Fundamental upper bound on the non-local model’s λ parameter

Determine whether there exists a fundamental upper bound on the parameter λ in the non-local spin entropic gravity model, in which mediator qubit frequencies are defined by ωα(x)=α f(x) with 1/f(x)=λ+ℓ^2/|x|, and where increasing λ suppresses intrinsic noise and makes the model’s predictions approach those of perturbative quantum gravity. If such an upper bound exists, identify and derive it, including its physical origin; otherwise, establish that λ can be taken arbitrarily large without inconsistency.

Background

In the non-local spin entropic gravity model, two masses interact via a bath-thermalized set of mediator qubits whose frequencies depend on their separation. The frequency function is chosen so that the emergent force reproduces Newton’s law in a thermodynamic limit, with 1/f(x)=λ+ℓ^2/|x|. The parameter λ (with dimensions of length) shifts the spectrum and does not affect the mean force but strongly controls noise and decoherence: larger λ suppresses fluctuations, allowing the model to become indistinguishable from perturbative quantum gravity in nonrelativistic regimes.

The authors note that tuning λ→∞ can, at least in their nonrelativistic analysis, reproduce the predictions of virtual graviton exchange. They explicitly state that they have not been able to identify whether there is a fundamental upper bound on λ. Establishing whether such a bound exists (and if so, its origin) would determine whether the model must necessarily differ observably from standard quantum gravity or can fully mimic it in appropriate limits.