Manuscript En01-C@1 · En01-C.tex · section · 00a2161c

Rigid-body self-energy

Model interpretation and external constraints › Rigid-body self-energy · lines 1989–2016

For fixed intrinsic density and orientation, translation-invariant internal pair energy has the form

U_{self} = - \frac{G}{2} \int \int μ_{m} (d r) μ_{m} (d r^{'}) W_{r_{c}} (∣ r - r^{'} ∣),

with the pair potential appropriate to the selected smearing. A common centre-of-mass translation cancels inside $r - r^{'}$ . Thus $U_{self}$ is a scalar on the retained rigid-body centre-of-mass Hilbert space and produces no centre-of-mass commutator. It does not remove the displaced-profile decoherence rate $Γ_{r_{c}} (d)$ .

External masses, deformable internal states, rotation, or centre-of-mass-dependent couplings change the model. Their potentials must be specified separately.

Measurement-feedback semiclassical gravity can prescribe both a regularized interaction and decoherence TilloyDiosi2017. Testing only (eq:G) does not test the complete feedback theory. This paper uses the decoherence-only interpretation.

Displayed formulas in this passage

unlabeled · line 1993
$U_{self} = - \frac{G}{2} \int \int μ_{m} (d r) μ_{m} (d r^{'}) W_{r_{c}} (∣ r - r^{'} ∣),$