Schrodinger: Difference between revisions

=== Schrodinger's Cat ===

While in Oxford, Schrodinger published four papers which have been very influential. These papers extended the debate on the appropriate interpretation of quantum mechanics.

The first of these papers was submitted to the Mathematical Proceedings of the Cambridge Philosophical Society on 14 August 1935. It was communicated by Max Born. "Communicated" refers to the process by which a scientific paper is submitted to a journal for publication by a third party, who is typically an established member of the academic community. Born acted as a mediator between the author of the paper and the journal. He would have reviewed the paper and deemed it appropriate for publication in the journal, and then submitted it on behalf of the author. In those days, to ensure the integrity of a paper submitted to a journal of a learned society, it needed to be communicated by a member of the society.

The paper, written in English, had the title "Discussion of Probability Relations between Separated Systems". It stated :

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When two systems, of which we know the states by their respective representatives, enter into temporary physical interaction due to known forces between them, and when after the time of mutual influence the systems separate again, they can no longer be described in the same way as before, viz, by endowing each of them with a representative of its own.

I would not call that "one", but rather "the" characteristic trait of quantum mechanics. The one that enforces its entire departure from classical lines of thought.

By the interaction, the two representatives (or ψ-functions) have become entangled. To disentangle them we must gather further information by experiment.

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This problem had become quite well known in quantum chemistry. When two electronic wave functions (orbitals) based on different atoms in a molecule which are placed quite far apart can still be mixed together if there is an interaction between them. The mixing becomes strongers if the two original states have similar energies, even if they are quite far apart in distance.

This paper has become highly cited in modern times as it is an early work discussing some of the principles behind quantum information processing and quantum computation. It also introduced the word "entangled" into quantum mechanics. The problem expressed in the final sentence above, with regards to disentangling the states in a practical experiment, remains one of the key challenges in quantum computation.

The paper referenced one published by Einstein, Podolsky and Rosen, in which it was argued that quantum mechancis provides an incomplete description of physical reality. That paper had considered two interacting particles. If the position of the first particle was measured, under the principles of quantum mechanics, the result of measuring the position of the second particle could be predicted. However, they claimed this was unsatisfactory as no action taken on the first particle could instantaneously influence the other particle, as information would then be transmitted faster than light.

Scrodinger then followed up his first paper on entanglement with a second one to the same journal entitled "Probability relations between separated systems". In this case, the paper was communicated to the Cambridge Philosophical Society by Paul Dirac. This paper develops the concept of mixtures of states that had been introduced by John von Neumann. The paper concludes by stating on mixed states that : "These conclusions, unavoidable within the present theory but repugnant to some physiscists including the author, are caused by applying non-relativistic quantum mechanics beyond its legitimate range".

The third paper from Schrodinger in Oxford was published on 29 November 1935 in Die Naturwissenschaften, the popular science journal whose editor had been Schrodinger's close friend, Arnold Berliner. In the paper, Schrodinger stated :

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A cat is penned in a steel chamber, along with a tiny bit of radioactive substance in a Geiger counter, which must be secured against direct interference by the cat. The radioactive substance is so small that perhaps in the course of the hour one of the atoms decay, but also, with equal probability, perhaps none of the atoms decay. If it decays, the counter tube discharges. Then, through a relay, it releases a hammer which 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 ψ-function of the entire system would express this by having in it the living and (pardon the expression) dead cat mixed or smeared out in equal parts.

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Because Schrodinger used the example of the life or death of a cat, it has caught the imagination of the public more than any other of his works to the present day. Accordingly, "Schrodinger's Cat states" is also a phrase used by physicists in connection with a microscopic quantum effect having an influence on a macroscopic phenomenon.