VASSILIOS KARAKOSTAS AND MICHAEL DICKSON
DECOHERENCE IN UNORTHODOX FORMULATIONS
OF QUANTUM MECHANICS
ABSTRACT. The conceptual structure of orthodox quantum mechanics has not provided
a fully satisfactory and coherent description of natural phenomena. With particular
attention to the measurement problem, we review and investigate two unorthodox formu-
lations. First, there is the model advanced by GRWP, a stochastic modification of the
standard Schr6dinger dynamics admitting statevector reduction as a real physical process.
Second, there is the ontological interpretation of Bohm, a causal reformulation of the
usual theory admitting no collapse of the statevector. Within these two seemingly quite
different approaches, we discuss in a comparative manner, several points: The meaning
of the state vector, the status of quantum probability, the legitimacy of attributing macro
objective properties to physical systems, and the possibility of retrieving the classical
limit. Finally, we consider aspects of non-locality and relevant difficulties with formulating
a relativistic generalization of the two approaches.
1. THE PROBLEM OF QUANTUM MEASUREMENT
Evolution in orthodox quantum mechanics is strangely dualistic. On the
one hand, the state-vector of a closed system evolves in a continuous,
deterministic and reversible manner according to the time dependent
Schr6dinger equation
(1) ~o--> ~, = eiH'~o, (~ = 1).
On the other hand, discontinuity, stochasticity and irreversibility are
introduced in measurement situations through the projection postulate,
which leads from linear superpositions in Hilbert-space vectors to classi-
cal statistical mixtures of states
(2) 2 CnC*ml't~n)(at~mt ~ 2 lCn[21a'Ifn)('f~nl.
nm r~
This second type of evolution is incompatible with the Schr0dinger
equation and consequently quantum theory is unable to consistently
provide a dynamical description of the measurement process. In parti-
cular, it is unclear where the transition between (1) and (2) occurs.
This unsatisfactory character of the standard formulation has been
pronounced as 'unprofessional' by Bell (1986, p. 54). "When I look at
Synthese 102: 61-97, 1995.
© 1995 Kluwer Academic Publishers. Printedin the Netherlands.