Philosophers are continually challenged to comprehend chance phenomena and probabilistic relationships. Those cases are especially intriguing in which we speak of chance or probability but can hardly attribute this manner of speaking to our being partially or totally ignorant of the situations in question. Those cases, then, can be taken to possess chance as an objective feature. In its intent, this paper is restricted to a discussion of such cases. Among objective chance relationships there is one kind which seems especially incomprehensible. These are stochastic relationships, i.e., chance relationships between consecutive states of physical systems.
Philosophers are continually challenged to comprehend chance phenomena and probabilistic relationships. Those cases are especially intriguing in which we speak of chance or probability but can hardly attribute this manner of speaking to our being partially or totally ignorant of the situations in question. Those cases, then, can be taken to possess chance as an objective feature. In its intent, this paper is restricted to a discussion of such cases. Among objective chance relationships there is one kind which seems especially incomprehensible. These are stochastic relationships, i.e., chance relationships between consecutive states of physical systems.
Among the philosophical issues raised by quantum theory, the alleged indeterminism of quantum-physical phenomena, as opposed to the determinism of classical physics, has stood at the center of discussion. There are various other much-debated problems which are directly or indirectly related to this issue or, more generally, the probabilistic character of quantum theory. Less attention has been paid to the questions of the stability of atoms and the specificity of their properties, which quantum theory was primarily designed to resolve. I argue that the indeterminism of quantum theory becomes less intriguing and can be better comprehended when seen in the light of these questions - or briefly, that “stability implies indeterminism, or chance.” Chance, in this respect, appears as an objective and legitimate mode of succession of otherwise stable and discrete well-determined states of certain physical systems.
There seems to be nothing short of a {\it double whammy} hitting the users of probability, and among them physicists, especially those involved in the foundations of quanta. First is the instant instinctual reaction that phenomena which interest one do sharply and clearly divide into the {\it dichotomy} of {\it two and only two} alternatives of being {\it either} ``deterministic", {\it or} on the contrary, being ``probabilistic". However, there is also a second, prior and yet deeper trouble, namely, the ``probabilistic" case is strongly believed to be equally clear and well-founded as is the ``deterministic" one. And the only difference seen between the two is that the latter can talk also about ``individual" phenomena, while the former can only do so about large enough ``ensembles" for which, however, it is believed to be equally clear, precise and rigorous with the ``deterministic" approach. Or briefly, ``probabilistic'' is seen as nothing else but the ``deterministic'' on the level of ``ensembles" ... \\The fact, however, is that there is a {\it deep gap} between the empirical world of ``random" phenomena, and on the other hand, theories of ``probability". Furthermore, any attempt to bridge that gap does inevitably involve {\it infinity}, thus aggravating the situation to the extent that even today, and even if not quite realized by many, theories of ``probabilities" have a {\it shaky} foundation. \\This paper tries to bring to the awareness of various users of ``probabilities", and among them, to physicists involved in quanta, the fact that - seemingly unknown to them - they are self-inflicted victims of the mentioned double whammy. \\ \\
Abstract Many theories and models from physics are probabilistic. This observation raises several philosophical questions: What are probabilities in physics? Do they reflect objective chances which exist independently of the human mind? Or do they only express subjective credences and thus capture our own uncertainty about the world? Finally, which metaphysical lessons, if at all, can one draw from the largely probabilistic character of physics? The chapters collected in this volume address these questions and provide a detailed philosophical appraisal of the status of probabilities in all of physics. Particular emphasis is laid upon statistical physics and quantum mechanics. Many chapters reflect a desire to understand probabilities from physics as objective chances. These chances are characterized, e.g., as time-averages, as probabilities from a best system in the terms of David Lewis, or using the Boltzmannian typicality approach. Other chapters are sympathetic to a Bayesian view of probabilities in physics. The chapters about quantum mechanics elucidate the peculiar characteristics of quantum correlations and discuss strategies to justify the Born Rule. Finally, the chapters of this volume demonstrate how closely interpretive issues about probabilities are entangled with other foundational problems of physics such as the Reversibility Paradox, the ontology of the quantum world and the question whether the world is deterministic.
This book examines in detail two of the fundamental questions raised by quantum mechanics. Is the world indeterministic? Are there connections between spatially separated objects? In the first part of the book after outlining the formalism of quantum mechanics and introducing the measurement problem, the author examines several interpretations, focusing on how each proposes to solve the measurement problem and on how each treats probability. In the second part, the author argues that there can be non-trivial relationships between probability (specifically, determinism and indeterminism) and non-locality in an interpretation of quantum mechanics. The author then re-examines some of the interpretations of part one of the book in the light of this argument, and considers how they are with regard to locality and Lorentz invariance. One of the important lessons that comes out of this discussion is that any examination of locality, and of the relationship between quantum mechanics and the theory of relativity, should be undertaken in the context of a detailed interpretation of quantum mechanics. The book will appeal to anyone with an interest in the interpretation of quantum mechanics, including researchers in the philosophy of physics and theoretical physics, as well as graduate students in those fields.
On a very intuitive way of thinking, if it is already determined that some event will happen, then there is no non-trivial chance of it failing to happen, and if it is already determined that some event will not happen, then there is no non-trivial chance of it happening. A different sort of worry that arises for an actual frequentist analysis of deterministic chance is that such an analysis seems unsuited to theories like Boltzmannian statistical mechanics or Bohmian mechanics insofar as those theories are supposed to describe the evolution of the Universe as a whole. It should be clear, then, that there are options available for understanding deterministic chance that are in keeping with several of the leading metaphysical analyses of chance. It is widely accepted that whatever chances are, they are to be contrasted with individual credences . According to classical statistical mechanics, the fundamental laws are Newtonian and thus deterministic.
The relationship between chance and determinism has been analyzed by philosophy, mathematics, and physics.With the aim of identifying the intersection between the two, the Law of Probability Equilibrium (LPE) was demonstrated.When the probabilities of natural phenomena differ from zero and one, the LPE shows that the observed probability is empirical and that the cumulative probability functions of these phenomena measure the imminence of their occurrence ("energy concentration").These functions behave like waves that carry information about the probabilistic ("energetic") potential for the materialization of such phenomena.Probability functions exhibit properties analogous to quantum systems, such as complementarity, superposition, uncertainty, collapse, duality, interference, and entanglement.The findings indicate that chance and determinism converge at a cumulative limit of 1/2, forming a self-regulating equilibrium within the probabilistic field.This implies both the certainty of occurrence and the unpredictability of its timing.Even events with infinitesimal probabilities will inevitably occur.The LPE shows that the probability potential decreases until it reaches zero ("maximum entropy").Accumulated randomness is restricted to a maximum value of 1/2, allowing for causal processes (e.g., emission and absorption).Each probabilistic event, before being observed, exists in two superposed states: presence and absence, and it possesses a simultaneous and distinct probabilistic duality.One of these values is derived from the density function at the final instant, while the other is accumulated and remains stationary at 1/2.Upon measurement, the two probability density functions collapse into presence or absence (1 or 0) ("particle modality").Meanwhile, the two cumulative probability distribution functions remain entangled, each How to cite this paper: Traversa, I.