Information is physically measurable as a selection from a set of possibilities, the domain of information. This defines the term "information". The domain of the information must be known together reproducibly beforehand. As a practical consequence, digital information exchange can be made globally efficient, interoperable, and searchable to a large extent by online definition of application-optimized domains of information. There are even more far-reaching consequences for physics. The purpose of this article is to present prerequisites and possibilities for a physical approach that is consistent with the precise definition of information. This concerns not only the discretization of the sets of possible experimental results but also the order of their definition over time. The access to or comparison with the domain of information is more frequent, the earlier it was defined. The geometrical appearance of our space is apparently a delayed statistical consequence of a very frequent connection with the common primary domain of information.
Information is physically measurable as a selection from a set of possibilities, the domain of information. This defines the term "information". The domain of the information must be known together reproducibly beforehand. As a practical consequence, digital information exchange can be made globally efficient, interoperable, and searchable to a large extent by online definition of application-optimized domains of information. There are even more far-reaching consequences for physics. The purpose of this article is to present prerequisites and possibilities for a physical approach that is consistent with the precise definition of information. This concerns not only the discretization of the sets of possible experimental results but also the order of their definition over time. The access to or comparison with the domain of information is more frequent, the earlier it was defined. The geometrical appearance of our space is apparently a delayed statistical consequence of a very frequent connection with the common primary domain of information.
What is information? A short answer could be: Anything that changes our minds and states of thinking! Information is virtual. It can be carried by speech, an image, scratches on a stone, patterns in a photon field, the connections of neurons in our brains or even by the wavefunction of an electron. Information does not depend on the actual means of transmission nor does its identity change when changing the carrier. Information is physical. It needs to be sustained by a physical substrate and rearranging that substrate to contain the wanted information requires to spend energy or work. Without a physical world, information can not be stored, processed, or transmitted. Our world is permeated with different representations of information. Actually Information about the physical laws governing our Universe can be found everywhere and in everything. Could it then be that the real fundamental elements of this world are tiny bits of information? Could we get it from bit?1 A number of researcher investigate this possibility, and several of their attempts to recover physical laws from the principles governing information are reported about in this special issue on physics of information. The articles by Gregg Jaeger,2 by Ariel Caticha,3 and by John Skilling and Kevin Knuth4 address the reconstruction of quantum mechanics from information theory. Furthermore, Kevin Knuth and James Walsh5 show how to recover space-time from particles sending each others signals in an initially geometry-free setting. A central element of most works on information is the concept of a probability. Probabilities can be defined via various routes. Most familiar might be their definitions by the frequentists school as relative frequencies of events (in the limit of infinite amounts of such). A more general definition of probabilities is the Bayesians' one, which regards probabilities as quantifiers of statements, expressing how much those should be expected to be true. Although this definition looks subjective on the first glance, it rests on a solid mathematical theorem by Richard Cox6 that any extension of binary logic to a continuum of single valued truthfulness quantifier that respects a minimum of requirements must be isomorphic to probability theory. And this definition turns out to embrace the frequentists' definition in case that infinite numbers of comparable events are actually available and can be counted. The majority of authors of this special issues seem to favor the Bayesian perspective, which is probably a result of our own, the guest editors', preference and not necessarily a reflection of the prevailing position of contemporary scientists. The different views on probabilities of frequentists and Bayesians are addressed by the article of Allen Caldwell.7 He builds a bridge between these antagonistic camps by explaining frequentists' constructions in a Bayesian language. In particular, his argumentation why the omnipresent p-value in statistical and experimental literature might often capture a relevant signal of model misfit is reassuring, given that a large fraction of our medical system is based on decisions backed up by p-values. A Bayesian might add that it would be even more reassuring, if a system rigorously build on logic and its continuous extension would be used for decisions affecting live-or-death questions. The laws governing probabilities themselves seem to reflect that of more elementary mathematical structures. Kevin Knuth shows how these emerge from lattice theory, which deals with relations in partially ordered sets like that of collections of possibilities.8 The sum rule of probability theory is a direct consequence of the underlying lattice structure. Interestingly, a number of other theories are resting also on such lattices and therefore exhibit their own versions of sum rules: measures of