Schild’s Ladder


Decoherence is a phenomenon that plays a role in many of the events in Schild’s Ladder. Beyond the novel, understanding decoherence is essential to understanding how classical physics emerges from quantum mechanics.

The basic idea is this: a quantum system, A, in isolation, behaves in a characteristically quantum-mechanical fashion, exhibiting interference effects that reflect the phase difference between the various components of its state vector. For example, if A consists of an electron in a state that is a superposition of equal parts spin up and spin down, there will be measurements that can be performed on the electron that will be sensitive to the phase relationship between these two components. This is quite different from the classical notion of probability: there isn’t merely a 50% chance for the electron’s spin to be up or down; rather, both possibilities exist simultaneously, and the phase describes a relationship between them that would be meaningless if either was absent.

If system A then interacts with another system, B, in such a manner that different components of A’s state vector influence B differently, the two systems become entangled, and observations on A alone will no longer exhibit quantum effects. System A appears to have “collapsed” down to just one component of its original state vector. In the example of the electron, it now acts as if there were merely a 50/50 chance for its spin to be either purely up or purely down.

However, no such “collapse” has really taken place. Measurements on the combined system, A+B, reveal that it is in a pure quantum state, and none of the original components of A’s state vector have been lost. Classical physics emerges, essentially, from the inability to observe everything we’d need to in order to detect quantum phenomena in the world at large. More details

This applet demonstrates three experiments that illustrate how quantum behaviour is hidden when a system becomes entangled, but can be recovered by observations on the complete system.

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Schild’s Ladder / Decoherence / created Tuesday, 1 January 2002 / revised Saturday, 5 January 2002
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Copyright © Greg Egan, 2002. All rights reserved.