Simple self‐referential algorithms can model the essential logic of quantum systems and the quantum formalism is sufficiently rich to be able to model the output states of self‐referential alogrithms. We identify a key feature of self‐referentiality and show that both quantum mechanics and general relativity exhibit this feature in distinct yet complementary ways. This implies that self‐referentiality must be a foundational principle, but causality protection prohibits it being directly observed. Examining two facets of causality protection we find that quantum mechanics implements one and general relativity the other. The implication is that there can be no mathematically consistent theory for quantum gravity. However we can gain understanding of the constraints imposed on physical law when viewing a noncausal reality as if it were a causal sequence. We derive the 3+1 dimensionality of spacetime and quantum non‐locality and also possible rationale for the U(1) × SU(2) × SU(3) symmetry of the Standard Model. We also identify a number of key open problems.
Simple self‐referential algorithms can model the essential logic of quantum systems and the quantum formalism is sufficiently rich to be able to model the output states of self‐referential alogrithms. We identify a key feature of self‐referentiality and show that both quantum mechanics and general relativity exhibit this feature in distinct yet complementary ways. This implies that self‐referentiality must be a foundational principle, but causality protection prohibits it being directly observed. Examining two facets of causality protection we find that quantum mechanics implements one and general relativity the other. The implication is that there can be no mathematically consistent theory for quantum gravity. However we can gain understanding of the constraints imposed on physical law when viewing a noncausal reality as if it were a causal sequence. We derive the 3+1 dimensionality of spacetime and quantum non‐locality and also possible rationale for the U(1) × SU(2) × SU(3) symmetry of the Standard Model. We also identify a number of key open problems.
Quantum mechanics has achieved unparalleled success as an operational theory, describing a wide range of experiments to remarkable accuracy. However, the physical foundations on which it rests remain as puzzling as they were a century ago, and a concise statement of the physical principles that underlie quantum mechanics is still outstanding. One promising approach holds that these principles should be formulated in terms of information, since many of the counter-intuitive effects in quantum theory concern questions such as what one can know about a quantum system and how the information encoded therein can be processed and distributed between parties. Another challenging feature of quantum theory is its incompatibility with the other cornerstone of modern physics, general relativity. In order to reconcile the two, one must identify and retain only the essential concepts and principles of each theory, and in the case of general relativity, causality has been identified as such a concept. This raises the question of how our classical understanding of causality must change when quantum theory is taken into account. In order to address these questions about information, knowledge and causality, I turn to the framework of causal models. In classical statistics, causal models explain the relations among a set of variables in terms of causal influences, which makes them a powerful tool for structuring our knowledge about complex systems and developing strategies for interacting with them. More importantly, the framework provides the conceptual underpinnings and mathematical methods for addressing questions about causation, information and knowledge in a rigorous manner. In this thesis, I develop a version of the classical causal models framework that is compatible with quantum theory and explore its physical implications. \n \n \nA first step is to define quantum versions of fundamental elements such as variables, conditionals and belief propagation rules. This allows one to consider the question of what one can come to know about a quantum variable from the point of view of causal modelling. The conditionals relating quantum variables are found to have a richer structure than their classical counterparts, which can be exploited for the task of discerning causal relations given limited data -- a central problem in classical causal modelling. The mathematical properties of quantum conditionals also establish a correspondence between various classes of two-party correlations, such as bound and distillable entanglement, and the types of causal structures that can give rise to them, which may become a useful tool for entanglement theory and quantum information processing. In the context of open quantum systems dynamics, quantum causal models provide a clear physical explanation of not completely positive maps and, more broadly, of non-Markovian quantum dynamics. Finally, I consider the possibility of non-classical effects in the way that different causal mechanisms are combined -- that is, non-classical causal structures. For the simple case of two causally ordered variables, I propose indicators that witness different classes of combinations of causal mechanisms, including a non-classical mixture, and describe an experiment realizing examples of the different classes. \n \n \nAs these results illustrate, the framework of quantum causal models provides both greater conceptual clarity and a comprehensive mathematical formalism for studying a diverse set of problems, ranging from foundational questions to applications in open systems dynamics and the exploration of non-classical causal structures, which are likely to feature in a future theory of quantum gravity. The material presented in this thesis is intended as a foundation and inspiration for further applications of quantum causal models.
Quantum theory, gauge fields, and general relativity traditionally rest on independent foundations. This paper argues that they can be understood within a unified logical framework when the Self-Consistent Reference Frame Principle (RCC) and causality are applied to a local Hilbert-space framework. The unifying object is the comparator U_{ij}, which translates states between sites. In gauge theory it becomes the parallel transporter yielding the Yang-Mills action; in quantum mechanics it forces the Born rule through a functional equation without Gleason's theorem; in gravity it becomes the Levi-Civita connection giving the Einstein-Hilbert action via Lovelock's theorem. Among the nine theorems and two lemmas, the Phase Unity Theorem establishes that the comparator Schur phase, the gauge transformation parameter, and the quantum global phase are structural correspondences of a single U(1) symmetry. The Coleman-Mandula separation of internal and spacetime symmetries follows from RCC as a consequence of distinct encoding schemes. The Higgs mechanism emerges as a corollary: RCC prohibits bare mass terms for gauge fields. The framework yields one parameter-free falsifiable prediction: a pattern of SMEFT Wilson coefficients that can be tested at colliders, albeit with current precision limitations.