sets, mutual information, the Euler characteristics of topological spaces, as well as quantum mechanical interactions that are quantified by pairs of numbers, the real and imaginary parts of complex probability amplitudes (see also4). The theory of information has very practical application in physics and elsewhere. Manfred Opper discusses how the solutions of stochastic differential equations can be inferred via variational methods, which have their origin in thermodynamics.9 Torsten Enßlin introduces information field theory (IFT), the information theory for fields, as a means to infer the configuration of a physical field from incomplete and noisy data.10 The mathematical apparatus for this is that of quantum field theory (QFT), just with ordinary probabilities instead of complex probability amplitudes as in the latter. Could it be that the difference between IFT and QFT is just be the same as between classical information theory and quantum mechanics, the transition from real valued to complex valued quantifier for statements? Anyhow, any practical inference machinery, be it for dynamical systems or for fields, requires sophisticated numerical methods. Michael Betancourt reviews Markov Chain Monte Carlo Methods to calculate expectation values over high dimensional probabilities.11 Theo Steininger and coworkers present the NIFTy3 software package for numerical information field theory calculations, which can handle very high dimensional field inference problems.12 Finally, in an article focused on the subtleties of the Monty Hall problem and mostly aiming at information theoretical entertainment, Torsten Enßlin and Margret Westercamp investigate the possibility that human intuition might be more rational than contemporary psychology thinks.13 A number of possible topics for an issue on physics of information are not addressed here. We would have loved to have articles on Landauer's principle, which states that erasing information has to cost energy, on QBism, a Bayesian version of quantum mechanics, on artificial and biological neural networks, as well as any other aspect of the information-soaked biological world. What has a reader of this special issue to be equipped with in order to follow the lines of thoughts? In addition to the usual physicist's education, the minimal additional equipment are the basics of probability theory and the concept of entropy. Most of the other concepts used in the articles rest on those and are introduced there. Let A, B, and C be propositions (or possibilities). The probability P ( A | B ) of A being true assuming that B is true is a number between 0 and 1, with P ( A | B ) = 1 expressing certainty of A under B ( B ⇒ A ) and P ( A | B ) = 0 expressing certainty of not A being the case under B ( B ⇒ ¬ A ).
A Reproducible Method for Checking Earlier Events and Later Choices in Quantum Experiments QDL Research Program — Paper 11 | Version V1.0.0 DOI: https://doi.org/10.5281/zenodo.23261100 Overview Quantum experiments can produce surprising results. Sometimes, an event is recorded first, and a measurement choice is made later. If these two events appear connected, an important question arises: Is this connection supported by the experimental data, or could it be explained by statistical variation, event selection, or measurement conditions? This paper presents a clear and reproducible method for investigating that question. It combines real experimental data, exact statistical calculations, source verification, and computer-based testing. The main goal is simple: make quantum-data calculations easier to understand, repeat, and independently check. What Does This Paper Study? The study examines how researchers can correctly compare an earlier recorded event with a later measurement setting. It focuses on five important questions: Were the earlier events and later settings correctly identified? Were all eligible events included using the original experimental rules? Do the observed numbers show a meaningful statistical relationship? Could selection effects, detection differences, or data-matching errors explain the result? Can another researcher reproduce the same calculations using the available sources? The paper provides mathematical formulas, numerical examples, source checks, and reproducible software for these questions. Three Main Research Applications 1. Munich Event-Ready Bell Experiment The first application studies data from a published quantum Bell experiment involving entangled atoms. The published dataset contains 55,568 events. We independently recalculated four-sector statistics from the published count tables. The main results are: Measurement Odds Ratio Fisher p-value Lab 1 0.997122 0.8653 Lab 2 0.980578 0.2486 These results do not provide stable evidence of an association between the selected variables in the full published counts. We also analyzed original event-level records from two experimental runs in April and June 2016. These files contain 20,403 valid paired events. By applying the original selection rule of 5,000 events per Bell-state class, we exactly reproduced the historical results. All 16 published sector counts matched, with zero differences. This demonstrates why correct event selection and source verification are important for reliable scientific calculations. 2. Photonic Quantum-Switch Experiment The second application examines published data from a 2026 photonic quantum-switch experiment. The original study reported a Bell-like causal-inequality value of approximately 1.8090 ± 0.0024, compared with a fixed-order bound of 1.75. We independently recalculated the relevant quantity using 256 published probability entries. Our calculated value was: 1.808954375 This agrees with the reported result at its published precision. We also examined six statistical comparisons involving measurement settings and marginal probabilities. These checks help distinguish an experimental causal-inequality result from a possible statistical relationship between an earlier event and a later setting. The two questions are different and should not be confused. 