GRAVITATIONAL RIVER

 

Anyone who has taken a leisurely trip by boat, dinghy, or canoe has likely noticed that when the current is weak and paddling ceases, the vessel often tends to drift towards the riverbank, getting caught in the grasses and trees along the edge.

 Let us explore the nature of gravitational attraction using the analogy of a boat navigating a river, representing an object moving through spacetime near a massive body (the riverbank). From the viewpoint of mechanical physics, particularly fluid dynamics, we can offer an initial explanation. Imagine the river flowing between its banks. Due to friction and resistance along the riverbanks, the water flow velocity is significantly reduced near the edges, approaching almost zero right at the bank, while it flows fastest in the centre. This interaction creates turbulence near the banks, a complex flow pattern where eddies can form, and significantly, parts of the turbulent flow can even move backward relative to the main river current. Now, consider the boat placed on this river. The boat, having a width roughly half the size of the river width, is subject to these varying currents. The velocity gradient across the river, combined with the complex turbulent motions including backward flows near the edge, exerts a net influence on the boat. This influence tends to draw the boat towards the nearest bank, the region where the forward flow velocity is weakest and where the turbulent structure dominates. This attraction towards the bank, explained through the mechanics of fluids and turbulence, provides a picture reminiscent of the framework suggested by Laurent Nottale, where non-differentiable paths and fractal structures govern motion.

Newton offers a different perspective. In this analogy, Newton doesn't concern himself with the underlying medium – he doesn't "see" the water beneath the boat. He simply observes the result: the boat is attracted to the bank. To explain this, he postulates a direct, invisible force exerted by the bank on the boat, pulling it closer. He provides a mathematical description of this force (dependent on mass and distance) but offers no mechanism for how this force is transmitted, assuming it acts instantaneously across the intervening space. It's a description of what happens, not why or how the interaction occurs through the medium.

Einstein, through General Relativity, brings the medium back into focus. He "sees" the water – the spacetime fabric. He explains the boat's attraction not through a direct force from the bank, but by observing that the flow of the water itself is altered near the bank. Specifically, the water flows more slowly near the bank compared to the centre. In relativistic terms, this corresponds to time flowing more slowly near a massive object. The boat, simply following the natural path available to it within this non-uniform flow (its geodesic in curved spacetime), finds its trajectory naturally bending towards the bank. The attraction arises fundamentally from the difference in the flow of time (the water's velocity) between one point and another, caused by the presence of the massive bank.

Nottale, with Scale Relativity, arguably completes this picture by providing a deeper explanation for the water's complex behaviour that Einstein described. While Einstein identified the varying flow (time dilation) as the key, Nottale explains why the flow might vary in such a way. The fractal spacetime proposed by Nottale is analogous to the turbulent river. The seemingly smooth flow observed at large scales (Einstein's curved spacetime) is, upon closer inspection (higher resolution), composed of an infinity of complex, non-differentiable fractal paths, akin to the turbulent eddies and even backward currents near the bank. The boat's journey isn't just about following a smoothly varying current; it's about navigating this intricate fractal structure. The slowing of time near the bank isn't just postulated due to mass; it arises because the effective distance the boat must travel through this "wrinkled," fractal medium is locally increased. The gravity observed by GR becomes an emergent property of the underlying fractal geometry and the associated scale-dependent dynamics described by SR.