Martin L. Shough*

Whether space determines trajectories, or trajectories determine space, remains a subtle question post-GR. The modern distinction tends to be in terms of geometry and mass-energy, the tension between Einstein’s ‘marble and straw’ - which is primary? In quantum theory the same dilemma, couched in terms of particles and fields, is turned into a principle of nature; the ‘resolution’ of the dilemma is to reify it. But everyone would agree that the conceptions of space and of ‘object’ are both logically and technically difficult ones in modern physics.

This article discusses the prospects for a more ‘primitive’ type of conception where this tension may in principle not arise, in which trajectories are space, or in which space is completely specified by a sum over all trajectories. The thrust of this approach is to construct, by a return to first principles, a space of basis states in which the traditional distinction between ‘far-action’ forces and modern relativistic ‘field contact’ forces can be subsumed. A particle- or wave-trajectory in such a space emerges with a radically different meaning. The trajectories live on a scale-free network from which space dimensionality and quantum mechanics are to be co-emergent.

Consistency with classical, relativistic and quantum mechanics is argued, and it is shown that a novel conception of gravitation might be possible on the basis of such a non-field theory. The focus is on conceptual foundational issues, and we do not pretend to arrive at the basis of a proper theory. The objective is only to establish that an alternative general framework is plausible in the sense that it allows an understanding of basic physical principles and has some potential for formal development.

© December 2003 *Martin L. Shough
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