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.
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.
A history of the discovery of `new' quantum mechanics and the paradoxes of its probabilistic interpretation are briefly reviewed from the modern point of view of quantum probability and information. Modern quantum theory, which has been developed during the last 20 years for the treatment of quantum open systems including quantum noise, decoherence, quantum diffusions and spontaneous jumps occurring under continuous in time observation, is not yet a part of the standard curriculum of quantum physics. It is argued that the conventional formalism of quantum mechanics is insufficient for the description of quantum events, such as spontaneous decays say, and the new experimental phenomena related to individual quantum measurements, but they have all received an adequate mathematical treatment in quantum stochastics of open systems. Moreover, the only reasonable probabilistic interpretation of quantum mechanics put forward by Max Born was, in fact, in irreconcilable contradiction with traditional mechanical reality and causality. This led to numerous quantum paradoxes, some of them due to the great inventors of quantum theory such as Einstein and Schrödinger. They are reconsidered in this paper from the modern point of view of quantum stochastics and information. The development of quantum measurement theory, initiated by von Neumann, indicated a possibility for resolution of this interpretational crisis by divorcing the algebra of the dynamical generators and the algebra of the actual observables, or Bell's be ables. It is shown that within this approach quantum causality can be rehabilitated in the form of a superselection rule for compatibility of the actual histories with the potential future. This rule, together with the self-compatibility of the measurements ensuring the consistency of the histories, is called the nondemolition, or causality principle in modern quantum theory. The application of this rule in the form of dynamical commutation relations leads to the derivation of the von Neumann projection postulate, and also to the more general reductions, instantaneous, spontaneous, and even continuous in time. This gives a dynamical solution, in the form of the quantum stochastic filtering equations, of the notorious measurement problem which was tackled unsuccessfully by many famous physicists starting with Schrödinger and Bohr. It has been recently proved that the quantum stochastic model for the continuous in time measurements is equivalent to a Dirac type boundary-value problem for the secondary quantized input `offer waves from future' in one extra dimension, and to a reduction of the algebra of the consistent histories of past events to an Abelian subalgebra for the `trajectories of the output particles'. This supports the corpuscular-wave duality in the form of the thesis that everything in the future are quantized waves, while everything in the past are trajectories of the recorded particles.
A physical theory is proposed that obeys both the principles of special relativity and of quantum mechanics. Time and space are treated on exactly the same footing, namely as quantum mechanical observables on a Hilbert space. The theory is not based upon Lagrangian or Hamiltonian mechanics and cannot be formulated within the framework of unitary dynamics. As a most important aspect, the theory breaks with the concept of a continuously flowing time in favour of a discrete jump process in spacetime. All physical statements are formulated in terms of detector events rather than particle states. The physical object under consideration is a spinless particle in empty space. Yet the theory also accounts for particle-antiparticle pair creation and annihilation, and is therefore not a single-particle theory in the strict sense. The Maxwell equations are derived as a straightforward consequence of some fundamental commutation relations. In the non-relativistic limit, and in the limit of infinitely small time uncertainties, one obtains the familiar Schr\\"odinger equation of a spinless particle exposed to an external electromagnetic field.
The Heisenberg uncertainty principle is conventionally interpreted as a constraint on the precision of future measurement outcomes. We argue that this temporal asymmetry is not justified by the underlying mathematics of quantum mechanics, which is fundamentally time-symmetric. We propose that uncertainty applies equally in both temporal directions: the past has no greater ontological determinacy than the future. Between collapse events, prior states were no more determined than future states are now. Only the present moment of collapse constitutes anything approaching a definite physical state, and that moment is immediately receding into a past that was never fully determined before collapse occurred. We formalize this interpretation through a timesymmetric reading of the existing uncertainty relations and discuss its implications for the ontological status of the past, the measurement problem, and the foundations of physical determinism.
This paper extends the temporal concept of Sequential Time Theory (STT) to the problem of metrology in the quantum domain. In STT, a time interval Δt is constructed by a counter n representing the number of realizations of a standard displacement ΔQ_unit, while time t serves as a coordinate label assigned to this sequence. STT explicitly posits that "time is a scaling of physical change" and that "time is constructed solely by clock phenomena subject to the same conditions within a local system." Consequently, in regimes where ΔQ is indistinguishable, time does not "cease to exist" but becomes "unconstructible (undefined)." Based on these definitions and axioms, this paper (i) organizes criteria for distinguishing between science and metaphysics, (ii) identifies conceptual confusions arising from the implicit assumption of an external classical clock in quantum theory, and (iii) proposes a relativity principle regarding differences in observation scale (e.g., macroscopic observation of microscopic systems). We demonstrate that issues such as measurement, classicality, and tunneling time can be unifiedly organized as problems of "choice of clock (ΔQ)" and "recording (event-token) protocols."Furthermore, we provide a mathematical derivation (Appendix A) showing that the intrinsic uncertainty of a physical clock (σ) naturally leads to the suppression of quantum interference terms (e−ω2σ2), thereby identifying the metrological origin of decoherence and the phenomenological arrow of time.Version 4 Update: Major revision including Appendix A (Mathematical Proof of Intrinsic Decoherence) and Appendix B (Definition of Phenomenon Arrow). This version provides the quantitative foundation for the theory.
Although time is one of our most intuitive physical concepts, its understanding at the fundamental level is still an open question in physics. For instance, time in quantum mechanics and general relativity are two distinct and incompatible entities. While relativity deals with events (points in spacetime), with time being observer dependent and dynamical, quantum mechanics describes physical systems by treating time as an independent parameter. To resolve this conflict, in this work, we extend the classical concept of an event to the quantum domain by defining an event as a transfer of information between physical systems. Then, by describing the universe from the perspective of a certain observer, we introduce quantum states of events with space-time-symmetric wave functions that predict the joint probability distribution of a measurement (observation) at $(t,\stackrel{P\vec}{x})$. Under these circumstances, without assuming collapse, we propose that a well-defined instant of time, like any other observable, arises from a single event, thus being an observer-dependent property. In this manner, we obtain a stationary quantum state written as a sum of a sequence of normalized states of events with increasing memories. As a consequence, a counterfactual asymmetry along this sequence of events gives rise to the flow of time as being successive ``snapshots'' from the observer's perspective. In this proposal, which contrasts strikingly to the view in which time is an illusion, it is the many distinguishable states in which the observer stores information that makes the existence of time possible.