This paper explores the fundamental nature of spacetime from the perspective of emergent causal structures, rooted in quantum mechanical principles. We propose a theoretical framework that treats spacetime not as a pre-existing background, but as a collective phenomenon arising from the interaction of quantum causal relations. By analyzing the constraints of causality and quantum coherence, we derive key implications for the emergence of classical spacetime geometry and the limits of local realism. Our results suggest a new way to bridge quantum mechanics and gravitational theory, providing a foundation for future studies in quantum gravity and spacetime physics.
Quantum theory, gauge fields, and general relativity traditionally rest on independent foundations. This paper argues that they share a single structural origin when the Self-Consistent Reference Frame Principle (RCC) and causality are applied to a local Hilbert-space framework. The unifying object is the comparator U_{ij}, which translates states between sites. In gauge theory it becomes the parallel transporter yielding the Yang-Mills action; in quantum mechanics it forces the Born rule through a functional equation without Gleason's theorem; in gravity it becomes the Levi-Civita connection giving the Einstein-Hilbert action via Lovelock's theorem. Among the ten theorems and two lemmas, the Phase Unity Theorem establishes that the comparator Schur phase, the gauge transformation parameter, and the quantum global phase are structural correspondences of a single U(1) symmetry. The Coleman-Mandula separation of internal and spacetime symmetries follows from RCC as a consequence of distinct encoding schemes. The Higgs mechanism emerges as a corollary: RCC prohibits bare mass terms for gauge fields. The framework yields one parameter-free falsifiable prediction: a pattern of SMEFT Wilson coefficients testable at colliders.
After the development of a self-consistent quantum formalism nearly a century ago, there ensued a quest to understand the often counterintuitive predictions of the theory. These endeavors invariably begin with the assumption of the "truth" of the mathematical formalism of quantum mechanics and then proceed to investigate the theory's implications for the physical world. One of the outcomes has been endless discussions of the quantum measurement problem, wave/particle duality, the non-locality of entangled quantum states, Schroedinger's cat, and other philosophical conundrums. In this essay, I take the point of view that quantum mechanics is a mathematical model, a human invention, and rather than pondering what the theory implies about our world, I consider the transposed question: what is it about our world that leads us to a quantum mechanical model of it? One consequence is the realization that discrete quanta, the quantum of action in particular, leads to the wave nature and statistical behavior of matter rather than the other way around.
A case study of quantum mechanics is investigated in the framework of the philosophical opposition “mathematical model – reality”. All classical science obeys the postulate about the fundamental difference of model and reality, and thus distinguishing epistemology from ontology fundamentally. The theorems about the absence of hidden variables in quantum mechanics imply for it to be “complete” (versus Einstein’s opinion). That consistent completeness (unlike arithmetic to set theory in the foundations of mathematics in Gödel’s opinion) can be interpreted furthermore as the coincidence of model and reality. The paper discusses the option and fact of that coincidence it its base: the fundamental postulate formulated by Niels Bohr about what quantum mechanics studies (unlike all classical science). Quantum mechanics involves and develops further both identification and disjunctive distinction of the global space of the apparatus and the local space of the investigated quantum entity as complementary to each other. This results into the analogical complementarity of model and reality in quantum mechanics. The apparatus turns out to be both absolutely “transparent” and identically coinciding simultaneously with the reflected quantum reality. Thus, the coincidence of model and reality is postulated as necessary condition for cognition in quantum mechanics by Bohr’s postulate and further, embodied in its formalism of the separable complex Hilbert space, in turn, implying the theorems of the absence of hidden variables (or the equivalent to them “conservation of energy conservation” in quantum mechanics). What the apparatus and measured entity exchange cannot be energy (for the different exponents of energy), but quantum information (as a certain, unambiguously determined wave function) therefore a generalized law of conservation, from which the conservation of energy conservation is a corollary. Particularly, the local and global space (rigorously justified in the Standard model) share the complementarity isomorphic to that of model and reality in the foundation of quantum mechanics. On that background, one can think of the troubles of “quantum gravity” as fundamental, direct corollaries from the postulates of quantum mechanics. Gravity can be defined only as a relation or by a pair of non-orthogonal separable complex Hilbert space attachable whether to two “parts” or to a whole and its parts. On the contrary, all the three fundamental interactions in the Standard model are “flat” and only “properties”: they need only a single separable complex Hilbert space to be defined.