Java でクラス変数をオーバーライドできますか?

class Dad {
    protected static String me = "dad";

    public void printMe() {
        System.out.println(me);
    }
}

class Son extends Dad {
    protected static String me = "son";
}

public void doIt() {
    new Son().printMe(); // Prints "dad"
}

public class Son extends Dad {
    private String me;

    public Son(String me) {
        this.me = me;
    }

    @Override
    public void printMe() {
        System.out.println(me);
    }
}