A model of a new version of Zeno's arrow paradox is presented in a plausible extension of Newtonian collision mechanics. In exploring various avenues for resolution of the paradox, it becomes evident that a prerelativistic classical physical topology which is locally deterministic can mechanically generate nonclassical ontological properties such as the appearance of a particle in many places at once. It can also mimic some properties of quantum physics, including unprepared spatially‐separated correlations. 1 Zeno's arrow paradox 2 Newtonian collision mechanics and extensions of it 3 Our initial condition (IC) 4 Demonstrating the model paradox 5 Resolving the paradox 6 Unprepared correlations in spatially‐separated events 7 Lessons
A model of a new version of Zeno's arrow paradox is presented in a plausible extension of Newtonian collision mechanics. In exploring various avenues for resolution of the paradox, it becomes evident that a prerelativistic classical physical topology which is locally deterministic can mechanically generate nonclassical ontological properties such as the appearance of a particle in many places at once. It can also mimic some properties of quantum physics, including unprepared spatially‐separated correlations. 1 Zeno's arrow paradox 2 Newtonian collision mechanics and extensions of it 3 Our initial condition (IC) 4 Demonstrating the model paradox 5 Resolving the paradox 6 Unprepared correlations in spatially‐separated events 7 Lessons
Quantum mechanics enables the calculation of the time evolution of a dynamical system provided the Hamiltonian is defined and the initial state is specified. Due to the time reversal invariance, the time evolution of a given initial state at t=0 does not have a time-arrow. These problems have been extensively studied by E. C. G. Sudarshan and collaborators, including myself. Here the survival probability, which is the square of the survival amplitude, is an even function of t. Using the survival amplitude as a common framework, we discuss Zeno effects in several processes: the decay of an unstable particle, pion productions in proton-nucleus collisions and the Aharonov-Vardi effect which is another manifestation of the Zeno effect.
The modern classical statistical physics, thermodynamics, quantum mechanics and gravity theory are developed and well-known theories. The described theories are developed and well studied for a long time. Nevertheless, it contains a number of paradoxes. It forces many scientists to doubt internal consistency of these theories. However, the given paradoxes can be resolved within the framework of the existing physics, without introduction of new laws. Further, in this paper we discuss the paradoxes underlying classical statistical physics, thermodynamics, quantum mechanics, and non-quantum and quantum gravities. We suggest the approaches to solution of these paradoxes on basis universal arrow of time. The first one relies on the influence of the external observer (environment), which disrupts the correlations in the system and results in time arrows alignment. The basis of the second one is the limits of self-knowledge of the system in case of the observed system; the external observer and the environment are included in the considered system. We introduce the concepts of observable dynamics, ideal dynamics, and unpredictable dynamics. We contemplate the phenomenon of complex (living) systems from the point of view of these dynamics. Perspectives of practical use of Unpredictable systems for artificial intellect are considered. c Chapter 1. The Universal Arrow of Time: Classical Mechanics. Abstract: Solution of paradox for the entropy increase in reversible systems. Statistical physics cannot explain why the thermodynamic time arrow does exist un- less very special and so it postulates unnatural initial conditions. However, we are ready to state that statistical physics is able to explain why the thermodynamic time arrow is
Many of the so‐called paradoxes of orthodox quantum mechanics can be shown to have parallel, more logical interpretations in the realm of nonlinear dynamics and chaos theory. Among these are violations of Bell‐type inequalities, which in comparing “classical” mechanics with quantum mechanics implicitly compare uncorrelated and correlated statistics. During the past decade research in the field of nonextensive thermodynamics (including Tsallis entropy) has demonstrated the existence of many statistical correlations in classical, nonlinear systems. When such correlations exist, the conventional classical upper limit on statistical correlations in Bell‐type experiments can easily be raised to overlap with quantum mechanical predictions involving correlated states such as the Bell singlet state, a favorite for deriving Bell inequalities. Thus, arguments based on experimental violations of Bell‐type inequalities, which rule out the existence of “local reality,” become moot. Perhaps quantum mechanics does have a deterministic, ontological basis, albeit one based in nonlinear dynamics and chaos theory. If so, deterministic chaos could provide Einstein’s longed‐for fundamental determinism, but because chaotic systems must be interpreted statistically, this also fits in quite well with the ideas of Bohr — Einstein and Bohr both could have been correct! It should be emphasized that the concept of nonlinear dynamics and chaos underpinning quantum mechanics does not involve hidden variables, nor does the fact that chaos is deterministic interlope on the existence of free will.
