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5.3.1 Hamiltonians, wave functions and measurements

In quantum physics, energy (the total of the kinetic and potential energies) is represented by the Hamiltonian operator . This operator enters into the Schrödinger wave equation which governs the time-dependence of all quantum wave forms. It thus generates all time evolution and all fields of probabilities for measurement outcomes, as discussed in Section 4.7. The principal dynamics in quantum physics are specified by knowing what the initial state is and what the Hamiltonian operator is. This applies to quantum mechanics as it is practised, by using Born’s statistical interpretation and then naively saying that the quantum state changes after a measurement to one of the eigenstates of the measurement operator. (This is the much discussed ‘reduction of the wave packet’, which we can agree at least appears to occur.)

We may consider quantum physics in the following ‘realistic’ way. We have the Hamiltonian which has to do with total energy. It is somehow ‘active’ since it is an operator which operates on the wave function and changes it. The Schrödinger equation is the rule for how the Hamiltonian operator produces the wave function. This wave function is a probabilistic disposition (a propensity) for action, since its squared modulus gives a probability for different macroscopic outcomes of experiments, and since the wave function changes according to the specific outcome.

Such is the structure of quantum physics as it is practised, and we may observe a sequence of derivative dispositions in operation:

We may draw this generative structure as



\includegraphics[width=0.8\textwidth]{figs/l3ap}

It appears again that we have multiple generative levels with the set of Hamiltonian, wave function and selection event. Note also that the final result is the weakest kind of minimal disposition, which influences merely by selection, because it is a selection. It appears as the last of a sequence of derivative dispositions, as a kind of ‘bottom line’ if we want to include it within the framework of multiple generative levels.

Admittedly, reductionist tendencies may be applied. It may be denied that there are distinct measurement outcomes in any ontological sense and that they may only be approximately defined within a coarse-grained ‘decoherent history’. Advocates of the Many Worlds Interpretation or Decoherence theories take this view. Others such as Bohr take the opposite view: he holds that only the measurement outcome is real and that the Hamiltonian and wave function are calculational devices and nothing real. These conflicting views will be discussed in Section 6.4.

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