8/21/2023 0 Comments Illuminate eup![]() , the Heisenberg uncertainty principle was generalized by the inclusion of the gravitational photon-electron interaction (acceleration) leading to the Generalized Uncertainty Principle (GUP)Īs usually assumed, the GUP takes into account the gravitational uncertainty of position related to the minimum fundamental length scale in physics. ![]() The standard uncertainty principle of quantum mechanics in its fundamental form does not take into account effects which are expected to arise from an underlying theory of quantum gravity. Our main achievement combines the method we introduce with the Generalized Uncertainty Principle (GUP) by virtue of deformed commutators to formulate a generic form of what we call the Asymptotic Generalized Extended Uncertainty Principle (AGEUP). This result is first verified for previously derived homogeneous space models and then applied to other non-trivial curvature related effects such as inhomogeneities, rotation and an anisotropic stress fluid leading to black hole “hair”. the expected position when performing a measurement. The leading 2nd order curvature induced correction is proportional to the Ricci scalar, while the 4th order correction features the 0th order Cartan invariant \(\Psi _2\) (a scalar quadratic in curvature tensors) and the curved space Laplacian of the Ricci scalar all of which are evaluated at the expectation value of the position operator i.e. Entering the realm of small position uncertainties, we derive a general asymptotic EUP. We present a formalism which allows for the perturbative derivation of the Extended Uncertainty Principle (EUP) for arbitrary spatial curvature models and observers.
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