To answer part of my own question, JSR 134: JavaTM Game Profile did propose to include a Physics Engine along with a kitchen sink of other features. This JSR was offcially withdrawn in July of 2003.
Perhaps it failed because it was too wide in scope. Focussing on just the Physics Engine might have a better chance.
Considering this a bit further, I'd say "Physics Engine" is quite wide definition. What kind of physics engine? I've only dwelled myself to some game oriented physics engines, they all share some common definitions but each has their own unique features.
Anyway, there might be possibility to create general proposal suitable for most physics engines. This proposal could contain e.g. positions, orientations, angular and linear velocities (add more here..), perhaps some joints or other constraints and general simulation definitions. Bindings to renderers could be also added to this proposal, they should be quite the same despite the physics engine used. All unique (more complex) features need to be defined through engine's own extension, this is something that is outside from the proposal.