Newton gave us a world where bodies move in a void and clocks tick the same for everyone. For three centuries, this picture worked flawlessly. But it relies on many invisible props: absolute position, the 'up-down' direction, and a single rhythm of time for the entire universe. We have never measured these directly — only through the relations between objects.

The authors of the new work step by step discard the superfluous. First, absolute position goes: only the distances between bodies matter, not where they are. Then orientation: it doesn't matter how the system is rotated in space. Next, universal time: only the order of events matters. Finally, scale: sizes and distances can only be compared to each other, not to a standard meter.

The most interesting part comes when this view is applied to the many-body problem with Newtonian attraction. A special quantity emerges — the 'shape complexity' V. It shows how complex the configuration of the system is. This quantity relentlessly increases with time, and provides a direction that was previously attributed to the ticking of a clock. Thus, from relations alone, the arrow of time is born.

This approach requires no new particles or fields. It simply removes from the description of the world what we have never seen. The idea traces back to Leibniz and his principle of sufficient reason: everything must have a cause. If there is no cause for absolute space — then it doesn't exist. The authors hope that this modest step in Newtonian mechanics will hint at something important for both general relativity and quantum mechanics. After all, nature might be simpler than we are used to thinking.