”, as he condensed his dissatisfaction with QM’s intrinsic randomness and (still to be resolved) counter-intuitivity.

The EPR paradox is a paradox in the following sense: if one takes quantum mechanics and adds some seemingly reasonable conditions (referred to as “locality”, “realism”, and “completeness”), then one obtains a contradiction. However, quantum mechanics by itself does not appear to be internally inconsistent, nor — as it turns out — does it contradict relativity. As a result of further theoretical and experimental developments since the original EPR paper, most physicists today regard the EPR paradox as an illustration of how quantum mechanics violates classical intuitions, and not as an indication that quantum mechanics is fundamentally flawed.

Description of the paradox
The EPR paradox draws on a phenomenon predicted by quantum mechanics, known as quantum entanglement, to show that measurements performed on spatially separated parts of a quantum system can apparently have an instantaneous influence on one another. This effect is now known as “nonlocal behaviour” (or colloquially as “quantum weirdness”). In order to illustrate this, let us consider a simplified version of the EPR thought experiment due to Bohm.

Measurements on an entangled state
We have a source that emits pairs of electrons, with one electron sent to destination A, where there is an observer named Alice, and another is sent to destination B, where there is an observer named Bob. According to quantum mechanics, we can arrange our source so that each emitted electron pair occupies a quantum state called a spin singlet. This can be viewed as a quantum superposition of two states, which we call I and II. In state I, electron A has spin pointing upward along the z-axis (+z) and electron B has spin pointing downward along the z-axis (-z). In state II, electron A has spin -z and electron B has spin +z. Therefore, it is impossible to associate either electron in the spin singlet with a state of definite spin. The electrons are thus said to be entangled.

The EPR thought experiment, performed with electrons. A source (center) sends electrons toward two observers, Alice (left) and Bob (right), who can perform spin measurements.
Alice now measures the spin along the z-axis. She can obtain one of two possible outcomes: +z or -z. Suppose she gets +z. According to quantum mechanics, the quantum state of the system collapses into state I. (Different interpretations of quantum mechanics have different ways of saying this, but the basic result is the same.) The quantum state determines the probable outcomes of any measurement performed on the system. In this case, if Bob subsequently measures spin along the z-axis, he will obtain -z with 100% probability. Similarly, if Alice gets -z, Bob will get +z.

There is, of course, nothing special about our choice of the z axis. For instance, suppose that Alice and Bob now decide to measure spin along the x-axis. According to quantum mechanics, the spin singlet state may equally well be expressed as a superposition of spin states pointing in the x direction. We’ll call these states Ia and IIa. In state Ia, Alice’s electron has spin +x and Bob’s electron has spin -x. In state IIa, Alice’s electron has spin -x and Bob’s electron has spin +x. Therefore, if Alice measures +x, the system collapses into Ia, and Bob will get -x. If Alice measures -x, the system collapses into IIa, and Bob will get +x.

In quantum mechanics, the x-spin and z-spin are “incompatible observables”, which means that there is a Heisenberg uncertainty principle operating between them: a quantum state cannot possess a definite value for both variables. Suppose Alice measures the z-spin and obtains +z, so that the quantum state collapses into state I. Now, instead of measuring the z-spin as well, Bob measures the x-spin. According to quantum mechanics, when the system is in state I, Bob’s x-spin measurement will have a 50% probability of producing +x and a 50% probability of -x. Furthermore, it is fundamentally impossible to predict which outcome will appear until Bob actually performs the measurement.

Incidentally, although we have used spin as an example, many types of physical quantities — what quantum mechanics refers to as “observables” — can be used to produce quantum entanglement. The original EPR paper used momentum for the observable. Actual experimental realizations of the EPR scenario often use the polarization of photons, because it is easy to prepare and to measure.

Reality and completeness
We will now introduce two concepts used by Einstein, Podolsky, and Rosen, which are crucial to their attack on quantum mechanics: (i) the elements of physical reality and (ii) the completeness of a physical theory.

The authors did not directly address the philosophical meaning of an “element of physical reality”. Instead, they made the assumption that if the value of any physical quantity of a system can be predicted with absolute certainty prior to performing a measurement or otherwise disturbing it, then that quantity corresponds to an element of physical reality. Note that the converse is not assumed to be true; there may be other ways for elements of physical reality to exist, but this will not affect the argument.

