Do physicists talk about the wavefunction of the universe? What does that wavefunction even mean? Usually, wavefunctions describe probabilities of measurements of a system. But in this case, every possible act of measurement is a part of the system. There's no outside observer to collapse the wavefunction of the universe.
Hypothetically, suppose I gave you the wavefunction of the universe by storing it in some hypothetical storage device. And assume that you are a being of infinite processing power. Could you use that wavefunction to make any predictions about the universe?
Suppose you are about to do an experiment on an isolated system. Could you use the wavefunction of the universe to predict (probabilistically predict) the outcome of this experiment? How would you do this (in principle, not practically)?
For simplicity, we assume that the universe obeys non-relativistic QM. So the wavefunction you're given is of the form $\psi (t, x_1, x_2, x_3, y_1, y_2, y_3,.......)$. $(x_i, y_i, z_i)$ are the co-ordinates of the i'th particle. This also includes all the particles that make up your brain. The variable $t$ is there because you're given the wavefunction at every single point of time. You do not have to compute the evolution yourself.
Also, it is assumed that you're given your own (and the experiment's) spacetime co-ordinates, in the same co-ordinate system used to express the wavefunction. I'm not even sure how you'd use this information. After all, that wavefunction describes your existence as a superposition.
To sum up, you're given the wavefunction $\psi$ of the universe at all points of time. Now $|\psi |^2$ does not have any meaning because there's no outside observer who can perform a measurement of the entire universe. All observers are part of the universe.
Now you're an observer inside this universe and you're about to do an experiment. Using the wavefunction, how would you, in principle, calculate the probabilistic predictions of your experiment?
