Schrödinger's cat

Schrödinger's cat: a cat, a flask of poison, and a radioactive source are placed in a sealed box. If an internal monitor detects radioactivity (i.e., a single atom decaying), the flask is shattered, releasing the poison that kills the cat. The Copenhagen interpretation of quantum mechanics implies that after a while, the cat is simultaneously alive and dead. Yet, when one looks in the box, one sees the cat either alive or dead, not both alive and dead. This poses the question of when exactly quantum superposition ends and reality collapses into one possibility or the other.

Schrödinger's cat is a thought experiment, sometimes described as a paradox, devised by Austrian physicist Erwin Schrödinger in 1935.^[1] 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 may be simultaneously both alive and dead,^{[2][3][4][5][6][7][8]} a state known as a quantum superposition, as a result of being linked to a random subatomic event that may or may not occur. The thought experiment is also often featured in theoretical discussions of the interpretations of quantum mechanics. Schrödinger coined the term Verschränkung (entanglement) in the course of developing the thought experiment.

Origin and motivation

Real-size cat figure in the garden of Huttenstrasse 9, Zurich, where Erwin Schrödinger lived 1921–1926. Depending on the light conditions, the cat appears either alive or dead.

Schrödinger intended his thought experiment as a discussion of the EPR article—named after its authors Einstein, Podolsky, and Rosen—in 1935.^[9] The EPR article highlighted the strange nature of quantum superpositions, in which a quantum system such as an atom or photon can exist as a combination of multiple states corresponding to different possible outcomes. The prevailing theory, called the Copenhagen interpretation, said that a quantum system remained in this superposition until it interacted with, or was observed by, the external world, at which time the superposition collapses into one or another of the possible definite states. The EPR experiment showed that a system with multiple particles separated by large distances could be in such a superposition. 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, Schrödinger described how one could, in principle, create a superposition in a large-scale system by making it dependent on a quantum particle that was in a superposition. He proposed a scenario with a cat in a locked steel chamber, wherein the cat's life or death depended on the state of a radioactive atom, whether it had decayed and emitted radiation or not. According to Schrödinger, the Copenhagen interpretation implies that the cat remains both alive and dead until the state is observed. Schrödinger did not wish to promote the idea of dead-and-alive cats as a serious possibility; on the contrary, he intended the example to illustrate the absurdity of the existing view of quantum mechanics.^[1] However, since Schrödinger's time, other interpretations of the mathematics of quantum mechanics have been advanced by physicists, some of which regard the "alive and dead" cat superposition as quite real. Intended as a critique of the Copenhagen interpretation (the prevailing orthodoxy in 1935), the Schrödinger's cat thought experiment remains a defining touchstone for modern 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.

Thought experiment

Schrödinger wrote:^[1][10]

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 first atomic decay would have poisoned it. 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.

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 begin 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 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.^[11]

Note that the charge of gunpowder is not 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 Einstein 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

The most commonly held interpretation of quantum mechanics is the Copenhagen interpretation.^[12] 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 thought 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.^[13] 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,^[14] although the validity of their design is disputed.^[15] The view that the "observation" is taken when a particle from the nucleus hits the detector can be developed into objective collapse theories. The thought experiment requires an "unconscious observation" by the detector in order for magnification to occur. In contrast, the many worlds approach denies that collapse ever occurs.

Many-worlds interpretation and consistent histories

The quantum-mechanical "Schrödinger's cat" paradox according to the many-worlds interpretation. In this interpretation, every event is a branch point. The cat is both alive and dead—regardless of whether the box is opened—but the "alive" and "dead" cats are in different branches of the universe that are equally real but cannot interact with each other.

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 possibly-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 the "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.^[16]

However, the mainstream view (without necessarily endorsing many-worlds) is that decoherence is the mechanism that forbids such simultaneous perception.^[17][18]

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 matter, or a 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.^[19] 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 its 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. This process, known as "decoherence", is among the fastest processes currently known to physics.^[20]

Applications and tests

Schrödinger's cat quantum superposition of states and effect of the environment through decoherence

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, e.g. superpositions of relatively large (by the standards of quantum physics) objects have been performed.^[21] 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.

