Schrödinger's cat

Schrödinger's cat is a seemingly paradoxical thought experiment devised by Erwin Schrödinger that attempts to illustrate the incompleteness of an early interpretation of quantum mechanics when going from subatomic to macroscopic systems. The experiment proposes:

''A cat is placed in a sealed box. Attached to the box is an apparatus containing a radioactive atomic nucleus and a canister of poison gas. This apparatus is separated from the cat in such a way that the cat can in no way interfere with it. The experiment is set up so that there is exactly a 50% chance of the nucleus decaying in one hour. If the nucleus decays, it will emit a particle that triggers the apparatus, which opens the canister and kills the cat. If the nucleus does not decay, then the cat remains alive. According to quantum mechanics, the unobserved nucleus is described as a superposition (meaning it exists partly as each simultaneously) of "decayed nucleus" and "undecayed nucleus". However, when the box is opened the experimenter sees only a "decayed nucleus/dead cat" or an "undecayed nucleus/living cat."

The question is: when does the system stop existing as a mixture of states and become one or the other? (See basis function.) The purpose of the experiment is to illustrate a paradox; as Schrödinger wrote,

"The href="http://articles.gourt.com/en/wavefunction">wavefunction for the entire system would the living and the dead cat (pardon the expression) [http://www.mtnmath.com/faq/meas-qm-3.html" target="_blank" >^* Because we cannot get along without making classical approximations, quantum mechanics is incomplete without some rules to relate the classical and quantum descriptions. One way of looking at this connection is to say that the wavefunction collapses and the cat becomes dead or remains alive instead of a mixture of both.

The point of view that this thought experiment most clearly refutes is that the laws of physics are different for experiments than for other interactions. In the case of the cat dying, a necropsy would show a time of death that would be before the opening of the box. The geiger counter, in moving to one outcome or the other, is, in effect, the "observer", the same as a human observing the outcome with senses.

The original article appeared in the German magazine Naturwissenschaften ("Natural Sciences") in 1935: E. Schrödinger: "Die gegenwärtige Situation in der Quantenmechanik" ("The present situation in quantum mechanics"), Naturwissenschaften, 48, 807, 49, 823, 50, 844 (November 1935). It was intended as a discussion of the EPR article published by Einstein, Podolsky and Rosen in the same year. Apart from introducing the cat, Schrödinger also coined the term "entanglement" (German: Verschränkung) in his article.

Albert Einstein was impressed; 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 gun powder + 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.

Nowadays, the mainstream view is that the thermodynamically irreversible triggering of the device acts as if it were an observation, in that the triggering apparatus generates decoherence that appears to "collapse" the wave function.

Copenhagen interpretation

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. Some interpret the experiment 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. More intuitively, some feel that the "observation" is taken when a particle from the nucleus hits the detector. Recent developments in quantum physics show that measurements of quantum phenomena taken by non-conscious "observers" (such as a wiretap) most definitely alter the quantum state of the phenomena from the point of view of conscious observers reading the wiretap, lending support to this idea.

A precise rule is that probability enters at the point where the classical approximation is first used to describe the system - almost by tautology, as the classical approximation is just a simplification of the quantum mathematics, and so must introduce imprecision in the measurement, which can be viewed as probability. Note, however, that this only applies to descriptions of the system, not the system itself.

Under Copenhagen, the amount of uncertainty for a complex quantum system is predicted by quantum decoherence. Particles which exchange photons (and possibly other atomic or subatomic particles) become entangled with each other from the point of view of an observer, meaning that these particles can only be described accurately with reference to each other, which decreases the total uncertainty of those particles from the point of view of our observer. By the time one has reached "macroscopic" levels - such as a cat, which is made up of a number of atomic particles almost too large to express with words - so many particles have become entangled with each other so as to decrease the uncertainty to almost zero. (Quantum effects in huge collections of particles are only seen in very rare, and often man-made, situations, such as a Bose-Einstein condensate). Thus, at least from the point of view of the observer, any improbability regarding the cat as a system of quantum particles has disappeared due to the massive amount of entanglement between all of the particles that make it up, meaning that the cat does not truly exist as both alive and dead at the same time, at least from the point of view of any observer viewing the cat.

It is interesting to note that even before observation was noted to be fundamentally distinct from consciousness through experimentation, the experiment always contained at least two "observers" - the physicist and the cat. Even had the physicist been unaware of the cat's state in the hypothetical experiment, one would have had to posit that the cat, at least, would have been quite sure of its status (at least, as long as the gas had not yet ended its ability to "observe"). However, since "observation" has been shown by experiment to have nothing to do with consciousness - or at the very least, any traditional definition of consciousness - most conjecture along these lines probably falls under the "interesting but physically irrelevant" category.

Steven Weinberg in "Einstein's Mistakes", Physics Today, November 2005, page 31, said:

All this familiar story is true, but it leaves out an irony. Bohr's version of quantum mechanics was deeply flawed, but not for the reason Einstein thought. The Copenhagen interpretation describes what happens when an observer makes a measurement, but the observer and the act of measurement are themselves treated classically. This is surely wrong: Physicists and their apparatus must be governed by the same quantum mechanical rules that govern everything else in the universe. But these rules are expressed in terms of a wavefunction (or, more precisely, a state vector) that evolves in a perfectly deterministic way. So where do the probabilistic rules of the Copenhagen interpretation come from?

Considerable progress has been made in recent years toward the resolution of the problem, which I cannot go into here. It is enough to say that neither Bohr nor Einstein had focused on the real problem with quantum mechanics. The Copenhagen rules clearly work, so they have to be accepted. But this leaves the task of explaining them by applying the deterministic equation for the evolution of the wavefunction, the Schrödinger equation, to observers and their apparatus.

