Dual-Time Supercausality (1989) Physics Essays 2/2 128-151 DUAL-TIME SUPERCAUSALITY

This article explores models of causality of the physical universe which extend beyond the usual quantum and classical descriptions. To facilitate discussion of this topic, a brief review of relevant areas of modern physics is included. Although mathematical logic is not directed in time, the causal description of the physical universe is classically performed in terms of temporal determinism , an initial-value problem in which subsequent states are determined through the action of differential equations, thus avoiding the paradox of effects preceding their causes. Quantum mechanics has reduced this description to the status of a stochastic-causal theory, in which individual future states of a system are not predictable because the probability interpretation of the wave function prevents a complete knowledge of a single reduction of the wave packet. The transactional interpretation of quantum mechanics provides a basis for examining the workings of stochastic causality in terms of time-symmetric advanced and retarded waves. Cosmic symmetry-breaking provides a contrasting description in which time-directed phenomena derive their explanation. Dual-time supercausality replaces the stochastic model with one in which two complementary causal processes, symmetrict ime and directed-time are operating. The mode of interaction of these avoids temporal paradox in the timedirected description, and also explains why quantum mechanics provides an incomplete stochastic model. An important role for supercausal processes in the structural evolution of the universe is proposed, including the emergence of biosystems, biological evolution, and consciousness. 1 : CAUSALITIES AND SUPERCAUSALITIES Since the development of calculus and the Newtonian model of the universe, the evolution of dynamical events has been described through the directional application of time as a parameter. The evolution of a classical system can in principle be causally described in terms of the initial conditions and the differential equations governing its action. In the classical Laplacian universe, the initial conditions and the dynamical equations taken together completely specify the ongoing state at subsequent times. We will refer to this model as temporal determinism. The classical Hamiltonian and Lagrangian dynamical equations are both expressed as differential equations expressing generalized coordinates in terms of increasing time, where = T V and in the case of a potential, = T + V, giving the total ( T kinetic & V potential ) energy : d dt ∂ ∂qi ∂ ∂qi = 0 i = 1, ..., N (1.1) = ∑ i p i qi ∂ ∂p i = q i ∂ ∂q i = p i (1.2) The essential features of this description are: (1) The spatial coordinates are expressed as differential functions of increasing time, and are completely determined by the differential equations and the initial conditions. (2) The energy and momentum are exactly specifiable simultaneously with time and position. (3) Space and time are independent parameters, and independent of the parameters of energy & momentum. Relativity introduces specific changes into this scenario, because the interdependence of spatial and temporal dimensions leads to natural negative energy solutions in which the temporal direction of evolution is reversed: (1) Although the temporal order of events is preserved under a Lorentz transformation with sub-luminal relative velocities, and the evolution of a positive-energy relativistic system along time-like world lines has the same directed causal description as classical physics, the relation below between relativistic energy and momentum ( c = 1 ) E2 = p2 + m2 leads immediately to dual energy solutions E = ± p + m 2 (1.3) in which the negative energy solution has reversed temporal behavior in space-time. (2) The planes of spatial simultaneity in the Newtonian view give way to the topology of space-time in which the light cone is divided into disjoint advanced and retarded regions forming the absolute past and future of O. A time-like world line as shown in 1,2,3 below has its time sequence preserved under Lorentz transformations, but space-like separations, such as 4,5 do not. Consequently transformations involving superluminal exchange, although permitted by the Lorentz transformations lead to temporality-reversing causality violations in which an event can contradict its own past causation (see fig 12).