Next, EPR defined a “complete physical theory” as one in which every element of physical reality is accounted for. The aim of their paper was to show, using these two definitions, that quantum mechanics is not a complete physical theory.

Let us see how these concepts apply to the above thought experiment. Suppose Alice decides to measure the value of spin along the z-axis (we’ll call this the z-spin.) After Alice performs her measurement, the z-spin of Bob’s electron is definitely known, so it is an element of physical reality. Similarly, if Alice decides to measure spin along the x-axis, the x-spin of Bob’s electron is an element of physical reality after her measurement.

We have seen that a quantum state cannot possess a definite value for both x-spin and z-spin. If quantum mechanics is a complete physical theory in the sense given above, x-spin and z-spin cannot be elements of reality at the same time. This means that Alice’s decision — whether to perform her measurement along the x- or z-axis — has an instantaneous effect on the elements of physical reality at Bob’s location. However, this violates another principle, that of locality.

Locality in the EPR experiment
The principle of locality states that physical processes occurring at one place should have no immediate effect on the elements of reality at another location. At first sight, this appears to be a reasonable assumption to make, as it seems to be a consequence of special relativity, which states that information can never be transmitted faster than the speed of light without violating causality. It is generally believed that any theory which violates causality would also be internally inconsistent, and thus deeply unsatisfactory.

It turns out that quantum mechanics violates the principle of locality without violating causality. Causality is preserved because there is no way for Alice to transmit messages (i.e. information) to Bob by manipulating her measurement axis. Whichever axis she uses, she has a 50% probability of obtaining “+” and 50% of obtaining “-”, completely at random; according to quantum mechanics, it is fundamentally impossible for her to influence what result she gets. Furthermore, Bob is only able to perform his measurement once: there is a fundamental property of quantum mechanics, known as the “no cloning theorem”, which makes it impossible for him to make a million copies of the electron he receives, perform a spin measurement on each, and look at the statistical distribution of the results. Therefore, in the one measurement he is allowed to make, there is a 50% probability of getting “+” and 50% of getting “-”, regardless of whether or not his axis is aligned with Alice’s.

However, the principle of locality appeals powerfully to physical intuition, and Einstein, Podolsky and Rosen were unwilling to abandon it. Einstein derided the quantum mechanical predictions as “spooky action at a distance”. The conclusion they drew was that quantum mechanics is not a complete theory.

It should be noted that the word locality has several different meanings in physics. For example, in quantum field theory “locality” means that quantum fields at different points of space do not interact with one another. However, quantum field theories that are “local” in this sense violate the principle of locality as defined by EPR.

Resolving the paradox

Hidden variables
There are several possible ways to resolve the EPR paradox. The one suggested by EPR is that quantum mechanics, despite its success in a wide variety of experimental scenarios, is actually an incomplete theory. In other words, there is some as-yet-undiscovered theory of nature to which quantum mechanics acts as a kind of statistical approximation (albeit an exceedingly successful one). Unlike quantum mechanics, the more complete theory contains variables corresponding to all the “elements of reality”. There must be some unknown mechanism acting on these variables to give rise to the observed effects of “non-commuting quantum observables”, i.e. the Heisenberg uncertainty principle. Such a theory is called a hidden variable theory.

To illustrate this idea, we can formulate a very simple hidden variable theory for the above thought experiment. One supposes that the quantum spin-singlet states emitted by the source are actually approximate descriptions for “true” physical states possessing definite values for the z-spin and x-spin. In these “true” states, the electron going to Bob always has spin values opposite to the electron going to Alice, but the values are otherwise completely random. For example, the first pair emitted by the source might be “(+z, -x) to Alice and (-z, +x) to Bob”, the next pair “(-z, -x) to Alice and (+z, +x) to Bob”, and so forth. Therefore, if Bob’s measurement axis is aligned with Alice’s, he will necessarily get the opposite of whatever Alice gets; otherwise, he will get “+” and “-” with equal probability.

Assuming we restrict our measurements to the z and x axes, such a hidden variable theory is experimentally indistinguishable from quantum mechanics. In reality, of course, there is an (uncountably) infinite number of axes along which Alice and Bob can perform their measurements, so there has to be an infinite number of independent hidden variables! However, this is not a serious problem; we have formulated a very simplistic hidden variable theory, and a more sophisticated theory might be able to patch it up. It turns out that there is a much more serious challenge to the idea of hidden variables.

