Contemporary physics relies extensively on mathematical formalisms to describe natural phenomena, often achieving remarkable predictive success. However, the relationship between mathematical description and physical explanation remains a subject of ongoing debate. In many cases, mathematical models are treated not only as tools for representation but also as implicit substitutes for the underlying physical mechanisms, which can obscure questions of causality and physical origin. This article examines this methodological issue using two fundamental physical phenomena—gravity and the tunneling effect— as representative examples. Both phenomena are commonly described by highly successful mathematical frameworks, namely general relativity and quantum mechanics, yet their physical interpretations remain incomplete or debated. The work argues that predictive accuracy alone does not necessarily constitute a full physical explanation and that mathematical consistency should be complemented by physically grounded mechanisms based on observable properties of matter and interaction. Alternative descriptions of gravity and the tunneling effect are proposed, grounded in experimental observations and established physical properties of matter at macroscopic and microscopic scales. These descriptions aim to clarify the physical processes underlying the phenomena while remaining compatible with empirical data. The proposed framework does not reject existing theories but seeks to supplement them by addressing conceptual gaps related to causality, physical mechanism, and interpretation. Such an approach may contribute to a more physically transparent understanding of fundamental phenomena and provide new directions for theoretical and applied research.
Contemporary physics relies extensively on mathematical formalisms to describe natural phenomena, often achieving remarkable predictive success. However, the relationship between mathematical description and physical explanation remains a subject of ongoing debate. In many cases, mathematical models are treated not only as tools for representation but also as implicit substitutes for the underlying physical mechanisms, which can obscure questions of causality and physical origin. This article examines this methodological issue using two fundamental physical phenomena—gravity and the tunneling effect— as representative examples. Both phenomena are commonly described by highly successful mathematical frameworks, namely general relativity and quantum mechanics, yet their physical interpretations remain incomplete or debated. The work argues that predictive accuracy alone does not necessarily constitute a full physical explanation and that mathematical consistency should be complemented by physically grounded mechanisms based on observable properties of matter and interaction. Alternative descriptions of gravity and the tunneling effect are proposed, grounded in experimental observations and established physical properties of matter at macroscopic and microscopic scales. These descriptions aim to clarify the physical processes underlying the phenomena while remaining compatible with empirical data. The proposed framework does not reject existing theories but seeks to supplement them by addressing conceptual gaps related to causality, physical mechanism, and interpretation. Such an approach may contribute to a more physically transparent understanding of fundamental phenomena and provide new directions for theoretical and applied research.
The predictive success of modern physics from rigid body mechanics to quantum field theory stands among the greatest achievements of the human mind. Yet this success does not necessarily entail completeness of explanatory understanding. This paper investigates the epistemological gap between mathematical description and causal explanation, taking the behavior of rotating bodies (gyroscopes) as a preliminary example, then extending to two central problems: the measurement problem in quantum mechanics and the nature of mass in particle physics. The study shows that concepts such as angular momentum and precession, despite their predictive accuracy, redescribe phenomena in mathematical language more than they provide intuitive causal mechanisms. It also demonstrates that Noether’s theorem and the principle of least action, for all their depth, reformulate fundamental questions rather than resolving them. The paper discusses the framework of structural realism as a philosophical stance that accommodates this gap, examines criticisms of this framework (the problem of structural individuation and the problem of abandoned theories), and concludes that acknowledging this gap is not an attack on physics but a condition for its philosophical maturity.
This article examines some experimental conditions that invite and possibly require recourse to quantum-mechanical-like mathematical models (QMLMs), models based on the key mathematical features of quantum mechanics, in scientific fields outside physics, such as biology, cognitive psychology, or economics. In particular, I consider whether the following two correlative features of quantum phenomena that were decisive for establishing the mathematical formalism of quantum mechanics play similarly important roles in QMLMs elsewhere. The first is the individuality and discreteness of quantum phenomena, and the second is the irreducibly probabilistic nature of our predictions concerning them, coupled to the particular character of the probabilities involved, as different from the character of probabilities found in classical physics. I also argue that these features could be interpreted in terms of a particular form of epistemology that suspends and even precludes a causal and, in the first place, realist description of quantum objects and processes. This epistemology limits the descriptive capacity of quantum theory to the description, classical in nature, of the observed quantum phenomena manifested in measuring instruments. Quantum mechanics itself only provides descriptions, probabilistic in nature, concerning numerical data pertaining to such phenomena, without offering a physical description of quantum objects and processes. While QMLMs share their use of the quantum-mechanical or analogous mathematical formalism, they may differ by the roles, if any, the two features in question play in them and by different ways of interpreting the phenomena they considered and this formalism itself. This article will address those differences as well.
Classical physics has enabled the acquisition of significant knowledge of the physical properties of nature on a standard macroscopic scale. These achievements were driven by use of the causal ontological approach (proposed originally by Aristotle) to formulate models of physical reality. At the beginning of the 20th century, however, the physics community began to prefer models based on a fundamentally different approach to human knowledge. Copenhagen quantum mechanics (CQM) was used to describe the micro-world. The special theory of relativity was used to describe the kinematics of objects moving at high velocity values in both the macroscopic and microscopic regions. This phenomenological approach to knowledge has been more focused on how things appear - instead of their actual properties and causal sequence. In the middle of the 20th century, the causal ontological approach was used to develop a significant scientific advance: the systematization of fundamental strongly interacting particles on the basis of unified algebra in three-dimensional isotopic spin space for spin values 1, 1/2, and 0. However, it was later strongly deformed under the influence of the phenomenological approach and the quark model. This paper will show that practically all contemporary theoretical models of physical reality contain mistakes or unresolved problems. Further scientific progress can be obtained if (and only if) scientists return to the successful causal ontological approach and falsification. Classical physics may be slightly generalized to enable the description of inertia mass increase in dependence on velocity, replacing the relativity theory and CQM. New assumptions may then be employed using generalized classical physics (GCP) to formulate new descriptions of observed phenomena that were previously inaccurately interpreted and used to promote fundamentally inadequate theories.
