Abstract I write as a physicist, with the knowledge that many physicists are studying the mathematical structure of our physical universe and hope to be able to find a ‘theory of everything’, or TOE, that will give a complete set of dynamical laws for this structure. This would essentially give the rules for how all the physical quantities in the universe evolve. Such a TOE would not by itself give the boundary conditions also necessary to determine the history of the universe, so it is a misnomer to say that it is a ‘theory of everything’, but it is convenient to retain the acronym TOE for this dynamical part of the laws of physics. Some physicists, such as Hartle and Hawking (1983), are also seeking to find rules specifying the boundary conditions (BC) of the universe. The combination of the TOE and the BC would then give a complete description of the mathematics of the state of the universe and its evolution.
Abstract I write as a physicist, with the knowledge that many physicists are studying the mathematical structure of our physical universe and hope to be able to find a ‘theory of everything’, or TOE, that will give a complete set of dynamical laws for this structure. This would essentially give the rules for how all the physical quantities in the universe evolve. Such a TOE would not by itself give the boundary conditions also necessary to determine the history of the universe, so it is a misnomer to say that it is a ‘theory of everything’, but it is convenient to retain the acronym TOE for this dynamical part of the laws of physics. Some physicists, such as Hartle and Hawking (1983), are also seeking to find rules specifying the boundary conditions (BC) of the universe. The combination of the TOE and the BC would then give a complete description of the mathematics of the state of the universe and its evolution.
The ideas of Sensible Quantum Mechanics are expressed in lay terms for philosophers of consciousness and others. A framework is proposed and explained for the `psycho-physical-parallelism' between conscious experiences and the mathematical structures of quantum physics (e.g., a set of quantum operators obeying some algebra, and a quantum state giving the expectation value of each operator). In particular, it is proposed that each set of possible conscious experiences has a measure given by the expectation value of a corresponding operator (a positive-operator-valued measure). Then one has a generalization of the Weak Anthropic Principle named the Conditional Aesthemic Principle: given that we are conscious beings, our conscious experiences are likely to be typical experiences in the set of all conscious experiences with its measure.
Sensible Quantum Mechanics or Mindless Sensationalism is a framework for relating consciousness to a quantum universe. It states that each conscious perception has a measure that is given by the expectation value of a corresponding quantum "awareness operator" in a fixed quantum state of the universe. The measures can be interpreted as frequency-type probabilities for a large set of perceptions that all actually exist with varying degrees of reality, so detailed theories within this framework are testable. The measures are not propensities for potentialities to be actualized, so there is nothing indeterministic in this framework, and no free will in the incompatibilistic sense. As conscious perceptions are determined by the awareness operators and the quantum state, they are epiphenomena. No fundamental relation is postulated between different perceptions (each being the entirety of a single conscious experience and thus not in direct contact with any other), so SQM or MS, a variant of Everett's "many-worlds" framework, is a "many-perceptions" framework but not a "many-minds" framework.
