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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?

Qmechanic
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Egg Man
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    What is this hypothetical storage device? - another Universe? See Is limited computational capacity a fundamental obstacle? – Roger V. May 12 '22 at 07:57
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    @RogerVadim Just assume it's a mythical device from Lord of the Rings lol – Egg Man May 12 '22 at 08:16
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    You know, quantum mechanics and relativity came into existence when one questioned some mythical assumptions (like being able to measure infinitely fast and with infinite precision). – Roger V. May 12 '22 at 08:23
  • If knowing the exact positions and velocities (that do not exist, but assume a classical picture) of particles in a gas is not particularly useful, imagine knowing the wavefunction of the Universe. How do you "discover" that there are stars, planets, black holes, animals from this wave function? Take a look at "More Is Different: Broken symmetry and the nature of the hierarchical structure of science" by P.W. Anderson https://www.science.org/doi/10.1126/science.177.4047.393 – Quillo May 12 '22 at 08:29
  • @Quillo Well if you're given the positions and velocities of every single particle at all points of time (assuming classical universe), then you already know the outcome of every single experiment. Nothing else to do there. If, however, you're given the wavefunction at every single point of time, there's still the remaining task of computing the probabilities of an experiment. I'm asking how you'd do that. – Egg Man May 12 '22 at 14:07
  • @EggMan Even if we know all the positions and and velocities, we need to store this information to specified precision - the memory must be made of atoms... likely more atoms than we want to store information about. Then, if we want to make predictions, we need to solve differential equations, which again involves hardware made of atoms. But all these atoms must still be a part of the Universe, and be accounted for in our calculation. – Roger V. May 12 '22 at 14:27
  • @RogerVadim First, you're given the information at all points of time. You do not have to compute the evolution yourself. Second, you are a being in a fantasy universe. That's where all of this information about this non-fantasy universe is stored. Now you, the fantasy being, has to make probabilistic predictions about what an observer in this non-fantasy universe will see when they do the experiment. – Egg Man May 12 '22 at 14:40
  • As I tried to hint earlier - the fact that you need a fantasy Universe means that we are not dealing here with something that can be studied scientifically... we are not dealing with physics. I understand that only physicists can entertain such fantasies... but still, the question is off topic, since it does not deal with mainstream physics. Please take no offense. – Roger V. May 12 '22 at 14:51
  • @RogerVadim I find your earlier objection to be valid. Because back then, I assumed the storage device, as well as the human of infinite processing power, to be a part of this universe. That'd have meant tampering with the physics of the universe that we're trying to study. However, I think my last comments deals with that issue. It's fine if you think otherwise. – Egg Man May 12 '22 at 15:12
  • EggMan: I am saying something a bit different. I give you the position and velocity of all the particles of this planet (stored in your God-provided computer). Now: given this accurate list of data, please describe how a giraffe is made, or that ants exist. You think that knowing all positions and velocities is useful just because you have the gas (or fluid) paradigm in mind (something uniform). From "raw" data it's extremely difficult, if not impossible to describe "emergent" behaviour. Read P.W Anderson, you will like it: https://www.science.org/doi/10.1126/science.177.4047.393 :-) – Quillo May 12 '22 at 15:15

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