• A "cat state" has been achieved with photons.^[22]
• A beryllium ion has been trapped in a superposed state.^[23]
• An experiment involving a superconducting quantum interference device ("SQUID") has been linked to the 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."^[24]
• A piezoelectric "tuning fork" has been constructed, which can be placed into a superposition of vibrating and non vibrating states. The resonator comprises about 10 trillion atoms.^[25]
• An experiment involving a flu virus has been proposed.^[26]
• An experiment involving a bacterium and an electromechanical oscillator has been proposed.^[27]

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; e.g.,

$|\psi \rangle ={\frac {1}{\sqrt {2}}}{\bigg (}|00\ldots 0\rangle +|11\ldots 1\rangle {\bigg )}.$

• Researchers at the Stanford PULSE Institute and the Department of Energy’s SLAC National Accelerator Laboratory have exploited this Schroedinger’s Cat behavior to create X-ray movies of atomic motion with much more detail than ever before. ^{[28] [29]}

Extensions

Wigner's friend is a variant on the experiment with two human observers: the first makes an observation on whether a flash of light is seen and then communicates his observation to a second observer. The issue here is, does the wave function "collapse" when the first observer looks at the experiment, 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.^[30][31]

See also

• Basis function
• Complementarity (physics)
• Consensus reality
• Double-slit experiment
• Elitzur–Vaidman bomb tester
• Half-life
• Heisenberg cut
• Interpretations of quantum mechanics
• Leggett–Garg inequality
• Maxwell's Demon
• Measurement problem
• Micro black hole
• Modal realism
• Observer (quantum physics)
• Observer effect (physics)
• Quantum Zeno effect
• Schroedinbug
• Schrödinger equation
• Schrödinger's cat in popular culture
• Wave function collapse
• Wigner's friend
• EPR Paradox

