Unit testing for object immutability

Question

I want to make sure that a given group of objects is immutable.

I was thinking about something along the lines of:

1. check if every field is private final

Answer 1

Pretty sure it is impossible. Consider this function:

public void doSomething() {
    if (System.currentTimeMillis() % 100000 == 0) {
        this.innerMember.changeState();
    }
}

First, you won't be able to detect it by running every class function, as this function changes the state of object precisely only once in 100 seconds.

Second, you won't be able to detect it by parsing code, as you do not know if changeState() function changes the state of innerMember or not.