Here an improved generalization of Feynman’s paradox of negative probabilities [1, 2] for observing three events is considered. This version of the paradox is directly related to the theory of quantum computing. Imagine a triangular room with three windows, where there are three chairs, on each of which a person can seat [4]. In any of the windows, an observer can see only the corresponding pair of chairs. It is known that if the observer looks at a window (to make a pairwise observation), the picture will be in the probabilistic sense the same for all windows: only one chair from the observed pair is occupied with a probability of 1/2, and there are never busy or free both chairs at once. Paradoxically, existing theories based on Kolmogorov’s probability theory do not answer the question that naturally arises after such pairs of observations of three events: «What is really happening in a triangular room, how many people are there and with what is the probability distribution they are sitting on three chairs?».
Here an improved generalization of Feynman’s paradox of negative probabilities [1, 2] for observing three events is considered. This version of the paradox is directly related to the theory of quantum computing. Imagine a triangular room with three windows, where there are three chairs, on each of which a person can seat [4]. In any of the windows, an observer can see only the corresponding pair of chairs. It is known that if the observer looks at a window (to make a pairwise observation), the picture will be in the probabilistic sense the same for all windows: only one chair from the observed pair is occupied with a probability of 1/2, and there are never busy or free both chairs at once. Paradoxically, existing theories based on Kolmogorov’s probability theory do not answer the question that naturally arises after such pairs of observations of three events: «What is really happening in a triangular room, how many people are there and with what is the probability distribution they are sitting on three chairs?».
This paper is devoted to foundations of probability theory. We discuss interpretations of probability, corresponding mathematical formalisms, and applications to quantum physics. One of the aims of this paper is to show that the probability model based on Kolmogorov's axiomatics cannot describe all stochastic phenomena, i.e., that quantum physics induces natural restrictions of the use of Kolmogorov's theory and that we need to develop non-Kolmogorov models for describing some quantum phenomena. The physical motivations are presented in a clear and brief manner. Thus the reader does not need to have preliminary knowledgeof quantum physics. Our main idea is that we cannot develop non-Kolmogorov models by the formal change of Kolmogorov's axiomatics. We begin with interpretations (classical, frequency, and proportional). Then we present a class of non-Kolmogorov models described by so-called p-adic numbers. Here, in particular, we obtain a quite natural realization of negative probabilities. These negative probability distributions might provide a solution of some quantum paradoxes.
Quantum non-locality and contextuality can be simulated with quasi-probabilities, i.e. probabilities that take negative values. Here, we show that another quantum phenomenon, the observer effect, admits a quasi-probabilistic description too. We also investigate post-quantum observer effects based on the Specker's triangle scenario. This scenario comprises three observables, with the possibility of measuring two simultaneously. Represented as three boxes with a hidden ball, this scenario exhibits counterintuitive behaviour: regardless of the chosen pair of boxes, one box always contains the ball. Moreover, the scenario demonstrates a strong observer effect. When an observer selects and opens the first box, finding it empty, the ball is guaranteed to be in the second box, thereby allowing the observer to determine the ball's location among the remaining two boxes. We extend this scenario to include additional boxes and multiple balls. By employing negative probabilities, we demonstrate amplification of the observer effect. This article is part of the theme issue 'Quantum contextuality, causality and freedom of choice'.
How can we use quantum theory to model other phenomena of interest to researchers in cognition and decision making? Quantum theory is not easy for researchers in cognition and decision making to accept. In fact, quantum mechanics was not easy for physicists to accept either, but it was forced on them by several paradoxical findings that could not be explained using classical physics. We have a similar problem in cognition and decision making – there are numerous paradoxical findings that just seem irrational according to classic probability theory. For example, under some conditions, people judge the probability of event A and B to be greater than the probability of event B , which is called the conjunction fallacy (Tversky & Kahneman, 1983). Also, under the same conditions, they judge the probability of A or B to be less than the probability of event A (Carlson & Yates, 1989), which is called the disjunction fallacy. In this chapter we examine how quantum probability theory explains these and other puzzling results from human probability judgment research. This chapter has two main parts. In the first part, we use a quantum model to derive qualitative predictions for conjunction errors, disjunction errors, and other closely related findings. The first section provides a general set of predictions that do not depend on specific assumptions about the features used to represent events, and the predictions are parameter free. In the second part, we examine the quantitative predictions of the quantum model for a Bayesian inference task, which we use to explain order effects on inference.
