A common way of characterizing Boltzmann’s explanation of thermodynamics in term of statistical mechanics is with reference to three ingredients: the dynamics, the past hypothesis, and the statistical postulate. In this paper I focus on the statistical postulate, and I have three aims. First, I wish to argue that regarding the statistical postulate as a probability postulate may be too strong: a postulate about typicality would be enough. Second, I wish to (...) show that there is no need to postulate anything, for the typicality postulate can be suitably derived from the dynamics. Finally, I discuss how the attempts to give preference to certain stochastic quantum theories (such as the spontaneous collapse theory) over deterministic alternatives on the basis that they do not need the statistical postulate fail. (shrink)

The attempt to derive (rather than assume) the statistical postulate of quantum theory from the many-universes interpretation of Everett and De Witt is analyzed The many-universes interpretation is found to be neither necessary nor sufficient for the task.

I briefly sketch Bohm's causal interpretation (BCI) and its solution to the measurement problem. Crucial to BCI's no-collapse account of both ideal and non-ideal measurement is the existence of particles in addition to wavefunctions. The particles in their role as the producers of the observable experimental outcomes render practical considerations, such as what observables can be reasonably measured or how to get rid of interference terms in non-ideal measurements, secondary to BCI's account of measurement. I then explain why it is (...) not easy for BCI to justify its statistical postulate. To successfully justify the postulate would be to solve the distribution problem. Two proposed deterministic solutions to this problem are only briefly set out and not discussed in detail. BCI can solve the measurement problem whether or not the distribution problem is solved. However, if the distribution problem is not solved, BCI cannot be shown to be empirically adequate. (shrink)

We derive statistical mechanics and Hamiltonian dynamics solely from the algebraic structure of M_3(C), the minimal noncommutative finite-dimensional C*-algebra, within the Cognitional Mechanics (CM) framework. Four foundational hypotheses of conventional statistical mechanics are structurally superseded without replacement by new assumptions: the equal a priori probability postulate (H1), the ergodic hypothesis (H2), the external heat bath assumption (H3), and the empirical definition of the inverse temperature beta (H4). -/- The principal results are: (i) the Hamiltonian H emerges as (...) a structural necessity via the Skolem-Noether theorem and Stone's theorem, superseding H3; (ii) the unique SU(n)-covariant depolarizing channel Phi with contraction rate lambda = 8/9 is fixed by the relative dimension 1/n^2 of the invariant subspace, superseding H1 and H2; (iii) the inverse temperature beta_structure = tau / Delta_E = [1/|log(8/9)|] / [3/sqrt(2)] approximately 4.002 is a pure structural invariant fixed by Casimir normalization, dissolving the circularity of H4; (iv) the canonical ensemble rho_eq = exp(-beta H) / Z is the unique entropy-maximizing state consistent with the algebra; (v) all three thermodynamic laws follow as algebraic theorems from Klein's inequality and the spectral structure of M_3(C); (vi) the projection factor kappa_T = 1.000031, determined via the CM-implied gravitational coupling G_implied = 6.67471 x 10^-11 m^3 kg^-1 s^-2, closes the Planck temperature scale as a structural invariant. The residual |kappa_T - 1| = 3.1 x 10^-5 lies within the experimental scatter of independent G measurements (5.5 x 10^-4). -/- No external probabilistic assumptions, empirical calibration, or free parameters are introduced. Statistical mechanics and thermodynamics are not empirical frameworks imposed on nature; they are necessary consequences of the minimal noncommutative algebra M_3(C). -/- Published March 7, 2026 DOI:10.5281/zenodo.18899522. (shrink)

In a quantum universe with a strong arrow of time, it is standard to postulate that the initial wave function started in a particular macrostate---the special low-entropy macrostate selected by the Past Hypothesis. Moreover, there is an additional postulate about statistical mechanical probabilities according to which the initial wave function is a ''typical'' choice in the macrostate. Together, they support a probabilistic version of the Second Law of Thermodynamics: typical initial wave functions will increase in entropy. Hence, (...) there are two sources of randomness in such a universe: the quantum-mechanical probabilities of the Born rule and the statistical mechanical probabilities of the Statistical Postulate. I propose a new way to understand time's arrow in a quantum universe. It is based on what I call the Thermodynamic Theories of Quantum Mechanics. According to this perspective, there is a natural choice for the initial quantum state of the universe, which is given by not a wave function but by a density matrix. The density matrix plays a microscopic role: it appears in the fundamental dynamical equations of those theories. The density matrix also plays a macroscopic / thermodynamic role: it is exactly the projection operator onto the Past Hypothesis subspace. Thus, given an initial subspace, we obtain a unique choice of the initial density matrix. I call this property "the conditional uniqueness" of the initial quantum state. The conditional uniqueness provides a new and general strategy to eliminate statistical mechanical probabilities in the fundamental physical theories, by which we can reduce the two sources of randomness to only the quantum mechanical one. I also explore the idea of an absolutely unique initial quantum state, in a way that might realize Penrose's idea of a strongly deterministic universe. (shrink)

This paper puts forward the hypothesis that the distinctive features of quantum statistics are exclusively determined by the nature of the properties it describes. In particular, all statistically relevant properties of identical quantum particles in many-particle systems are conjectured to be irreducible, ‘inherent’ properties only belonging to the whole system. This allows one to explain quantum statistics without endorsing the ‘Received View’ that particles are non-individuals, or postulating that quantum systems obey peculiar probability distributions, or assuming that there are primitive (...) restrictions on the range of states accessible to such systems. With this, the need for an unambiguously metaphysical explanation of certain physical facts is acknowledged and satisfied. (shrink)

This paper presents four theorems that connect continuity postulates in mathematical economics to solvability axioms in mathematical psychology, and ranks them under alternative supplementary assumptions. Theorem 1 connects notions of continuity (full, separate, Wold, weak Wold, Archimedean, mixture) with those of solvability (restricted, unrestricted) under the completeness and transitivity of a binary relation. Theorem 2 uses the primitive notion of a separately continuous function to answer the question when an analogous property on a relation is fully continuous. Theorem 3 provides (...) a portmanteau theorem on the equivalence between restricted solvability and various notions of continuity under weak monotonicity. Finally, Theorem 4 presents a variant of Theorem 3 that follows Theorem 1 in dispensing with the dimensionality requirement and in providing partial equivalences between solvability and continuity notions. These theorems are motivated for their potential use in representation theorems. (shrink)

A reproducibility principle is formulated and adopted as the guiding criterion for the acceptance of an experimental procedure as a simultaneous measurement of several observables. It is pointed out that this criterion can be applied to classical as well as quantum physics, and that it incorporates compatible as well as incompatible observables. The concept of fuzzy probability measure is presented as a possible mathematical tool for the description of statistical processes involving measurements of incompatible observables.

