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Schrödinger's cat

Schrödinger's cat

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Schrödinger's cat is a thought experiment
Thought experiment
A thought experiment or Gedankenexperiment considers some hypothesis, theory, or principle for the purpose of thinking through its consequences...

, usually described as a paradox
Paradox
Similar to Circular reasoning, A paradox is a seemingly true statement or group of statements that lead to a contradiction or a situation which seems to defy logic or intuition...

, devised by Austrian physicist Erwin Schrödinger
Erwin Schrödinger
Erwin Rudolf Josef Alexander Schrödinger was an Austrian physicist and theoretical biologist who was one of the fathers of quantum mechanics, and is famed for a number of important contributions to physics, especially the Schrödinger equation, for which he received the Nobel Prize in Physics in 1933...

 in 1935. It illustrates what he saw as the problem of the Copenhagen interpretation
Copenhagen interpretation
The Copenhagen interpretation is one of the earliest and most commonly taught interpretations of quantum mechanics. It holds that quantum mechanics does not yield a description of an objective reality but deals only with probabilities of observing, or measuring, various aspects of energy quanta,...

 of quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

 applied to everyday objects. The scenario presents a cat that might be alive or dead, depending on an earlier random
Quantum indeterminacy
Quantum indeterminacy is the apparent necessary incompleteness in the description of a physical system, that has become one of the characteristics of the standard description of quantum physics...

 event. Although the original "experiment" was imaginary, similar principles have been researched and used in practical applications. The Cat paradox is also often featured in theoretical discussions of the interpretation of quantum mechanics
Interpretation of quantum mechanics
An interpretation of quantum mechanics is a set of statements which attempt to explain how quantum mechanics informs our understanding of nature. Although quantum mechanics has held up to rigorous and thorough experimental testing, many of these experiments are open to different interpretations...

. In the course of developing this experiment, Schrödinger coined the term Verschränkung (entanglement
Quantum entanglement
Quantum entanglement occurs when electrons, molecules even as large as "buckyballs", photons, etc., interact physically and then become separated; the type of interaction is such that each resulting member of a pair is properly described by the same quantum mechanical description , which is...

).

Origin and motivation


Schrödinger intended his thought experiment as a discussion of the EPR article
EPR paradox
The EPR paradox is a topic in quantum physics and the philosophy of science concerning the measurement and description of microscopic systems by the methods of quantum physics...

—named after its authors Einstein, Podolsky
Boris Podolsky
Boris Yakovlevich Podolsky , was an American physicist of Russian Jewish descent.-Education:In 1896, Boris Podolsky was born into a poor Jewish family in Taganrog, in what was then the Russian Empire, and he moved to the United States in 1913...

, and Rosen
Nathan Rosen
Nathan Rosen was an American-Israeli physicist noted for his study on the structure of the hydrogen molecule and his work with Albert Einstein and Boris Podolsky on entangled wave functions and the EPR paradox.-Background:Nathan Rosen was born into a Jewish family in Brooklyn, New York...

—in 1935. The EPR article highlighted the strange nature of quantum entanglement
Quantum entanglement
Quantum entanglement occurs when electrons, molecules even as large as "buckyballs", photons, etc., interact physically and then become separated; the type of interaction is such that each resulting member of a pair is properly described by the same quantum mechanical description , which is...

, which is a characteristic of a quantum state that is a combination of the states of two systems (for example, two subatomic particles), that once interacted but were then separated and are not each in a definite state. The Copenhagen interpretation implies that the state of the two systems undergoes collapse into a definite state when one of the systems is measured. Schrödinger and Einstein exchanged letters about Einstein's EPR article, in the course of which Einstein pointed out that the state of an unstable
Instability
In numerous fields of study, the component of instability within a system is generally characterized by some of the outputs or internal states growing without bounds...

 keg of gunpowder
Gunpowder
Gunpowder, also known since in the late 19th century as black powder, was the first chemical explosive and the only one known until the mid 1800s. It is a mixture of sulfur, charcoal, and potassium nitrate - with the sulfur and charcoal acting as fuels, while the saltpeter works as an oxidizer...

 will, after a while, contain a superposition
Quantum superposition
Quantum superposition is a fundamental principle of quantum mechanics. It holds that a physical system exists in all its particular, theoretically possible states simultaneously; but, when measured, it gives a result corresponding to only one of the possible configurations.Mathematically, it...

 of both exploded and unexploded states.

