If all Special Relativity did was dictate the fact that there were different reference frames, and that none of them was preferred, it wouldn't be a very interesting theory, nor would have done much to advance our understanding of physics.
The true magic of Special Relativity is that it deals with concepts which are subjective, and ties them together with concepts that are objective.
Special Relativity states that: knowing that there is no preferred reference frame, the laws of physics must apply in every reference frame.
This statement provides the mechanism for determining if a physical model is correct or incorrect. It also gives us a hint as to how to construct correct physical models. A correct physical model must be constructed from quantities that are the same in every reference frame. These quantities are called Invariants. If a concept is physically significant, it can and should be expressed in terms of Invariants. If it cannot be expressed in terms of Invariants, then it is not a physically significant concept.
Special Relativity identifies two particularly useful invariants. One Invariant is global - the speed of light. The speed of light is measured to be the same value in every reference frame. The other Invariant is subjective - the proper time of an observer. The proper time is the time as measured in the observers own reference frame, and there is a prescription for calculating it, which results in the same value if measured in any reference frame.
It is interesting that Special Relativity successfully connects a subjective act (measurement within a reference frame) with a universal objective reality: the speed of light is constant.
A Moral Invariant should be a moral concept which is the same in every Moral Reference Frame. There may exist both global as well as subjective Moral Invariants, however the act of observing them will always be a necessarily subjective exercise.
The search for ethical truth must involve a search for Moral Invariants. And a test of absolute correctness of an ethical model will be that it is framed in terms of Moral Invariants. Concepts that can be phrased in terms of Moral Invariants are called Morally Significant concepts.
One hint that a concept is a Morally Significant is that it crosses cultural boundaries. The ethic space has more boundaries than just cultural boundaries, but the cultural boundaries are the most visible, as well as the hardest for complex concepts to bridge.
The best way for two Moral Observers to seek "common ground" is to phrase their discussion in a Morally Significant way.
Morally Significant statements are likely not the type of thing that can be phrased as "A good person does X". Rather it will be things like "It makes me feel good when someone I love spends time with me," or "I don't like it when someone forces me to do something." Statements like this cross all cultural boundaries. Statements like this give us hints as to what the underlying Moral Invariant is.
I'm not sure if I can, at this time, claim a specific concept as THE Moral Invariant, though I have a few likely candidates, the primary one being Love. Love is a concept that is extolled in the texts of religions who seem to have nothing else to agree on. It is held as something that is at least desirable amongst those who are religious, as well as those who aren't.
Another likely candidate for a Moral Invariant is self preservation. This is an inborn desire that manifests itself incredibly early, and in fact manifests across species.
My personal bias produces the ethical expectation that Love is "higher" than self preservation, in that it may require a higher level of intelligence to comprehend principles of love.
Even if we don't have an exact identification of what a Moral Invariant actually is, the promise of Moral Covariance (as well as common experience with other members of the Human Race) is that they exist, and that if we want to construct Morally Significant models, we should try to determine what the Moral Invariants are.
In the absence of a well identified Moral Invariant, an indication that two Moral Observers are employing Morally Significant models, is that the models are based on the common ground of the two Moral Observers.