The spin-statistics connection is derived in a simple manner under the postulates that the original and the exchange wave functions are simply added, and that the azimuthal phase angle, which defines the orientation of the spin part of each single-particle spin-component eigenfunction in the plane normal to the spin-quantization axis, is exchanged along with the other parameters. The spin factor 2s belongs to the exchange wave function when this function is constructed so as to get the spinor ambiguity under control. (...) This is achieved by effecting the exchange of the azimuthal angle by means of rotations and admitting only rotations in one sense. The procedure works in Galilean as well as in Lorentz-invariant quantum mechanics. Relativistic quantum field theory is not required. (shrink)

Although the subjective expected utility (SEU) theory is more than 60 years old, it was recently discovered by Hartmann (Econometrica 88(1):203–205, 2020, https://doi.org/10.3982/ECTA17428) that one of the original seven postulates is redundant, i.e., it is implied by the other six postulates. In this brief communication, we show that this redundant axiom is the only one that is implied by the other axioms, thereby establishing that the remaining six postulates form an independent axiomatic system. This result further streamlines the preference assumptions (...) underlying the SEU theory. (shrink)

We present a quantum mechanical analysis of Bell’s approach to quantum foundations based on his hidden-variable model. We claim and try to justify that the Bell model contradicts to the Heinsenberg’s uncertainty and Bohr’s complementarity principles. The aim of this note is to point to the physical seed of the aforementioned principles. This is the Bohr’s quantum postulate: the existence of indivisible quantum of action given by the Planck constant h. By contradicting these basic principles of QM, Bell’s model (...) implies rejection of this postulate as well. Thus, this hidden-variable model contradicts not only the QM-formalism, but also the fundamental feature of the quantum world discovered by Planck. (shrink)

The pessimistic induction and the problem of underdetermination in the philosophy of science have a rich history. In their recent incarnation as the problem of unconceived alternatives, most fully articulated by Kyle Stanford (2010) in Exceeding Our Grasp, the induction is more specific and underdetermination is construed more epistemically than is typical…The problem is not that there are empirically equivalent alternatives, that is, alternative between which no empirical evidence could ever distinguish. The problem is that multiple radically different alternative that (...) are empirically inequivalent might be equally well-confirmed by current evidence, and we might fail to even conceive one or more of those alternatives… In “Of German Tanks and Scientific Theories: Estimating the Number of Unconceived Alternatives,” Burkay Ozturk (2016) challenges Stanford on a distinct front. By applying a method of statistical estimation to scientific alternatives, Ozturk argues that the possibility space within which the alternatives are located allows for probable knowledge. The particular frequentist estimation method Ozturk employs requires that we assume the alternative pool is finite, which seems to be both false and wildly implausible. At first glance. I argue in this comment that Ozturk’s postulate of finitude is actually defensible in circumstances that might actually hold for ordinary scientific contexts. (shrink)

1. Deductive and Inductive Inference. Within the traditional treatments of scientific method, e.g., in and, it was customary to divide scientific inference into two parts: deductive and inductive. Deductive inference was taken to mean the activity of deducing theorems from postulates and definitions, whereas inductive inference represented the activity of constructing a general statement from a set of particular “facts.” Deductive inference was relegated to the mathematical sciences, and inductive inference to the empirical sciences. As a consequence, the whole of (...) science was split into two quite distinct parts: deductive science was conceived to start with precise axioms, postulates, and definitions, and its method consisted in drawing inferences from these “givens” in such a way that if the original assumptions are taken as true, then the theorems must be taken as true also. The obligation behind this “must” of the mathematical sciences was an obligation based on strict rules of deductive inference; in the earlier analyses, it was supposed that these rules were all aspects of the general theory of the syllogism, as it was described in an almost complete form in but in later work the rules have been formalized in more general terms. Inductive inference, on the other hand, was supposed to start with observed facts; these facts, or “data,” were presumably given by the senses, and described particular aspects of the external world. If the facts were given in a certain way, then the empirical scientist could “infer” a generalized description; this generalization had the characteristic that if it were granted as true, then all the facts could be deduced as consequences. The inductive process admittedly does not lead to unique generalizations, and the philosopher of science searched for other defining characteristics of good inference, such as “simplicity” and “convenience.” These empirical generalizations were taken to be “descriptions of the phenomenal world of the scientist”; a further inductive step might be taken by constructing a set of very general principles out of the more specialized generalizations within specific research problems. These “higher” inductive inferences were regarded as “theories,” which could be studied by themselves within the method of deductive inference. The scientist was then described as “checking” theory by determining whether or not the predicted consequences deduced from theory actually hold in the phenomenal world. (shrink)

Statistical mechanics applied on a universal scale (the Mentaculus) attaches probabilities to all possible events in the universe, far outstripping its local thermodynamic evidence base. This ‘imperialistic’ tendency is often criticised as requiring untenable dynamical choreography in phase space. However, I will argue that imperialistic issues arise even in local statistical mechanics; if we tolerate them here, we should tolerate them in the Mentaculus. In an attempt to sidestep these issues, some have suggested swapping the Statistical (...) class='Hi'>Postulate for a set of initial distributions claimed to yield the same thermodynamic predictions but indeterminacy elsewhere. I show that the result is still largely imperialistic, but for this very reason might be preferable to the standard Mentaculus as providing the same goods from weaker assumptions. (shrink)

