Search Results (19)

The details of the contents and formulations of the Born rule have changed considerably from its inception by Born in 1926 to the present day. This paper traces the early history of the Born rule 100 years ago, its generalization (essential for today’s quantum optics and quantum information theory) to POVMs around 50 years ago, and a modern derivation from an intuitive definition of the notion of a quantum detector. Also discussed is the extent to which the various forms of the Born rule have, like any other statement in physics, a restricted domain of validity, which leads to problems when applied outside this domain. Full article

The POVM theorem is a central result in Bohmian mechanics, grounding the measurement formalism of standard quantum mechanics in a statistical analysis based on the quantum equilibrium hypothesis (the Born rule for Bohmian particle positions). It states that the outcome statistics of an experiment are described by a positive operator-valued measure (POVM) acting on the Hilbert space of the measured system. In light of recent debates about the scope and status of this result, we provide a systematic presentation of the POVM theorem and its underlying assumptions with a focus on their conceptual foundations and physical justifications. We conclude with a brief discussion of the scope of the POVM theorem—especially the sense in which it does (and does not) place limits on what is “measurable” in Bohmian mechanics. Full article

Einstein’s 1919 distinction between “principle theories” and ”constructive theories” has been applied by Jeffrey Bub to classify the Copenhagen interpretation of quantum mechanics (QM) as a principle theory agree with this classification. Additionally, I argue that Bohm’s interpretation of QM fits Einstein’s concept of a constructive theory. Principle theories include empirically established laws or principles, such as the first and second laws of thermodynamics or the principles of special relativity, including the Born Rule of QM. According to Einstein, principle theories offer ”security in their foundations and logical perfection”. However, ultimate understanding requires constructive theories, which build complex phenomena from simpler models. Constructive theories provide intelligible models of physical phenomena. Bohm’s QM, with its added microstructure, presents such a model. In this framework, quantum phenomena appear from statistical ensembles of microparticles in motion, with deterministic particle trajectories guided by the wave function. This reveals how Bohm’s account offers a constructive model for understanding quantum phenomena. Full article

One of the most common mitigations against network-borne security threats is the deployment of firewalls, i.e., systems that can observe traffic and apply rules to let it through if it is benign or drop packets that are recognized as malicious. Cheap and open-source (a feature that is greatly appreciated in the security world) software solutions are available but may be too slow for high-rate channels. Hardware appliances are efficient but opaque and they are often very expensive. In this paper, an open-hardware approach is proposed for the design of a firewall, implemented on off-the-shelf components such as an FPGA (the Xilinx KC705 development board), and it is tested using controlled Ethernet traffic created with a packet generator as well as with real internet traffic. The proposed system can filter packets based on a set of rules that can use the whitelist or blacklist approach. It generates a set of statistics, such as the number of received/transmitted packets and the amount of received/transmitted data, which can be used to detect potential anomalies in the network traffic. The firewall has been experimentally validated in the case of a network data throughput of 1 Gb/s, and preliminary simulations have shown that the system can be upgraded with minor modifications to work at 10 Gb/s. Test results have shown that the proposed firewall features a latency of 627 ns and a maximum data throughput of 0.982 Gb/s. Full article

Quantum states containing records of incompatible outcomes of quantum measurements are valid states in the tensor-product Hilbert space. Since they contain false records, they conflict with the Born rule and with our observations. I show that excluding them requires a fine-tuning to an extremely restricted subspace of the Hilbert space that seems “conspiratorial”, in the sense that (1) it seems to depend on future events that involve records (including measurement settings) and on the dynamical law (normally thought to be independent of the initial conditions), and (2) it violates Statistical Independence, even when it is valid in the context of Bell’s theorem. To solve the puzzle, I build a model in which, by changing the dynamical law, the same initial conditions can lead to different histories in which the validity of records is relative to the new dynamical law. This relative validity of the records may restore causality, but the initial conditions still must depend, at least partially, on the dynamical law. While violations of Statistical Independence are often seen as non-scientific, they turn out to be needed to ensure the validity of records and our own memories and, by this, of science itself. A Past Hypothesis is needed to ensure the existence of records and turns out to require violations of Statistical Independence. It is not excluded that its explanation, still unknown, ensures such violations in the way needed by local interpretations of quantum mechanics. I suggest that an as-yet unknown law or superselection rule may restrict the full tensor-product Hilbert space to the very special subspace required by the validity of records and the Past Hypothesis. Full article