3. Testing the Method with 80,000 Synthetic Trials The third application uses 80,000 computer-generated trials, divided into four controlled scenarios. The scenarios represent: A system with no inserted effect. A system with a deliberately inserted statistical difference. A system affected by detection-efficiency differences. A system with information leakage before the earlier result was fully recorded. The software reproduced the expected numerical results for all four scenarios. These tests show how the method can identify known statistical patterns and distinguish them from possible experimental artifacts. The synthetic trials are software-validation data, not new laboratory observations. Main Contributions This paper brings together several important elements in one reproducible research workflow. 1. Clear event identification It defines which event happened earlier, which setting was chosen later, and how the records should be matched. 2. Exact statistical calculations It uses four-sector count tables, odds ratios, log-affinity measures, uncertainty estimates, and Fisher's exact tests. 3. Original-data verification It demonstrates how the correct historical event-selection rule can reproduce published results exactly. 4. Independent source comparisons It uses different quantum datasets without incorrectly treating their measurements as equivalent. 5. Reproducible software It provides a computational framework for repeating the calculations, checking results, and recording source limitations. Why Is This Work Useful? Scientific results become more valuable when other researchers can independently verify them. This paper offers a practical way to investigate complex quantum-data questions without depending only on interpretations or assumptions. The method can help researchers: Recheck published quantum experiments. Find problems caused by event selection or data matching. Compare statistical results across experimental runs. Separate real experimental measurements from simulated examples. Design more reliable tests for future quantum experiments. Understand which conclusions are supported by the available evidence. Scientific Scope This work is primarily about statistical verification, experimental-data interpretation, and reproducibility. It does not establish backwards-time signalling or a new fundamental physical law. The Munich published-count analysis and the two recovered original runs have different levels of source access. The quantum-switch experiment measures a different physical quantity. The synthetic trials are used only to test the software. These distinctions are maintained throughout the study. Data and Software Availability The calculations are supported by QDL Research Suite, a Python-based scientific software package containing tools for reproducible mathematical and statistical analysis. QDL Research Suite — All Versions: https://doi.org/10.5281/zenodo.22952901 QDL Research Suite v1.10.0 — Version Used: https://doi.org/10.5281/zenodo.23256494 The software provides calculation modules, reproducibility tools, automated tests, and verification outputs. The study also identifies the original experimental publications and available source datasets so that the calculations can be checked against their sources. Conclusion The central contribution of Paper 11 is a clear, source-linked method for checking quantum experimental data. It combines published experimental results, original event records, exact statistical methods, and controlled software tests. The work shows how careful data selection, transparent calculations, and independent verification can improve confidence in scientific analysis. Its purpose is to help make complex quantum research more understandable, reproducible, and reliable, while keeping mathematical results, experimental evidence, and physical interpretations clearly separated. Author: Roshankumar Chandaliya Research Program: Quantum Diverter Loop (QDL) Paper: 11 Version: V1.0.0 DOI: https://doi.org/10.5281/zenodo.23261100
The quantum–classical transition is one of the most frequently invoked concepts in modern physics. Yet the notion of classicality itself is far from unique. Depending on the physical context, classical behavior may be associated with decoherence, the semiclassical limit, thermodynamic averaging, suppression of correlations, emergence of collective order, or geometric simplification of statistical state space. These viewpoints are often presented as if they described a single phenomenon, although they emphasize different physical mechanisms and different operational criteria. In this article we examine the principal notions of classicality that appear across quantum theory, statistical physics, condensed matter physics, and information geometry. We compare the corresponding mechanisms of classical emergence and analyze the physical quantities commonly used to characterize them, including coherence, entanglement, fluctuations, correlation length, Fisher information, statistical complexity, and information-geometric curvature. We argue that many apparently distinct routes toward classical behavior share a common structural feature: a reduction of effective fluctuation freedom. From this perspective, classicality may be interpreted as an emergent regime in which the accessible fluctuation manifold becomes progressively constrained, stabilized, or geometrically simplified. This viewpoint naturally unifies decoherence, semiclassical localization, thermodynamic averaging, decorrelation, and collective organization within a common conceptual framework. Rather than representing a unique physical process, the quantum–classical transition appears as a family of related mechanisms through which complex quantum fluctuation structure gives rise to effective macroscopic classical behavior.
