I’ve claimed for some time that quantum computing can be realized on a single processor Von Neumann machine and published a paper explaining the basic intuition. All that is necessary is to represent information using sparse distributed codes (SDC) rather than localist codes. With SDC, all informational states (hypotheses) represented in a system (e.g., computer) are represented in physical superposition and therefore all such states are partially active in proportion to their similarity with the current most likely (most active) state. My Sparsey® system operates directly on superpositions, transforming the superposition over hypotheses at T into the superposition at T+1 in time that does not depend on the number of hypotheses represented (stored) in the system. This update occurs via passage of signals via a recurrent channel, i.e., a recurrent weight matrix. In addition to a serial (in time) updating of the superposition, mediated by the recurrent matrix, the system may also have an output channel (a different, non-recurrent weight matrix) that “taps” off, i.e., observes, the superposition at each T. Thus the system can generate a sequence of collapsed outputs (observations) which can be thought of as a sequence of maximum likelihood estimates, as well as continuously update the superposition (without requiring collapse).
This has led me to the following interpretation of the quantum theory of the physical universe itself. Projecting a universe of objects in a low dimensional space, e.g., 3 dimensions, up into higher dimensional spaces, causes the average distance between objects to increase exponentially with the number of dimensions. (The same is true of sparse distributed codes living in a sparse distributed code space.) But now imagine that the objects in the low dimensional space are not point masses, but rather have extension. Specifically, let’s imagine that these objects are something like ball-and-stick lattices, or 3D graphs consisting of edges and nodes. The graph has extension in 3 dimensions, but is mostly just space. Further, imagine that the graph edges simply represent forces between the nodes (and not constrained to be pairwise forces), where the nodes are the actual material constituents of objects (similar to how an atom is mostly space…and perhaps even a proton is mostly empty space).
Now suppose that the actual universe is of huge dimension, e.g., a million dimensions, or an Avogadro’s number of dimensions, but let’s stick with one million for simplicity. Furthermore, imagine that these are all macroscopic dimensions (as opposed to the Planck-scale rolled up dimensions of string theory). Now imagine that this million-D universe is filled with macroscopic “graph” objects. They would have macroscopic extent on perhaps a large fraction or even all of those 1 million dimensions, but they would be almost infinitely sparse or diffuse, i.e., ghost-like, so diffuse that numerous, perhaps exponentially numerous such objects, could exist in physical superposition with each other, i.e., physically intermingled. They could easily pass through each other. But, as they did so, they would physically interact.
Suppose that we can consider two graphs to be similar in proportion to how many nodes they share in common. Thus two graphs that had a high fraction of their nodes in common might represent two similar states of the same object.
But suppose that instead of thinking of a single graph as representing a single object, we think of it as representing a collection of objects. In this case, two graphs having a certain set of nodes in common (intersection), could be considered to represent similar world states in which some of the same objects are present and perhaps where some of the those objects have similar internal states and some of the inter-object relations are similar. Suppose that such a graph, S, consisted of a very large number (e.g., millions) of nodes and that a tiny subset, for concreteness, say, 1000, of those nodes corresponded to the presence of some particular object x. Then imagine another instance of the overall graph, S’, in which 990 of those nodes are present. We could imagine that that might represent another state of reality in which x manifests almost identically as it did in the original instance; call that version of x, x‘. Thus, if S was present, and thus if x was present, we could say that x‘ is also physically present, just with 990/1000 strength rather than with full strength. In other words, the two states of reality can be said to be physically present, just with varying strength. Clearly, there are an exponential number of states around x that could also be said to be partially physically present.
Thus we can imagine that the actual physical reality that we experience at each instant is a physical superposition of an exponentially large number of possible states, where that superposition, or world state, corresponds to an extremely diffuse graph, consisting of a very large number of nodes, living in a universe of vastly high dimension.
This constitutes a fundamentally new interpretation of physical reality in which, in contrast to Hugh Everett’s “many worlds” theory, there is only one universe. In this single universe, objects do physically interact via all the physical forces we already know of. It’s just that the space itself has such high dimension and these object’s constituents are so diffuse that they can simply exist on top of each other, pass through each other, etc. Hence, we have found a way for actual physical superposition to be the physical realization of quantum superposition.
Imagine projecting this 1 million dimensional space down into 3 dimensions. These “object-graphs”, which are exponentially diffuse in the original space, will appear dense in the low dimensional manifold. Specifically, the density of such objects increases exponentially with decreasing number of dimensions. I submit that what we experience (perceive) as physical reality is simply an extremely low dimensional, e.g. 3 or 4 dimensions, projection of a hugely-high dimensional universe, whose objects are macroscopic but extremely diffuse. Note that these graphs (or arbitrary portions thereof) can have rigid structure (due to the forces amongst the nodes).
In particular, this new theory obviates the need for the exponentially large number of physically separate universes that Everett’s theory requires. Any human easily understands the massive increase in space in going from 1-D to 2-D or from 2-D to 3-D. There is nothing esoteric or spooky about it. Anyone can also understand how this generalizes to adding an arbitrary number of dimensions. In contrast, I submit that no human, including Everett, could offer a coherent explanation of what it means to have multiple, physically separate universes. We already have the concept, which we are all easily taught in childhood, that the “universe” is all there is. There is no Physical room for any additional universes. The “multiverse”—a hypothesized huge or infinite set of physical universes—is simply an abuse of language.
Copenhagen maintains that all possible physical states exist in superposition at once and that when we observe reality, that superposition collapses to one state. But Copenhagen never provided an intuitive physical explanation for this quantum superposition. What Copenhagen simply does not explain, and what Everett solves by positing an exponential number of physically separate, low-dimensional universes, filled with dense, low-D objects, I solve by positing a single super-high dimensional universe filled with super-diffuse, high-D objects.
Slightly as an aside, this new theory helps resolve a problem I’ve always had with Schrodinger’s cat. The two states, “cat alive” and “cat dead” are constructed to seem very different. This misleads people into thinking that at every instant and in every physical subsystem, a veritable infinity of states coexist in superposition. I mean…why stop at just “cat alive” and “cat dead”? What about the state in which a toaster has appeared, or a small nuclear-powered satellite? I suppose it is possible that some vortex of physical forces, perhaps designed by a supercomputer, could instantly rearrange all the atoms in the box from one in which there was a live cat to one in which there is the toaster, or the satellite. But I think it is better to think of transformations like this to have zero probability. My point here is that the number of physical states to which any physical subsystem might collapse at any given moment, i.e., the cardinality of the superposition that exists at that moment, is actually vastly smaller than one might naively think having been misled by the typical exposition of Schrodinger’s cat. Thus, it perhaps becomes more plausible that my theory can accommodate the number of physical states that actually do coexist in superposition.
Again, this theory of what physical reality actually is came to me by first understanding and constructing a similar theory about representing physical reality. In that SDC theory, the universe is a high-D “codespace”, the “objects” are “representations” or “codes”, and these codes are high-D but are extremely diffuse (sparse) in that codespace.