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Appendix 12 THE SURREALISM OF SUPERPOSITIONS OF STATES: THE CASE OF SCHRÖDINGER’S CAT The surrealistic nature of superpositions of states is revealed when a system is suspended in a superposition of contradictory states. For example, the solution of Schrödinger’s equation for a free particle can be expressed as a superposition of states in which the particle is moving along an axis in two ways, both to the right ψ(→), and to the left, ψ(←). In this composite state, momentum has no definite value. If you speak out of both sides of your mouth, you say nothing. If you move in opposite directions at the same time, you go nowhere. Thus, there is no motion and such a state could be adequately termed a Parmenidian state. In the same way, the traditional notions of motion lose their meaning, when an unobserved particle is nowhere because it can be everywhere. If you are both here and there, you are nowhere. If you take all possible paths at the same time, you take no definite path at any time. In a superposition of states, no definite properties. Thus, when the concept is applied to ordinary things, paradoxical situations arise. To illustrate this point, Schrödinger invented what is now called the Paradox of Schrödinger’s Cat. In Schrödinger’s paradox a live cat is locked up in a box with a bottle containing a deadly poison and an atom of a radioactive element. When the atom decays, the bottle breaks, the poison is released, and the cat dies. As long as the atom does not decay, the cat lives. The decay process of a radioactive element is a random event— a quantum process—that is characterized by its half-life. After the half-life of an atom, the probability is ½ that it has decayed, and ½ that it has not yet decayed. Thus, after a time corresponding to the half-life of the radioactive element in the box with the cat, the probability is ½ that the cat is dead, and ½ that it is alive. Unobserved,  1SCHÄFER_PAGES:SCHÄFER PAGES 4/29/10 11:14 AM Page 183 the quantum cat is now in a superposition of states in which it is both dead and alive. As Schrödinger put it, “The half-live and the half-dead cat are smeared throughout the whole box.” According to some interpretations of quantum mechanics the wave function collapses and an actual situation arises, when an observation is made. But what does that mean—making an observation? If the measuring instrument, too, is considered a quantum system, its wave function will itself evolve in a superposition of states in which different outcomes of a measurement are possible. To relieve it from superposition, another instrument is needed, and for that one, yet another, and so on. There is an infinite chain of measuring devices, and the question is where ψ will collapse. In a variation of Schrödinger’s cat experiment, the cat is replaced by a human observer, usually called Wigner’s friend. Open the box and ask the friend what happened. The question is, in what state is the friend immediately before his mind is being probed? In a superposition of states? And what state will you be in, probing Wigner’s friend, prior to being probed yourself by a friend of your own? At what link in the chain does the wave function collapse? In a general way, the most reasonable assumption seems to be that the collapse occurs when a system in a superposition of states interacts with one in a state of ordinary reality. For the half-live and halfdead cat, the question as to whether or not it existed in a superposition of states before it was observed can be answered by a simple experiment : The first observer of the phenomenon should open the box and take a deep breath: the stinking cat has been real dead for a long time.  1SCHÄFER_PAGES:SCHÄFER PAGES 4/29/10 11:14 AM Page 184 ...

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