Every physical measuring needs a finite, different from zero measurement time and provides information in form of the choice of a measurement result from all possible measurement results. If infinitely many (different) measurement results would be possible, the choice of a measurement result could deliver an infinite quantity of information. But the results of physical measurings (of finite duration) never deliver an infinite quantity of information, they describe past, finite reality. Therefore the set of all possible measurement results a priori is finite. In the physical reality only a finite information quantity can be processed within a finite time interval. For mathematical models whose representation requires a processing of an infinite quantity of information, for example irrational numbers, no (exact) equivalent exists in the physical reality. So mathematical calculations, which have an equivalent in physical reality, can include only rational (finitely many elementary) combinations of rational numbers. Conclusions arise from this for the foundations of mathematical physics.
A conceptual variable is any variable defined by a person or by a group of persons. Such variables may be inaccessible, meaning that they cannot be measured with arbitrary accuracy on the physical system under consideration at any given time. An example may be the spin vector of a particle; another example may be the vector (position and momentum). In this paper, a space of inaccessible conceptual variables is defined, and group actions are defined on this space. Accessible functions are then defined on the same space. Assuming this structure, the basic Hilbert space structure of quantum theory is derived: Operators on a Hilbert space corresponding to the accessible variables are introduced; when these operators have a discrete spectrum, a natural model reduction implies a new model in which the values of the accessible variables are the eigenvalues of the operator. The principle behind this model reduction demands that a group action may also be defined also on the accessible variables; this is possible if the corresponding functions are permissible, a term that is precisely defined. The following recent principle from statistics is assumed: every model reduction should be to an orbit or to a set of orbits of the group. From this derivation, a new interpretation of quantum theory is briefly discussed: I argue that a state vector may be interpreted as connected to a focused question posed to nature together with a definite answer to this question. Further discussion of these topics is provided in a recent book published by the author of this paper.
There are several links between information theory — between »information as such« whatever that might mean — and the foundations of nature, i e, basic physics. Well, since physics a science still evolving (despite propositions that »the end of science« now in sight), some of the links between information and physics are hypothetical. One linkage fairly obvious — thermodynamics depends upon entropy or some measure of order or disorder, and that clearly has something to do with information. The other possible relationship might be between the uncertainty that a key characteristic of quantum mechanics. We can never know everything on the quantum scale; the Heisenberg uncertainty principle tells that the more information we gain in one direction the less we know in another. If we, on that scale, obtain certainty as to one factor, then another will stay entirely undecided — try to affix a position to a quantum particle, and the momentum will be out of bounds entirely. (This the established dogma currently, though there are some deviating ideas.1) Then the question arises: who does the actual measuring, with what — what particles, at what level, are involved in this act of, as it pronounced, forcing the wave function to collapse? This wave function is the indeterminate particle: the various statistics describing the probabilities that the particle (which simultaneously takes on aspects of a wave) may be in one state or another. We will now attempt to discuss these different — or are they really different? — interdependencies, starting with black holes.