On June 7 of 1935, Erwin Schroedinger wrote to Albert Einstein to congratulate him on what is now known as the EPR paper, a famous problem in the interpretation of Quantum Mechanics. Soon thereafter, he published what was to become one of the most celebrated paradoxes in quantum theory:
A cat is placed in a box, together with a radioactive atom. If the atom decays, and the geiger-counter detects an alpha particle, the hammer hits a flask of prussic acid (HCN), killing the cat. The paradox lies in the clever coupling of quantum and classical domains. Before the observer opens the box, the cat's fate is tied to the wave function of the atom, which is itself in a superposition of decayed and undecayed states. Thus, said Schroedinger, the cat must itself be in a superposition of dead and alive states before the observer opens the box, ``observes'' the cat, and ``collapses'' its wave function. You may ask in respect to cold fusion, what does all this have to do with Schroedinger's cat? Well, when the proton who is a member of a coherent ensemble: a classical macroscopic domain has coherently tunneled into a nickel atom who lives on the surface of a nickel lattice, Quantum Mechanics tells us the state of the proton must be described by a ``superposition''. The proton inside this nickel nucleus is at the same time as it were, much like the cat is in a superposition between dead and alive because its fate is coupled to the quantum coherence decay. However, as our proton/nickel nucleus system shows, the effect of an environment on a quantum superposition can be drastic, even destroying the superposition, thus hinting that for all practical purposes, the cat's wave function will be ``collapsed'' into either the dead or the alive state. Finite temperature behavior of the lattice is interesting in and of itself. The rate of decoherence turns out to be proportional to the temperature to the power (2alpha -1), and thus increases with increasing temperature if alpha < 1/2, mimicking the so-called Quantum Zeno effect. The Quantum Zeno effect, also known by terms such as "a watched pot never boils", was named after Zeno, the fourth century Greek philosopher famed for his paradoxes and conumdrums. It is usually invoked for a class of effects in which constant monitoring of a quantum subsystem drastically slows down its dynamics. As the temperature rises, the substrate vibrates more, more phonons are excited, and the combined effect of each phonon ``measuring'' the position of the proton and increases QM decoherence. We can exactly calculate the coupling constant alpha in terms of the elastic constants, the density and the force difference between the positions of the atoms. These can be independently measured, and thus an experiment could carefully test all these theories of how the environment (phonons) affects an embedded quantum system (our tunneled coherent proton).
