We argue that modern physics—including classical mechanics, relativity, and quantum mechanics—suffers from a fundamental incompleteness rooted in the treatment of time as a variable. Starting from parity violation and the absence of intrinsic lifetime in quantum wave functions, we show that: (1) only matter can observe change, yet physics uses light (which has no time) to define spacetime; (2) the time coordinate is either meaningless (without motion) or not independent (with motion); (3) physics writes equations from a God's eye view but performs measurements from a material observer's view; (4) matter, change, and time form a circular dependency that cannot be resolved within the current framework. The incompleteness of physics is not technical but structural.
We argue that modern physics—including classical mechanics, relativity, and quantum mechanics—suffers from a fundamental incompleteness rooted in the treatment of time as a variable. Starting from parity violation and the absence of intrinsic lifetime in quantum wave functions, we show that: (1) only matter can observe change, yet physics uses light (which has no time) to define spacetime; (2) the time coordinate is either meaningless (without motion) or not independent (with motion); (3) physics writes equations from a God's eye view but performs measurements from a material observer's view; (4) matter, change, and time form a circular dependency that cannot be resolved within the current framework. The incompleteness of physics is not technical but structural.
The understanding of time in physics has undergone profound changes from classical mechanics to relativity and quantum mechanics. In Newtonian mechanics, time is regarded as an absolute and uniform passage, independent of external phenomena, and is a fundamental parameter of the equations of motion. Relativity emphasises the relativity of time and its close connection with the motion of matter, proposes an operational definition of the simultaneity of distant events, and develops Minkowski’s view of spacetime and Riemannian curved spacetime. In quantum mechanics, time is often regarded as a parameter external to the microscopic system rather than an observable quantity. Although some scholars have attempted to introduce time operators, they have not yet gained widespread recognition. Overall, the understanding of time in physics continues to deepen with the development of theory. Still, the unity of classical and quantum mechanics in time remains an unsolved problem.
INTRODUCTION The purpose of this article is to bring out in as conceptually clear terms as possible what seems to be a major incompleteness in the probability theory of particles offered by classical quantum mechanics. The exact nature of this incompleteness is illustrated by consideration of some simple quantum-mechanical examples. In addition, these examples are contrasted with the fundamental assumptions of Brownian motion in classical physics on the one hand, and with a controversy of a decade ago in mathematical psychology. (The psychological example is described in detail in the appendix). Our central claim is that classical quantum mechanics is radically incomplete in its probabilistic account of the motion of particles. In the last part of the article we derive the time-dependent joint distribution of position and momentum of the linear harmonic oscillator, and show how the apparently physically paradoxical statistical independence of position and momentum has a natural explanation. The explanation is given within the framework of the non-quantum-mechanical stochastic theory we construct for such oscillators. Before entering into any technical details, we shall attempt to spell out in intuitive terms our incompleteness claim. To begin with, there are two senses of completeness that we want to distinguish. One sense of completeness is that demanded by any hidden variable theories of quantum mechanics. States should be found, or be theoretically characterizable at least, that lead to precise values for all observables; that is, no observable is to have a variance greater than zero.
We argue that (1) our perception of time through change and (2) the gap between reality and our observation of it are at the heart of both quantum mechanics and the dynamical mechanism of physical systems. We suggest that the origin of quantum uncertainty lies with the absence of infinities or infinitesimals in observational data and that our concept of time derives from observing changing data (events). We argue that the fundamentally important content of the Superposition Principle is not the "probability amplitude" of posterior state observation but future state availability conditional only on prior information. Since event detection also implies posterior conditions (e.g. a specific type of detectable event occurred) as well as prior conditions, the probabilities of detected outcomes are also conditional on properties of the posterior properties of the observation. Such posterior conditions cannot affect the prior state availabilities and this implies violation of counter-factual definiteness. A component of a quantum system may be chosen to represent a clock and changes in other components can then be expected to be correlated with clocks with which they are entangled. Instead of traditional time-dependent equations of motion we provide a specific mechanism whereby evolution of data is instead quasi-causally related to the relative \availability\ of states and equations of motion are expressed in terms of quantized clock variables. We also suggest that time-reversal symmetry-breaking in weak interactions is an artifice of a conventional choice of co-ordinate time-function. Analysis of a "free" particle suggests that conventional co-ordinate space-time emerges from how we measure the separation of objects and events.
