Interpreting Quantum Mechanics
The world of atoms and molecules is described by exactly the same expressions as the determinisric world described in the previous chapter, yet here, a world consisting of ‘real things’, seems to be missing. As soon as one makes some very basic assumption
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Interpreting Quantum Mechanics
This book will not include an exhaustive discussion of all proposed interpretations of what quantum mechanics actually is. Existing approaches have been described in excessive detail in the literature [1, 6–8, 10, 11, 35], but we think they all contain weaknesses. The most conservative attitude is what we shall call the Copenhagen Interpretation. It is also a very pragmatic one, and some mainstream researchers insist that it contains all we need to know about quantum mechanics. Yet it is the things that are not explained in the Copenhagen picture that often capture our attention. Below, we begin with indicating how the cellular Automaton interpretation will address some of these questions.
3.1 The Copenhagen Doctrine It must have been a very exciting period of early modern science, when researchers began to understand how to handle quantum mechanics, in the late 1920s and subsequent years [64]. The first coherent picture of how one should think of quantum mechanics, is what we now shall call the Copenhagen Doctrine. In the early days, physicists were still struggling with the equations and the technical difficulties. Today, we know precisely how to handle all these, so that now we can rephrase the original starting points much more accurately. Originally, quantum mechanics was formulated in terms of wave functions, with which one referred to the states electrons are in; ignoring spin for a moment, they were the functions ψ( x , t) = x |ψ(t). Now, we may still use the words ‘wave function’ when we really mean to talk of ket states in more general terms. Leaving aside who said exactly what in the 1920s, here are the main points of what one might call the Copenhagen Doctrine. Somewhat anachronistically,1 we employ Dirac’s notation: 1 Let me stress here again that from our use of terms such as “Copenhagen Interpretation”, or “Copenhagen doctrine”, it should not be inferred that our descriptions would be attempts to rewrite history; the philosophical debates that did take place among the “Copenhagen group”, whoever
© The Author(s) 2016 G. ’t Hooft, The Cellular Automaton Interpretation of Quantum Mechanics, Fundamental Theories of Physics 185, DOI 10.1007/978-3-319-41285-6_3
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Interpreting Quantum Mechanics
A system is completely described by its ‘wave function’ |ψ(t), which is an element of Hilbert space, and any basis in Hilbert space can be used for its description. This wave function obeys a linear first order differential equation in time, to be referred to as Schrödinger’s equation, of which the exact form can be determined by repeated experiments. A measurement can be made using any observable O that one might want to choose (observables are Hermitian operators in Hilbert space). The theory then predicts the average measured value of O , after many repetitions of the experiment, to be O = ψ(t)|O|ψ(t).
(3.1)
As soon as the measurement is made, the wave function of the system collapses to a state in the subspace of Hilbert space that is an eigenstate of the
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