Abstract Quantum mechanics and relativity are two of the most successful theoretical frameworks in modern physics, yet their conceptual foundations remain difficult to reconcile at the deepest level. Quantum theory describes physical systems through states, observables, probabilities, measurement contexts, superposition, entanglement, and nonclassical correlations. Relativity describes physical processes through space-time structure, causal order, invariant physical law, observer-dependent decomposition of time and space, and constraints on signal propagation. This article examines the conceptual relationship between quantum measurement, relativistic causality, and space-time description. The purpose is not to present a mathematical unification but to analyze how the two frameworks organize physical explanation differently and where their interpretive tensions arise. Special attention is given to the measurement problem, the status of quantum states, the role of observers and reference frames, the meaning of locality, the distinction between correlation and causal influence, and the challenge of describing quantum processes without privileging a single global time. The article argues that many apparent conflicts between quantum theory and relativity result from importing classical intuitions into domains where they no longer apply. Quantum entanglement does not permit controllable faster-than-light communication, yet it challenges classical separability. Relativity forbids superluminal signaling, yet it does not require that all physically meaningful correlations be reducible to local classical properties. Measurement introduces another difficulty because standard quantum theory often describes state update in a way that appears instantaneous, while relativistic space-time does not provide a universal present. The discussion develops a conceptual framework in which quantum measurement is treated as a physical interaction, relativistic causality as a constraint on operational influence, and space-time description as an organizing structure for events rather than a simple background stage. This analysis is relevant for quantum field theory, quantum information, relativistic quantum foundations, and future approaches to quantum gravity.
This work presents a conceptual and representational framework aimed at clarifying the structural relationships among established physical theories across relativistic, quantum, and cosmological regimes. Rather than proposing new dynamical laws, particles, or experimentally testable predictions, the manuscript focuses on how existing physical descriptions may be consistently interpreted within a unified representational structure. The proposed Dual-Spacetime Projection Framework distinguishes between an underlying descriptive domain and an observed effective spacetime, connected through a scale-dependent projection. This distinction is intended as a formal and interpretative tool, not as an ontological claim about the existence of multiple physical spacetimes. Within this perspective, several foundational features of modern physics—such as Lorentz invariance, finite signal propagation, quantum uncertainty, and large-scale cosmological behavior—are discussed as consequences of representational structure rather than as independent postulates. The manuscript is positioned as a contribution to the foundations of theoretical physics, offering a coherent conceptual lens for organizing and interpreting existing theories. It is intended for readers interested in foundational questions, conceptual unification, and the representational aspects of physical law, and does not rely on experimental data or numerical simulation.
Mathematics is an artificial symbolic logical system whose evaluation standard lies only in internal self consistency. Its core function is to fit observed phenomena. When deduction hits obstacles, mathematics can expand definitions extend number fields or change calculation frameworks to bypass difficulties. As long as logic forms a closed loop this operation is valid within the scope of mathematics. Imaginary number systems and calculus are typical examples. They are internally self consistent and efficient for calculation as computing tools but the tools themselves do not equal objective reality. Mathematical systems face no punishment from objective reality. When contradictions appear in deduction researchers only need to adjust rules and refit data. Physics takes objective reality and causal chains independent of human cognition as its foundation. The only judging standard comes from the real natural world. Physics cannot bypass fundamental contradictions by makeshift assumptions. This paper clarifies a critical dividing line. Success in engineering application never proves the correctness of the underlying physical theory supporting that engineering. Many technical achievements come from empirical exploration and repeated trial and error. Researchers build devices and obtain effects first. Theories are proposed later to fit collected data. Those theories do not reveal the real causal mechanism in advance. Newtonian mechanics is an approximate description valid under limited conditions. It has clear application boundaries and its underlying causal framework does not deliberately avoid core contradictions. Interpretations such as superposition and Schrodinger cat that describes simultaneous life and death are different. They deliberately bypass microscopic dynamic mechanisms and modify the inherent properties of matter to adapt to mathematical frameworks. These two cases have essential differences. Even if a deviated underlying physical mechanism can produce usable calculation schemes or even drive engineering progress it does not prove the foundation is correct. If basic assumptions depart from reality all derived conclusions must be revised from the root instead of adding surface patches. Part of the difficulties in modern fundamental physics arise from three types of confusion. Confusion between mathematical fitting and physical reality. Confusion between empirical engineering success and the truth of underlying physical mechanism. Confusion between well bounded approximate theories and patchwork assumptions made to avoid contradictions. If researchers keep stacking derived models on a shifted physical foundation the system will accumulate internal inconsistencies. Even with delicate local mathematical fitting the whole theory will eventually collapse logically just like a tall dangerous building built on skewed ground. This paper analyzes the differences between mathematics and physics the long term theoretical risks of bypassing contradictions and the boundary between engineering success and physical theoretical success. It proposes that fundamental physics must stick to objective reality and closed causality.