Consider a complete state of the universe. Call it U.
This state contains all objects, all relations, all conditions, all hidden structures, all positions, and the complete description of the event itself. Nothing relevant exists outside it. Nothing is missing.
I do not mean a partial laboratory setup or a limited collection of observable conditions. It is the total state.
If U is truly complete, then the next state must follow from U alone.
Now suppose someone claims that the same complete state U can produce two different future states, U₁ and U₂, where:
U₁ ≠ U₂
Then a simple question appears:
Where does the difference come from?
If the source of the difference is contained within U, then the two cases were never actually the same. The difference was already present inside the initial state.
If the source of the difference is not contained within U, then it must come from outside U. But this contradicts the assumption that U is complete and self-contained.
If the difference comes from nowhere, then we have introduced a difference without a cause, a distinction without a distinction.
Therefore: A genuinely complete state cannot produce genuinely different outcomes without some difference existing somewhere in the total description.
If the outcome differs, the total state differed.
If the total state is identical, the outcome cannot differ.
Otherwise, the meaning of "same" disappears.