Bell’s inequality
In 1964, John Bell showed that the predictions of quantum mechanics in the EPR thought experiment are actually slightly different from the predictions of a very broad class of hidden variable theories. Roughly speaking, quantum mechanics predicts much stronger statistical correlations between the measurement results performed on different axes than the hidden variable theories. These differences, expressed using inequality relations known as “Bell’s inequalities”, are in principle experimentally detectable. For a detailed derivation of this result, see the article on Bell’s theorem.

After the publication of Bell’s paper, a variety of experiments were devised to test Bell’s inequalities. (As mentioned above, these experiments generally rely on photon polarization measurements.) All the experiments conducted to date have found behavior in line with the predictions of standard quantum mechanics.

However, the book is not completely closed on this issue. First of all, Bell’s theorem does not apply to all possible “realist” theories. It is possible to construct theories that escape its implications, and are therefore indistinguishable from quantum mechanics, though these theories are generally non-local — they are believed to violate both causality and the rules of special relativity. Some workers in the field have also attempted to formulate hidden variable theories that exploit loopholes in actual experiments, such as the assumptions made in interpreting experimental data. However, no one has ever been able to formulate a local realist theory that can reproduce all the results of quantum mechanics.

Implications for quantum mechanics
Most physicists today believe that quantum mechanics is correct, and that the EPR paradox is only a “paradox” because classical intuitions do not correspond to physical reality. Several different conclusions can be drawn from this, depending on which interpretation of quantum mechanics one uses. In the old Copenhagen interpretation, one concludes that the principle of locality does not hold, and that instantaneous wavefunction collapse really does occur. In the many-worlds interpretation, locality is preserved, and the effects of the measurements arise from the splitting of the observers into different “histories”.

The EPR paradox has deepened our understanding of quantum mechanics by exposing the fundamentally non-classical characteristics of the measurement process. Prior to the publication of the EPR paper, a measurement was often visualized as a physical disturbance inflicted directly on the measured system. For instance, when measuring the position of an electron, one imagines shining a light on it, thus disturbing the electron and producing the quantum mechanical uncertainties in its position. Such explanations, which are still encountered in popular expositions of quantum mechanics, are debunked by the EPR paradox, which shows that a “measurement” can be performed on a particle without disturbing it directly, by performing a measurement on a distant entangled particle.

Technologies relying on quantum entanglement are now being developed. In quantum cryptography, entangled particles are used to transmit signals that cannot be eavesdropped upon without leaving a trace. In quantum computation, entangled quantum states are used to perform computations in parallel, which may allow certain calculations to be performed much more quickly than they ever could be with classical computers.

Book Description
“Scientists other than quantum physicists often fail to comprehend the enormity of the conceptual change wrought by quantum theory in our basic conception of the nature of matter,” writes Henry Stapp. Stapp is a leading quantum physicist who has given particularly careful thought to the implications of the theory that lies at the heart of modern physics. In this book, which contains several of his key papers as well as new material, he focuses on the problem of consciousness and explains how quantum mechanics allows causally effective conscious thought to be combined in a natural way with the physical brain made of neurons and atoms. The book is divided into four sections. The first consists of an extended introduction. Key foundational and somewhat more technical papers are included in the second part, together with a clear exposition of the “orthodox” interpretation of quantum mechanics. The third part addresses, in a non-technical fashion, the implications of the theory for some of the most profound questions that mankind has contemplated: How does the world come to be just what it is and not something else? How should humans view themselves in a quantum universe? What will be the impact on society of the revised scientific image of the nature of man? The final part contains a mathematical appendix for the specialist and a glossary of important terms and ideas for the interested layman. This new edition has been updated and extended to address recent debates about consciousness.

Why Classical Mechanics Cannot Naturally Accommodate Consciousness_But Quantum Mechanics Can by Henry P. Stapp

Advanced Reading

Quantum suicide

In quantum mechanics, quantum suicide is a thought experiment which was independently proposed in 1987 by Hans Moravec and in 1988 by Bruno Marchal, and further developed by Max Tegmark in 1998, that attempts to distinguish between the Copenhagen interpretation of quantum mechanics and the Everett many-worlds interpretation by means of a variation of the Schrödinger’s cat experiment. The experiment essentially involves looking at the Schrödinger’s cat experiment from the point of view of the cat.