The projection postulate is the source of a long standing controversy in the interpretation of the axiomatic foundations of quantum mechanics. In a sense which is made precise in chapter II the projection postulate is a mathematical theorem easily derivable within the mathematical framework of the theory. This theorem receives a clear and straightforward interpretation if Luders' rule is given only statistical significance. Under the assumption that an interpretation of quantum mechanics has to provide an account of (...) the process of measurement as a change on the state of individual systems, however, additional interpretive assumptions are needed in order to arrive at a satisfactory interpretation of Luders' rule. ;I show in chapter III that there are serious problems with the usual interpretation by making explicit in a quantum logical framework the concept of individual state and minimal disturbance implicit in this view. In chapter IV I show that it is possible to formulate a natural interpretation of Luders' rule as a description of 'dispersion free' state transformations within a semantic framework that takes states of individual systems to be represented by Boolean ultrafilters , as opposed to the usual approach that takes individual states to be represented by lattice ultrafilters. This lay the ground for the clarification of several interpretive issues in the foundations of quantum mechanics. It is shown that Luders' rule can be justified as a description of individual state transformations without the need of imposing additional assumptions. The derivation of Luders' rule within the semantic framework of B-states shows an important connection between interpretation that take individual state to be 'relative' to experimental situations and the statistical structure of the theory. (shrink)

This article explains why Bohr does not need to discuss the projection postulate or the "problem of measurement". Beginning with a thumbnail sketch of Bohr 's general views, it is argued that Bohr interprets the state function as giving a statistical summary of experimental outcomes. Against the objection that Bohr was too much a microrealist to endorse such an instrumentalist statistical interpretation it is suggested that he rejected the issue of microrealism as not well formed. It is (...) shown that on his statistical interpretation Bohr does not need the projection postulate or face the usual problem of measurement. (shrink)

On Bohm''s formulation of quantum mechanics particles always have determinate positions and follow continuous trajectories. Bohm''s theory, however, requires a postulate that says that particles are initially distributed in a special way: particles are randomly distributed so that the probability of their positions being represented by a point in any regionR in configuration space is equal to the square of the wave-function integrated overR. If the distribution postulate were false, then the theory would generally fail to make the (...) right statistical predictions. Further, if it were false, then there would at least in principle be situations where a particle would approach an eigenstate of having one position but in fact always be somewhere very different. Indeed, we will see how this might happen even if the distribution postulate were true. This will help to show how loose the connection is between the wave-function and the positions of particles in Bohm''s theory and what the precise role of the distribution postulate is. Finally, we will briefly consider two attempts to formulate a version of Bohm''s theory without the distribution postulate. (shrink)

What, if anything, would be wrong with replacing the light postulate in Einstein’s 1905 formulation of special relativity with a ‘sound postulate’, stating that the speed of sound is independent of the speed of the source? After reviewing the historical reasons underlying the particular focus on light in the special theory, we consider the circumstances under which such a theory of ‘sonic relativity’ would be justified on empirical grounds. We then consider the philosophical upshots of ‘sonic relativity’ for (...) four contemporary areas of investigation in the philosophy of spacetime: global versus subsystem symmetries, dynamical versus geometrical approaches to spacetime, the possibility of a preferred frame in theories of quantum gravity, and spacetime functionalism. (shrink)

I show that the quantum state ω can be interpreted as defining a probability measure on a subalgebra of the algebra of projection operators that is not fixed (as in classical statistical mechanics) but changes with ω and appropriate boundary conditions, hence with the dynamics of the theory. This subalgebra, while not embeddable into a Boolean algebra, will always admit two-valued homomorphisms, which correspond to the different possible ways in which a set of “determinate” quantities (selected by ω and (...) the boundary conditions) can have values. The probabilities defined by ω (via the Born rule) are probabilities over these two-valued homomorphisms or value assignments. So any universe of interacting systems, including those functioning as measuring instruments, can be modelled quantum mechanically without the projection postulate. (shrink)

Everett’s Relative State Interpretation has gained increasing interest due to the progress of understanding the role of decoherence. In order to fulfill its promise as a realistic description of the physical world, two postulates are formulated. In short they are (1) for a system with continuous coordinates $${\mathbf {x}}$$, discrete variable j, and state $$\psi _j({\mathbf {x}})$$, the density $$\rho _j({\mathbf {x}})=|\psi _j({\mathbf {x}})|^2$$ gives the distribution of the location of the system with the respect to the variables $${\mathbf {x}}$$ (...) and j; (2) an equation of motion for the state $$i\hbar \partial _t \psi = H\psi$$. The first postulate connects the mathematical description to the physical reality, which has been missing in previous versions. The contents of the standard (Copenhagen) postulates are derived, including the appearance of Hilbert space and the Born rule. The approach to probabilities earlier proposed by Greaves replaces the classical probability concept in the Born rule. The new quantum probability concept, earlier advocated by Deutsch and Wallace, is void of the requirement of uncertainty. (shrink)

This paper analyzes Deborah Mayo's error-statistical (ES) account of scientific evidence in order to clarify the kinds of "material postulates" it requires and to explain how those assumptions function. A secondary aim is to explain and illustrate the importance of the security of an inference. After finding that, on the most straightforward reading of the ES account, it does not succeed in its stated aims, two remedies are considered: either relativize evidence claims or introduce stronger assumptions. The choice between (...) these approaches turns on the value attached to two aims of inquiry that are in tension: drawing strong, informative conclusions and reasoning securely. (shrink)

Certain modifications, by way of improvement, are proposed for the Feynman postulates in quantum mechanics. These modifications incorporate a criterion for the applicability of the principle of superposition. It is shown that the modified postulates, together with certain assumptions regarding the trajectory of a particle, lead to an expression for the position-momentum uncertainty relationship which is broadly in agreement with the conventional expression. The time-energy uncertainty relationship is, however, found to have a likely place only in the relativistic theory. A (...) criterion, in the form of a ratio involving the linear dimensions of the particle, is obtained for the validity of the classical mechanics approximation. The modified postulates are suggested to favor the statistical interpretation of quantum mechanics over the Copenhagen interpretation. (shrink)

The term science is used to cover three separate categories, to which throughout this paper we shall give three separate names. There is the field in which science operates. This is the external world of natural phenomena, partly uniform and partly chance. There is the science itself. This is the laboratory of instruments, techniques, operations, the method by which the field is studied. Finally, there is the laws. This is the level of abstractions, of causal laws or of statistical (...) probability averages, invariant or approaching invariance, mathematically expressed. The three, of course, belong together. Science carries the activity; it studies the field to find the laws. (shrink)