To further illustrate the putative incompleteness of quantum mechanics, Schrödinger describes how one could, in principle, transpose the superposition of an atom to large-scale systems of a live and dead cat by coupling cat and atom with the help of a diabolical mechanism. He proposed a scenario with a cat in a sealed box, wherein the cat's life or death depended on the state of a subatomic particle. According to Schrödinger, the Copenhagen interpretation implies that the cat remains both alive and dead (to the universe outside the box) until the box is opened. Schrödinger did not wish to promote the idea of dead-and-alive cats as a serious possibility; quite the reverse, the paradox is a classic reductio ad absurdum
Reductio ad absurdum
In logic, proof by contradiction is a form of proof that establishes the truth or validity of a proposition by showing that the proposition's being false would imply a contradiction...

. The thought experiment illustrates the counterintuitiveness of quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

 and the mathematics necessary to describe quantum states. Intended as a critique of just the Copenhagen interpretation
Copenhagen interpretation
The Copenhagen interpretation is one of the earliest and most commonly taught interpretations of quantum mechanics. It holds that quantum mechanics does not yield a description of an objective reality but deals only with probabilities of observing, or measuring, various aspects of energy quanta,...

 (the prevailing orthodoxy
Orthodoxy
The word orthodox, from Greek orthos + doxa , is generally used to mean the adherence to accepted norms, more specifically to creeds, especially in religion...

 in 1935), the Schrödinger cat thought experiment remains a typical touchstone
Touchstone (metaphor)
As a metaphor, a touchstone refers to any physical or intellectual measure by which the validity or merit of a concept can be tested. It is similar in use to an acid test, litmus test in politics, and a shibboleth.-Touchstone in literature:...

 for all interpretations of quantum mechanics. Physicists often use the way each interpretation deals with Schrödinger's cat as a way of illustrating and comparing the particular features, strengths, and weaknesses of each interpretation.

The thought experiment


Schrödinger wrote:
The above text is a translation of two paragraphs from a much larger original article that appeared in the German magazine Naturwissenschaften ("Natural Sciences") in 1935.

Schrödinger's famous thought experiment
Thought experiment
A thought experiment or Gedankenexperiment considers some hypothesis, theory, or principle for the purpose of thinking through its consequences...

 poses the question, when does a quantum system stop existing as a superposition
Quantum superposition
Quantum superposition is a fundamental principle of quantum mechanics. It holds that a physical system exists in all its particular, theoretically possible states simultaneously; but, when measured, it gives a result corresponding to only one of the possible configurations.Mathematically, it...

 of states and become one or the other? (More technically, when does the actual quantum state stop being a linear combination of states, each of which resembles different classical states, and instead begins to have a unique classical description?) If the cat survives, it remembers only being alive. But explanations of the EPR experiments that are consistent with standard microscopic quantum mechanics require that macroscopic objects, such as cats and notebooks, do not always have unique classical descriptions. The thought experiment illustrates this apparent paradox. Our intuition says that no observer can be in a mixture of states—yet the cat, it seems from the thought experiment, can be such a mixture. Is the cat required to be an observer, or does its existence in a single well-defined classical state require another external observer? Each alternative seemed absurd to Albert Einstein, who was impressed by the ability of the thought experiment to highlight these issues. In a letter to Schrödinger dated 1950, he wrote:

Note that no charge of gunpowder is mentioned in Schrödinger's setup, which uses a Geiger counter as an amplifier
Quantum decoherence
In quantum mechanics, quantum decoherence is the loss of coherence or ordering of the phase angles between the components of a system in a quantum superposition. A consequence of this dephasing leads to classical or probabilistically additive behavior...

 and hydrocyanic poison instead of gunpowder. The gunpowder had been mentioned in Einstein's original suggestion to Schrödinger 15 years before, and apparently Einstein had carried it forward to the present discussion.