In this experiment, a physicist sits in front of a gun which is triggered or not triggered depending on the decay of some radioactive atom. With each run of the experiment there is a 50-50 chance that the gun will be triggered and the physicist will die. If the Copenhagen interpretation is correct, then the gun will eventually be triggered and the physicist will die. If the many-worlds interpretation is correct then at each run of the experiment the physicist will be split into a world in which he lives and one in which he dies. In the worlds where the physicist dies, he will cease to exist. However, from the point of view of the non-dead physicist, the experiment will continue running without his ceasing to exist, because at each branch, he will only be able to observe the result in the world in which he survives, and if many-worlds is correct, the physicist will notice that he never seems to die.

Unfortunately, the physicist will be unable to report the results because, from the viewpoint of an outside observer, the probabilities will be the same whether many worlds or Copenhagen is correct.

A variation of this thought experiment suggests a controversial outcome known as quantum immortality, which is the argument that if the many-worlds interpretation of quantum mechanics is correct then a conscious observer can never cease to exist.

Quantum immortality

Quantum immortality is the controversial speculation deriving from the quantum suicide thought experiment that states the Everett many-worlds interpretation of quantum mechanics implies that conscious beings are immortal.

Explanation of the thought experiment
Imagine that a physicist detonates a nuclear bomb beside him. In almost all parallel universes, the nuclear explosion will vaporize the physicist. However, there should be a small set of alternative universes in which the physicist somehow survives (ie. the set of universes which support a “miraculous” survival scenario). The idea behind quantum immortality is that the physicist will remain alive in, and thus able to experience, at least one of the universes in this set, even though these universes form a tiny subset of all possible universes. Over time the physicist would therefore consider himself to be living forever. There are some parallels with this concept in the anthropic principle.

Another example is that provided by quantum suicide where a physicist sits in front of a gun which is triggered, or not triggered, by radioactive decay. With each run of the experiment there is a fifty-fifty chance that the gun will be triggered and the physicist will die. If the Copenhagen interpretation is correct, then the gun will eventually be triggered and the physicist will die. If the many-worlds interpretation is correct, then at each run of the experiment the physicist will be split into a world in which he lives and one in which he dies. In the worlds where the physicist dies, he will cease to exist. However, from the point of view of the physicist, the experiment will continue running without his ceasing to exist, because at each branch, he will only be able to observe the result in the world in which he survives, and if many-worlds is correct, the physicist will notice that he never seems to die, therefore “proving” himself to be immortal, at least from his own point of view in probability.

strong>Required assumptions and controversy
Proponents point out that while it is highly speculative, quantum immortality violates no known laws of physics assuming two controversial assumptions are true:

1. The many-worlds interpretation of quantum mechanics is the correct one, as opposed to the Copenhagen interpretation, which does not indicate the existence of parallel universes.

2. All of the possible scenarios in which the proposed physicist (or any entity being argued about in the thought experiment) can die support at least a small subset of survival scenarios.

A potential criticism of the theory is that the second assumption is not a necessary consequence of the many-worlds interpretation and may require the violation of laws that are still thought to be conserved across *all* possible realities. The many-worlds interpretation of quantum physics does not necessarily imply that “everything is possible”, only that all outcomes that *are* possible will branch off from any given instant in time. Most physical laws of the universe still cannot be broken - for example, the second law of thermodynamics is still considered to be conserved in all probabilities, theoretically preventing a parallel universe in which this law is violated from ever branching off. This has implications that, from the point of view of the physicist, it is possible to reach a particular configuration of reality where the physicist’s survival actually becomes impossible, because a survival scenario in that reality would at that point require a violation of a law of the universe that is not thought to be violated in any possible reality.

For example, in the nuclear-bomb scenario above, once the bomb detonates, it is difficult to effectively describe a scenario in which the physicist continues living that does not violate basic biological principles. Living cells simply cannot remain alive at the temperatures found at the core of a nuclear reaction under any known subsets of modern science. For quantum immortality to be true, either the bomb would have to misfire (or otherwise not detonate) or an event would have to take place which made use of scientific principles that are not yet proven or discovered. Another example is natural biological death from old age, which may not be escapable in any parallel universe (at least without more advanced technology than is currently known).

Another potentially problematic area is that quantum immortality would also imply that a conscious being could “cause” itself to experience highly improbable events in its own probability simply by repeatedly placing itself in situations in which it is highly likely that the being will die. Even though in most parallel universes the being would die, the only ones that the being could possibly subjectively experience would be the ones in which it experiences the unlikely survival scenario. This may turn out to be a violation of some sort of property of causality, the nature of which is still not well understood in quantum physics.