The concept of position and its measurement are fundamental to modern navigation technology as well as to theoretical physics. Nevertheless, a consistent notion of position has not been found in modern physics because of apparent inconsistencies between quantum mechanics and relativity. In quantum mechanics the probability distribution for a particle's position is determined by its wave function. A wave function strictly localized in space describes a particle within that locality, and nowhere else. But the quantum equations of motion predict the function will disperse, after any length of time at all, to occupy all space. Therefore the theoretical prediction is that, shortly after detection in a laboratory, a particle may be found anywhere in the universe, including regions requiring faster-than-light travel to reach. This contradicts the theory of relativity, which precludes a body traveling faster than the speed of light. The conflict arises from unexamined assumptions regarding the time of the measurement event and the time of the system under measurement. The prevailing view in physics is that time is only a parameter, having a definite value, describing dynamic changes in physical systems. This view endures even though quantum mechanics recognizes position as a quantum variable with inherent uncertainty, and relativity indicates that time should be placed on the same footing as position. But if time is recognized as a quantum variable with inherent uncertainty, the conceptual problems with position are resolved. The particle has finite probability of being in the past (or future) of the observer, while the quantum mechanical operator describing the position measurement contains a term which extrapolates from the intrinsic time of the particle to the time of the observer. Being potentially well in the past of the measurement event, the particle has time to travel to remote regions without exceeding the speed of light, and the conflict with relativity is resolved. A relativistic quantum theory can therefore be constructed incorporating a well-defined concept of position.
The paper sketches out an ontology of physics in terms of matter being primitive stuff distributed in space and all the properties physics is committed to being dispositions that fix the temporal development of the distribution of matter in space. Whereas such properties can be conceived as intrinsic properties of particles in classical mechanics, in quantum physics, there is a holistic property or structure that relates all matter and that fixes its temporal development. 1. Classical physics and intrinsic properties At the end of the “Opticks ” (1704), Newton writes: … it seems probable to me, that God in the Beginning form’d Matter in solid, massy, hard, impenetrable, moveable Particles …; no ordinary Power being able to divide what God himself made one in the first Creation. … the Changes of corporeal Things are to be placed only in the
Twentieth-century physics was shaped by two profound revolutions. The first, Einstein's relativity, banished absolute space and time from the foundations of physics. Motion, Einstein showed, possesses no absolute meaning—only relative motion between observers merits physical description. The second, quantum mechanics, dismantled the classical notion of determinacy. A physical quantity, before measurement, is not merely unknown but genuinely indefinite, suspended in a superposition of possibilities. These two revolutions, for all their splendor, have never spoken a common language. General relativity describes a world of continuous, deterministic geometry; quantum mechanics, a world of discrete, probabilistic events. Their unification—a theory of quantum gravity—remains the central unsolved problem of theoretical physics. We diagnose this impasse not as a technical failure, but as a conceptual incompleteness. The two revolutions, in their original domains, stopped short of questioning a premise both inherited from classical thought: that physical reality, determinacy, and facts themselves are absolute—that they exist independently of the framework through which they are described. Einstein relativized motion but left the existence of spacetime geometry absolute. Quantum mechanics relativized the values of observables but left the fact of an outcome unexplained, consigning it to the mysterious "measurement process." Neither theory asked: in what sense is a fact—that a quantity has a definite value, that an event has occurred, that a physical reality is thus and not otherwise—itself relative to a descriptive framework? This is the question the present work undertakes to answer. In doing so, it completes the program of relativity—not by appending new terms to old equations, but by extending the principle of relativity to its ultimate domain: being itself.