Interpretations of the experiment


Since Schrödinger's time, other interpretations of quantum mechanics have been proposed that give different answers to the questions posed by Schrödinger's cat of how long superpositions last and when (or if) they collapse.

Copenhagen interpretation



The most commonly held interpretation of quantum mechanics is the Copenhagen interpretation
Copenhagen interpretation
The Copenhagen interpretation is one of the earliest and most commonly taught interpretations of quantum mechanics. It holds that quantum mechanics does not yield a description of an objective reality but deals only with probabilities of observing, or measuring, various aspects of energy quanta,...

  In the Copenhagen interpretation, a system stops being a superposition of states and becomes either one or the other when an observation takes place. This experiment makes apparent the fact that the nature of measurement
Measurement in quantum mechanics
The framework of quantum mechanics requires a careful definition of measurement. The issue of measurement lies at the heart of the problem of the interpretation of quantum mechanics, for which there is currently no consensus....

, or observation, is not well-defined in this interpretation. The experiment can be interpreted to mean that while the box is closed, the system simultaneously exists in a superposition of the states "decayed nucleus/dead cat" and "undecayed nucleus/living cat," and that only when the box is opened and an observation performed does the wave function collapse into one of the two states.

However, one of the main scientists associated with the Copenhagen interpretation, Niels Bohr
Niels Bohr
Niels Henrik David Bohr was a Danish physicist who made foundational contributions to understanding atomic structure and quantum mechanics, for which he received the Nobel Prize in Physics in 1922. Bohr mentored and collaborated with many of the top physicists of the century at his institute in...

, never had in mind the observer-induced collapse of the wave function, so that Schrödinger's Cat did not pose any riddle to him. The cat would be either dead or alive long before the box is opened by a conscious observer. Analysis of an actual experiment found that measurement alone (for example by a Geiger counter) is sufficient to collapse a quantum wave function before there is any conscious observation of the measurement. The view that the "observation" is taken when a particle from the nucleus hits the detector can be developed into objective collapse theories. In contrast, the many worlds approach denies that collapse ever occurs.

Many-worlds interpretation and consistent histories


In 1957, Hugh Everett
Hugh Everett
Hugh Everett III was an American physicist who first proposed the many-worlds interpretation of quantum physics, which he termed his "relative state" formulation....

 formulated the many-worlds interpretation of quantum mechanics, which does not single out observation as a special process. In the many-worlds interpretation, both alive and dead states of the cat persist after the box is opened, but are decoherent
Quantum decoherence
In quantum mechanics, quantum decoherence is the loss of coherence or ordering of the phase angles between the components of a system in a quantum superposition. A consequence of this dephasing leads to classical or probabilistically additive behavior...

 from each other. In other words, when the box is opened, the observer and the already-dead cat split into an observer looking at a box with a dead cat, and an observer looking at a box with a live cat. But since the dead and alive states are decoherent, there is no effective communication or interaction between them.

