One of the classic debates in metaethics/moral psychology is between motivation externalism and motivational internalism. This debate seems to be in the process of being resolved by neuroscience, in favor of motivational externalism.

Moral motivation for humans is an empirical question, but no universally compelling arguments = externalism for minds-in-general, no? And internalism, not "objective morality", is the precise term we should be using for the spooky thing we don't believe in.