During the last forty years, the use of strontium isotopes in archaeology and biogeochemical research has spread widely. These isotopes, alone or in combination with others, can contribute to trace past and present environmental conditions. However, the interpretation of the isotopic values of strontium is not always simple and requires good knowledge of geochemistry and geology. This short paper on the use of strontium isotopes is aimed at those who use this tool (archaeologists, but not only) but who do not have a thorough knowledge of mineralogy, geology, and geochemistry necessary for a good understanding of natural processes involving these isotopes. We report basic knowledge and suggestions for the correct use of these isotopes. The isotopic characteristics of bio-assimilable strontium depend not so much on the isotopic characteristics of the bulk rock as, rather, on those of its more soluble minerals. Before studying human, animal and plant remains, the state of conservation and any conditions of isotopic pollution should be carefully checked. Samples should be collected according to random sampling rules. The data should be treated by a statistical approach. To make comparisons between different areas, it should be borne in mind that the study of current soils can be misleading since the mineralogical modification of soil over time can be very rapid. Full article

Following the inauguration, the Trump administration authorized a series of anti-immigrant policies, including modifications to the public charge regulation. This study analyzed the effect of the publication of a proposed public charge rule in 2018 on the risk of preterm birth between uninsured and privately insured Latinx birthing people in the United States by using natality files from the National Center for Health Statistics. In total, 1,375,580 Latinx birthing people reported private insurance as their primary source of delivery from 2014 to 2019, while 317,056 Latinx birthing people reported self-pay as their primary source of delivery during the same period. After the publication of the proposed public charge rule in 2018, the odds of preterm birth among uninsured foreign-born Latinx birthing people increased by 6.2% compared with privately insured foreign-born Latinx birthing people (OR: 1.062; 95% CI: 1.016, 1.110). On the other hand, the odds of preterm births among uninsured US-born Latinx birthing people did not significantly increase after the publication of the proposed rule compared with privately insured US-born Latinx birthing people. These findings suggest the publication of the public charge rule proposed in 2018 may be associated with adverse birth outcomes among uninsured foreign-born Latinx birthing people in the United States. Full article

A longstanding issue in the Everettian (Many-Worlds) interpretation is to justify and make sense of the Born rule that underlies the statistical predictions of standard quantum mechanics. The paper offers a reappraisal of Everett’s original account in light of the recent literature on the concept of typicality. It argues that Everett’s derivation of the Born rule is sound and, in a certain sense, even an optimal result, and defends it against the charge of circularity. The conclusion is that Everett’s typicality argument can successfully ground post-factum explanations of Born statistics, while questions remain about the predictive power of the Many-Worlds interpretation. Full article

The argument of environment-assisted invariance (known as envariance) implying Born’s rule is widely used in models for quantum measurement to reason that they must yield the correct statistics, specifically for linear models. However, it has recently been shown that linear collapse models can never give rise to Born’s rule. Here, we address this apparent contradiction and point out an inconsistency in the assumptions underlying the arguments based on envariance. We use a construction in which the role of the measurement machine is made explicit and shows that the presence of envariance does not imply that every measurement will behave according to Born’s rule. Rather, it implies that every quantum state allows a measurement machine to be constructed, which yields Born’s rule when measuring that particular state. This resolves the paradox and is in agreement with the recent result of objective collapse models necessarily being nonlinear. Full article

We investigate the dependence of elemental abundances on physical constants, and the implications this has for the distribution of complex life for various proposed habitability criteria. We consider three main sources of abundance variation: differing supernova rates, alpha burning in massive stars, and isotopic stability, and how each affects the metal-to-rock ratio and the abundances of carbon, oxygen, nitrogen, phosphorus, sulfur, silicon, magnesium, and iron. Our analysis leads to several predictions for which habitability criteria are correct by determining which ones make our observations of the physical constants, as well as a few other observed features of our universe, most likely. Our results indicate that carbon-rich or carbon-poor planets are uninhabitable, slightly magnesium-rich planets are habitable, and life does not depend on nitrogen abundance too sensitively. We also find suggestive but inconclusive evidence that metal-rich planets and phosphorus-poor planets are habitable. These predictions can then be checked by probing regions of our universe that closely resemble normal environments in other universes. If any of these predictions are found to be wrong, the multiverse scenario would predict that the majority of observers are born in universes differing substantially from ours, and so can be ruled out, to varying degrees of statistical significance. Full article