When opening the box, the observer becomes entangled with the cat, so "observer states" corresponding to the cat's being alive and dead are formed; each observer state is entangled or linked
Quantum entanglement
Quantum entanglement occurs when electrons, molecules even as large as "buckyballs", photons, etc., interact physically and then become separated; the type of interaction is such that each resulting member of a pair is properly described by the same quantum mechanical description , which is...

 with the cat so that the "observation of the cat's state" and the "cat's state" correspond with each other. Quantum decoherence
Quantum decoherence
In quantum mechanics, quantum decoherence is the loss of coherence or ordering of the phase angles between the components of a system in a quantum superposition. A consequence of this dephasing leads to classical or probabilistically additive behavior...

 ensures that the different outcomes have no interaction with each other. The same mechanism of quantum decoherence is also important for the interpretation in terms of consistent histories
Consistent histories
In quantum mechanics, the consistent histories approach is intended to give a modern interpretation of quantum mechanics, generalising the conventional Copenhagen interpretation and providing a natural interpretation of quantum cosmology...

. Only the "dead cat" or "alive cat" can be a part of a consistent history in this interpretation.

Roger Penrose
Roger Penrose
Sir Roger Penrose OM FRS is an English mathematical physicist and Emeritus Rouse Ball Professor of Mathematics at the Mathematical Institute, University of Oxford and Emeritus Fellow of Wadham College...

 criticises this:
Although the mainstream view (without necessarily endorsing many-worlds) is that decoherence is the mechanism that forbids such simultaneous perception.

A variant of the Schrödinger's Cat experiment, known as the quantum suicide machine, has been proposed by cosmologist Max Tegmark
Max Tegmark
Max Tegmark is a Swedish-American cosmologist. Tegmark is a professor at the Massachusetts Institute of Technology and belongs to the scientific directorate of the Foundational Questions Institute.-Early life:...

. It examines the Schrödinger's Cat experiment from the point of view of the cat, and argues that by using this approach, one may be able to distinguish between the Copenhagen interpretation and many-worlds.

Ensemble interpretation


The ensemble interpretation
Ensemble Interpretation
The ensemble interpretation, or statistical interpretation of quantum mechanics, is an interpretation that can be viewed as a minimalist interpretation; it is a quantum mechanical interpretation that claims to make the fewest assumptions associated with the standard mathematical formalization...

 states that superpositions are nothing but subensembles of a larger statistical ensemble. The state vector would not apply to individual cat experiments, but only to the statistics of many similarly prepared cat experiments. Proponents of this interpretation state that this makes the Schrödinger's Cat paradox a trivial non-issue.

This interpretation serves to discard the idea that a single physical system in quantum mechanics has a mathematical description that corresponds to it in any way.

Relational interpretation


The relational interpretation
Relational quantum mechanics
Relational quantum mechanics is an interpretation of quantum mechanics which treats the state of a quantum system as being observer-dependent, that is, the state is the relation between the observer and the system. This interpretation was first delineated by Carlo Rovelli in a 1994 preprint, and...

 makes no fundamental distinction between the human experimenter, the cat, or the apparatus, or between animate and inanimate systems; all are quantum systems governed by the same rules of wavefunction evolution
Time evolution
Time evolution is the change of state brought about by the passage of time, applicable to systems with internal state . In this formulation, time is not required to be a continuous parameter, but may be discrete or even finite. In classical physics, time evolution of a collection of rigid bodies...

, and all may be considered "observers." But the relational interpretation allows that different observers can give different accounts of the same series of events, depending on the information they have about the system. The cat can be considered an observer of the apparatus; meanwhile, the experimenter can be considered another observer of the system in the box (the cat plus the apparatus). Before the box is opened, the cat, by nature of it being alive or dead, has information about the state of the apparatus (the atom has either decayed or not decayed); but the experimenter does not have information about the state of the box contents. In this way, the two observers simultaneously have different accounts of the situation: To the cat, the wavefunction of the apparatus has appeared to "collapse"; to the experimenter, the contents of the box appear to be in superposition. Not until the box is opened, and both observers have the same information about what happened, do both system states appear to "collapse" into the same definite result, a cat that is either alive or dead.

Objective collapse theories


According to objective collapse theories, superpositions are destroyed spontaneously (irrespective of external observation) when some objective physical threshold (of time
Time
Time is a part of the measuring system used to sequence events, to compare the durations of events and the intervals between them, and to quantify rates of change such as the motions of objects....