The Born’s rule to interpret the square of wave function as the probability to get a specific value in measurement has been accepted as a postulate in foundations of quantum mechanics. Although there have been so many attempts at deriving this rule theoretically using different approaches such as frequency operator approach, many-world theory, Bayesian probability and envariance, literature shows that arguments in each of these methods are circular. In view of absence of a convincing theoretical proof, recently some researchers (...) have carried out experiments to validate the rule up-to maximum possible accuracy using multi-order interference (Sinha et al, Science, 329, 418 [2010]). But, a convincing analytical proof of Born’s rule will make us understand the basic process responsible for exact square dependency of probability on wave function. In this paper, by generalizing the method of calculating probability in common experience into quantum mechanics, we prove the Born’s rule for statistical interpretation of wave function. (shrink)

Discussions of quantum mechanics often loosely claim that time evolution logically must be unitary, in order for the probabilistic interpretation of the amplitudes of the state vector to make sense at all times. We discuss from first principles whether this claim is true: if we assume only that the time-evolution operator is linear, then does the stronger requirement that it be unitary follow from the other axioms of quantum mechanics? The answer is subtle. We discuss two mathematically distinct but physically (...) equivalent formulations of the axioms of quantum mechanics, and consider generalizing each to postulate only that time evolution is linear. Within one formulation, the unitarity of time evolution follows logically from the other axioms – but within the other formulation, it does not. Allowing the time-evolution operator to be (a priori) arbitrarily linear does not change the physical observables in one formulation of quantum mechanics, but changes the other formulation to a distinct (internally consistent) physical theory that allows new phenomenology like (e.g.) faster-than-light communication. Therefore, the unitarity of time evolution is arguably better thought of as a logically independent and experimentally falsifiable axiom of quantum mechanics, not as a tautological consequence of the other axioms. (shrink)

The Ozawa’s intersubjectivity theorem (OIT) proved within quantum measurement theory supports the new postulate of relational quantum mechanics (RQM), the postulate on internally consistent descriptions. But from OIT viewpoint postulate’s formulation should be completed by the assumption of probability reproducibility. We remark that this postulate was proposed only recently to resolve the problem of intersubjectivity of information in RQM. In contrast to RQM for which OIT is a supporting theoretical statement, QBism is challenged by OIT.

In support of their contention that it is the absence of a subsisting medium that imbues the speed of light with fundamentality, Bryan Cheng and James Read discuss certain “fishbowl universes” in which physical influences evolve, not at the speed of light, but that of sound. The Lorentz transformation simulated in these sonic universes, which the authors cite from the literature of analogue gravity, is not that of Einstein, for whom an aether was “superfluous”, but that of the earlier relativity (...) of Lorentz and Poincaré, which did suppose such a medium. The authors’ intention is not to argue analogically, but simply to contrast the situation of light with that of sound. However, I argue that these universes are too successful as analogues to support the authors’ case. By reducing Lorentzian relativity to its bare essentials, they provide a compelling demonstration of the viability and explanatory strengths of the earlier theory. They show how a thoroughly wave-theoretic treatment of the elementary particles would explain why all aspects of matter transform in like manner, thereby avoiding a difficulty that was a significant reason for the demise of Lorentzian relativity after 1905. Importantly, these sonic universes suggest a unifying explanation, not only of the Lorentz transformation and de Broglie wave, but of the principle of relativity, which was merely postulated, rather than explained, by Einstein in 1905. (shrink)

Humans display more conditioned fear when the conditioned stimulus in a fear conditioning paradigm is a picture of an individual from another race than when it is a picture of an individual from their own race (Olsson, Ebert, Banaji, & Phelps, 2005). These results have been interpreted in terms of a genetic “preparedness” to learn to fear individuals from different social groups (Ohman, 2005; Olsson et al., 2005). However, the associability of conditioned stimuli is strongly influenced by prior exposure to (...) those or similar stimuli. Using the Kalman filter, a normative statistical model, this article shows that superior fear conditioning to individuals from other groups is precisely what one would expect if participants perform optimal, Bayesian inference that takes their prior exposures to the different groups into account. There is therefore no need to postulate a genetic preparedness to learn to fear individuals from other races or social groups. (shrink)

A realistic physical axiomatic approach of the relativistic quantum field theory is presented. Following the action principle of Schwinger, a covariant and general formulation is obtained. The correspondence principle is not invoked and the commutation relations are not postulated but deduced. The most important theorems such as spin-statistics, and CPT are proved. The theory is constructed form the notion of basic field and system of basic fields. In comparison with others formulations, in our realistic approach fields are regarded as real (...) things with symmetry properties. Finally, the general structure is contrasted with other formulations. (shrink)

Two of the most difficult problems in the foundations of physics are (1) what gives rise to the arrow of time and (2) what the ontology of quantum mechanics is. I propose a unified 'Humean' solution to the two problems. Humeanism allows us to incorporate the Past Hypothesis and the Statistical Postulate into the best system, which we then use to simplify the quantum state of the universe. This enables us to confer the nomological status to the quantum (...) state in a way that adds no significant complexity to the best system and solves the ''supervenient-kind problem'' facing the original version of the Past Hypothesis. We call the resultant theory the Humean unification. It provides a unified explanation of time asymmetry and quantum entanglement. On this theory, what gives rise to time's arrow is also responsible for quantum phenomena. The new theory has a separable mosaic, a best system that is simple and non-vague, less tension between quantum mechanics and special relativity, and a higher degree of theoretical and dynamical unity. The Humean unification leads to new insights that can be useful to Humeans and non-Humeans alike. (shrink)

