I can see why this would keep you up all night. Have you looked into the 10 Dimensions Theory?
Not specifically 10, in that I view this number to be more of a longer answer required by a formulation of string theory that is mostly superseded, and because of the nature of these dimensions (which are wholly unlike the 4D spacetime of either special or general relativity). These dimensions are far more mathematical, as one can see in e.g., the equating of 10-dimensional superstring theory with a 4D gauge theory. Then there's the fact that the preference for 10 dimensions rather than an equally consistent 26 is, I think, one of economy. Finally, there's the nature of the dimensions and the space to consider. For example, we describe quantum physics only as they exist in a space that extends infinitely along infinitely many "directions" called Hilbert space. The 4D spacetime of special relativity is geometrically different from that of general relativity (which is actually a rather big problem, as the latter allows for causal paradoxes such as closed timelike curves or CTCs). There's a pretty good monograph by Bars & Terning (2010).
Extra dimensions in space and time (
Multiversal Journeys) that goes over various proposals and is important in how thoroughly it addresses the ways different models "split" the dimensions (e.g., two-time physics isn't ever 2D) and the various alterations on the more standard models beyond the "standard models". I came into physics more through mathematics than anything else, so I got used to thinking about 1,000th dimensional spaces or more before I know more than the basics of QM. To me, the ontology of spacetime is more of a daunting question than posited solutions of extra-dimensions that resolve mathematical difficulties in cosmology & theoretical physics.
While this doesn't seem too astounding, think of it in the context of how the general theory of relativity was first criticized as a radical proposition. The theory stipulated that from one perspective, in real-time, an object moving in space took 5 seconds to travel from point A to point B which was measured from Perspective 1 as 10 meters. However, from Perspective 2, the distance traveled in those 5 seconds from point A to point B was 20 meters.
Actually these "paradoxes" were introduced 10 years earlier by Einstein's 1905 paper founding special relativity (and with it length contraction and time dilation). Things get even more troublesome in general relativity, even though we are still dealing with 4-dimensions.
The insight is that we may lack a dimension of measurement to understand the unexplained problems that arise in quantum theory like wave-particle contradictions and entanglement, to name just two.
I don't know if I'd call the wave-like nature of all matter (wave-particle duality is a misnomer, as in reality QM posits that everything is wave-like but becomes increasingly localized the larger the system is). It's counterintuitive, yes, but it's only a problem if it doesn't reflect reality (also, I'm not sure I follow you regarding how nonlocality, entanglement, etc., are addressed by physics beyond the standard model in ways that "resolve" these).
My purpose for explaining all this is to reach the point that our understanding of the universe should be described as 'incomplete' as an alternative to 'incorrect'.
Good point. Although one could argue that incomplete knowledge entails incorrect knowledge, or at least that it can.
If we are incorrect, then our methods for understanding the universe and everything in it (scientific method, logic, capacity to reason, etc) would be flawed.
Many a scientific theory has been held that turned out not incomplete but incorrect. Certainly, before another 1905 paper by Einstein which really sparked the development of quantum physics, it was thought that classical physics was incomplete. However, it was barely incomplete (so barely that the general view was work in physics was basically done). It turned out that what was incomplete was incomplete because most of classical physics was fundamentally incorrect.
This, though, is not something I see as a problem for logic or scientific methods. There's an oft-quoted dictum "all models are wrong, but some are useful." It's one thing if inaccuracies, failures, and being incorrect prevented us from making progress. It's another to recognize that we'll be wrong most of the time to some degree, but this doesn't prevent us form making firm statements about the nature of the world/cosmos.
I understand, I think, where you are coming from (and certainly your concern) but I think the failure of classical physics was one of the most important wake-up calls without which modern sciences wouldn't really be possible. Two different experiments continually confirmed mutually exclusive results, until we were forced to realize that the entire theoretical framework was flawed, and the experiments and their findings closely related to and motivated by theory. Now we know this is so.
This is a hazardous idea because of the conclusion (that I believe you came to) that we must doubt conclusions that we rationally came to since they are based on methods embedded with flaws.
What we realized, and one of the most important results of the failure of classical physics, was that all hypotheses are theory-laden. That is, when we develop hypotheses we wish to test we do so relying on theory to generate them, theory to inform how we set-up our experiments, and theory to interpret the results. The idea that there is The Scientific Method (always an idealization) consisting of
1) Develop hypothesis
2) Try to disprove hypothesis repeatedly
3) If repeatedly confirmed, hypothesis becomes theory
is alien to the sciences and has been for a century. If we don't recognize that the inter-relationship between theory, methods, hypotheses, and interpretations we run the risk of repeating the catastrophic failure of physics during the early 20th century. Given any field, there are numerous disagreements over aspects of theories in that field, or theories in that field. One of the reasons that a theory I mentioned in an earlier post, embodied cognition, has been around alongside an incompatible theory for ~30 years is because of the ways in which methods and findings are theory-laden.