On Wave Function Collapse in Quantum Mechanics in the Case of a Spin System Having Three Anticommuting Operators: the Reason Because it is so Difficult to Realize a Theory of Collapse in Quantum Mechanics
We use a two states quantum spin system S, and thus considering the particular case of three anticommuting elements and the measurement of . We evidence that, during the wave collapse, we have a transition of standard commutation relation of the spin to new commutation relations and this occurs during the interaction of the S system with the macroscopic measurement system M. The reason to accept such view point is that it causes the destruction of the interferential factors and of the fermion creation and annihilation operators of the S system without recourse to further elaborations based on the use of Hamiltonians or other methods. By this formulation we propose a new method in attempting to solve the problem of wave function collapse. The concept of Observable , in use in standard quantum mechanics, is resolved in an abstract entity to which is connected a linear hermitean operator that signs mathematically the operation that we must perform on the wave function in order to obtain the potential and possible values of the observable. It does not commute with a number of other operators characterizing the system and the non commuting rules have a fundamental role in quantum mechanics .They have a logic that must be analyzed in each phase of the non measuring and the measuring processes. When we consider the dynamics of wave function collapse we must account that the observed observable becomes a number ,with proper unity of measurements ,during the measurement, thus the linear hermitean operator to which is connected before the measurement, disappears and in its place it appears a new operator that maintain the non commutativity with the other operators to which the old and disappeared operator was connected.
We use a two states quantum spin system S, and thus considering the particular case of three anticommuting elements and the measurement of . We evidence that, during the wave collapse, we have a transition of standard commutation relation of the spin to new commutation relations and this occurs during the interaction of the S system with the macroscopic measurement system M. The reason to accept such view point is that it causes the destruction of the interferential factors and of the fermion creation and annihilation operators of the S system without recourse to further elaborations based on the use of Hamiltonians or other methods. By this formulation we propose a new method in attempting to solve the problem of wave function collapse. The concept of Observable , in use in standard quantum mechanics, is resolved in an abstract entity to which is connected a linear hermitean operator that signs mathematically the operation that we must perform on the wave function in order to obtain the potential and possible values of the observable. It does not commute with a number of other operators characterizing the system and the non commuting rules have a fundamental role in quantum mechanics .They have a logic that must be analyzed in each phase of the non measuring and the measuring processes. When we consider the dynamics of wave function collapse we must account that the observed observable becomes a number ,with proper unity of measurements ,during the measurement, thus the linear hermitean operator to which is connected before the measurement, disappears and in its place it appears a new operator that maintain the non commutativity with the other operators to which the old and disappeared operator was connected.
Abstract The problem of the wave function collapse (a problem of measurement in quantum mechanics) is considered. It is shown that it can be solved based on quantum mechanics and does not require any additional assumptions or new theories. The particle creation and annihilation processes, which are described based on quantum field theory, play a key role in the measurement processes. Superposition principle is not valid for the system of equations of quantum field theory for particles and fields, because this system is a non-linear. As a result of the creation (annihilation) of a particle, an additional uncertainty arises, which “smears” the interference pattern. The imposition of such a large number of uncertainties in the repetitive measurements leads to the classical behavior of particles. The decoherence theory also implies the creation and annihilation of particles, and this processes are the consequence of non-linearity of quantum mechanics. In this case, the term “collapse of the wave function” becomes a consequence of the other statements of quantum mechanics instead of a separate postulate of quantum mechanics.
The problem of measurement in quantum mechanics is that the quantum particle in the course of evolution, as described by the linear Schrodinger equation, exists in all of its possible states, but in measuring, the particle is always detected in only one of its states. This property is called the "collapse of the wave function" and was formulated by Von Neumann as one of the postulates of quantum mechanics. However, it remains unclear at what point in time and under what laws this transition occurs. This article demonstrates that the collapse of the wave function may be due to the creation or annihilation of particles (quasi-particles). The processes of the creation or annihilation of particles play a key role in the measurements and are described on the basis of quantum field theory. The system of equations of quantum field theory of particles and fields is non-linear; as a result, the principle of superposition does not hold for the theory. The collapse of the wave function is a consequence of this non-linearity and occurs at the moment of creation (annihilation) of a particle. This result demonstrates that the wave function collapse can occur in both microscopic and macroscopic systems. Understanding the mechanisms of the collapse of the wave function can lead to the creation of microscopic devices involved in the calculations based on quantum computing.
