  We consider the effect of gravity on extended quantum systems (EQS) in the
low energy regime. We model the gravitational effect due to a nearby source
mass as a redshift in the internal Hamiltonian of the EQS. Due to the
dependence of the energy spectrum of the EQS on the position of the massive
particle (via the redshift) at zero temperature, our model predicts
gravitational decoherence of the massive particle in the position basis. We
show that the decoherence effect is multiplicative, in the sense that the
increase in number of EQS gravitationally interacting with a single massive
particle leads to an increase in its decoherence. If the considered model of
gravitational redshift holds alongside the linearity of quantum mechanics (as
an appropriate limit of an accepted theory for coupling quantum matter with
gravity) to allow for a spatial superposition of the source mass, we propose
that the same methodology can be applied to continuous fields, which are
essentially EQS. This could provide an upper limit on the number of
undiscovered fields by observing coherent superpositions of masses, e.g., in a
matter wave interferometer. Besides, by taking a spin chain as a toy model of
an EQS, we analyse the dependence of the new effect on relevant system
parameters and identify the number of independent spin chains that can cause a
detectable effect.