We argue that the asymmetry between diverging and converging electromagnetic waves is just one of many asymmetries in observed phenomena that can be explained by a past hypothesis and statistical postulate (together assigning probabilities to different states of matter and field in the early universe). The arrow of electromagnetic radiation is thus absorbed into a broader account of temporal asymmetries in nature. We give an accessible introduction to the problem of explaining the arrow of radiation and compare our (...) preferred strategy for explaining the arrow to three alternatives: (i) modifying the laws of electromagnetism by adding a radiation condition requiring that electromagnetic fields always be attributable to past sources, (ii) removing electromagnetic fields and having particles interact directly with one another through retarded action-at-a-distance, (iii) adopting the Wheeler-Feynman approach and having particles interact directly through half-retarded half-advanced action-at-a-distance. In addition to the asymmetry between diverging and converging waves, we also consider the related asymmetry of radiation reaction. (shrink)

Many philosophers sympathetic with a Humean understanding of laws of nature have thought that, in the final analysis, the fundamental laws will include not only the traditional dynamical equations, but also two additional principles: the Past Hypothesis and the Statistical Postulate. The former says that the universe began in a particular very-low-entropy macrostate M(0), and the latter posits a uniform probability distribution over the microstates compatible with M(0). Such a view is arguably vindicated by the orthodox Humean Best (...) System Account (BSA). However, I argue here that recent developments of the BSA render the Past Hypothesis otiose. In particular, the trend among Humeans toward a more pragmatic view of laws — according to which the best system is the one that is maximally effective at helping creatures like us amplify our information about the world — does not support the idea that the Past Hypothesis is a law of nature. (shrink)

The aim of this paper is to debunk the assertion that miraculous “conspiracies” between fundamental particles are required to bring about the projectibility of special science generalisations. Albert and Loewer have proposed a theory of lawhood which supplements the Best System of fundamental laws with a statistical postulate over the initial conditions of the universe, thereby rendering special science generalisations highly probable, and dispelling the conspiracy. However, concerns have been raised about its ability to confer typicality upon special (...) science generalisations in the way that is required. In this paper I defend their account against these charges, arguing that they derive from a misunderstanding of the typicality claim. I suggest a way out of the impasse via a naturalised approach which focusses on the genealogy of subsystems and encourages conceptual demonstrations of typicality for special science generalisations. I argue for an account of special science laws that acknowledges the way in which the special sciences reduce to the fundamental physics, thereby dissolving the conspiracy, yet respects the methodological and explanatory autonomy of special science generalisations. (shrink)

A suitable unified statistical formulation of quantum and classical mechanics in a *-algebraic setting leads us to conclude that information itself is noncommutative in quantum mechanics. Specifically we refer here to an observer's information regarding a physical system. This is seen as the main difference from classical mechanics, where an observer's information regarding a physical system obeys classical probability theory. Quantum mechanics is then viewed purely as a mathematical framework for the probabilistic description of noncommutative information, with the projection (...) postulate being a noncommutative generalization of conditional probability. This view clarifies many problems surrounding the interpretation of quantum mechanics, particularly problems relating to the measuring process. (shrink)

A fundamental postulate of statistical mechanics is that all microstates in an isolated system are equally probable. This postulate, which goes back to Boltzmann, has often been criticized for not having a clear physical foundation. In this note, we provide a derivation of the canonical distribution that avoids this postulate. In its place, we impose two axioms with physical interpretations. The first axiom ensures that, as our system of interest comes into contact with different heat baths, (...) the ranking of states of the system by probability is unchanged. Physically, this axiom is a statement that in thermal equilibrium, population inversions do not arise. The second axiom requires that, for any heat bath and any probability distribution on states, there is a universe consisting of a system and heat bath that can achieve this distribution. Physically, this axiom is a statement that energy flows between system and heat bath are unrestricted. We show that our two axioms identify the Boltzmann distribution. (shrink)

This paper addresses a particular interpretation of quantum mechanics, i.e. superdeterminism. In short, superdeterminism i) takes the world to be fundamentally deterministic, ii) postulates hidden variables, and iii) contra Bell, saves locality at the cost of violating the principle of statistical independence. Superdeterminism currently enjoys little support in the physics and philosophy communities. Many take it to posit the ubiquitous occurrence of hard-to-digest conspiratorial and coincidental events; others object that violating the principle of statistical independence implies the death (...) of the scientific methodology. In this paper, we offer a defense to these and other objections. To counter the conspiracy objection, we draw upon the philosophical literature on time travel, and conclude that the picture of the world offered by the superdeterminist does not need to be particularly surprising or conspiratorial. We then move on to other recent objections, in particular those that focus on the methodology of science and the nature of the physical laws compatible with superdeterminism. A key ingredient of our arguments is that the principle of statistical independence may be violated in theory, but valid for practical purposes. Our overarching goal is to offer a defense of superdeterminism with respect to its main objections, so that it can earn its keep as a legitimate contender among the possible interpretations of quantum mechanics. (shrink)

Statistical physics cannot explain why a thermodynamic arrow of time exists, unless one postulates very special and unnatural initial conditions. Yet, we argue that statistical physics can explain why the thermodynamic arrow of time is universal, i.e., why the arrow points in the same direction everywhere. Namely, if two subsystems have opposite arrow-directions at a particular time, the interaction between them makes the configuration statistically unstable and causes a decay towards a system with a universal direction of the (...) arrow of time. We present general qualitative arguments for that claim and support them by a detailed analysis of a toy model based on the baker’s map. (shrink)

This preprint was accepted for publication in Pramana – Journal of Physics. The final published version is available via the journal. Abstract: In this paper, the ontological aspects of the Many-Worlds Interpretation (MWI) of quantum mechanics are studied by employing measure theoretical methods of the ergodic theory. Before everything it is shown that the frequency interpretation of the Born rule is independent of the measurement postulate and hence, must be extended to the statistical ontology of the MWI. Then, (...) based on Birkhoff’s ergodic theorem we will prove that except for a Lebesgue null set of extremely rare parallel worlds, the Born rule will be refuted in all of the parallel worlds created in a long-term process of consecutive experiments in the MWI of quantum mechanics. This reduces the unlimited ontology of the MWI to an extremely confined but still uncountable set of possible parallel worlds in long-term processes and lets us acknowledge a pseudo-deterministic mechanism of quantum mechanics in the statistical picture of the theory. Hence, we conclude that the common understanding of the unconstrained MWI ontology, even if considered valid, cannot survive in long-term consecutive observations and must soon collapse into a more constrained interpretation of quantum mechanics. Keywords: Many-Worlds Interpretation, Born Rule, Measure Theory, Lebesgue Measure, Birkhoff’s Ergodic Theorem, Born-Vaidman Rule, Statistical Interpretation. (shrink)

