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It seems to me that several quantum interpretations rely on the idea that there exists a wavefunction that completely specifies the state of the universe. Of these, the Many Worlds Interpretation is perhaps the most famous but it seems even the Bohm Interpretation requires a Universal Wavefunction in order to specify the complete, nonlocal waveguide that determines the trajectories of locally isolated particles.

This Universal Wavefunction is difficult to explicitly construct as it requires a specification of a complete set of observables. However, one can imagine that in the limit of infinite experiments, it might be possible to enumerate a complete set of observables and determine the form of the Universal Wavefunction on these observables (or more specifically on some maximal subset of commuting observables).

The difficulty I'm encountering is that I do not see how this limit necessarily converges to a fully specified Universal Wavefunction. Just considering how the final object would have to be constructed, a simple paradox immediately arises: There must be a self-encoding (i.e. a model) of the Universal Wavefunction within a subset of itself. This model would be constructed using strictly less information than the "real" Universal Wavefunction. Naively this seems not only unlikely to me, but completely contradictory. One could consider the universe itself as the model, but this is not a representation of the universe and it contains no physical content about its laws or any means of prediction.

It's clear that some approximate model might exist in a subset of the Universal Wavefunction, but a number of these quantum interpretations rely on the existence of such a wavefunction in order to justify their ontological ramifications. Often the stipulation is made, "if calculated from an outside observer," but it isn't fair to assume that an "observer outside the universe" is a sensible ontological framework to work with either.

I haven't really been able to find discussions of the Universal Wavefunction from this angle, are there any resources that are able to define the Universal Wavefunction in such a way and circumvent (or show the potential naive flaw of) my concerns?

Is there an argument that such a Universal Wavefunction need not exist in order to carry out the program implied by these interpretations?

Are the ontological pictures of Bohmian mechanics and the many worlds interpretation insensitive to the existence of a Universal Wavefunction in the first place?

I apologize if this is a repost but similar questions seem to be focused on the existence of the many worlds that follow from this stipulation in the many worlds interpretation or whether the universal wavefunction exists and neither approach seem to be getting at my question.

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  • $\begingroup$ Is your objection specific to quantum mechanics? In classical mechanics, the analog of the "universal wavefunction" is just a set of real numbers specifying the position of all the particles. But presumably this also contains too much information to be described within the universe itself (or a subset of it). $\endgroup$ – Dominic Else Oct 18 '18 at 22:15
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    $\begingroup$ Isn't this like saying 'I don't believe the earth is a single planet, because that would mean that a geology textbook describes the whole earth, but the geology textbook is just a small part of earth and so can't contain a description of the whole?' $\endgroup$ – Mitchell Porter Oct 19 '18 at 0:03
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    $\begingroup$ It is, you shouldn't expect the geography book to have a complete description of every particle on Earth's position and momenta. That is indeed the inference. $\endgroup$ – Daniel Kerr Oct 19 '18 at 1:24
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    $\begingroup$ For a constructivist approach, see arxiv.org/abs/1512.06845 $\endgroup$ – Stéphane Rollandin Oct 19 '18 at 8:06
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    $\begingroup$ See also arxiv.org/abs/quant-ph/0005095 $\endgroup$ – Stéphane Rollandin Oct 19 '18 at 8:10
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I agree with some of the comments that the Universal Wavefunction $\Psi$ is in no principle way different to a collection of all positions and momenta $(p_i,q_i)$, for $i=1,...,N$, where $N$ is the number of particles in the universe. The latter would be the "full description" of the state of the universe in classical mechanics.

Of course, if we seriously write down a theory (classical mechanics/quantum mechanics), we postulare some mathematical objects ($p_i$ and $q_i$/$\Psi$) for the description of our world. Some people might even claim they exist, and then we have the word ontology in the games. But even more clearly, no one thinks that these can be known, or written down explicitly, or whatever.

It is not a problem: Why should we even think that we can fully know anything that exists? It is very similar to the oceans on earth: Before people could fly, nobody had seen more than very small parts of the ocean, and everybody saw different parts. It was, however, the natural assumption that actually all the space between, say, Europe and America, is filled with water and the Atlantic ocean actually exists. This is a simpler concept than anything else I could think of to explain what we see.

In the same way, we assume that the whole universe is described by a wave function because the use of wave functions for all kinds of subsystems of the universe has proven very fruitful. Where would you stop, what should be the largest system that still has a wave function? Since the whole universe is the only real "isolated system" that there is, we need at least in principle to consider it as a whole. For all practical purposes, of course, this is an irrelevant question. For ontology, the question is then more if the mathematical objects as $\Psi$ are really "there" or just a convenient invention by us. Maybe this latter opinion suits you better.

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  • $\begingroup$ Inferring the existence of the whole universe does not also allow us to infer it has a wavefunction or the properties of one. Even if you assume the mathematical wavefunctions are "there," an inconsistent wavefunction for the Universe is still an issue. Take MWI for example, if you cannot assume that the Universal Wavefunction branches in environmentally-selected eigenstates, you cannot postulate the existence of other worlds. If this were true, MWI would not be problematic for interpreting specific experiments, but it couldn't serve as an ontology for the universe. $\endgroup$ – Daniel Kerr Oct 31 '18 at 18:14
  • $\begingroup$ Maybe it's true that Many-Worlds are problematic, but if you take e.g. Bohmian mechanics, no problems arise. $\endgroup$ – Luke Nov 2 '18 at 15:01
  • $\begingroup$ I'm not sure I follow how Bohmian mechanics avoids this. If you cannot assume that the Universe has the properties of a wavefunction, how do we have an ontological basis for the universal pilot wave that determines the complete set of particle trajectories? $\endgroup$ – Daniel Kerr Nov 2 '18 at 17:48

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