The overall purpose of this paper is to clarify the physical meaning and epistemological status of the term ‘measurement’ as used in quantum theory. After a review of the essential logical structure of quantum physics. Part I presents interpretive discussions contrasting the quantal concepts observable and ensemble with their classical ancestors along the lines of Margenau's latency theory. Against this background various popular ideas concerning the nature of quantum measurement are critically surveyed. The analysis reveals that, in addition to internal mathematical difficulties, all the so-called quantum theories of measurement are grounded in unjustifiable, classical presuppositions.
We consider the effects of weak measurements on the quantum critical ground state of the one-dimensional (a) tricritical and (b) critical quantum Ising model, by measuring in (a) the local energy and in (b) the local spin operator in a lattice formulation. By employing a controlled renormalization group (RG) analysis we find that each problem exhibits highly complex novel scaling behavior, arising from the intrinsically indeterministic ('random') nature of quantum mechanical measurements, which is governed by a measurement-dominated RG fixed point that we study within an
ε expansion. In the tricritical Ising case (a) we find (i): multifractal scaling behavior of energy and spin correlations in the measured groundstate, corresponding to an infinite hierarchy of independent critical exponents and, equivalently, to a continuum of universal scaling exponents for each of these correlations; (ii): the presence of logarithmic factors multiplying powerlaws in correlation functions, a hallmark of 'logarithmic conformal field theories' (CFT); (iii): universal 'effective central charges'
cn(eff) for the prefactors of the logarithm of subsystem size of the
nth Rényi entropies, which are independent of each other for different
n, in contrast to the unmeasured critical ground state, and (iv): a universal ("Affleck-Ludwig") 'effective boundary entropy'
Seff which we show, quite generally, to be related to the system-size independent part of the Shannon entropy of the measurement record, computed explicitly here to 1-loop order. - A subset of these results have so-far also been obtained within the
ε expansion for the measurement-dominated critical point in the critical Ising case (b).
At the time of publication of H. Everett's Relative-State Formulation (1957) and DeWitt's Many-Worlds Interpretation (1970), quantum mechanics was available in a more modern and adequate version than the one used by these authors. We show that with the more modern quantum theory, quantum measurement could have been analyzed along more conventional lines in a one-world cosmology. Bell criticized the Everett-DeWitt theory quite sharply in 1987 but this seems not to have affected the acceptance of the old quantum mechanics as the framework for analysis of measurement.