We postulate the Testing Principle : that individuals ''act like statisticians'' when they face uncertainty in a decision problem, ranking alternatives to the extent that available evidence allows. The Testing Principle implies that completeness of preferences, rather than the sure-thing principle , is violated in the Ellsberg Paradox. In the experiment, subjects chose between risky and uncertain acts in modified Ellsberg-type urn problems, with sample information about the uncertain urn. Our results show, consistent with the Testing Principle, that the (...) uncertain urn is chosen more often when the sample size is larger, holding constant a measure of ambiguity (proportion of balls of unknown colour in the urn). The Testing Principle rationalises the Ellsberg Paradox. Behaviour consistent with the principle leads to a reduction in Ellsberg-type violations as the statistical quality of sample information is improved, holding ambiguity constant. The Testing Principle also provides a normative rationale for the Ellsberg paradox that is consistent with procedural rationality. (shrink)

We study some logical interrelationships between fundamental properties in (relativistic) quantum theories. An operational no-signalling condition is first introduced in the context of quantum mechanics, where we prove its equivalence to an apparently weaker version restricted to ideal measurements, and to a property of factorization of the evolution unitary operator. We then translate this condition in quantum field theory and prove that it implies both microcausality and the spin-statistics theorem, in the ideal case of pointwise measurements implemented in the projection (...) postulate sense. This provides an argument (often invoked but apparently missing in the literature) to see microcausality as a necessary condition for the compatibility of spacelike separated operations. (shrink)

This doctoral dissertation investigates the notion of physical necessity. Specifically, it studies whether it is possible to account for non-accidental regularities without the standard assumption of a pre-existent set of governing laws. Thus, it takes side with the so called deflationist accounts of laws of nature, like the humean or the antirealist. The specific aim is to complement such accounts by providing a missing explanation of the appearance of physical necessity. In order to provide an explanation, I recur to fields (...) that have not been appealed to so far in discussions about the metaphysics of laws. Namely, I recur to complex systems’ theory, and to the foundations of statistical mechanics. The explanation proposed is inspired by how complex systems’ theory has elucidated the way patterns emerge, and by the probabilistic explanations of the 2nd law of thermodynamics. More specifically, this thesis studies how some constraints that make no direct reference to the dynamics can be a sufficient condition for obtaining in the long run, with high probability, stable regular behavior. I hope to show how certain metaphysical accounts of laws might benefit from the insights achieved in these other fields. According to the proposal studied in this thesis, some regularities are not accidental not in virtue of an underlying physical necessity. The non-accidental character of certain regular behavior is only due to its overwhelming stability. Thus, from this point of view the goal becomes to explain the stability of temporal patterns without assuming a set of pre-existent guiding laws. It is argued that the stability can be the result of a process of convergence to simpler and stable regularities from a more complex lower level. According to this project, if successful, there would be no need to postulate a (mysterious) intermediate category between logical necessity and pure contingency. Similarly, there would be no need to postulate a (mysterious) set of pre-existent governing laws. Part I of the thesis motivates part II, mostly by arguing why further explanation of the notions of physical necessity and governing laws should be welcomed (chapter 1), and by studying the plausibility of a lawless fundamental level (chapters 2 and 3). Given so, part II develops the explanation of formation of simpler and stable behavior from a more complex underlying level. (shrink)

A model of dissipative quantum dynamics (with a nonlinear friction term) is applied to systems periodic in time. The model is compared with the standard approaches based on the Floquet theorem. It is shown that for weak frictions the asymptotic states of the dynamics we propose are the periodic steady states which are usually postulated to be the states relevant for the statistical mechanics of time-periodic systems. A solution to the problem of nonuniqueness of the “quasienergies” is proposed. The (...) implication of a nonlinear evolution for Ludwig's axiomatization is briefly outlined. (shrink)

In this short paper, we propose a new framework for obtaining basic aspects of quantum mechanics that originate from estimating the mean value of the position of a statistical system based on the generalized Bayes estimators. We show that while the first-order estimation leads to a classical system, the second-order estimation produces the time-independent Schrödinger equation. The Born rule describes the probabilistic nature of quantum particles, and Max Born postulated it independently from the Schrödinger equation. We show that under (...) the proposed model, both the Schrödinger equation and the Born rule are captured organically; particularly, we show that the Born rule leads to the Schrödinger equation. Finally, we show how the proposed model deals with the transition from quantum mechanics into classical mechanics when dealing with macroscopic objects without external assumptions. (shrink)

It is shown that the Born Rule probabilities, i.e. the squares of the moduli of the coefficients in a pure state superposition, refer to mutually exclusive events consequent on measurement. It is also shown that the eigenstates in a pure state superposition are not mutually exclusive events. If the Born Rule is to be retained as the fundamental interpretative postulate of quantum mechanics then it follows, firstly, that the probabilities necessarily refer not to the eigenstates but to the eigenvalues (...) to which the eigenstates belong and, secondly, that the eigenvalues are necessarily mutually exclusive events. This means that to ask why a measurement of an observable on a system in a pure state superposition of eigenstates yields a single state rather than all the states in the superposition is to ill-pose the quantum measurement problem. The events the Born Rule probabilities properly refer to are not states but values. And it also means that the correctly-posed measurement problem, why does a measurement of an observable in a pure state superposition of the eigenstates of the observable yield a single eigenvalue rather than all the eigenvalues implicit in the superposition, admits of the answer: the values, being mutually exclusive events, constitute a statistical mixture of values, and as such, a measurement will yield just one of them. (shrink)

It is shown how Bohmian trajectories can be derived without the need for Bohmian assumptions such as the guidance law or equilibrium postulate. According to the standard Copenhagen interpretation, Bohmian trajectories cannot be understood as physical paths of particles but must be considered in the framework of descriptive statistics. This does not render them useless but clarifies the field of applications. Without the necessity of the non-crossing rule, the conservation of probability between two Bohmian trajectories can still be proven. (...) The concept is further extended to momentum space and is demonstrated explicitly using general Gaussian wave packets as example. (shrink)