Extremely many worlds would exist mathematically where the results of quantum processes happen to occur from now on outside earth always according to completely other probability distributions then the known ones. At first glance it seems to be extremely improbable to perceive ourselves in a world where the probability distributions will remain those according to the simple rules of quantum theory. This is called a probability paradox, and further similar paradoxes are presented. A strategy is described to search for solutions, an information theoretic approach. In that approach infinitely many worlds are considered in parallel.
Abstract We argue that there is a simple, unique, reason for all quantum paradoxes, and that such a reason is not uniquely related to quantum theory. It is rather a mathematical question that arises at the intersection of logic, probability, and computation. We give our ‘weirdness theorem’ that characterises the conditions under which the weirdness will show up. It shows that whenever logic has bounds due to the algorithmic nature of its tasks, then weirdness arises in the special form of negative probabilities or non-classical evaluation functionals. Weirdness is not logical inconsistency, however. It is only the expression of the clash between an unbounded and a bounded view of computation in logic. We discuss the implication of these results for quantum mechanics, arguing in particular that its interpretation should ultimately be computational rather than exclusively physical. We develop in addition a probabilistic theory in the real numbers that exhibits the phenomenon of entanglement, thus concretely showing that the latter is not specific to quantum mechanics.
Four people sit down to dinner. Physics can tell you exactly where they are, but not what happens between them. This preprint proposes six measurable coordinates for what’s missing, and states how each one could be proven wrong. At 6:00 PM, four people meet at a restaurant. Standard 4D spacetime maps the event perfectly: x, y and z locate the table, and t marks the time. Four worldlines meet at one point. That description is correct, and it’s incomplete. It says where the bodies are. It says nothing about what the meeting is: breathing that falls into rhythm, four different points of view on the same evening, moods that colour every sentence, and a shared state that belongs to no single person and fades when they leave. So the meeting is not 1 + 1 + 1 + 1 = 4. It is a + b + c + d = x, where x includes everything that exists only while they are together. The gravity of the meeting. Now change who is at the table. Seat both You and Me, the President of the United States, Donald J. Trump, and the President of the People’s Republic of China, Xi Jinping. The physical mass in the room is about the same as at any other dinner, but the gravity of the meeting is very different. Each leader brings the institutions, decisions and consequences of their office, and what is said at that table spreads into markets, policies and lives far beyond the room. Physics already knows that a system’s mass is not the sum of its parts (an atomic nucleus weighs less than its protons and neutrons). MW Theory proposes a parallel quantity for events, event weight (W). W depends on who is present, what is at stake, what came before the meeting and what follows from it. As an example - the restaurant meeting is the followup of 6 months project finalizing international teams work, lead by neutral facilitator and oriented on alternative, data driven realistic scenarios that can be implemented in areas like: high-stakes resolve and perception shift of fentanyl crisis, oil price scenarios and pathways to ending the war in Ukraine. The solutions are business deals, data driven and created in a win-win formats. Measure the E=mc2 of that meeting against first one, and add the fact that there is a superobserver scenario. MW Dimension Theory extends 4D spacetime with six additional coordinates: β, Pneumodynamic: respiratory phase π, Point of View: the observer’s reference frame Σ, Sensory-Emotional State: inner condition μ, Relational-Kinetic: movement, communication and connection Γ, Group Entanglement: the shared state of the group Α, Conscious Architecture: the designed environment The framework draws on relational quantum mechanics (Rovelli, 1996), quantum reference frames (Giacomini, Castro-Ruiz & Brukner, 2017), EEG hyperscanning and collective intelligence research. It describes a group from the superobservers perspective, a frame that covers every observer without giving priority to any one of them and keeps the ledger of the event balanced, possibility to rebalance events due to nature of quantum physics and superposition. It is developed in three formulations: Relational-Biological, Field-Theoretic and Quantum-Information. Every claim is tagged by strength of evidence, and the paper sets out 12 testable predictions, each with an explicit kill criterion. Applications include facilitating complex problem-solving for governments, multinational teams and think tanks, on high-stakes questions such as the fentanyl crisis, oil price scenarios and paths to ending the war in Ukraine. The paper also proposes a new field, Quantum Andragogy, which studies how adults learn and solve problems together, using Quantum Physics, Quantum Biology and related fields. Working preprint, v0.00.03. Feedback and research collaboration welcome, located at last page.