Scho Dingers Cat and the Law

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Schrödinger’s Cat and the Law

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This essay and the story it contains are inspired by the all-to-common abuse ofSchrödinger’s cat by treating her as if “live cat/dead a quantum states” weresensible concepts.

A cat is not like an isolated electron or even a macroscopic chunk ofsuperconductor. A cat continuously interacts with its environment, even if thatenvironment is confined to a sealed box; it’s not in a ‘live’ quantum state. Itsinteractions – breathing, eating, urinating, etc. -- define ‘live’. A dead cat is alsointeracting with its environment – cooling, decaying, etc. Both dead and live catsinteract irreversibly with their environment causing the entropy of the sealed,isolated box to rise and causing any quantum state that may have existed todecoher rapidly.

The absurdity of Schrödinger’ cat has been pointed out before ( e.g ., by Carpenterand Anderson a). The following parable - ‘Schrödinger’s Cat and the Law’ - isintended to illustrate this absurdity vividly and simply.

The Parable of Schrödinger’s Cat and the Law

It is little-known fact that Schrödinger had a cat. He loved his cat Flaumig somuch that he left her his considerable fortune in his will. The will also provided

that in the event Flaumig predeceased Schrödinger the fortune would revert toCERN theorist John Ellis (see figure 1A). Flaumig, as it turned out, loved Einsteinor, at least, his sweater (see figure 1B), and left him her estate should she haveone.

When Schrödinger conceived his cat experiment, he decided actually to performit. Flaumig was the only cat he had access to and as much as he loved her, heloved physics more, so decided to use her in the experiment.

Schrödinger built a lethal apparatus, to be placed the sealed box, designed sothat the probability of the cat being dead would be 50% one hour into theexperiment.

a Carpenter RHS, Anderson AJ (2006). "The death of Schrodinger’s cat and of consciousness-based wave-functioncollapse" (PDF). Annales de la Foundation Louis de Broglie 31 (1): 45–52.


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The device consisted of the long-lived radioactive, source Polonium-210 (seetable 1) with its quantity adjusted so that the probability of at least one decayoccurring in an hour was 1/2. The source was sealed in a container made of

plastic scintillator which produces a flash of light when transited by an

particle produced by the radioactive decays of the source. The scintillator wassurrounded by phototubes arranged to detect the scintillation light with highefficiency and wired to trigger a hammer to break a container of hydrogencyanide gas, releasing the gas and rapidly killing the cat i .

Schrödinger put his cat Flaumig in the box, closed it, sealed it, and started atimer. Things were thus arranged so that according to Bohr’s Copenhageninterpretation the “live cat” and “dead cat” states would have equal amplitudes

at one hour. See figure 2.

Schrödinger, thinking about what was happening to Flaumig, becameincreasingly agitated as the time ticked by. He regretted using her in theexperiment.

At one hour he started reaching to open to box and to pull her out and preventher from becoming completely dead when the stress triggered a heart attack,and he died. The timer was knocked on the floor by his fall, and stopped, but thesealed box was unperturbed.

The disposition of the will, of course, ended up in court.

John Ellis’ lawyers called quantum physicists (e.g., John Wheeler, Niels Bohr) asexpert witnesses who testified that as Schrödinger had not succeeded inobserving the cat before he expired, the cat was at that point half dead and halfalive. His lawyers argued concludenter donatio mortis causa that theinheritance should be shared equally. His lawyers far from understanding thearguments of their experts did not wish to risk entirely losing their contingency

fees and, thus, their argument was more an effort at compromise rather thanone of trying to get at the truth.

Einstein employed the forensic pathologist Michael Baden as his expert. Badenmeasured the oxygen left in the conveniently sealed box and determined that


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the cat died 23 minutes after Schrödinger and was thus wealthy at the time ofher death.

The Judge Phyllida Erskine-Brown ruled in Einstein’s favor as she hadn’t been

able to make sense of anything said by the physicists!

This fable illustrates just how silly most discussions of Schrödinger’s cat are. They assume that a live-cat/dead-cat superposition is a sensible conceptand completely fail to appreciate Schrödinger’s original intention of mocking theCopenhagen interpretation b.

The ‘information’ interpretation c based on John Von Neumann’s mathematicalformulation of quantum measurement d provides a straightforward view of whathappens. In the information interpretation the collapse of the ‘wave function’ isprecipitated by the first thermodynamically irreversible event, e.g ., a scintillationflash produced by a particle hitting a piece of scintillator. There is no need to waitfor, say, Lord Rutherford e, to observe the flash or look at the cat. Von Neumann’smath shows the results to be the same whether one takes the measurement tocorrespond to the first irreversible interaction or waits for a conscious ‘observer’to see it. The ‘conscious observer’ is not needed.