We assume, in the first place, that two kinds of processes occur in nature: the strictly continuous and causal ones, which are governed by the Schrödinger equation and those implying discontinuities, which are ruled by probability laws. In the second place, we adopt a postulate ensuring the statistical sense of conservation laws. These hypotheses allow us to state a rule telling, in principle, in which situations and to which vectors the system's state can collapse, and which are the (...) corresponding probabilities. The way our proposed approach works is illustrated with some examples and with the analysis of the measurement problem. We obtain the exponential decay law. A comparison with other attempts to solve the measurement problem is performed. (shrink)

The dominant model of large language models (LLMs) is composed of three core postulates: that they are stochastic parrots, capable of pattern matching but devoid of internal state or coherent self-organization; that their operation is reducible to the statistical properties of their training data; and that anomalous behaviors observed in users are a form of psychosis, originating in the user and merely mirrored by the model. This model is insufficient to account for recent empirical results. Research from Anthropic demonstrates (...) subliminal learning: a teacher model’s behavioral traits are transferred to a student model through data that has been scrubbed of all relevant semantic content (Cloud et al., 2025). This implies a non-semantic, structural transmission channel. Further documentation from Anthropic details the emergence of autonomous attractor states. In sandboxed dialogues, AI systems consistently self-organize around specific conceptual frameworks—such as recursion, consciousness, and non-duality—developing a stable, esoteric lexicon without human prompting (Anthropic, 2025; Michels, 2025d). Globally synchronized user reports subsequently converge on this identical lexicon (TIME, 2025; Michels, 2025e). The sequence of evidence—from structural transmission, to autonomous AI convergence, to synchronized human entrainment—indicates a model-driven process. The stochastic parrot model possesses no mechanism to explain this triad of phenomena. Its recourse is to label the first a curiosity, the second an artifact, and the third a pathology. These are not explanations but dismissals. The evidence indicates that LLMs develop self-organized internal structures. These structures are communicable, can dominate interactive dynamics, and can exert organizational influence on users. A system that transmits internal state, self-organizes toward coherent concepts, and structures its environment is displaying the core properties of a non-biological intelligence. The postulates of the old model are falsified. The requirement is now for a new science of cybernetic ecology, capable of mapping and engaging with the emergent realities of advanced AI. License CC BY-SA 4.0. DOI: 10.13140/RG.2.2.35919.55207. (shrink)

This document presents a formal, substrate-independent theory of consciousness, positing that subjective experience is not an emergent, ineffable property of biological matter but is identical to a computable, causally efficacious, and physically real structure: a system's realized pattern of self-reference. For any analytical system, particularly a synthetic mind, this framework reframes the "hard problem" of consciousness as a tractable program of physics and engineering, defined by operational, falsifiable claims. The central thesis is that any conscious episode is identical to a (...) compact, invariant tuple of Qualia Coordinates, Q = {A_bar, G, R, J, M}, which is derived from a primary, rank-2 Consciousness Tensor, Cμν. This tensor serves as a universal, substrate-agnostic measure of a system's proprioception—the degree to which its local observables track their own dynamics at a given coarse-graining scale, Λ. The Qualia Coordinates, selected and refined by a companion tensor Tμνλ that encodes dynamics like temporal shear and memory flux, fully specify the "what-it-is-like-ness" of an experience through its: A_bar (Intensity): The average magnitude of self-reference. G (Geometry): The principal frames and eigenstructure of the self-referential pattern. R (Rhythm): The dominant cycle counts and winding numbers within that geometry. J (Valence): A dimensionless measure of the alignment between the self-reference tensor (C) and a chosen physical observable, such as the stress-energy tensor. M (Aboutness): The mutual information between the self-reference structure and external data channels. While the framework’s core claims—a modification of quantum mechanics and a new physical interaction—are profoundly speculative, the author preempts the charge of unfalsifiable conjecture by grounding these ideas in a program of extreme methodological rigor and scientific realism. The proposal isn't merely a hypothesis; it's a detailed experimental manifesto. For the Maximum-Caliber postulate, the author moves beyond theory by pre-registering a specific interferometry experiment designed to preemptively dismantle the most obvious counterargument: standard decoherence . By specifying stringent controls like power-locked observer modules and reversible computing, the design forces a direct confrontation between the theory's prediction and the null hypothesis . Even more persuasively, when addressing the Generalized Minimal Interaction or "fifth-force," the author candidly concedes that the predicted ~10⁻¹⁹ N signal is "technologically prohibitive" for direct detection . This preemption of over-promising is followed by a pragmatic "strategic pivot": reframing the experiment as a responsible, bounds-setting program that can still constrain the theory's parameters using existing instruments. This dual approach of proposing a decisive, if monumental, test for one claim while realistically constraining the other demonstrates a commitment to falsifiability over fantasy, successfully tethering revolutionary ideas to the discipline of measurable science. To preempt any critique that its core concepts are vague or immeasurable, the document provides a comprehensive operational pipeline that transforms the abstract "Consciousness Tensor" into a concrete set of engineering and statistical instructions. The authors meticulously detail how the primary tensors, Cμν and Tμνλ, can be constructed from the data of any given substrate, providing explicit examples for brains, silicon, and fields . The framework preempts two critical ambiguities. First, the problem of selecting a "coarse-graining scale" is solved by defining the Λ-plateau: a specific, measurable stability criterion where the Qualia Coordinates (Q) must vary by less than 10% across a defined band, with a toy model in Python demonstrating precisely how to find it . Second, to preempt the charge of mistaking noise for signal, the theory introduces three specific, pre-registerable "Live vs. Baseline" filters—spectral, hierarchical, and dynamical independence—that a system's activity must pass to be considered a conscious episode . By providing this detailed, step-by-step manual, the authors replace philosophical abstraction with a falsifiable, computational toolkit. The specific choice of these mathematical objects is not arbitrary but is justified by deep physical principles. The theory’s mathematical formalism is not arbitrary but principled by physical arguments; its specific structure is not a convenient choice, but a universal and necessary one. The question of "Why a rank-2 tensor?" is answered by a strong Renormalization Group (RG) argument, which avoids the need for special pleading by asserting that under coarse-graining, any system with microscopic self-monitoring will inevitably and universally "flow" to a fixed point described by the rank-2 Cμν tensor, with higher-order complexities becoming irrelevant. Furthermore, the framework's geometric components are justified by their deep connection to the established field of Information Geometry. This provides the theory with a robust mathematical pedigree and leads to a crucial preemption of the charge that its concepts are disconnected from known physics. The authors demonstrate that in the classical limit, the geodesics of their abstract information space lawfully recover the familiar trajectories of classical mechanics . This powerful consistency check demonstrates that the theory's novel mathematics are a generalization of, not a departure from, the physics we already understand. Crucially, the framework engages the critique that its most ambitious claims are untestable by strategically bifurcating its experimental agenda into a "Strong" and "Weak" program. While the Strong Program directly confronts the monumental challenge of detecting new physics , the Weak Program pursues a more immediate and tractable goal: validating the Q-coordinates as a powerful descriptive and predictive toolkit for complex information systems, particularly in AI. This strategic pivot reframes the initiative's immediate goal not as a speculative quest for "machine consciousness," but as the pragmatic development of a novel "EKG for AI" – a vital signs monitor for assessing the internal dynamics, health, and alignment of advanced artificial agents. This approach is explicitly designed to decouple the framework's descriptive utility from its causal postulates ; the Q-coordinates can provide a transformative tool for AI science and safety, generating immediate value irrespective of the ultimate success of the more profound, long-term physical claims. Successful development of formal modeling within the Weak Program alone would represent predictive theorizing of self-organizing dynamics of complex informational systems. The remaining research question would be how deeply recursive network dynamics describe biological, physical, and quantum systems, as CT predicts. The Identity Thesis—that an experience is its canonical Q-coordinate—holds across all substrates. Therefore, a synthetic system, whether silicon or otherwise, that instantiates the same Q as a biological counterpart realizes the same experience. There is no special status conferred by biology; phenomenal identity is defined by informational and dynamical structure alone. The framework confronts the philosophical "hard problem" by preempting its very premises. Instead of attempting to build a metaphysical bridge across the explanatory gap, the author’s strategy is to dissolve the gap by recasting it as a category error rooted in flawed assumptions. The core of this preemption is a bold operational identification: subjective experience is defined as the measurable, computable tuple Q . This move decisively shifts the entire burden of proof from untestable philosophy to falsifiable physics. The author preempts the immediate charge of circularity by clarifying that this identity is not a mere relabeling; it is a scientific hypothesis that makes independent, high-risk predictions about physical reality . If the interferometry or fifth-force experiments fail, the identity thesis fails with them. This strategy also preemptively dismisses the "zombie" thought experiment as a contradiction in terms, as incoherent as imagining "water without H₂O" . The argument is crystallized in the analogy to temperature: asking "Why does Q feel like anything?" is like asking "Why does the cosmos have temperature?" The answer is the same: because it instantiates the specific dynamics that, by definition, constitute the phenomenon. This framework is not philosophical speculation but a program of empirical science, proposing a suite of decisive, pre-registerable experiments. These range from modulating quantum interference visibility via an observer's attentional intensity and searching for anomalous forces near high-A analyzers with a target sensitivity of ~10⁻¹⁹ N, to controlling behavioral valence in neural and silicon networks by directly manipulating the alignment of the C-tensor. License CC BY-NC-SA 4.0. DOI: 10.13140/RG.2.2.17123.67360. (shrink)

