To date, there has been no experimental evidence that invalidates quantum theory. Yet it may only be an effective description of the world, in the same way that classical physics is an effective description of the quantum world. We ask whether there exists an operationally defined theory superseding quantum theory, but which reduces to it via a decoherence-like mechanism. We prove that no such post-quantum theory exists if it is demanded that it satisfy two natural physical principles: causality and purification. Causality formalizes the statement that information propagates from present to future, and purification that each state of incomplete information arises in an essentially unique way due to lack of information about an environment. Hence, our result can be viewed either as evidence that the fundamental theory of Nature is quantum or as showing in a rigorous manner that any post-quantum theory must abandon causality, purification or both.
To date, there has been no experimental evidence that invalidates quantum theory. Yet it may only be an effective description of the world, in the same way that classical physics is an effective description of the quantum world. We ask whether there exists an operationally defined theory superseding quantum theory, but which reduces to it via a decoherence-like mechanism. We prove that no such post-quantum theory exists if it is demanded that it satisfy two natural physical principles: causality and purification. Causality formalizes the statement that information propagates from present to future, and purification that each state of incomplete information arises in an essentially unique way due to lack of information about an environment. Hence, our result can be viewed either as evidence that the fundamental theory of Nature is quantum or as showing in a rigorous manner that any post-quantum theory must abandon causality, purification or both.
We find a process satisfying the axioms of hyper-decoherence which produces standard quantum theory from the theory of quantum boxes (higher-order quantum theory with the non-signalling tensor product). This hyper-decoherence map evades the no-go theorem of Lee and Selby by relaxing constraints on signalling to the past and the uniqueness of purifications. We discuss some natural opposing conclusions: that the existence of this map might be evidence of a genuine hyper-decoherence process producing causal quantum theory from its causally-indefinite higher-order theory; or that it serves as an indication that the axioms of hyper-decoherence might need careful re-consideration, especially regarding the subtle albeit central role that purity plays.
To date, there has been no experimental evidence that invalidates quantum theory. Yet it may only be an effective description of the world, in the same way that classical physics is an effective description of the quantum world. We ask whether there exists an operationally defined theory superseding quantum theory, but which reduces to it via a decoherence-like mechanism. We prove that no such post-quantum theory exists if it is demanded that it satisfy two natural physical principles: causality and purification . Causality formalizes the statement that information propagates from present to future, and purification that each state of incomplete information arises in an essentially unique way due to lack of information about an environment. Hence, our result can be viewed either as evidence that the fundamental theory of Nature is quantum or as showing in a rigorous manner that any post-quantum theory must abandon causality, purification or both.
Quantum theory describes our universe incredibly successfully. To our classically-inclined brains, however, it is a bizarre description that requires a reimagining of what fundamental reality, or “ontology”, could look like. This thesis examines different ontological features in light of the success of quantum theory, what it requires, and what it rules out. While these investigations are primarily foundational, they also have relevance to quantum information, quantum communication, and experiments on quantum systems. The way that quantum theory describes the state of a system is one of its most unintuitive features. It is natural, therefore, to ask whether a similarly strange description of states is required on an ontological level. This thesis proves that almost all quantum superposition states for d > 3 dimensions must be real—that is, present in the ontology in a well-defined sense. This is a strong requirement which prevents intuitive explanations of the many quantum phenomena which are based on superpositions. A new theorem is also presented showing that quantum theory is incompatible with macro-realist ontologies, where certain physical quantities must always have definite values. This improves on the Leggett-Garg argument, which also aims to prove incompatibility with macro-realism but contains loopholes. Variations on both of these results that are error-tolerant (and therefore amenable to experimentation) are presented, as well as numerous related theorems showing that the ontology of quantum states must be somewhat similar to the quantum states themselves in various specific ways. Extending these same methods to quantum communication, a simple proof is found showing that an exponential number of classical bits are required to communicate a linear number of qubits. That is, classical systems are exponentially bad at storing quantum data. Causal influences are another part of ontology where quantum theory demands a revision of our classical notions. This follows from the outcomes of Bell experiments, as rigorously shown in recent analyses. Here, the task of constructing a native quantum framework for reasoning about causal influences is tackled. This is done by first analysing the simple example of a common cause, from which a quantum version of Reichenbach’s principle is identified. This quantum principle relies on an identification of quantum conditional independence which can be defined in four ways, each naturally generalising a corresponding definition for classical conditional independence. Not only does this allow one to reason about common causes in a quantum experiments, but it can also be generalised to a full framework of quantum causal models (mirroring how classical causal models generalise Reichenbach’s principle). This new definition of quantum causal models is illustrated by examples and strengthened by it’s foundation on a robust quantum Reichenbach’s principle. An unusual, but surprisingly fruitful, setting for considering quantum ontology is found by considering time travel to the past. This provides a testbed for different ontological concepts in quantum theory and new ways to compare classical and quantum frameworks. It is especially useful for comparing computational properties. In particular, time travel introduces non-linearity to quantum theory, which brings (sometimes implicit) ontological assumptions to the fore while introducing strange new abilities. Here, a model for quantum time travel is presented which arguably has fewer objectionable features than previous attempts, while remaining similarly well-motivated. This model is discussed and compared with previous quantum models, as well as with the classical case. Together, these threads of investigation develop a better understanding of how quantum theory affects possible ontologies and how ontological prejudices influence quantum theory.
