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A chameleonic solution to the cosmological constant problem and thenon-equivalence of different conformal frames at the quantum level have beenrecently suggested [Phys. Rev. D82 (2010) 044006]. In this article we furtherdiscuss the theoretical grounds of that model and we are led to a chameleonicequivalence postulate (CEP). Whenever a theory satisfies our CEP (and someother additional conditions), a density-dependence of the mass of matter fieldsis naturally present. Let us summarize the main results of this paper. 1) TheCEP can be considered the microscopic counterpart of the Einstein's EquivalencePrinciple and, hence, a chameleonic description of quantum gravity is obtained:in our model, (quantum) gravitation is equivalent to a conformal anomaly. 2) Toillustrate one of the possible applications of the CEP, we point out aconnection between chameleon fields and quantum-mechanical wave functioncollapse. The collapse is induced by the chameleonic nature of the theory. Wediscuss the collapse for a Stern-Gerlach experiment and for a diffractionexperiment with electrons. More research efforts are necessary to verifywhether these ideas are compatible with phenomenological constraints.

Chameleonic equivalence postulate and wave function collapse