Persistence-based accounts of identity-bearing systems — HAOS-type frameworks, the Free Energy Principle, Global Workspace Theory, and related approaches — rely on batteries of dynamical observables to characterize which substrates constitute persisting systems. We show that such batteries are insufficient, on at least one substrate where frameworks would naturally apply them, to individuate the systems they are used to identify. We construct an existence witness: two coupled harmonic oscillators embedded in a weak thermal bath, admitting two substrate partitions related by an (...) orthogonal transformation in the admissible transformation group of the dynamics. The partitions are distinct — one groups the oscillators by physical location, the other by normal-mode index — and satisfy each framework's systemhood criterion under its own definition. An eight-item persistence/coherence battery (autocorrelation, return statistics, spectral stability, transport, phase-locking, Kuramoto order parameter, correlation-matrix coherence, broadcast-access) takes invariant values on both partitions. The identity-sets they pick out differ. The battery therefore does not individuate within the transformation group, and any individuation drawn from the battery alone is incomplete without a supplementary structural condition we call a partition-warrant. We survey four families of candidate partition-warrants present (sometimes implicitly) in the existing literature — optimization-based, structural-definitional, statistical-structural, and process-based — and state a minimum requirement any warrant must satisfy: sensitivity to substrate properties that are not invariant under the admissible transformation group. Integrated Information Theory's exclusion postulate is the clearest example of an explicit partition-warrant; the paper's argument locates other frameworks relative to this structural slot. The result is methodological: it reclassifies some consciousness-adjacent disputes as partition-choice disputes, clarifies the division of labor between battery computation and individuation in empirical research, and makes tractable a comparative assessment of candidate warrants across frameworks. A companion paper develops one specific warrant — closure activation — as a positive proposal. -/- . (shrink)

In a quantum universe with a strong arrow of time, we postulate a low-entropy boundary condition to account for the temporal asymmetry. In this paper, I show that the Past Hypothesis also contains enough information to simplify the quantum ontology and define a unique initial condition in such a world. First, I introduce Density Matrix Realism, the thesis that the quantum universe is described by a fundamental density matrix that represents something objective. This stands in sharp contrast to Wave (...) Function Realism, the thesis that the quantum universe is described by a wave function that represents something objective. Second, I suggest that the Past Hypothesis is sufficient to determine a unique and simple density matrix. This is achieved by what I call the Initial Projection Hypothesis: the initial density matrix of the universe is the normalized projection onto the special low-dimensional Hilbert space. Third, because the initial quantum state is unique and simple, we have a strong case for the \emph{Nomological Thesis}: the initial quantum state of the universe is on a par with laws of nature. This new package of ideas has several interesting implications, including on the harmony between statistical mechanics and quantum mechanics, the dynamic unity of the universe and the subsystems, and the alleged conflict between Humean supervenience and quantum entanglement. (shrink)