Emergent Causality Through Decoherence An imaginary hypothesis, not a theory. What if causality were not fundamental? What if it emerged, like temperature, from the degree of decoherence in a system? This hypothesis proposes that there is no single causality, but three regimes of the same process. The core idea:There is no single causality. There are causalities that emerge according to the degree of decoherence in a system. In other words: causality is not a property of the universe. It is a property of the level of description. The three regimes: Quantum causality (zero or low decoherence). The system is isolated. What exists are pure correlations: entanglement, superposition. There is no causality in the classical sense. There is correlation without direction. There is no defined "before" or "after." Relativistic causality (medium decoherence). The system interacts with the environment, but not completely. There is a causal structure defined by spacetime. There is causality, but it is relative: it depends on the observer. Classical causality (high decoherence). The system is fully coupled to the environment. It is classical. There is absolute, local causality: cause → effect, without ambiguity. The mechanism: decoherence.The more degrees of freedom interact with the system, the more decoherence. More decoherence → more classical → more causal. There is no "line" that is crossed. There is a continuum. Causality emerges gradually, just as temperature emerges from the number of particles. Why this makes the three regimes fit together: They are not separate levels. They are degrees of the same process. Time emerges together with causality. Without decoherence, there is no defined time. With decoherence, irreversibility emerges. And with it, the arrow of time. Relativity is the intermediate regime. What it would resolve: The problem of time: it emerges with decoherence. The arrow of time: it is the irreversibility of decoherence. The relativity–quantum clash: it is not a clash. They are different regimes of the same process. Causality: it is not fundamental. It is emergent. What it does not resolve: What decoherence exactly is. How to quantize gravity. Why there is decoherence. The information paradox. The label (important):This is an imaginary hypothesis, not a theory. It is coherent with what we know, but it is not demonstrated. It lacks mathematics, predictions, and confirmation. It does not say that time does not exist. It says that time could emerge. It does not say that causality does not exist. It says that causality could emerge. All of this, if one takes decoherence seriously, without adding anything else. But no one has demonstrated it. That is why it is a hypothesis, not a theory. A note on the anchor:This hypothesis does not invent its premise. It takes it from established physics: quantum mechanics already treats information as correlation, not as substance. Entanglement is pure correlation. Decoherence is entanglement with the environment. If information is always relational, then causality could be relational too. Related work: "Measure Reinforcement: Emergent Causality From Quantum Interactions" (Zenodo, 2025). Proposes emergent causality from quantum interactions without predefined time. Difference: includes a conscious observer. This hypothesis does not. Here decoherence is the mechanism, without consciousness. "Spacetime as an Emergent Causal Structure: A Quantum Mechanical Perspective" (Preprints.org, 2026). Derives proper time from the degree of decoherence. Difference: focuses on time, not causality as a regime. This hypothesis unifies the three regimes (quantum, relativistic, classical) into a single continuum. "Causal Space-Time: Emergent Physics from Causality" (2010). Proposes that physics emerges from a causal network. Difference: opposite direction. There causality is fundamental; here it emerges from decoherence. "Radial Coherential Dynamics: Emergent Causality" (2025). Proposes collapse as a decoherence front that generates time and causality. Difference: it is radial and has specific predictions. This hypothesis is more general: it describes causality as a regime of description, not as a radial process. The gap: no one has unified the three regimes (quantum, relativistic, classical) into a continuum parametrized by the degree of decoherence, nor has proposed that causality is a property of the level of description, not of the universe. Keywords: decoherence, emergent causality, quantum mechanics, foundations of physics, emergent time, quantum-classical transition.
In the wake of relativistic field theories in physics, all of our most fundamental physical theories shared three properties regarding the way that they described the world. First, properties of objects were always determined. Second, systems always evolved deterministically. Thirdly, no causal relationship between two separate regions in space was immediate or had superluminal effect. These properties of theories are called determinacy, determinism and local causality, respectively. These properties all correspond to classical metaphysical principles about the structure of the world. It will be shown that the theory of quantum mechanics has none of these properties and so therefore introduces a tension between the classical metaphysical description of the world and the descriptions given by our most fundamental physical theories. John Stewart Bell showed that no entirely correct theory of quantum mechanics has the property of local causality. I argue that this implies that local causality is metaphysically untenable.
When we are presented with apparently bizarre properties of microsystems governed by quantum mechanics (as in our discussion of the double-slit experiment in the previous chapter), we naturally ask whether it might be possible to find another theory, or at least another story to go with the equations, that would make more sense to us. We might seek a theory and a view of fundamental physical processes that would accord more with our classically based, everyday common sense. This typically takes the form of the question of the possibility of the existence of a more detailed description of atomic processes than that afforded by the wave function (that is, by the Copenhagen interpretation of the previous chapter). In this chapter we discuss some of the central interpretive problems of the Copenhagen version of quantum mechanics. Then, in the next two chapters, we look at the severe, general restrictions that are placed on any such completion of quantum mechanics and at one particular extension of quantum mechanics. First, though, we begin here with the struggle that ensued over the status of causality in quantum theory. THE COMPLETENESS OF QUANTUM MECHANICS Although the Heisenberg uncertainty principle (Section 20.4) and the lack of absolute predictive power are an inherent feature of quantum mechanics, there have been attempts to preserve an in principle completely deterministic structure for physics. Even classically, in a macroscopic sample of gas there are so many molecules that it would be hopeless, as a practical matter, to predict the future locations of all these molecules from Newton's laws of motion.