We outline a new model in which generalised uncertainty relations are
obtained without modified commutation relations. While existing models
introduce modified phase space volumes for the canonical degrees of freedom, we
introduce new degrees of freedom for the background geometry. The phase space
is therefore enlarged but remains Euclidean. The spatial background is treated
as a genuinely quantum object, with an associated state vector, and the model
naturally gives rise to the extended generalised uncertainty principle (EGUP).
Importantly, this approach solves (or rather, evades) well known problems
associated with modified commutators, including violation of the equivalence
principle, the `soccer ball’ problem for multiparticle states, and the velocity
dependence of the minimum length. However, it implies two radical conclusions.
The first is that space must be quantised on a different scale to matter and
the second is that the fundamental quanta of geometry are fermions. We explain
how, in the context of the model, these do not contradict established results
including the no go theorems for multiple quantisation constants, which still
hold for species of material particles, and the spin-$2$ nature of gravitons.