Quantum mechanics is usually defined in terms of some loosely connected axioms and rules. Such a foundation is far from the beauty of, e.g., the `principles' underlying classical mechanics. Motivated, in addition, by notorious interpretation problems, there have been numerous attempts to modify or `complete' quantum mechanics. A first attempt was based on so-called hidden variables; its proponents essentially tried to expel the non-classical nature of quantum mechanics. More recent proposals intend to complete quantum mechanics not within mechanics proper but on a `higher (synthetic) level'; by means of a combination with gravitation theory (R Penrose), with quantum information theory (C M Caves, C A Fuchs) or with psychology and brain science (H P Stapp). I think it is fair to say that in each case the combination is with a subject that, per se , suffers from a very limited understanding that is even more severe than that of quantum mechanics. This was acceptable, though, if it could convincingly be argued that scientific progress desperately needs to join forces. Quantum mechanics of a closed system was a beautiful and well understood theory with its respective state being presented as a point on a deterministic trajectory in Liouville space---not unlike the motion of a classical N -particle system in its 6N -dimensional phase-space. Unfortunately, we need an inside and an outside view, we need an external reference frame, we need an observer. This unavoidable partition is the origin of most of the troubles we have with quantum mechanics. A pragmatic solution is introduced in the form of so-called measurement postulates: one of the various incompatible properties of the system under consideration is supposed to be realized (i.e. to become a fact, to be defined without fundamental dispersion) based on `instantaneous' projections within some externally selected measurement basis. As a result, the theory becomes essentially statistical rather than deterministic; furthermore there is an asymmetry between the observed and the observing. This is the point where consciousness may come in. Complemented by an introduction and several appendices, Henry Stapp's book consists essentially of three parts: theory, implications, and new developments. The theory part gives a very readable account of the Copenhagen interpretation, some aspects of a psychophysical theory, and, eventually, hints towards a quantum foundation of the brain--mind connection. The next part, `implications', summarizes some previous attempts to bridge the gap between the working rules of quantum mechanics and their possible consequences for our understanding of this world (Pauli, Everett, Bohm, Heisenberg). The last section, `new developments', dwells on some ideas about the conscious brain and its possible foundation on quantum mechanics. The book is an interesting and, in part, fascinating contribution to a field that continues to be a companion to `practical' quantum mechanics since its very beginning. It is doubtful whether such types of `quantum ontologies' will ever become (empirically) testable; right now one can hardly expect more than to be offered some consistent `grand picture', which the reader may find more or less acceptable or even rewarding. Many practicing quantum physicists, though, will remain unimpressed. The shift from synthetic ontology to analytic ontology is the foundation of the present work. This means that fundamental wholes are being partitioned into their ontologically subordinate components by means of `events'. The actual event, in turn, is an abrupt change in the Heisenberg state describing the quantum universe. The new state then defines the tendencies associated with the next actual event. To avoid infinite regression in terms of going from one state of tendencies to the next, consciousness is there to give these events a special `feel', to provide a status of `intrinsic actuality'. The brain of an alert human observer is similar in an important way to a quantum detection device: it can amplify small signals to large macroscopic effects. On the other hand, actual events are not postulated to occur exclusively in brains. They are more generally associated with the formation of records. Records are necessarily part of the total state of the universe: it is obvious that the state of the universe cannot undergo a Schrödinger dynamics and at the same time record its own history. `The full universe consists therefore of an exceedingly thin veneer of relatively sluggish, directly observable properties resting on a vast ocean or rapidly fluctuating unobservable ones.' The present ideas also bear on how the world should be seen to develop. While conventional cosmology encounters problems as to how to define the intial conditions, which would enter the governing equations of motion, here `the boundary conditions are set not at some initial time, but gradually by a sequence of acts that imposes a sequence of constraints. After any sequence of acts there remains a collection of possible worlds, some of which will be eliminated by the next