Quantum theory of measurement and related philosophical problems

Martin Kober

The Copenhagen interpretation of quantum theory is investigated from a philosophical point of view. It is justified the opinion that the philosophical attitude the Copenhagen interpretation is based on is in principle inevitable for a real comprehension of quantum theory. This attitude is mainly related to epistemological arguments. However, the measurement problem often seems not to be treated clearly enough within the interpretation. By referring to the property of the necessity to use macroscopic measurement instruments obeying classical concepts it is made the attempt to solve the measurement problem. According to this consideration the indeterministic character of quantum theory seems to have its origin in a lack of knowledge and thus it appears in a similar but more principle way than in statistical mechanics. It is emphasized the ontological character of the uncertainty relation and the related non locality of quantum theory suggesting that the existence of a position space is not as fundamental as the assumptions of general quantum theory.

Wolfgang Weidlich

PEKKA J. LAHTI, Peter Mittelstaedt

Richard A. Mould

Robert Weingard

Before we, as philosophers, take a look at string theory I want to mention that more than one person has suggested to me that it is still too early for philosophical and foundational studies of string theory. Indeed, the suggestion emphasizes, since string theory is still in the process of development, and its physical and mathematical principles are not completely formulated, there is, in a sense, no theory for the philosopher to analyse. And I must admit that I think there is something to this suggestion. In a sense I hope I will make clear, there does not yet exist a precise mathematical formulation for string theory as there is Hilbert space for (elementary) quantum theory, and Riemann spacetime for general relativity. Because these latter formulations exist, we can ask precise questions and prove precise theorems about their interpretation. The Kochen–Specker theorem about non-contextualist hidden variable theories, the Fine–Brown proof of the insolvability of the quantum measurement problem, and the current determinism–hole argument debate are some examples. Without a clearly formulated mathematical structure, I don't think we can expect to get analogous distinctly stringy results. This suggests a related worry. String theory, at least in the first quantized theory, is a relativistic quantum theory of strings (one-dimensional extended objects). One may well agree that of course all of the standard philosophical and foundational issues of quantum theory and relativity are still there, but be sceptical about whether string theory will either shed any light on these old problems, or give rise to stringy problems.