Although quantum immortality is motivated by the quantum suicide thought experiment, Max Tegmark, one of the inventors of this experiment, has stated that he does not believe that quantum immortality is a consequence of his work. He argues that under any sort of normal conditions, before someone dies they undergo a period of diminishment of consciousness, a non-quantum decline (which can be anywhere from seconds to minutes to years), and hence there is no way of establishing a continuous existence from this world to an alternate one in which the person continues to exist.

Fictional depictions
The Greg Egan novel Quarantine explores topics related to quantum immortality.

Other science fiction stories exploring these and related ideas include “All the Myriad Ways” by Larry Niven, and “Divided by Infinity” by Robert Charles Wilson.

The film Donnie Darko loosely explores quantum immortality.

Terry Pratchett’s short story Death, and What Comes Next has a philosopher arguing the principle with Death, who has come for him.

In the Hitchhiker’s Guide To The Galaxy series, it could be argued that the Infinite Improbability Drive resembles this idea when the Heart of Gold rescues Arthur Dent and Ford Prefect - Ford and Arthur should certainly die when thrown out of an airlock into outer space - but instead, they experience a rescue wherein the basic laws of the universe seem to have been rewritten, which is similar to what some conjecture would happen were a consciousness to perceive its death as so inevitable as to require a massively improbable event.

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

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

Being an observer of the non-linear (spiritual realm), I am aware of the fact that science, i.e. Quantum Mechanics has the capability of going to the very end of the linear realm. Scientists, in recent years, have finally come to the realization that reality can only be explained to the edge of the cliff, (so to speak) through science and mathematics, and beyond that we must enter that which one has no actual physical explanation. Having experienced the world of the non linear, I can attest to the fact that it is entirely experiential. Although there are wonderful studies and writings by many scientists in their respective fields regarding the world of non duality, as David Hawkins calls it, much of science is lacking the capacity to prove what humans have long been searching for…Proof that something lies beyond our physical reality. To bring science and the non linear together in one place would most likely take the rest of my life and add an unending list of references as well as objective and subjective studies to this website. I feel no obligation to prove what it is I already know, but for the sake of bringing the two together here, I will give these subjects my best attempt at explanations.

All of the information provided here, is reiterated through various reference materials. Please be aware that although articles from the Wiki Encyclopedia contain fact, they also reflect the opinions of the writers. See future articles on the subjects of linear, non linear, duality and non duality and the spiritual realms.
Myswizard

Quantum Mechanics
Quantum Mechanics is a theory in physics which primarily tries to explain the behaviour of extremely small bodies, such as atoms and molecules. Scientists generally agree that it is a very accurate and successful theory, and it has very important applications in today’s world as all electronic devices depend on Quantum Mechanics in some way. It is also important in understanding how large objects such as stars and even the whole Universe are the way they are.

Despite how successful Quantum Mechanics is, it does have some controversial elements. For example, the behaviour of microscopic objects is very different from our everyday experience, and some of its results appear to contradict other successful theories, such as the Theory of Relativity - simplified.

In quantum physics, the Heisenberg uncertainty principle, expresses a limitation on accuracy of (nearly) simultaneous measurement of observables such as the position and the momentum of a particle. It furthermore precisely quantifies the imprecision by providing a lower bound (greater than zero) for the product of the standard deviations of the measurements. The uncertainty principle is one of the cornerstones of quantum mechanics and was discovered by Werner Heisenberg in 1927.

It is sometimes called the Heisenberg indeterminacy principle (a title prefered by Niels Bohr),
Understanding uncertainty
Consider an experiment in which a particle is prepared in a definite state and two successive measurements are performed on the particle. The first one measures the particle’s position and the second immediately after measures its momentum. Each time the experiment is performed, some value x is obtained for position and some value p is obtained for momentum. These values, however, may be different for each trial. In other words, there is an uncertainty in the outcome of the measurements. The Heisenberg uncertainty principle provides a quantitative relationship between the uncertainties of p and x as measured by their standard deviations in the following way: If the particle state is such that the first measurement yields a dispersion of values Δx, then the second measurement will have a distribution of values whose dispersion Δp is at least inversely proportional to Δx.