act.' Connected with those acts is `meaning': there has always been some speculation about the special significance of local properties in our understanding of the world. One could argue that correlations (even the quantum correlations found, e.g., in the EPR-experiments) were as real as anything else. But also Stapp stresses the special role of locality: the `local observable properties, or properties similar to them are the natural, and perhaps exclusive, carriers of meaning in the quantum universe. From this point of view the quantum universe tends to create meaning.' This sounds like an absolute concept: meaning not with respect to something else, but defined intrinsically---not easy to digest. The role of consciousness in the developing quantum universe requires more attention. `The causal irrelevance of our thoughts within classical physics constitutes a serious deficiency of that theory, construed as a description of reality.' This is taken to be entirely different within quantum mechanics. `The core idea of quantum mechanics is to describe our activities as knowledge-seeking and knowledge-using agents.' `21st century science does not reduce human beings to mechanical automata. Rather it elevates human beings to agents whose free choices can, according to the known laws, actually influence their behaviour.' An example with respect to perception is discussed: `Why, when we look at a triangle, do we experience three lines joined at three points and not some pattern of neuron firings?' The brain `does not convert an actual whole triangle into some jumbled set of particle motions; rather it converts a concatenation of separate external events into the actualization of some single integrated pattern of neural activity that is congruent to the perceived whole triangle.' How convincing is this proposal? It is hard to tell. I think Henry Stapp did a good job, but there are tight limitations to any such endeavour. Quantum mechanics is often strange indeed, but it also gives rise to our classical world around us. For the emergence of classicality jumps and measurement projections (the basic phenomena connected with those fundamental events of choice) are not needed. Therefore, I doubt whether the explanation of the evolution of our world really allows (or requires) that much free choice. On the other hand, most scientist will agree that empirical science was not possible without free will: we could not ask independent questions if this asking was part of a deterministic trajectory. The fact that the result of a quantum measurement is indeterminate (within given probabilities) does certainly not explain free will. How about the type of measurment? The experimentalist will have to assume that he can select the pertinent observable within some limits. But given a certain design the so-called pointer basis (producing stable measurement results) is no longer a matter of free choice. `The main theme of classical physics is that we live in a clocklike universe.' Today it is often assumed that the universe was a big (quantum-) computer or a cellular automaton. Many would be all too happy to leave that rather restrictive picture behind. But where to go? Stapp suggests giving consciousness a prominent role: `The most profound alteration of the fundamental principles was to bring consciousness of human beings into the basic structure of the physical theory.' How far we are able to go in this direction will depend on the amount of concrete research results becoming available to support this view.
✨On the Significance and Implications of the Obidi Probability Law Derived from the Principles of the Theory of Entropicity (ToE) The Obidi probability law is a central result in John Onimisi Obidi's Theory of Entropicity (ToE), and it marks a radical departure from classical probability theory. In standard Kolmogorov or quantum mechanics, the rule that the sum of all probabilities equals one is taken as an axiom with no dynamical origin. In ToE, Obidi derives this rule from the geometry and dynamics of the universe's Hilbert space, elevating probability from an epistemic bookkeeping rule to an ontological conservation law. The Connection Between Usual Probability and the Obidi Probability Law The simplest and perhaps clearest way to express the relationship between the usual [traditional] probability law and Obidi's entropic probability law is this: usual probability tells you what you might see, while the Obidi probability tells you why you see what you see. Usual probability is a predictive rule; Obidi probability is a structural law. They share a mathematical surface, but they arise from entirely different conceptual foundations. Understanding this distinction is essential for appreciating the depth of the Obidi Probability Law and its implications for physics. Mathematically, the two frameworks look deceptively similar. Usual probability is built on the normalization condition ∑iPi=1, while the Obidi Probability Law expresses a unique conservation law through the relation Po(t)+Pe(t)=1. Both involve quantities between 0 and 1 that sum to