I. Introduction: remote connectedness and coherent phenomena

A new view of the role of human consciousness is emerging in terms of its role in the structure of physical theories, particularly in quantum mechanics. The rapid development of the structure, content ant interpretation of quantum theory in the 1930's, as exemplified by the Heisenberg Uncertainty Principle and Schrödinger Cat Paradox, opened the door for the passive observer to become an active participant. Heisenberg ant Bohr demonstrated that the act of observation necessarily leaves the system in a new state through what J.A.Wheeler terms ''participation''.⁽¹⁾

What is termed the Schrödinger Cat Paradox arises over the issue of the collapse of the wave function. For two equally probable states arising from a microscopic process, only observation can determine which state exists.⁽²⁾

The Copenhagen interpretation of quantum mechanics (that the theory can only predict the probability of the outcome of a specific experiment) was an attempt to dismiss the observer's participation, but by this dismissal, we can no longer built a motel of reality. Certainly the most desirable consequence of scientific discovery is the ability to refine our concept of reality.

What are some of the possible implications from the quantum description, if we choose to pursue the development of motels of reality ant perhaps relax the pure objectivity constraint in physical theory? This issue is well exemplified by the Bell's theorem formulation of the EPR paradox.⁽³⁾

An indication that non-locality is a principle in Nature is contained in Bell's theorem, which asserts that no deterministic local "hitter variable" theories can give all the predictions of quantum theory.⁽⁴⁾ However, most physicists believe that nature is non-deterministic ant that there are no hidden variables. The prevailing view is that Bell's theorem merely confirms these ideas, rather than that it is an indication of a fundamental statement of non-locality.

H. P. Stapp demonstrates that determinism ant hiddle variables occupy no essential role in the proof of Bell's theorem, which Stapp has reformulated.⁽⁵⁾ Stapp asserts that no theory which predicts the outcome of individual observations which conform to the predictions of quantum theory can be local. A less restrictive interpretation of Bell's theorem is that either locality or realism fail.⁽⁶⁾

Realism is a philosophical view in which external reality is assumed to exist and have definite properties fundamentally independent of an observer.^(6,7) Stapp presents reasonable and comprehensive models of reality in which non-locality, as implied by Bell's theorem, is inconsistent with "objective reality", in which observable attributes can become definite, independent of the observer, the so-called "collapse of the wave function".⁽⁸⁾

In Young's double slit experiment, photons from a source can go through one of two slits or openings of a double slit interference arrangement. Through which slit did the photon go that blackens a photographic plate at the other end of the apparatus? The answer is not yet defined because of the Heisenberg Uncertainty Principle. One can observe interference fringes when both slits are open, but at the cost of not knowing through which slit the photon went. Or, one can know through which slit the photon went when one slit is closed, but at the cost of not having any interference fringes. Again, the choice is that of the observer.⁽⁹⁾

In our research, we have introduced a complex multi-dimensional geometry consisting of the four real dimensions of space, X₁, X₂, ,X₃ and X₄ = t and four imaginary dimensions of iX₁, iX₂, iX₃, and iX₄ such that we can describe non-local macroscopic connections of events that do not violate causality.^(10,11) There are several motivations for introducing such a model; one of which relates to a possible macroscopic formulation of a Bell's theorem-like non-local correlation function that may have macroscopic ant astrophysical consequences and fits some recently observed data, as well as reconciling precognition and causality. The additional imaginary dimensions allow for a description in which they make it possible, in "mental space", for remote spacetime events to be contiguous to the observer, thus causality is preserved, yet acquisition of remote information is allowed.

We have solved the Schrödinger equation in the complex eight dimensional space and, with the inclusion of a small non-linear term, g² (i), we find soliton or solitary wave solutions. The non-linear term, which depends on the imaginary time component, overcomes dispersion giving the non-dispersive soliton waves. The coherence over remote space and time of these waves may relate to a macroscopic related phenomena to that exemplified by Bell's theorem ant Young's double-slit experiment. The non-linear form of the Schrödinger equation can be related more readily to non-linear gravitational phenomena and also has implications for the quantum measurement problem. Resolution of the observer/participant problem may be at hand as demonstrated by a new interpretation of the Schrödinger Cat Paradox. Issues involving the mind/matter problem are also involved.^(12,13)

The existence of consciousness may create an intrinsic subjective aspect to reality. It may be that the intervention of mind in the universe of matter is what leads the processes of observation to be one of participation.

Let us examine a geometrical model which demands a remote connoctedness by its structure. Also we will examine solutions to Schrödinger's equation which are coherent and non-"dispersive" over relatively long times. The connection of the observer ant the observed is discussed and also the quantum measurement problem as exemplified by the Schrödinger Cat Paradox. Lack of dispersion in the solutions may be "vehicles" for describing remote connectedness.