The r\^{o}le of observers and observations in physics theories is considered in the light of G\{o}del's incompleteness theorem. Incompleteness arises in G\{o}del's theorem with self-referential propositions, when the system asks to define itself in its own terms. Self-referencing occurs in physics whenever the observer is recognized as being part of the observed system, so the acts of observation are also observables and should become part of the phenomena considered by the theory. This is emphasized by the fact that in many instances the same physical phenomenon may be viewed in more than one way, hence its interpretation depends on the mode of observation. Observations of observations imply a potentially endless hierarchy of levels of observations. Each higher level suggests a larger overview with more profound insight into the universe, empirically implying essentially new discoveries and realizations. New discoveries imply new first principles in the foundation of the theory, so the theory remains open and cannot be complete.
The r^{o}le of observers and observations in physics theories is considered in the light of G{o}del's incompleteness theorem. Incompleteness arises in G{o}del's theorem with self-referential propositions, when the system asks to define itself in its own terms. Self-referencing occurs in physics whenever the observer is recognized as being part of the observed system, so the acts of observation are also observables and should become part of the phenomena considered by the theory. This is emphasized by the fact that in many instances the same physical phenomenon may be viewed in more than one way, hence its interpretation depends on the mode of observation. Observations of observations imply a potentially endless hierarchy of levels of observations. Each higher level suggests a larger overview with more profound insight into the universe, empirically implying essentially new discoveries and realizations. New discoveries imply new first principles in the foundation of the theory, so the theory remains open and cannot be complete.
Abstract Is it possible to encompass the full extent of the universe within a theory based on a finite set of first principles and inference rules? The r^ole of observers and observations in physics theories is considered here in the light of G¨odel’s incompleteness theorem. Physics theories are the sum-total that we – humans, scientists, physicists – can make in interpreting our observations of the universe. We are integral part of the universe, together with our observations, therefore acts of observation are also observables and should become part of the phenomena considered by the theory, especially in view of the fact that arbitrarily chosen modes of observations may essentially determine empirical results. Incompleteness arises in G¨odel’s theorem with self-referential propositions. Observations and interpretations are acts of referencing, and self-referencing occurs in physics whenever the observer is recognized as being part of the observed system. If self-reference appears in physics in simile to G¨odel’s theorem, then incompleteness seems unavoidable in physics. The article discusses observers and observations as referencing in physics, culminating with the understanding that they are hierarchically inter-related so that a universal physics theory cannot be complete.
We show how Gödel's first incompleteness theorem has an analog in quantum theory. Gödel's theorem implies endless opportunities for appending axioms to arithmetic, implicitly showing a role for an agent, namely an agent that asserts an axiom. There is an analog of this theorem in physics, to do with the set of explanations of given evidence. We prove that the set of explanations of given evidence is uncountably infinite, thereby showing how contact between theory and experiment depends on activity beyond computation and measurement -- physical activity characterized as agency.
Why do physicists discover different equations to describe the same universe? This paper proposes a new answer by introducing the Observer Hierarchy of Physics, a general framework in which physical theories are understood as exact observer equations, each preserving the information accessible within a particular observational regime rather than replacing one another. Instead of treating Newtonian mechanics, Maxwell's equations, the Schrödinger equation, the Dirac equation, thermodynamics, and other successful theories as competing descriptions, the framework argues that each is the minimal mathematical description required to preserve the measurements available to a specific observer algebra. The central idea is that the observer algebra is not chosen arbitrarily. It is generated by the observer's physical coupling to the underlying substrate together with finite spatial resolution, temporal resolution, energy access, detector sensitivity, and measurement precision. Once that coupling-generated observer algebra is specified, the minimal sufficient field representation, observer state, and observer equation follow naturally. In this view, the universe continuously evolves its full microscopic state, while observer equations describe only the information that survives physical coupling and projection into observable records. The paper introduces five new theoretical results: • Observer Hierarchy Theorem — demonstrating that a single physical system may admit multiple exact observer equations corresponding to different observational regimes. • Observer Sufficiency Theorem — establishing that an equation may be non-fundamental while remaining mathematically exact within the regime whose observables it preserves. • Representation Sufficiency Theorem — showing that reduced field representations are selected by observer algebras rather than by different physical laws or runtime modes. • Information Preservation Theorem — proving that observer equations are characterized by the information they preserve, not by the information they discard. • Observer Reduction Theorem, together with the Coupling-Determined Algebra Principle, showing that observer algebras arise from physical coupling to the substrate and that transitions between observer equations correspond to information-preserving projections rather than changes in physical reality. The framework is then illustrated using the Lattice Field Medium (LFM), where a continuously evolving second-order computational substrate gives rise to observer-selected field registers, a stable electron solution, the relativistic Dirac observer equation, and finally the low-energy Schrödinger observer equation. Importantly, the substrate itself never changes representation; only the observer's retained description changes as additional observables become experimentally accessible. Seven numerical information-projection diagnostics accompany the theoretical development, validating observer compression, register sufficiency, information preservation, bandwidth-dependent validity, and representation selection through controlled computational experiments. Rather than proposing that future theories replace existing ones, this work argues that scientific progress should explain why existing equations remain exact within their domains of applicability. If correct, the Observer Hierarchy provides a unified organizing principle for theoretical physics in which the evolution of physical theory is understood as the progressive discovery of observer equations emerging from an underlying computational reality.
Zero Subjectivity Physics presents a foundations-level framework that removes subjectivity from the base ontology of physical theory while preserving the full operational role of observation. Modern physics successfully predicts what systems do, yet foundational discussions often reintroduce subjectivity—explicitly or implicitly—through observer primacy, awareness, or experiential assumptions. This paper argues that such moves are unnecessary and stem from an inherited anthropomorphic interpretation of observation rather than from physical necessity. In this framework, observation is treated as an operational regime: a physically instantiated pattern of constrained dynamics and information flow that can arise wherever certain stability, memory, self-reference, and latency conditions are satisfied. Observation is not owned by a subject, localized at a privileged vantage point, or endowed with intrinsic awareness. Like light, it is defined entirely by what it does, not by what it is. Duality and non-duality are reframed as observer-dependent descriptive modes applied to the same underlying physical processes, rather than as competing ontologies. Subjectivity, if it arises at all, is treated as a higher-level organizational feature of certain systems, not as a primitive ingredient of physical law. The framework is compatible with classical mechanics, relativity, quantum theory, decoherence-based measurement theory, and operational or relational approaches, while taking a stronger stance against any foundational role for subjectivity. By enforcing zero subjectivity at the base level, the paper clarifies the physics–philosophy boundary, dissolves persistent observer paradoxes, and constrains consciousness-first interpretations without denying the reality of observers as physical systems.
We develop a mathematical and philosophical framework in which conscious obser- vation is the fundamental act that brings reality into existence. Before observation, nothing exists in an actualized sense: not space, time, laws, or structures. Reality is purely a manifold of potential universes, each containing possible laws and possible observers. When a conscious observer emerges, the act of observation actualizes the unique minimal universe consistent with its existence. This is not a selection among alternatives but an ontological crystallization that transforms possibility into actuality, retroactively defining the universe’s laws, constants, structure, and history. Within this actualized universe, unobserved properties remain probabilistic un- til collapsed by observation. We formalize sensory collapse, observer priority, multi- observer shared reality, emergent time, retroactive history, and the closed feedback loop between observers and their universe. This framework unifies consciousness, existence, physics, and cosmology into a single observer-centric formalism.
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.