Verdie Michael Dreyer

Now consider a Popperian-type conjecture on the time of an instant and the problem of motion, when setting the rational endeavour of modern physics, with a focus on Bohr’s complementarity, before the logical challenge of ancient paradox, specifically Zeno’s Flying Arrow, and so for demonstrating the philosophical power of reason over such combinatory reflection as thereby to yield novel scientific insight. By addressing the arrow argument precisely on its own logical terms, and by adaptively applying a core principle of quantum mechanical theory, the study argues that the possibility of motion, from little atoms to large arrows, is contingent upon space and time acting as dynamical properties of forms in motion – and crucially, as such properties that possess both a quantitative and a qualitative character. The reasoning engages with the pertinent thought of influential philosophers, mathematicians and physicists, both past and present, hence drawing the ‘common science’ issue of an emphatic quantitative mindset into the identification of a Kantian-style antinomy of the pure quantum instant. The results show that certain core conundrums – like the measurement problem in quantum mechanics about the ‘collapse’ of the wavefunction, and that of quantum gravity, with so many conflicting conceptions of space, time and motion dividing the canonical, covariant and other approaches – must persist for so long as Zeno’s challenge is not formally answered with the philosophical grasp and scientific understanding of a fundamentally qualitative instant of motion.