The irreversible event (scintillation) causes an increase in information, i.e ., thetime scintillation flash occurs, and the cyanide bottle breaks has been, in effect,‘recorded’.

Neither the ‘wave function’ nor its confusing ‘collapse’ everywhere are neededeither. I find it simpler to think of it, in the manner of Feynman f , as the amplitudefor the particle to be measured at a given location and/or time. The probability of

a specified measurement is given by the absolute value of the amplitude ( )

b https://en.wikipedia.org/wiki/Schr%C3%B6dinger%27s_cat#Origin_and_motivation c http://www.informationphilosopher.com/introduction/physics/interpretation d Mathematical Foundations of Quantum Mechanics , Beyer, R. T., trans., Princeton Univ. Press. 1996 edition: ISBN0-691-02893-1e E. Rutherford, The Scattering of α and β Particles by Matter and the Structure of the Atom , PhilosophicalMagazine. Series 6, vol. 21 . May 1911f Feynman, R. P. and Hibbs, A. R. (1965). Quantum Mechanics and Path Integrals. New York: McGraw-Hill. ISBN 0-07-020650-3


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squared ( Prob= | | 2). Feynman’s view might by summarized by Wittgenstein’sdictum g “Whereof one cannot speak, thereof one must be silent.”

As they predict the same results, other interpretations don’t need to be

abandoned along with silly interpretations of Schrödinger’s cat. Everett’s “ManyWorlds” interpretation h is still viable though at some considerable cost. Instead oftwo worlds with a dead and live cat, there needs to be a world for eachdistinguishable possible time of death. It’s unclear to me whether this is a finite,infinite or even an unaccountably infinite i number of worlds; in any case, it’s a lot.“Many Worlds” is complicated and might be rejected based on Occam’s razor j.

However, complexity and simplicity are in the eye of the beholder. Whether ornot the need for two processes (propagation and measurement) is more complexthan a very large, possibly infinite, number of worlds is arguable.

The Feynman ‘path integral’ approach k seems simple and straight forward. Itdodges separate propagation phase as well as the ‘collapse of the wavefunction’by doing away the ‘wave-function’ and replacing it with the sum of theamplitudes along all possible paths between an initial state and a measurement ofa defined final state determined by irreversible (measurable) interactions. It givesup knowledge of exactly what happens in between (reality, if you insist) andexplicitly abandons determinism. The amplitude is just a device for calculating theprobabilities; there is no quasi-physical ‘wave function’ to collapse. Quantummechanical calculations yield only probabilities, and the world is explicitly,intrinsically random.

However, it’s hard to avoid ‘speaking’ about how the detector ‘knows’ not todetect a particle in more than one place; it would violate conservation laws (likeenergy and lepton number) to detect a particle twice, and it has, of course, never

g https://en.wikipedia.org/wiki/Tractatus_Logico-Philosophicush Everett, Hugh (1957). "Relative State Formulation of Quantum Mechanics" . Reviews of Modern Physics 29 : 454– 46 i Georg Cantor (1892). "Ueber eine elementare Frage der Mannigfaltigkeitslehre" (PDF). Jahresbericht derDeutschen Mathematiker-Vereinigung 1890–1891 1: 75–78 (84–87 in pdf file). (in german).

j https://en.wikipedia.org/wiki/Occam%27s_razork Feynman, R. P. (1948). "Space-Time Approach to Non-Relativistic Quantum Mechanics". "Reviews of ModernPhysics" 20 (2): 367–387


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been seen to happen. It seems like some kind of non-local ‘entanglement’ isneeded. Wittgenstein’s rule is hard to obey; Occam might not like it any morethan a little action at a distance.

However, Schrödinger’s cat is either dead or alivel

at any given time!

Figure 1 :(A): Theoretical physicist John Ellis; (B) Albert Einstein in hiscat beloved sweater

l Well ‘dead or alive ‘apart from strictly classical, biological/social/religious questions. Perhaps Flaumig is alive andwell on the ‘ rainbow bridge .’ See figure 3… and In many worlds interpretation the cat might be alive in some worlds and dead in others at various times, butwill be either dead or alive in our your world.


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Figure 2 : Cartoon of quantum cat experiment

Figure 3: Flaumig and friends ambling across the rainbow bridge. Given thenumber of cats dying all the time, the traffic seems light.


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Table 1: Poloniums-210 source properties

Description Activity Half-Life

Polonium-210

0.05, 0.1 & 1uCi 138 days

Primary Radiation Type Energies KeV

Alpha (α) 5304.5


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Scho Dingers Cat and the Law