Wave function collapse has long been regarded as a fundamental element of the quantum measurement process, providing a mechanism by which a superposed quantum state yields a single observed outcome. Despite its widespread use, the physical meaning of collapse remains conceptually controversial. In particular, it is often assumed that the quantities associated with a quantum state before measurement and the values obtained after measurement belong to the same conceptual category. This assumption leads naturally to the image of a discontinuous transition in which one value is selected from a superposition of possibilities. In the present work, we reexamine the concept of quantum collapse from the perspective of observability. We argue that pre-measurement quantities do not constitute observable values in the ordinary operational sense. Rather, they represent a structure of potential observability associated with possible measurement outcomes. By contrast, post-measurement outcomes correspond to operationally realized observability, in which a specific result becomes accessible through measurement. From this viewpoint, the apparent collapse does not represent a physical jump of an already existing value, but a transition from potential observability to operationally realized observability. Based on this distinction, we propose that many conceptual difficulties traditionally associated with wave function collapse arise from treating these two fundamentally different forms of observability as if they were physically equivalent. The apparent discontinuity of collapse may therefore originate not from a discontinuous change in reality itself, but from a conceptual conflation of potential observability and operationally realized observability. Within the Intrinsic Observability Framework (IOF), this interpretation naturally leads to the concept of accessibility transition, in which the emergence of a definite outcome is understood as a change in accessible structure rather than as a fundamental non-unitary state reduction. The present analysis suggests that wave function collapse may not be a fundamental physical phenomenon, but instead a consequence of the transition from potential observability to operationally realized observability. This perspective provides a conceptual reorganization of the measurement problem and clarifies the role of observability in the emergence of definite quantum outcomes.
The many-Hilbert-space approach to the measurement problem in quantum mechanics is applied to a typical ``yes-no'' experiment relative to two branch routes corresponding to mutually exclusive propositions. First, we reformulate the notion of wave-function collapse by measurement as a dephasing process between the two branch waves of an interfering particle (from our own point of view as opposed to the conventional Copenhagen interpretation). In this way, the concept of ``wave-function collapse'' is replaced by that of a statistically defined dephasing process. One of the most important points of this paper is the introduction of an order parameter \ensuremath{\epsilon} that quantitatively describes the degree of decoherence. Its value ranges from \ensuremath{\epsilon}=0 (which describes the case in which the two waves are perfectly coherent) to \ensuremath{\epsilon}=1 (which describes the case in which coherence is totally lost); for this reason \ensuremath{\epsilon} is named the ``decoherence parameter.'' In terms of this parameter we formulate a definite criterion to judge whether an instrument works well or not as a measuring apparatus. Then, we study the interaction between a microscopic particle and a macroscopic system (a detector), by modeling the macrosystem with a linear array of complex \ensuremath{\delta} potentials, which undergo several kinds of statistical fluctuations. This leads us, under particular conditions, to the so-called wave-function collapse, which is attained in the limit \ensuremath{\epsilon}=1. We also examine in some detail which kind of elastic and/or inelastic collisions can give the wave-function collapse. Some connections with recent experimental results in neutron interferometry and quantum optics are also stressed.
The present paper contains a new attack on the measurement problem. The point of departure is a realist view according to which i) state functions in quantum theory describe physical states of affairs and not information states attributed to observers, and ii) in theses states, some observables are indeterminate and not merely unknown, i.e., value determinism is rejected. Furthermore, quantisation of interaction is accepted as an empirically established fact, independently of any interpretations of quantum theory. From these assumptions it follows that Hermitian operators replacing classical variables may be viewed as representing actions from the environment done on physical systems represented by the state functions upon which the operators operate. Sometimes this influence is followed by a discontinuous, indeterministic and irreversible state change; in other words, the system undergoes a collapse, which is represented by a projection operator. Thus, assuming a realistic view on quantum states and their changes, we have an explanation for the collapse of the wave function. Since the collapse is a discontinuous, random and irreversible state change, the classical form of physical explanation in terms of a mechanism which describes how a system continuously changes its state is impossible. Hence, if we accept quantisation of interaction, we must give up our demand for a ordinary mechanical explanation for the collapse. Neither can we state, in advance, sufficient conditions for the collapse, since it is an indeterministic theory.
Abstract This article presents a revised and conceptually refined formulation of a previously proposed Temporal Interpretation of quantum measurement, explicitly addressing the physical nature of wavefunction collapse. While the original proposal emphasised relativistic aspects of momentum superpositions, the present work clarifies the interpretation within the standard formalism of quantum mechanics, without introducing new dynamics or experimental predictions. Unitary evolution is read as a process of differentiated phase accumulation between branches of a quantum state. In relativistic contexts, phase differentials can be structurally related to effective proper-time differentials, allowing the introduction of a notion of temporal compatibility that provides a physically grounded account of decoherence. When such differentials exceed a characteristic scale, interference between branches becomes operationally inaccessible, while global unitarity is preserved. The observer is treated as a physical system endowed with an irreversible proper time associated with macroscopic, entropic dynamics. Within this framework, collapse is explained as an emergent physical phenomenon arising from the irreversibility of the observer’s proper time, which prevents the reconstruction of phase coherence after an interaction. Collapse is therefore neither a fundamental dynamical mechanism nor an objective event in space-time, but a necessary consequence of temporal irreversibility in physical observers. This formulation sharpens the distinction between decoherence and collapse, preserves full consistency with the Born rule, and positions the Temporal Interpretation as a competing interpretative framework that provides a concrete physical explanation for the quantum–classical transition, improving and clarifying the original proposal. This version clarifies the operational status of the interaction time, refines Sections 5.3 and 5.4, and standardises references and editorial structure. No changes to the formalism or conclusions.