There is a very reason to consider that to solve Zeno's paradoxes is to propose the theory of mechanical world view. We believe that this is not only our opinion but also most philosophers' opinion. Recently, in order to justify Heisenberg`s uncertainty principle (cf. Rep. Math. Phys Vol. 29, No. 3, 1991) more firmly. we proposed the linguistic interpretation of quantum mechanics (called quantum and classical measurement theory), which was characterized as the metaphysical and linguistic turn of the Copenhagen interpretation. This turn from physics to language does not only extend quantum mechanicsto classical systems but also yield the (quantum and classical) mechanical world view (and therefore, establish the method of science). If it be so, we may assert that Zeno's paradoxes (Flying Arrow Paradox, Achilles and the tortoise, etc.) were already solved in measurement theory. The purpose of this paper is to examine this assertion.
This work offers a foundational, ontological re-examination of the Einstein-Podolsky-Rosen (EPR) paradox and the violation of Bell inequalities. It argues that the apparent "nonlocality" in quantum mechanics stems not from a physical mechanism of interaction, but from an inadequate ontological premise shared by classical reasoning and many interpretations of quantum theory. Core Thesis: The paradox arises from the implicit assumption that measurement outcomes in entangled systems represent independent, local facts that pre-exist or can be defined separately. The work rejects this premise. Instead, it proposes that entangled states describe indivisible ontological structures, where correlated outcomes are not separate entities to be coordinated, but inseparable aspects of a single whole. Key Conceptual Innovations: The JED Postulate (Ontological Simultaneity): The cornerstone of the framework. It posits a global constraint on the co-realization of facts: for an entangled state, individual outcomes cannot exist as autonomous facts. They can only be realized as elements of an admissible pair (e.g., {Alice+, Bob-} or {Alice-, Bob+}). This is not a temporal or causal constraint, but a structural condition for existence. Formalism of Frames and Admissibility Relations: The ontology is formalized using "frames" (sets of co-existing facts) and an "admissibility relation" R, which encodes the structure of an entangled state (e.g., for a singlet: R = {(+, -), (-, +)}). The JED postulate ensures that a frame containing one element of a related pair must contain its counterpart. The "Broken Mirror" Metaphor: A central heuristic. Entanglement is likened to a mirror broken into two complementary halves. The halves do not "communicate" to match; their perfect fit is a consequence of their common origin in a single act of breaking. Asking "which half appeared first?" or "how does one half know about the other?" is ontologically meaningless—there is no process that produces only one isolated half. Resolution of the EPR Paradox: The paradox dissolves because its first step—treating Alice's local outcome as an independent fact—is invalid within the JED ontology. There is no independent fact for locality to protect, hence no contradiction between correlations and relativistic locality. Interpretation of Bell's Theorem: The work reframes Bell's theorem. Its violation is not proof of nonlocality, but empirical evidence against the ontology of independent local facts. Bell's mathematics is correct, but its physical significance depends on ontological axioms that may not hold. The JED ontology provides a local, realistic (but not fact-local) framework consistent with the correlations. Distinction from Hidden Variables: The approach is explicitly not a hidden-variable theory. It introduces no hidden parameters λ governing individual outcomes. The relation R is a structural definition of the entangled whole, not a hidden cause of correlations. Probabilities are treated as a descriptive layer over the admissible ontological structures. Methodology: The work is developed in the spirit of the "pencil-case" methodology, constructing minimal ontological models to analyze the logical roots of physical puzzles without adding new dynamical mechanisms. Scope and Intent: The present work should be read as a contribution to the philosophy of physics: it does not aim at proposing a new physical theory, but at clarifying the ontological assumptions underlying existing formalisms. It seeks to shift the discussion from "how do the parts communicate?" to "what kind of whole do the parts constitute?" The formalism is shown to be logically consistent with the standard quantum correlation function (e.g., E(θ,φ) = -cos(θ-φ)), without deriving it, thereby separating the ontological question of admissibility from the empirical-statistical question of probability distribution. Keywords: EPR Paradox, Bell's Theorem
One of the basic assumptions underlying Bell's theorem is the causal arrow of time, having to do with temporal order rather than spatial separation. Nonetheless, the physical assumptions regarding causality are seldom studied in this context, and often even go unmentioned, in stark contrast with the many different possible locality conditions which have been studied and elaborated upon. In the present work, some retrocausal toy-models which reproduce the predictions of quantum mechanics for Bell-type correlations are reviewed. It is pointed out that a certain toy-model which is ostensibly superdeterministic-based on denying the free-variable status of some of quantum mechanics' input parameters-actually contains within it a complete retrocausal toy-model. Occam's razor thus indicates that the superdeterministic point of view is superfluous. A challenge is to generalize the retrocausal toy-models to a full theory-a reformulation of quantum mechanics-in which the standard causal arrow of time would be replaced by a more lenient one: an arrow of time applicable only to macroscopically-available information. In discussing such a reformulation, one finds that many of the perplexing features of quantum mechanics could arise naturally, especially in the context of stochastic theories.