A Novel Mathematical Formalism for Modeling Physical Phenomena

The action principle, which had successfully guided physicists for centuries, now appears to be leading them into dead ends. The reason for this is conjectured to be its inability to properly represent scale covariant physics. As a result, absolute notions of large and small emerge, with the size of a human observer determining which is which. An alternative to the action principle is proposed, rectifying this relic of anthropocentric bias by postulating that physicists could exist at any scale, all on equal footing. The consistency between their descriptions of physical phenomena severely restricts the set of their possible observations. So much so that the set of well-behaved, scale-dependent and compatible fields, φ(x,λ), representing spacetime phenomena at any scale, λ, could replace the set of fields which are local extrema of an action, in its role as a ``physical law". Observations which appear inexplicable or bizarre when analyzed at any given scale become inevitable when viewed as mere constant-scale `sections', φ(x,λ=const), of such `scale-orbits'. Among them: Why particles rather than a continuum, and why must they not be represented by mathematical points? Why Einsteinian/Newtonian gravity seem to break down at small accelerations? What is the origin of quantum nonlocality? Quantitative agreement with observations is demonstrated in simple cases while in more complicated cases, exact paths to solutions are provided.