unity. This superficial resemblance is precisely why the Obidi formulation feels familiar at first glance: it preserves the algebraic structure of probability. Yet the meaning of these quantities is entirely different. In usual probability, the numbers represent degrees of belief or frequencies of outcomes. In the Obidi probability, they represent the partitioning of physical reality between coherent and entropic sectors of the universe's informational geometry. Usual probability is fundamentally epistemic. It answers the question, "Given what I know, what outcome should I expect?" It depends on the observer's knowledge, uncertainty, and measurement context. It is a rule of inference, not a physical law. The Born Rule, Bayesian updating, and the Kolmogorov axioms all fall into this category: they describe how observers assign probabilities, not how the universe itself behaves. In this sense, usual probability is a tool for reasoning about outcomes, not a description of the underlying structure of reality. Obidi probability is ontological. It answers a different question entirely: "How is reality partitioned between coherence and entropy?" It is observer‑independent, conserved, and rooted in the entropic geometry of the universe. It does not describe ignorance or uncertainty; it describes the physical distribution of amplitude between the coherent sector Po and the entropic sector Pe. It is not optional, not interpretive, and not dependent on measurement. It is a law of nature, not a rule of reasoning. In this sense, Obidi probability is a structural invariant of the universe's informational architecture. The connection between the two emerges when the entropic sector becomes negligible. When Pe(t)≈0, the coherent sector satisfies Po(t)≈1, and the usual Born‑rule probability appears as the projection of the coherent sector onto the observer's measurement basis. In this limit, usual probability is recovered as a special case of the Obidi Probability Law. This relationship mirrors other major correspondences in physics: Newtonian mechanics as a limit of relativity, classical thermodynamics as a limit of statistical mechanics, and classical geometry as a limit of quantum geometry. In each case, the familiar theory is not wrong - it is simply the low‑entropy, low‑curvature, or low‑energy approximation of a deeper structure. Usual probability plays the same role relative to Obidi probability. Measurement provides the final bridge between the two frameworks. In standard quantum mechanics, measurement is modeled as a discontinuous collapse of the wavefunction, with probabilities jumping abruptly according to the Born Rule. In Obidi's Theory of Entropicity (ToE), measurement is reinterpreted as an irreversible flow of amplitude from the coherent sector Po into the entropic sector Pe. This entropic transfer supplies a physical mechanism for what usual probability merely describes. The Born Rule becomes the visible cast or projection of a deeper entropic process unfolding beneath the surface of quantum mechanics. In summary, usual probability is what the observer computes, while the Obidi probability is what the universe is doing underneath. How the Obidi Probability Law Is Formulated In the Theory of Entropicity (ToE), the total quantum state of the universe is written as: Ψ(t) = ψ_o(t) + ψ_e(t) where: ψ_o(t) = the component of the state in the observer (coherent) sector ψ_e(t) = the component of the state in the entropic (irreversible) sector ψ_o(t) is orthogonal to ψ_e(t) This orthogonality is written as: ψ_o ⟂ ψ_e The total state always has unit norm: ‖Ψ(t)‖² = 1 If you decompose a vector into orthogonal components: Ψ = A + B then automatically: ‖Ψ‖² = ‖A‖² + ‖B‖² This is not the Born rule. This is Pythagoras in Hilbert space. Here, we are not assuming probability. We are deriving a conservation identity. From this, the Obidi Probability Law follows immediately: P_o(t) + P_e(t) = 1 where: P_o(t) = ‖ψ_o(t)‖² P_e(t) = ‖ψ_e(t)‖² This means that: P_o(t) is the probability associated with the coherent observer sector P_e(t) is the probability associated with the entropic sector Their sum is always 1, because they partition the entire Hilbert space of reality This is the entropic probability conservation law in ToE. In other words: The Theory of Entropicity (ToE) begins by decomposing the universe's total Hilbert space into two orthogonal sectors: Hₒ - The Coherent Observer Sector This is where quantum amplitudes evolve unitarily. It contains all accessible information. It is the sector in which observers, measurements, and coherent quantum states live. 2. Hₒ - The Entropic Sector This is the domain into which amplitude flows irreversibly. It represents informationally inaccessible states. It is responsible for decoherence, irreversibility, and the arrow of time. The total state of the universe is written as: Ψ(t) = ψₒ(t) + ψₑ(t) with the orthogonality condition: ψₒ ⟂ ψₑ We then write the probabilities as: Pₒ(t) = |ψₒ(t)|² Pₑ(t) = |ψₑ(t)|² In the Theory of Entropicity (ToE), the above [Pₒ(t) = |ψₒ(t)|² and Pₑ(t) = |ψₑ(t)|²] is NOT the