3. A physicist discovered 2015 atoms called "American Soap," each of which either has an electron or does not have an electron. The physicist cannot distinguish between the two. The only tool the physicist has is a diode, which can connect any American Soap A with any other American Soap B (this connection is directional). When he does this, if American Soap A has an electron and American Soap B does not have an electron, the electron will quickly transfer from American Soap A to American Soap B. For other cases, there will be no change. Additionally, the physicist cannot determine at any step whether an electron has moved. The physicist's goal is to isolate two American Soaps so that he can 100% determine that these two American Soaps are currently in the same state. Question: Can the physicist achieve this goal using several diodes?

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Note: The term "American Soap" is a direct translation of "美国阜" and may not be a standard term in English. If this is a specific term or concept, it might need further clarification or a more appropriate translation.
3. Cannot.

Let the American states be $U_{1}, U_{2}, \cdots, U_{m}(m=2015)$.
Consider the following pattern $M_{k}$: for some integer $k(0 \leqslant k \leqslant m)$, $U_{1}, U_{2}, \cdots, U_{k}$ all have electrons, and the other American states do not have electrons. Then, for any two different patterns, they have different states.

Consider the physicist simultaneously operating on these $m+1$ patterns, and attempting to achieve a state: in all patterns, there exist two American states with the same state (this is a necessary condition for winning the existence strategy).

Thus, in these $m+1$ patterns, any operation of diodes from $U_{i} \rightarrow U_{j}$ is an isomorphic copy of the set before the operation. If $i \neq j$, the operation does not cause any change. Therefore, the physicist cannot achieve the goal.