Would the existence of a universal wave function automatically mean the Many Worlds Interpretation?

Question

If the Universal Wave Function definitely existed, would that mean the Many-Worlds Interpretation was automatically true or would it only imply that?

Answer 1

The concept of "wavefunction"is inherent in the definition of Quantum Mechanics,in the same way the concept of mass is inherent in the definition of classical mechanics: it is a mathematical function which is used to model data and predict physical behavior of matter at small dimensions .

Present physics modeling assumes that the underlying microscopic interactions obey quantum mechanical equations, and it has been shown that the classical theories emerge from this underlying level. In this sense a universal wave function, assuming extreme measurement accuracies, exists and has been modeled with the density matrix formalism .

[The many-worlds interpretation] (MWI) is an interpretation of quantum mechanics that asserts that the universal wavefunction is objectively real, and that there is no wavefunction collapse. This implies that all possible outcomes of quantum measurements are physically realized in some "world" or universe

As in principle a universal wave function exists, the crucial word is "interpretation". It means that the proposal gives exactly the same numerical predictions for new studies , just a different way of interpreting the internal functions.

would that mean the Many-Worlds Interpretation was automatically true or would it only imply that?

The universal wavefunction exists, can be formulated mathematically . The mathematics is true, but the many-worlds interpretation of the mathematics is just a different optical angle,there are no new predictions to be able to distinguish if it is valid or not.

Answer 2

It would imply that we are entities bound by the laws of quantum mechanics, and thus there are no truly classical observers to observe the system. The QM interpretations are only needed to explain their behavior with respect to a classical observer.

Decoherence based theories would be the natural winner.

Answer 3

If the Universal Wave Function definitely existed, would that mean the Many-Worlds Interpretation was automatically true or would it only imply that?

There are quite a lot of different issues being mixed up in this question.

If the Universal Wave Function definitely existed

It's a bit unclear what you mean by this. Knowledge is created by noticing a problem with our existing understanding of some aspect of how the world works, proposing solutions to those problems and critically discussing the solutions until we find one with no known criticisms despite our best attempts to find such a criticism. In science, the criticism step includes looking for experiments that could distinguish between different theories and performing those experiments to rule out theories that contradict experiments. Since we haven't looked throughout the whole of physical reality it is always possible that some experiment that could be done would contradict and existing theory. So there is no prospect of proving any scientific theory to be definitely true. For some more explanation see the recommended reading here:

https://fallibleideas.com/books#popper

There is an entirely separate issue in this question of whether a universal wave function implies the MWI.

The many worlds interpretation (MWI) is what you get if you take the equations of motion of quantum theory seriously as a description of how the world actually works and work out their implications as you would for any other scientific theory.

In classical physics the equations of motion for the $x$ position of a particle are written in terms of a function $x(t)$ such that if you measure $x$ at time $t$, you get the answer $x(t)$.

In quantum physics the equations of motion are written in terms of matrices called observables. The eigenvalues of those observables are the possible results of measuring the relevant quantity. Quantum physics predicts the probability of each of those possible outcomes.

In many experiments, the result of an experiment depends on what happens to all of the possible values of the relevant observable: this is called quantum interference. For an example see Section 2 of this paper

https://arxiv.org/abs/math/9911150

When you walk through a doorway you don't have to take account of all of the possible routes through the doorway. A commonly stated explanation for this fact is that somehow all of the possible values of the observables describing your trajectory vanish except the one you see: this is called collapse. Collapse is incompatible with the equations of motion of quantum theory. Some physicists have tried to modify the equations of motion of quantum theory to include collapse:

https://arxiv.org/abs/2310.14969

Another proposed modification of quantum theory involves sprinkling particles on top of reality as described by quantum theory with specific equations of motion: pilot wave theory. There are proposals for ways to test pilot wave theory against quantum theory:

https://arxiv.org/abs/2408.05403

Quantum theory without collapse models measurements as interactions that produce records of some property of the measured system. A record is a piece of information that can be copied and copying information out of a quantum system suppresses interference. This is called decoherence:

https://arxiv.org/abs/1911.06282

Any object you can see in everyday life is undergoing such interactions on scales of space and time smaller than those over which they change significantly, e.g. - light reflecting off an object conveys information about its position to other systems, as does the pressure an object exerts on whatever it is resting on and so on. As a result of decoherence such objects tend to obey the laws of classical physics to a good approximation.

Decoherence doesn't eliminate the other values of the monitored observable, it just prevents interference between them. As a result quantum theory describes a reality in which all of the systems around you exist in multiple versions that form layers each of which acts approximately like the world as described by classical physics, hence the name of the MWI:

https://arxiv.org/abs/1111.2189

https://arxiv.org/abs/quant-ph/0104033

Spontaneous collapse and pilot wave theories both have a wavefunction so strictly the mere existence of a wavefunction doesn't imply the MWI. But those theories also also don't currently reproduce the predictions of relativistic quantum theories, which are the vast bulk of experimentally tested predictions of quantum theory:

https://arxiv.org/abs/2205.00568

and there are other problems too

https://arxiv.org/abs/quant-ph/0403094

https://arxiv.org/abs/1407.4746

So you can have variants of quantum theory that claims to eliminate many worlds.

Answer 4

If all elementary particles are part of the quantum system described by the universal wavefunction, then there are no elementary particles left over to "build" an observer.

If no observer can exist outside of the universal wavefunction (i.e. outside of the universe), then no observation can be made of the wavefunction, and if no observation can be made of the wavefunction, then the wavefunction cannot collapse.

If there can be no collapse, then no eigenstate can be said to be the "real one", since we usually define that to be the eigenstate that is observed. So all possible eigenstates are equally valid, or equally real. We just happen to inhabit one of them.

Answer 5

No, there is no universal wave function. You need a universal density matrix, but to store it would require hardware bigger than the universe itself. At least in the subclass of many worlds that I and my many copies are inhabiting.