Sound analogy
There is a precise, quantitative analogy between the Heisenberg uncertainty relations and properties of waves or signals. Consider a time-varying signal such as a sound wave. It is meaningless to ask about the frequency spectrum of the signal at a moment in time. In order to determine the frequencies accurately, the signal needs to be sampled for a finite (non zero) time. This necessarily means that time precision is lost. In other words, a sound cannot have both a precise time, as in a short pulse, and a precise frequency, as in a continuous pure tone. The time and frequency of a wave in time are analogous to the position and momentum of a particle in space.

Overview
An uncertainty relation arises between any two observable quantities that can be defined by non-commuting operators. The uncertainty principle in quantum mechanics is sometimes explained by claiming that the measurement of position necessarily disturbs a particle’s momentum. Heisenberg himself may have offered explanations which suggest this view, at least initially. That disturbance plays no role in the uncertainty principle can be seen as follows: Consider a particle prepared in a definite state, and measure either the momentum or the position of the particle, but not both. After repeating this experiment a large number of times, we will obtain probability distributions of values for both these quantities and the uncertainty relation still holds for the dispersions Δp, Δx of the values.

The Heisenberg uncertainty relations are a theoretical bound over all measurements. They hold for so-called ideal measurements, sometimes called von Neumann measurements. They hold even more so for non-ideal or Landau measurements.

Correspondingly, any one particle cannot be described simultaneously as a “classic point particle” and as a wave. The fact that either one of these descriptions is appropriate at least in separate cases is called wave-particle duality; a change of appropriate descriptions according to measured values is known as wavefunction collapse.) The uncertainty principle, as initially considered by Heisenberg, is concerned with cases in which neither of these two descriptions is fully and exclusively appropriate, such as a particle in a box with a particular energy value; i.e. systems which are characterized neither by one unique “position” (one particular value of distance from a potential wall) nor by one unique value of momentum (incl. its direction).

Formulation
If several identical copies of a system in a given state are prepared, measurements of position and momentum will conform to a determined probability distributions. This is a fundamental postulate of quantum mechanics. If we compute the standard deviation Δx of the position measurements and the standard deviation Δp of the momentum measurements, then where is Planck’s constant (h) divided by 2π. (In some treatments, the “uncertainty” of a variable is taken to be the smallest width of a range which contains 50% of the values, which, in the case of normally distributed variables, leads to a larger lower bound of h/2π for the product of the uncertainties.) Note that this inequality allows for several possibilities: the state could be such that x can be measured with high precision, but then p will only approximately be known, or conversely p could be sharply defined while x cannot be precisely determined. In yet other states, both x and p can be measured with “reasonable” (but not arbitrarily high) precision.

In everyday life, we do not usually observe these uncertainties because the value of Planck’s constant (h) is extremely small.

Other characterizations
A number of additional characterizations have been developed including the ones below.

Expression of finite available amount of Fisher information
The uncertainty principle alternatively derives as an expression of the Cramér-Rao inequality of classical measurement theory. This is in the case where a particle position is measured. See Stam (1959). The mean-squared particle momentum enters as the Fisher information in the inequality. See also extreme physical information.

Generalized applications
The uncertainty principle does not just apply to position and momentum. In its general form, it applies to every pair of conjugate variables. An example of a pair of conjugate variables is the x-component of angular momentum (spin) vs. the y-component of angular momentum. In general, and unlike the case of position versus momentum discussed above, the lower bound for the product of the uncertainties of two conjugate variables depends on the system state.

History and interpretations of the principle
Main article: Interpretation of quantum mechanics

Albert Einstein was not happy with the uncertainty principle, and he challenged Niels Bohr and Werner Heisenberg with a famous thought experiment (See the Bohr-Einstein debates for more details): we fill a box with a radioactive material which randomly emits radiation. The box has a shutter, which is opened and immediately thereafter shut by a clock at a precise time, thereby allowing some radiation to escape. So the time is already known with precision. We still want to measure the conjugate variable energy precisely. Einstein proposed doing this by weighing the box before and after. The equivalence between mass and energy from special relativity will allow you to determine precisely how much energy was left in the box. Bohr countered as follows: should energy leave, then the now lighter box will rise slightly on the scale. That changes the position of the clock. Thus the clock deviates from our stationary reference frame, and again by special relativity, its measurement of time will be different from ours, leading to some unavoidable margin of error. In fact, a detailed analysis shows that the imprecision is correctly given by Heisenberg’s relation.

