What is the wavefunction of the observer himself?

Solution 4

Hugh Everett is often misunderstood. His interpretation of quantum mechanics is taken by most physicists today to mean a many worlds interpretation with splittings. His interpretation was actually something else, the relative state interpretation. Most physicists narrowed in on the the part of his thesis where he gave a reduced density matrix analysis, but his real interpretation lies in the concept of a relative state. Decompose the universe into the observer and everything else. The internal states of the observer are entangled with the rest of the universe. Relative to a choice of a classical internal state of the observer, the term in the entanglement expansion given by the tensor product of this internal state with the wave function of the rest of the universe is the relative state.

Let me give you a consistent histories overview for more precision. An Information Gathering and Utilization System, or IGUS in short, is some cybernetic system taking in information from the outside world through its senses, processing them internally, storing some information as memories, and as a result of all the processing, it decides how to act in or manipulate the external world. An IGUS may be an animal, human, robot, computer or whatnot. In a succession of moments in time, the IGUS makes consecutive measurements of its environment and also its internal states through its senses and introspection. This can be modeled as coarse grained measurements in consistent histories. The end result stored in the memory banks of the IGUS is not a simple transcript of all of these measurements but the result of a classical computational processing of these measurements. It is undoubtedly classical because scientists have successfully simulated the brains of worms, or cortical columns of a rat using classical simulations and nothing else. Consistent histories can be adapted so that the choice of successive measurements by the senses is dependent upon the outcomes of earlier measurements, and a further coarse graining of these measurements by combining collections of histories into a further coarse grained history reflecting the actual memory contents of the IGUS after elaborate processing. The wave function of the universe is an entanglement between the memory contents of the IGUS and the rest of the universe. The memories are encoded in synaptic connections, magnetic disks, solid state drives, or what not, with all the attendant coarse grained fuzziness.

Now choose a classical configuration for the memories. The relative state of the universe with respect to this classical configuration is what we want. A particular history. It contains limited information about the universe out there and most of the world out there remains in a macroscopic superposition.

You might ask, why classical memories? Can quantum IGUSes exist? Suppose for the sake of argument that there are quantum memory registers. Because of no cloning, either the register is representing classical information of the external world in some basis, it does not represent anything out there, or it is the incorporation of some quantum information which once existed out there but now only exists inside the register. In the latter case, such quantum information can only be useful with respect to the goal of successful action if it is entangled with something out there. The information must have its coherence preserved right until the decision to determine which action. Because most actions decohere, this has to be an essentially classical command and we can fix the classical information stored in the memories right before it was used to determine the action in the appropriate basis. Unless the action is some communication over a quantum channel. In that case, it's pretty safe to say the IGUS was never conscious of the quantum information passing through it because of no cloning. Unconscious processing.

In string theory, the universe is in a superposition of multiverses, and the relative state picks out multiverses hospitable to IGUSes. The classical memories manifest the right anthropic laws and the right environment in the past.

This is an epistemic interpretation, more or less, with radical epistemological uncertainty. The central concept is the internal consistency and coherence of the story the contents of the memory tell. What sort of branches in the world out there correspond to the relative state of the classical memories? For very high internal story consistency, a good contribution comes from an external world which more or less match the contents of the story at a coarse grained level. But the contributions coming from being in a realistic computer simulation are also high... For slightly less internal consistency, it could be from something which more or less matches but with inaccurate recall/perception and distortions along the way, or maybe the IGUS had been systematically deceived. For even less consistency, it could be fiction or a not so naturalistic computer simulation or a brain in a vat. For very low consistencies like near randomness, the most likely contribution to the relative state comes from Boltzmann type statistical fluctuations conspiring together. There is no objective reality in quantum mechanics. This is what the math tells us.

How is the IGUS selected if there are many IGUSes? Pool the memory contents of many IGUSes together to form a supra-IGUS. The individual IGUSes are like drops of water and the supra-IGUS the ocean, and the drops of water merge into the collective consciousness of the ocean.

Let me tell you the meaning of consistent histories. Consistent histories are about what an observer external to our universe in some higher plane can measure and record externally in some Akashic records about our universe without being detected from the inside. The selection of framework is now transparently what the external observer chooses to measure. Why should the external observer select quasiclassical histories? Because that tells him a coherent meaningful story. Why should the external observer select the memories of IGUSes? Because that gives him a predigested condensed high information coarse grained meaningful description of the universe.

Solution 5

Think in terms of the anthropic principle. In the universal wave function of the universe, the probability for the existence of observers is exponentially small. The probability is definitely smaller than the fine-tuning in the cosmological constant, $10^{-123}$, most likely much much smaller than that. Anthropic selection effects.

Ask yourself, what is the Shannon entropy of consciousness? What is your naive estimate of the Shannon entropy of human consciousness as encoded within neuronal firing and encoding patterns within the brain? The capacity of working memory is $7 \pm 2$, and the logarithm of the number of possible neural network symbols parseable by working memory is relatively small. Is the product of this with $7\pm 2$ still less than the log of $10^{123}$? If so, statistically speaking, will Boltzmann brain fluctuations predominate over evolved life?

Something isn't quite right here. Should we add short term memory into the contents of consciousness, and not just working memory? Maybe consciousness isn't what we think it is?

Why digital encoding in terms of discrete symbols for working memory? Why not analog encoding? Surely the particular form of the encoding of the symbols within the neural network ought to be irrelevant to consciousness? Or not?

What physical process searches through the haystack of the universal wave function looking for needles looking like the "conscious states" of observers encoded in a messy form of neural networks anyway so that it can attach "consciousness" to those states?