Schrödinger's cat

Quantum mechanics
\Delta x\, \Delta p \ge \frac{\hbar}{2}
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Delayed choice quantum eraser
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Wheeler's delayed choice

Schrödinger's cat is a thought experiment, usually described as a paradox, devised by Austrian physicist Erwin Schrödinger in 1935. It illustrates what he saw as the problem of the Copenhagen interpretation of quantum mechanics applied to everyday objects. The scenario presents a cat that might be alive or dead, depending on an earlier random 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. In the course of developing this experiment, Schrödinger coined the term Verschränkung (entanglement).

Contents

Origin and motivation

Schrödinger intended his thought experiment as a discussion of the EPR article—named after its authors Einstein, Podolsky, and Rosen—in 1935.[1] The EPR article highlighted the strange nature of quantum entanglement, 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 keg of gunpowder will, after a while, contain a superposition 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.[2] The thought experiment illustrates the counterintuitiveness of quantum mechanics and the mathematics necessary to describe quantum states. Intended as a critique of just the Copenhagen interpretation (the prevailing orthodoxy in 1935), the Schrödinger cat thought experiment remains a typical touchstone 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:

One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, along with the following device (which must be secured against direct interference by the cat): in a Geiger counter, there is a tiny bit of radioactive substance, so small that perhaps in the course of the hour, one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges, and through a relay releases a hammer that shatters a small flask of hydrocyanic acid. If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The psi-function of the entire system would express this by having in it the living and dead cat (pardon the expression) mixed or smeared out in equal parts. It is typical of these cases that an indeterminacy originally restricted to the atomic domain becomes transformed into macroscopic indeterminacy, which can then be resolved by direct observation. That prevents us from so naively accepting as valid a "blurred model" for representing reality. In itself, it would not embody anything unclear or contradictory. There is a difference between a shaky or out-of-focus photograph and a snapshot of clouds and fog banks.[3]

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.[2]

Schrödinger's famous thought experiment poses the question, when does a quantum system stop existing as a superposition 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:

You are the only contemporary physicist, besides Laue, who sees that one cannot get around the assumption of reality, if only one is honest. Most of them simply do not see what sort of risky game they are playing with reality—reality as something independent of what is experimentally established. Their interpretation is, however, refuted most elegantly by your system of radioactive atom + amplifier + charge of gunpowder + cat in a box, in which the psi-function of the system contains both the cat alive and blown to bits. Nobody really doubts that the presence or absence of the cat is something independent of the act of observation.[4]

Note that no charge of gunpowder is mentioned in Schrödinger's setup, which uses a Geiger counter as an amplifier 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 whether) they collapse.

Copenhagen interpretation

Main article: Copenhagen interpretation

The most commonly held interpretation of quantum mechanics is the Copenhagen interpretation.[5] 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, 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, 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.[6] 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.[7] 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

Main article: Many-worlds interpretation

In 1957, Hugh Everett 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 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 with the cat so that the "observation of the cat's state" and the "cat's state" correspond with each other. Quantum decoherence 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. Only the "dead cat" or "alive cat" can be a part of a consistent history in this interpretation.

Roger Penrose criticises this:

"I wish to make it clear that, as it stands, this is far from a resolution of the cat paradox. For there is nothing in the formalism of quantum mechanics that demands that a state of consciousness cannot involve the simultaneous perception of a live and a dead cat",[8]

Although the mainstream view (without necessarily endorsing many-worlds) is that decoherence is the mechanism that forbids such simultaneous perception.[9][10]

A variant of the Schrödinger's Cat experiment, known as the quantum suicide machine, has been proposed by cosmologist Max Tegmark. 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 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 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, 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.[11] 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, mass, temperature, irreversibility, 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.[12] 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.

In quantum computing the phrase "cat state" often refers to the special entanglement of qubits wherein the qubits are in an equal superposition of all being 0 and all being 1; i.e.,

| \psi \rangle = \frac{1}{\sqrt{2}} \bigg( | 00...0 \rangle %2B |11...1 \rangle \bigg) .

Extensions

Wigner's friend 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 in the universe in 1998 may have "reduced its life expectancy" through a pseudo-Schrödinger's Cat scenario, although this is a controversial viewpoint.[18][19]

In popular culture

Main article: Schrödinger's cat in popular culture

See also

References

  1. ^ EPR article: Can Quantum-Mechanical Description Reality Be Considered Complete?
  2. ^ a b Schrödinger, Erwin (November 1935). "Die gegenwärtige Situation in der Quantenmechanik (The present situation in quantum mechanics)". Naturwissenschaften. 
  3. ^ Schroedinger: "The Present Situation in Quantum Mechanics"
  4. ^ Pay link to Einstein letter
  5. ^ Hermann Wimmel (1992). Quantum physics & observed reality: a critical interpretation of quantum mechanics. World Scientific. p. 2. ISBN 9789810210106. http://books.google.com/books?id=-4sJ_fgyZJEC&pg=PA2. Retrieved 9 May 2011. 
  6. ^ Faye, J (2008-01-24). "Copenhagen Interpretation of Quantum Mechanics". Stanford Encyclopedia of Philosophy. The Metaphysics Research Lab Center for the Study of Language and Information, Stanford University. http://plato.stanford.edu/entries/qm-copenhagen/. Retrieved 2010-09-19. 
  7. ^ Carpenter RHS, Anderson AJ (2006). "The death of Schroedinger's Cat and of consciousness-based wave-function collapse". Annales de la Fondation Louis de Broglie 31 (1): 45–52. Archived from the original on 2006-11-30. http://web.archive.org/web/20061130173850/http://www.ensmp.fr/aflb/AFLB-311/aflb311m387.pdf. Retrieved 2010-09-10. 
  8. ^ Penrose, R. The Road to Reality, p 807.
  9. ^ Wojciech H. Zurek, Decoherence, einselection, and the quantum origins of the classical, Reviews of Modern Physics 2003, 75, 715 or [1]
  10. ^ Wojciech H. Zurek, "Decoherence and the transition from quantum to classical", Physics Today, 44, pp 36–44 (1991)
  11. ^ Rovelli, Carlo (1996). "Relational Quantum Mechanics". International Journal of Theoretical Physics 35: 1637–1678. arXiv:quant-ph/9609002. Bibcode 1996IJTP...35.1637R. doi:10.1007/BF02302261. 
  12. ^ What is the World's Biggest Schrodinger Cat?
  13. ^ Schr%C%B6dingers Cat Now Made of Light
  14. ^ C. Monroe, et. al. A “Schrodinger Cat” Superposition State of an Atom
  15. ^ Physics World: Schrodinger's cat comes into view
  16. ^ Scientific American : Macro-Weirdness: "Quantum Microphone" Puts Naked-Eye Object in 2 Places at Once: A new device tests the limits of Schrödinger's cat
  17. ^ How to Create Quantum Superpositions of Living Things>
  18. ^ Chown, Marcus (2007-11-22). "Has observing the universe hastened its end?". New Scientist. http://www.newscientist.com/channel/fundamentals/mg19626313.800-has-observing-the-universe-hastened-its-end.html. Retrieved 2007-11-25. 
  19. ^ Krauss, Lawrence M.; James Dent (April 30, 2008). "Late Time Behavior of False Vacuum Decay: Possible Implications for Cosmology and Metastable Inflating States". Phys. Rev. Lett. (US: APS) 100 (17). arXiv:0711.1821. Bibcode 2008PhRvL.100q1301K. doi:10.1103/PhysRevLett.100.171301. 

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