View Full Version : Schrödinger's cat and quantum entanglement.

04-07-2011, 08:01 AM
This digs heavily into whether or not reality is even real itself. Both deep scientific and religious principles are involved.

Best discussed IMHO among a few reasonably bright to genius level people ... and a buzz doesn't hurt things at all.

A bit long, but it includes the needed background on the history and science behind it:

<div class="ubbcode-block"><div class="ubbcode-header">Quote:</div><div class="ubbcode-body">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 thought experiment presents a cat that might be alive or dead, depending on an earlier random event. In the course of developing this experiment, he coined the term Verschränkung (entanglement).

Schrödinger's thought experiment was intended as a discussion of the EPR article, named after its authors—Einstein, Podolsky, and Rosen—in 1935.[1] The EPR article had 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. <span style='font-size: 11pt'>The Copenhagen interpretation implies that the state of the two systems undergoes collapse into a definite state when one of the systems is measured.</span>

Schrödinger and Einstein had exchanged letters about Einstein's EPR article, in the course of which Einstein had pointed out that the state of an unstable keg of gunpowder will, after a while, contain a superposition of both exploded and unexploded states.

<span style='font-size: 11pt'>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</span> 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 was dependent 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.

<span style='font-size: 11pt'>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 serves to illustrate the bizarreness of quantum mechanics and the mathematics necessary to describe quantum states.</span> Intended as a critique of just the Copenhagen interpretation (the prevailing orthodoxy in 1935), the Schrödinger cat thought experiment remains a topical touchstone for all interpretations of quantum mechanics. How each interpretation deals with Schrödinger's cat is often used as a way of illustrating and comparing each interpretation's particular features, strengths, and weaknesses.

The thought experiment

Schrödinger wrote:

<span style='font-size: 14pt'>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]</span>

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 purpose of the thought experiment is to illustrate 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:

<span style='font-size: 14pt'>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]</span>

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.

In the Copenhagen interpretation of quantum mechanics, 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.<span style='font-size: 14pt'> 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.</span></div></div>