When a large trade hits a market, the price moves. The standard economic explanation is informational: the trade reveals that the trader knows something the market does not. The price adjusts to incorporate the new information. The size of the move reflects the amount of information the trade conveys.
Tóth et al. (arXiv:2502.16246), analyzing six years of Tokyo Stock Exchange data, find that price impact follows a “double” square-root law. Impact scales as the square root of order volume at the individual-order level — each additional share moves the price less than the last. Then the impact decays inversely with the square root of time. Volume in, square root. Time out, inverse square root.
The double square-root structure is entirely mechanical. When an order arrives, it consumes the available liquidity at each price level. The order book is not uniformly populated — liquidity is sparse near the best quote and denser further away. Consuming the first few levels of liquidity moves the price a lot. Consuming the next few levels moves it less. This geometric compression of the book produces the square-root dependence on volume. No information is needed. The impact would be identical if the order were placed by a coin flip.
The decay follows the same logic in reverse. After the order is absorbed, other participants refill the depleted levels. The refilling is not instantaneous, and the rate at which liquidity returns produces the inverse square-root decay in time. Again, no information processing is involved. The book was mechanically depleted and is mechanically restored.
The structural point is that the dominant empirical law of price impact — the one that governs how every large trade moves every market — arises from plumbing, not epistemology. The order book is a physical structure with finite depth and finite resilience. A large order compresses the book like a spring. The spring relaxes. The square-root law is the natural mode of a mean-reverting elastic medium under impulse loading. The information story is a post-hoc rationalization applied to a phenomenon that is already fully explained by the mechanics of supply at each price level.