The GRW model supports robust macroscopic locations, but not universal exact point locations supplied by a list of particle coordinates. It modifies the wave function rather than adding the actual particle configuration of Bohmian mechanics. A claim that objects are located must therefore specify both the collapse dynamics and the proposed ontology. “Localized” is not synonymous with “has compact support” or “is a position eigenstate”.
Using one standard convention, a collapse on constituent with centre acts by the GRW localization operator
Its centre has probability density . Independent constituent collapse rates give a body with relevant constituents an approximately localization rate. Correlations within a macroscopic superposition allow one constituent's localization to suppress an entire alternative configuration: the GRW amplification mechanism.[ref]
For two narrow packets separated by , a hit near one multiplies the other's relative amplitude approximately by . This explains a sharply concentrated pointer reading. Yet the Gaussian function is never zero at finite separation. A nonzero distant tail therefore remains, and a finite-width packet is not an exact position eigenstate. This is the tails problem in collapse theories.[ref] The assertion that each hit produces exact bounded support is false; an initially everywhere nonzero Gaussian wave packet is a concrete counterexample.
A GRW matter-density ontology specifies matter in ordinary SPACE by
A macroscopic body's density is concentrated near one region, making its approximate location physically meaningful. The formula is the proposed matter field itself, not a probability distribution over a hidden set of exact point positions. Residual tails correspond to very low density elsewhere, motivating the further question of why such tails do not constitute ordinary rival objects. Concentration provides a practical account of records; a full ontology must also address that structured-tail objection.
A GRW flash ontology instead identifies the primitive events with collapse centres in spacetime. Individual flashes have definite locations and times, while a persisting macroscopic object is a dense pattern of flashes. There is no continuous particle trajectory between them. An isolated microscopic system may flash rarely, so the model must not be read as assigning it an ordinary point location at every instant. Matter-density and flash accounts express distinct ontologies with related empirical predictions.[ref]
An approximate-location rule, such as requiring almost all matter density inside a suitably sized region, is meaningful if its tolerance and scale are stated. It does not turn the small tail into zero, and arbitrary sharp property thresholds can create artificial counting puzzles. The defensible result is emergent, highly stable macroscopic localization, or exact locations of flashes, depending on the ontology. Exact Bohmian positions are a different theoretical commitment and cannot be attributed to the collapse equation alone.