Everett many-worlds interpretation & consistent histories

In the many-worlds interpretation of quantum mechanics, which does not single out observation as a special process, both states persist, but decoherent from each other. When an observer opens the box, he becomes entangled with the cat, so observer-states corresponding to the cat being alive and dead are formed, and each can have no interaction with the 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.

In other words, when the box is opened, the universe (or at least the part of the universe containing the observer and cat) is split into two separate universes, one containing an observer looking at a box with a dead cat, one containing an observer looking at a box with a live cat.

Practical applications

The experiment is a purely theoretical one, and the machine proposed does not exist.

This has some practical use in quantum computing and quantum cryptography. It is possible to send light that is in a superposition of states down a fiber optic cable. Placing a wiretap in the middle of the cable which intercepts and retransmits the transmission will collapse the wavefunction (in the Copenhagen interpretation, "perform an observation") and cause the light to fall into one state or another. By performing statistical tests on the light received at the other end of the cable, one can tell whether it remains in the superposition of states or has already been observed and retransmitted. In principle, this allows the development of communication systems that cannot be tapped without the tap being noticed at the other end. This experiment (which can be performed, although a workable quantum cryptographic communications system which can transmit large quantities of data has not yet been constructed) also illustrates that "observation" in the Copenhagen interpretation has nothing to do with consciousness, in that a perfectly unconscious wiretap will cause the statistics at the end of the wire to be different.

In quantum computing, the phrase "cat state" often refers to the special entanglement of qubits where the qubits are in an equal superposition of all being 0 and all being 1, i.e. $|00...0\rangle$ + $|11...1\rangle$ .

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 this may be able to distinguish between the Copenhagen interpretation and many worlds. Another variant on the experiment is Wigner's friend.

Physicist Stephen Hawking once exclaimed, "When I hear of Schrödinger's cat, I reach for my gun," paraphrasing German playwright and Nazi "Poet Laureate", Hanns Johst's famous phrase "Wenn ich 'Kultur' höre, entsichere ich meinen Browning!" ("When I hear the word 'culture', I release the safety on my Browning!")

In fact, Hawking and many other physicists are of the opinion that the "Copenhagen School" interpretation of quantum mechanics unduly stresses the role of the observer. A final consensus on this point among physicists seems still to be out of reach.

Related humor

Curiosity may have killed the cat, Schrödinger only killed half of it.

Many pet cats have been named "Schrödinger" as an allusion to Schrödinger's thought experiment.

In 1982 Cecil Adams, in his column The Straight Dope, wrote a concise and humourous description of the thought experiment, and Einstein's refutation of same, in the form of an epic poem. "The story of Schroedinger's cat (an epic poem)" ^*

"Schrödinger's Cat" is a novel by Robert Anton Wilson in which the Many-Worlds Interpretation is explored. Wilson refers to this model as the "Everett-Wheeler-Graham Model (after its postulators)". In his DVD biography entitled "Maybe Logic", Wilson suggests that our general misconceptions and confusion about quantum mechanics may stem from the use of logical constructs that are inadequate for describing the universe. See General Semantics.

The term "Schrödinger's Terrorist" has been used to semi-humorously label terrorists whose status as living or dead is unknown and/or subject to contradictory rumors such as Osama bin Laden.

A "Schrödinger's Date" is a meeting between two people that may or may not be a date, and whose status cannot be determined. Only the odds of it being one or the other can be estimated.

Novelist Douglas Adams posits an amusing anecdote in his novel Dirk Gently's Holistic Detective Agency, wherein Schrödinger's cat is neither alive nor dead when the box is opened, and is, in fact, not there. It is later revealed that the cat simply became bored with the experiment and wandered off. They should have used a rat. A rat indeed obediently stays put until the cat shows up.

The manga version of Hellsing features a catboy character named Schrödinger, who has the ability to be "everywhere and nowhere" at once. He is killed in one chapter, only to return unscathed and with no explanation shortly after.

There's also the mock headline "Schrödinger's cat found half-alive: quantum theory a mistake!"

From the syndicated comic strip, "Brewster Rockit": "Schrödinger's cat-litter box. If you don't observe it, you won't have to change it."

In Stargate SG-1, Carter gives a friend from a race of highly advanced physicists a tabby cat called Schrödinger as a gesture of good will.

In in the pilot episode of Sliders, Quinn has a pet cat named Schrödinger.

In the NetHack computer game, one occasionally finds a quantum mechanic with a box containing a cat named "Schrödinger's Cat". It is dead in half of the instances.

Schrödinger's Fridge, from the comic Bob the Angry Flower.

In The Last Hero by Terry Pratchett, Albert tries to explain the Schrödinger's Cat experiment to Death, who doesn't quite grasp the concept of not knowing if something is alive or dead. Death finally gives up the experiment, remarking, "I don't hold with cruelty to cats." Also, in Lords and Ladies, Pratchett describes the results of the experiment in three possible states: "Alive", "Dead", and "Bloody Furious."

Tears for Fears Track on their Saturnine Martial & Lunatic Album is called Schrödinger's cat.

The online retailer ThinkGeek sells a t-shirt that has the words "Schrödinger's cat is dead" on the front and "Schrödinger's Cat is not dead" on the back.

Cartoon: You see a picture of a refrigerator with a post-it-note saying "I'm out of town for a few days. Please be so nice and feed my cat. Thanks. Schrödinger".

External links

Thought experiments | Physical paradoxes | Quantum measurement

Gourt Home::Gourt :: Schrödinger's cat

Copenhagen interpretation

Everett many-worlds interpretation & consistent histories

Practical applications

Related humor

See also

External links