References

1. Schrödinger, Erwin (November 1935). "Die gegenwärtige Situation in der Quantenmechanik (The present situation in quantum mechanics)". Naturwissenschaften. 23 (48): 807–812. Bibcode:1935NW.....23..807S. doi:10.1007/BF01491891.
2. Moring, Gary (2001). The Complete Idiot's Guide to Theories of the Universe. Penguin. pp. 192–193. ISBN 1440695725.
3. Gribbin, John (2011). In Search of Schrodinger's Cat: Quantum Physics And Reality. Random House Publishing Group. p. 234. ISBN 0307790444.
4. Greenstein, George; Zajonc, Arthur (2006). The Quantum Challenge: Modern Research on the Foundations of Quantum Mechanics. Jones & Bartlett Learning. p. 186. ISBN 076372470X.
5. Tetlow, Philip (2012). Understanding Information and Computation: From Einstein to Web Science. Gower Publishing, Ltd. p. 321. ISBN 1409440400.
6. Herbert, Nick (2011). Quantum Reality: Beyond the New Physics. Knopf Doubleday Publishing Group. p. 150. ISBN 030780674X.
7. Charap, John M. (2002). Explaining The Universe. Universities Press. p. 99. ISBN 8173714673.
8. Polkinghorne, J. C. (1985). The Quantum World. Princeton University Press. p. 67. ISBN 0691023883.
9. Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47, 777 (1935)
10. "The Present Situation in Quantum Mechanics: A Translation of Schrödinger's 'Cat Paradox' Paper" by John D. Trimmer, Proceedings of the American Philosophical Society 124:5 (Oct. 10, 1980), 323-338, 328. , reproduced with some inaccuracies here: Schroedinger: "The Present Situation in Quantum Mechanics." 5. Are the Variables Really Blurred?
11. Pay link to Einstein letter
12. Hermann Wimmel (1992). Quantum physics & observed reality: a critical interpretation of quantum mechanics. World Scientific. p. 2. ISBN 978-981-02-1010-6. Retrieved 9 May 2011.
13. 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. Retrieved 2010-09-19.
14. Carpenter RHS, Anderson AJ (2006). "The death of Schroedinger's cat and of consciousness-based wave-function collapse" (PDF). Annales de la Fondation Louis de Broglie. 31 (1): 45–52. Archived from the original (PDF) on 2006-11-30. Retrieved 2010-09-10. External link in |journal= (help)
15. Okón E, Sebastián MA (2016). "How to Back up or Refute Quantum Theories of Consciousness". Mind and Matter. 14 (1): 25–49.
16. Penrose, R. The Road to Reality, p 807.
17. Wojciech H. Zurek, Decoherence, einselection, and the quantum origins of the classical, Reviews of Modern Physics 2003, 75, 715 or
18. Wojciech H. Zurek, "Decoherence and the transition from quantum to classical", Physics Today, 44, pp. 36–44 (1991)
19. Rovelli, Carlo (1996). "Relational Quantum Mechanics". International Journal of Theoretical Physics. 35 (8): 1637–1678. arXiv:quant-ph/9609002. Bibcode:1996IJTP...35.1637R. doi:10.1007/BF02302261.
20. Roland Omnès (1999). Quantum Philosophy.
21. What is the World's Biggest Schrödinger Cat?
22. Schrödingers Cat Now Made of Light
23. C. Monroe, et al. A "Schrödinger Cat" Superposition State of an Atom
24. Physics World: Schrödinger's cat comes into view
25. 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
26. How to Create Quantum Superpositions of Living Things
27. Could 'Schrödinger's bacterium' be placed in a quantum superposition?>
28. Glownia, J.M; Natan, A; Cryan, J.P; Hartsock, R (October 2016). "Self-Referenced Coherent Diffraction X-Ray Movie of Ångstrom- and Femtosecond-Scale Atomic Motion". Physical Review of Letters. doi:10.1103/physrevlett.117.153003. PMID 27768351.
29. 'Schroedinger's Cat' Molecules Give Rise to Exquisitely Detailed Movies>
30. Chown, Marcus (2007-11-22). "Has observing the universe hastened its end?". New Scientist. Retrieved 2007-11-25.
31. 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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More spoken articles

• Erwin Schrödinger (1935) The Present Situation in Quantum Mechanics (translation of 3-part Schrödinger, Erwin (November 1935). "Die gegenwärtige Situation in der Quantenmechanik (The present situation in quantum mechanics)". Naturwissenschaften. 23 (48): 823807–828812. Bibcode:1935NW.....23..807S. doi:10.1007/BF014918914. and pp. 823–828, 844–849) Schrödinger's cat paper
• A. Einstein, B. Podolsky, N. Rosen (1935) Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?, Physical Review, Vol. 47, p. 777. The EPR paper
• Phillip Yam (October 10, 2012) Bringing Schrödinger's Cat to Life, Scientific American. Describes investigations of quantum "cat states" and wavefunction collapse by Serge Haroche and David J. Wineland for which they won the 2012 Nobel Prize in Physics
• Tony Leggett (August 2000) New Life for Schrödinger's Cat, Physics World, p. 23-24. Article on experiments with "cat state" superpositions in superconducting rings, in which the electrons go around the ring in two directions simultaneously.
• Information Philosopher on Schrödinger's cat More diagrams and an information creation explanation.
• Poliakoff, Martyn (2009). "Schrödinger's Cat". Sixty Symbols. Brady Haran for the University of Nottingham.
• Schrödinger's cat in audio produced by Sift
• J.Foukzon, A.A.Potapov, S.A.Podosenov SCHRODINGER'S CAT PARADOX RESOLUTION USING GRW COLLAPSE MODEL,International Journal of Recent advances in Physics (IJRAP) Vol.3, No.3, August 2014.