There is a clear example I have in mind of a modal transformer. The primary winding is in possible world, W1. The secondary winding is in possible world, W2. W1 and W2 are not causally linked in any way. There is no magnetic flux that flows between the worlds. The transformer halves, primary and secondary, are at arbitrary space-time locations in each of the worlds. There is no law of conservation of energy in W1 or W2. However, both halves act in the way we would expect a transformer in our world with this difference. In W1, the primary coil loses energy. In W2, the secondary coil gains energy. They act as if they are causally linked but they are not. The W1 coil can best be described as an energy losing inductor. The W2 coil can best be described as an energy creating inductor. Suppose, they gain and lose energy in the proportions we would expect if the two halves were connected in our world.
Now, the following is true of this trans world modal transformer:
Across both worlds, no energy is lost by this system.
The energy lost in W1 = the energy gained in W2 without ANY causal links between W1 and W2.
The question is:
Is the modal transformer described above consistent with our best possible world semantics?
Does this example or one's like it suggest that we modify our definition of a necessary truth in modal logic?
The counterfactual truth involves W1 and W2, that when combined it matches a transformer in a world W3 which has a physical law for transformers. W1 does not have W3's law, nor does W2, so a statement of the relevant physical law is false in W1 and false in W2, and also false in W3, but analogous to a true statement in W3. The analogy breaks down specifically because of a lack of causal continuity between W1 and W2. So, the W1+W2 truth is necessarily false taking the worlds on an individual basis, but contingently true of W1+W2 taken together.