Born rule - it is a sector‑weight derived from Hilbert‑space geometry. With the norm conservation of the full state which demands that: |Ψ(t)|² = 1, this immediately yields the Obidi Probability Law: Pₒ(t) + Pₑ(t) = 1 This is the entropic probability conservation law in ToE. Explore: Entropic Field Significance of the Obidi Entropic Probability Law From axiom to conservation principle Unlike classical probability, which partitions events, the Obidi law partitions sectors of physical reality. The sum is not imposed but follows from the Hilbert‑space structure and the combined unitary–entropic evolution . Ontological status of probability Probability becomes a structural invariant of the universe's geometry and dynamics, not just a measure of ignorance. This reframes probability as a fundamental physical law rather than a statistical convention. Mechanism for irreversibility and decoherence The entropic operator transfers amplitude from the observer sector to the entropic sector, generating irreversibility, decoherence, and the arrow of time while keeping total probability constant. Unified explanation of physical phenomena In ToE, this law underpins explanations of wavefunction collapse, classical irreversibility, and even the black hole information paradox: measurement outcomes correspond to irreversible amplitude transfer into the entropic sector. Conceptual shift in physics By embedding probability conservation in the geometry of reality rather than in human observation, the Obidi law challenges the Copenhagen interpretation and suggests a deeper, sector‑based ontology of quantum processes. In short: The Obidi probability law is significant because it redefines probability as a derived, conserved quantity rooted in the universe's Hilbert‑space structure, linking quantum coherence, entropy, and the arrow of time in a single, unified framework. The Obidi Probability Law is precisely a theory of the visible and invisible sectors of reality. This is one of its deepest conceptual achievements, and it's why it feels so different from anything in standard physics. In the following sections, we lay it out clearly and technically for the reader, so as not to lose sight of the elegance of the idea. The Obidi Probability Law teaches us about the visible and invisible sectors of reality The Obidi Probability Law divides the universe into two complementary informational sectors: the coherent sector Po - the visible, reversible, interference‑preserving part of reality the entropic sector Pe - the invisible, irreversible, information‑absorbing part of reality And the law states: Po(t)+Pe(t)=1 This is not a bookkeeping identity. It is a conservation law describing how reality is partitioned between what can be observed and what cannot [what we can reasonably access and what we cannot; and this has nothing to do with the limits of our laboratory or experimental apparatus or devices, but the inherent constraints of nature itself, independent of how accurate or efficient our tools are]. 1. The "visible sector": the coherent part of reality The coherent sector Po corresponds to: superposition interference unitary evolution reversible dynamics the part of the wavefunction that can produce observable outcomes This is the sector that standard quantum mechanics foc
Scientific theories need to be testable by observations, say using Bayes' theorem. A complete theory needs at least the three parts of dynamical laws for specified physical variables, the correct solution of the dynamical laws (boundary conditions), and the connection with observations or experience or conscious perceptions (laws of psycho-physical parallelism). Principles are proposed for Bayesian meta-theories. One framework that obeys these principles is Sensible Quantum Mechanics (SQM), which is discussed. In principle, it allows one to test between single-history and many-worlds theories, and to discuss threats to certain theories from fake universes and Boltzmann brains. The threat of fake universes may be dismissed if one doubts the substrate-independence of consciousness, which seems very implausible in the SQM framework. Boltzmann brains seem more problematic, though there are many conceivable solutions. SQM also suggests the possibility that past steps along our evolutionary ancestry may be so rare that they have occurred nowhere else within the part of the universe that we can observe.
Reading Paul Davies recent book The New Physics [6], one cannot help but marvel at the immense success of modern physics in describing the physical world. Yet that very success leads one reviewer [9] to pause and consider where amongst the successes “may lurk some tiny murkiness destined to become the seed of the next scientific revolution” just as the quantum behaviour of light turned out to be the seed which overthrew classical physics. Davies himself notes that the role of consciousness in a quantum observation still remains an unresolved issue, “..it may be that this frontier — the interface of mind and matter — will turn out to be the most challenging legacy of the New Physics.” [6, p6]