, mass
Mass
Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...

, temperature
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...

, irreversibility
Irreversibility
In science, a process that is not reversible is called irreversible. This concept arises most frequently in thermodynamics, as applied to processes....

, etc.) is reached. Thus, the cat would be expected to have settled into a definite state long before the box is opened. This could loosely be phrased as "the cat observes itself," or "the environment observes the cat."

Objective collapse theories require a modification of standard quantum mechanics to allow superpositions to be destroyed by the process of time evolution.

Applications and tests


The experiment as described is a purely theoretical one, and the machine proposed is not known to have been constructed. However, successful experiments involving similar principles, i.e. superpositions of relatively large (by the standards of quantum physics) objects have been performed. These experiments do not show that a cat-sized object can be superposed, but the known upper limit on "cat states" has been pushed upwards by them. In many cases the state is short-lived, even when cooled to near absolute zero
Absolute zero
Absolute zero is the theoretical temperature at which entropy reaches its minimum value. The laws of thermodynamics state that absolute zero cannot be reached using only thermodynamic means....

.
  • A "cat state" has been achieved with photon
    Photon
    In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...

    s.
  • A beryllium
    Beryllium
    Beryllium is the chemical element with the symbol Be and atomic number 4. It is a divalent element which occurs naturally only in combination with other elements in minerals. Notable gemstones which contain beryllium include beryl and chrysoberyl...

     ion
    Ion
    An ion is an atom or molecule in which the total number of electrons is not equal to the total number of protons, giving it a net positive or negative electrical charge. The name was given by physicist Michael Faraday for the substances that allow a current to pass between electrodes in a...

     has been trapped in a superposed state.
  • An experiment involving a superconducting quantum interference device ("SQUID") has been linked to theme of the thought experiment: " The superposition state does not correspond to a billion electrons flowing one way and a billion others flowing the other way. Superconducting electrons move en masse. All the superconducting electrons in the SQUID flow both ways around the loop at once when they are in the Schrödinger’s cat state.".
  • A piezoelectric "tuning fork
    Tuning fork
    A tuning fork is an acoustic resonator in the form of a two-pronged fork with the prongs formed from a U-shaped bar of elastic metal . It resonates at a specific constant pitch when set vibrating by striking it against a surface or with an object, and emits a pure musical tone after waiting a...

    " has been constructed, which can be placed into a superposition of vibrating and non vibrating states. The resonator comprises about 10 trillion atoms.
  • An experiment involving a flu virus has been proposed.


In quantum computing the phrase "cat state" often refers to the special entanglement of qubit
Qubit
In quantum computing, a qubit or quantum bit is a unit of quantum information—the quantum analogue of the classical bit—with additional dimensions associated to the quantum properties of a physical atom....

s wherein the qubits are in an equal superposition of all being 0 and all being 1; i.e.,
.

Extensions


Wigner's friend
Wigner's friend
Wigner's friend is a thought experiment proposed by the physicist Eugene Wigner; it is an extension of the Schrödinger's cat experiment designed as a point of departure for discussing the Quantum mind/body problem.- The thought experiment :...

 is a variant on the experiment with two external observers: the first opens and inspects the box and then communicates his observations to a second observer. The issue here is, does the wave function "collapse" when the first observer opens the box, or only when the second observer is informed of the first observer's observations?

In another extension, prominent physicists have gone so far as to suggest that astronomers observing dark energy
Dark energy
In physical cosmology, astronomy and celestial mechanics, dark energy is a hypothetical form of energy that permeates all of space and tends to accelerate the expansion of the universe. Dark energy is the most accepted theory to explain recent observations that the universe appears to be expanding...

 in the universe in 1998 may have "reduced its life expectancy" through a pseudo-Schrödinger's Cat scenario, although this is a controversial viewpoint.

External links