Could Spontaneous Transitions be Spontaneous ? 1 Bernd

It is considered to re-formulate quantum theory as it appears: A theory of continuous and causal time evolution, interrupted by discontinuous and stochastic jumps. Relying on a global reduction process, a hypothesis is introduced postulating spontaneous collapse of superpositions of states which describe spontaneous absorption or emission. The collapse probability determines a mean collapse time τ c = bh̄/△E, where b is a dimensionless constant and△E is the difference in energy distribution between alternative branches. Ramsey atomic beam spectroscopy yields a lower bound on b and avalanche photodiodes give an upper bound, such that 1.35 · 10 < b < 3.8 · 10. Work partially supported by the Department of Energy under contract DE-FG05-87ER40319. Department of Physics, The Florida State University, Tallahassee, FL 32306, USA. Supercomputer Computations Research Institute, Tallahassee, FL 32306, USA. E-mail: [email protected]; Fax: (850) 644 6735. A photographic plate consists of an emulsion which separates grains of AgCl (or similar) molecules. Let me present a simplified discussion of the detection of a single photon. The photon may dissociate an AgCl molecule. The Cl escapes, whereas the Ag radical starts, upon photographic development, a chemical reaction which leaves a small, visible spot. Before detection the one-particle photon wave may pass through both parts of a double slit, see for instance ref.[1]. The geometry of the device (distance between the slits etc.) can be chosen such that the photon is spread out over a region covering distances much larger than a single grain, which determines the size of the finally visible spot. The physics which causes the photon wave to collapse is not understood. Let us first recall where the Schrödinger equation leaves us. For simplicity we assume that each grain consists of precisely one AgCl molecule. We label the AgCl molecules on the plate by i = 1, ..., n and assume that the relevant features of the photographic plate are described by products of AgCl molecule wave functions. Initially the state is