Diverse phenomena such as feedback, interconnectedness, causality, network dynamics, and complexity are all born from Relationships. They are fundamentally important, as they are transdisciplinary and synonymous with connections, links, edges, and interconnections. The foundation of systems thinking and systems themselves consists of four universals, one of which is action–reaction Relationships. They are also foundational to the consilience of knowledge. This publication gives a formal description of and predictions of action–reaction Relationships (R) or “R-rule”. There are seven original empirical studies presented in this paper. For these seven studies, experiments for the subjects were created on software (unless otherwise noted). The experiments had the subjects complete a task and/or answer a question. The samples are generalizable to a normal distribution of the US population and they vary for each study (ranging from N = 407 to N = 34,398). With high statistical significance the studies support the predictions made by DSRP Theory regarding action–reaction Relationships including its universality as an observable phenomenon in both nature (ontological complexity) and mind (cognitive complexity); mutual dependencies on other universals (i.e., Distinctions, Systems, and Perspectives); role in structural predictions; internal structures and dynamics; efficacy as a metacognitive skill. In conclusion, these data suggest the observable and empirical existence, parallelism (between cognitive and ontological complexity), universality, and efficacy of action–reaction Relationships (R). Full article

Lyme disease is the most prevalent tick-borne disease in Eastern Europe. This study focuses on the development of a machine learning model based on a neural network for predicting the dynamics of the Lyme disease epidemic process. A retrospective analysis of the Lyme disease cases reported in the Kharkiv region, East Ukraine, between 2010 and 2017 was performed. To develop the neural network model of the Lyme disease epidemic process, a multilayered neural network was used, and the backpropagation algorithm or the generalized delta rule was used for its learning. The adequacy of the constructed forecast was tested on real statistical data on the incidence of Lyme disease. The learning of the model took 22.14 s, and the mean absolute percentage error is 3.79%. A software package for prediction of the Lyme disease incidence on the basis of machine learning has been developed. Results of the simulation have shown an unstable epidemiological situation of Lyme disease, which requires preventive measures at both the population level and individual protection. Forecasting is of particular importance in the conditions of hostilities that are currently taking place in Ukraine, including endemic territories. Full article

The mathematical formalism of quantum mechanics is derived or “reconstructed” from more basic considerations of the probability theory and information geometry. The starting point is the recognition that probabilities are central to QM; the formalism of QM is derived as a particular kind of flow on a finite dimensional statistical manifold—a simplex. The cotangent bundle associated to the simplex has a natural symplectic structure and it inherits its own natural metric structure from the information geometry of the underlying simplex. We seek flows that preserve (in the sense of vanishing Lie derivatives) both the symplectic structure (a Hamilton flow) and the metric structure (a Killing flow). The result is a formalism in which the Fubini–Study metric, the linearity of the Schrödinger equation, the emergence of complex numbers, Hilbert spaces and the Born rule are derived rather than postulated. Full article

In this work, we derive Born’s rule from the pilot-wave theory of de Broglie and Bohm. Based on a toy model involving a particle coupled to an environment made of “qubits” (i.e., Bohmian pointers), we show that entanglement together with deterministic chaos leads to a fast relaxation from any statistical distribution $\rho \left(x\right)$ of finding a particle at point x to the Born probability law ${|\Psi \left(x\right)|}^2$. Our model is discussed in the context of Boltzmann’s kinetic theory, and we demonstrate a kind of H theorem for the relaxation to the quantum equilibrium regime. Full article

Max Born’s statistical interpretation made probabilities play a major role in quantum theory. Here we show that these quantum probabilities and the classical probabilities have very different origins. Although the latter always result from an assumed probability measure, the first include transition probabilities with a purely algebraic origin. Moreover, the general definition of transition probability introduced here comprises not only the well-known quantum mechanical transition probabilities between pure states or wave functions, but further physically meaningful and experimentally verifiable novel cases. A transition probability that differs from 0 and 1 manifests the typical quantum indeterminacy in a similar way as Heisenberg’s and others’ uncertainty relations and, furthermore, rules out deterministic states in the same way as the Bell-Kochen-Specker theorem. However, the transition probability defined here achieves a lot more beyond that: it demonstrates that the algebraic structure of the Hilbert space quantum logic dictates the precise values of certain probabilities and it provides an unexpected access to these quantum probabilities that does not rely on states or wave functions. Full article