8.1 Schrö­din­ger’s Cat

Schrö­din­ger, ap­par­ently not an an­i­mal lover, came up with an ex­am­ple il­lus­trat­ing what the con­cep­tual dif­fi­cul­ties of quan­tum me­chan­ics re­ally mean in every­day terms. This sec­tion de­scribes the ex­am­ple.

A cat is placed in a closed box. Also in the box is a Geiger counter and a tiny amount of ra­dioac­tive ma­te­r­ial that will cause the Geiger counter to go off in a typ­i­cal time of an hour. The Geiger counter has been rigged so that if it goes off, it re­leases a poi­son that kills the cat.

Now the de­cay of the ra­dioac­tive ma­te­r­ial is a quan­tum-me­chan­i­cal process; the dif­fer­ent times for it to trig­ger the Geiger counter each have their own prob­a­bil­ity. Ac­cord­ing to the or­tho­dox in­ter­pre­ta­tion, mea­sure­ment is needed to fix a sin­gle trig­ger time. If the box is left closed to pre­vent mea­sure­ment, then at any given time, there is only a prob­a­bil­ity of the Geiger counter hav­ing been trig­gered. The cat is then alive, and also dead, each with a nonzero prob­a­bil­ity.

Of course no rea­son­able per­son is go­ing to be­lieve that she is look­ing at a box with a cat in it that is both dead and alive. The prob­lem is ob­vi­ously with what is to be called a mea­sure­ment or ob­ser­va­tion. The count­less tril­lions of air mol­e­cules are hardly go­ing to miss ob­serv­ing that they no longer en­ter the cat's nose. The bi­o­log­i­cal ma­chin­ery in the cat is not go­ing to miss ob­serv­ing that the blood is no longer cir­cu­lat­ing. More di­rectly, the Geiger counter is not go­ing to miss ob­serv­ing that a de­cay has oc­curred; it is re­leas­ing the poi­son, isn't it?

If you pos­tu­late that the Geiger counter is in this case do­ing the “mea­sure­ment“ that the or­tho­dox in­ter­pre­ta­tion so de­vi­ously leaves un­de­fined, it agrees with our com­mon sense. But of course, this Deus ex Machina only rephrases our com­mon sense; it pro­vides no ex­pla­na­tion why the Geiger counter would cause quan­tum me­chan­ics to ap­par­ently ter­mi­nate its nor­mal evo­lu­tion, no proof or plau­si­ble rea­son that the Geiger counter is able to fun­da­men­tally change the nor­mal evo­lu­tion of the wave func­tion, and not even a shred of hard ev­i­dence that it ter­mi­nates the evo­lu­tion, if the box is truly closed.

There is a strange con­clu­sion to this story. The en­tire point Schrö­din­ger was try­ing to make was that no sane per­son is go­ing to be­lieve that a cat can be both dead and kick­ing around alive at the same time. But when the equa­tions of quan­tum me­chan­ics are ex­am­ined more closely, it is found that they re­quire ex­actly that. The wave func­tion evolves into de­scrib­ing a se­ries of dif­fer­ent re­al­i­ties. In our own re­al­ity, the cat dies at a spe­cific, ap­par­ently ran­dom time, just as com­mon sense tells us. Re­gard­less whether the box is open or not. But, as dis­cussed fur­ther in sec­tion 8.6, the math­e­mat­ics of quan­tum me­chan­ics ex­tends be­yond our re­al­ity. Other re­al­i­ties de­velop, which we hu­mans are ut­terly un­able to ob­serve, and in each of those other re­al­i­ties, the cat dies at a dif­fer­ent time.