Within the widely but not universally accepted Copenhagen interpretation of quantum mechanics, the uncertainty principle is taken to mean that on an elementary level, the physical universe does not exist in a deterministic form—but rather as a collection of probabilities, or potentials. For example, the pattern (probability distribution) produced by millions of photons passing through a diffraction slit can be calculated using quantum mechanics, but the exact path of each photon cannot be predicted by any known method. The Copenhagen interpretation holds that it cannot be predicted by any method.

It is this interpretation that Einstein was questioning when he said “I cannot believe that God would choose to play dice with the universe.” Bohr, who was one of the authors of the Copenhagen interpretation responded, “Einstein, don’t tell God what to do.”

Einstein was convinced that this interpretation was in error. His reasoning was that all previously known probability distributions arose from deterministic events. The distribution of a flipped coin or a rolled dice can be described with a probability distribution (50% heads, 50% tails). But this does not mean that their physical motions are unpredictable. Ordinary mechanics can be used to calculate exactly how each coin will land, if the forces acting on it are known. And the heads/tails distribution will still line up with the probability distribution (given random initial forces).

Einstein assumed that there are similar hidden variables in quantum mechanics which underlie the observed probabilities.

Neither Einstein nor anyone since has been able to construct a satisfying hidden variable theory, and the Bell inequality illustrates some very thorny issues in trying to do so. Although the behavior of an individual particle is random, it is also correlated with the behavior of other particles. Therefore, if the uncertainty principle is the result of some deterministic process, it must be the case that particles at great distances instantly transmit information to each other to ensure that the correlations in behavior between particles occur.

The uncertainty principle in popular culture
The uncertainty principle is often misunderstood or misstated in the popular press. One common incorrect formulation is that observation of an event changes the event. This may be true in some cases for some events, but it has nothing to do with the uncertainty principle in quantum mechanics.

In some science fiction stories, a device to circumvent the uncertainty principle is called a Heisenberg compensator, most famously in Star Trek for use on the transporter; however, it is not clear what circumventing means.

In Stephen Donaldson’s Gap Cycle science fiction book series, one of the characters postulates a socio-political version of the uncertainty principle: namely, that by determining his precise “location” in the current political landscape, he is prevented from simultaneously calculating the likely direction of political events in the near future.

Humor
The unusual nature of Heisenberg’s uncertainty principle, and its distinctive name, has made it the source of several jokes. It is said that a popular item of graffiti at the physics department of university campuses is the slogan “Heisenberg may have been here.”

In another uncertainty principle joke, a quantum physicist is stopped on the highway by a police officer who asks “Do you know how fast you were going, sir?”, to which the physicist responds, “No, but I know exactly where I am!”.

In the show Futurama there is a close finish in a horse race, a “quantum finish” they say, and a photograph reveals who won, when the professor yells out “No fair! By oberserving the results you’ve changed them!”

Consciousness causes collapse
Consciousness causes collapse is the speculative theory that observation by a conscious observer is responsible for the wavefunction collapse. It is an attempt to solve the Wigner’s friend paradox by simply stating that collapse occurs at the first “conscious” observer. Supporters claim this is not a revival of substance dualism, since (in a ramification of this view) consciousness and objects are entangled and cannot be considered as distinct. The consciousness causes collapse theory can be considered as a speculative appendage to almost any interpretation of quantum mechanics and most physicists reject it as unverifiable and introducing unnecessary elements into physics.

The process of “measurement” in quantum mechanics is regarded as consciousness itself. However, it is not explained by this theory which animals, living creatures, or objects have consciousness, that is, the right to collapse the wavefunction. It is also not clear whether measuring devices might also be considered conscious, though generally measuring devices are considered simply a “chain of observations” that only ends at a conscious entity. Some even suggest that some beings have a “higher consciousness” and therefore more capability to collapse the wavefunction, whereas others believe all conscious entities have an equal capability.

It has been claimed that the theory that meshes well with ancient Eastern mysticism and philosophy, including Hinduism and Taoism, which stress “Oneness”.

Amit Goswami, a retired theoretical physicist, supported this theory in some of his writings, including The Self-Aware Universe. The Hungarian physicist Eugene Wigner also supported it.

The view is also presented in the popular and controversial documentary What the Bleep Do We Know!?, alongside some unrelated biological discussions.

The Stanford Encyclopedia of Philosophy(Quantum Mechanics)

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article “Heisenberg Principle and Consciousness causes collapse”.

The Stanford Encyclopedia of Philosophy(Quantum Mechanics)

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”.