A thought experiment is discussed to clarify the concept of decoherence. Superposition of states consisting of ground state of a single hydrogen atom and its excited state after a huge amount of time is discussed to show that the decoherence of the state, more precisely the loss of coherence, is literally the loss of ability of interference. The loss of superposition of states is just apparent or even superfacial. Applications of this example in its relation to many-world interpretation of observation of a quantum state, decoherence in usual cases, and weak collapse of wavepackets are discussed.
A thought experiment is discussed to clarify the concept of decoherence. Superposition of states consisting of ground state of a single hydrogen atom and its excited state after a huge amount of time is discussed to show that the decoherence of the state, more precisely the loss of coherence, is literally the loss of ability of interference. The loss of superposition of states is just apparent or even superfacial. Applications of this example in its relation to many-world interpretation of observation of a quantum state, decoherence in usual cases, and weak collapse of wavepackets are discussed.
Abstract The measurement problem has long been a fundamental challenge in quantum mechanics. The mainstream decoherence theory attributes the transition from quantum superposition to classical determinacy to the entanglement between the system and its environment. However, this theory still leaves several foundational issues unresolved: decoherence can only eliminate observable interference fringes but cannot explain why a single measurement yields only one definite outcome; nor can it fully account for the phenomena observed in recent attosecond tunneling experiments. The author first published the temporal relativity hypothesis on the Zenodo preprint platform on June 20, 2026[4]. This theory proposes that quantum superposition is not an intrinsic property of microscopic particles, but rather an apparent effect arising from the relative relationship between the temporal sampling frequency of the detection system and the evolution frequency of the quantum object. When the detector's temporal resolution frequency far exceeds the characteristic evolution frequency of the microscopic particle, the interference fringes from wavefunction superposition gradually disappear, and continuous classical trajectories become observable. On July 11, 2026, the author systematically proposed the qualitative three-stage criterion of temporal relativity within the original preprint framework (also published on Zenodo[8]): when the sampling frequency , the system exhibits classical determinacy; when , the system resides in a critical transition state; when , the system manifests as a quantum superposition state. The precise threshold corresponding to this ratio requires calibration through subsequent continuous attosecond imaging experiments, establishing a natural collaborative pathway between theory and experiment. The attosecond scanning tunneling experiment published by the University of Regensburg on July 3, 2026[3], is in strong agreement with the independent theoretical predictions and the experimentally designed predictions presented in the above preprint (June 20). Furthermore, after the publication of the author's Zenodo preprint on July 11, 2026[8], it was found that the experimental results from the Weizmann Institute of Science group in early 2026[5] are also highly isomorphic with the three-stage evolution predicted by this hypothesis. This paper is an advanced revision building upon two previous versions published by the author on the Zenodo preprint platform: the initial temporal relativity hypothesis incorporating the concept of "consciousness" was proposed on June 20, 2026[4]; the July 11, 2026 version[8] removed the consciousness concept and established a purely physical "detector temporal resolution frequency" qualitative framework with the explicit three-stage model; this version fully inherits the qualitative three-stage model while adding a complete unified mathematical framework—built upon the three pillars of the time-dependent Schrödinger equation, time-domain sampling boundary conditions, and critical phase criteria—upgrading the theory from a qualitative hypothesis to a complete mathematical system capable of quantitative computation and experimental data fitting.
The act of measurement on a quantum state is supposed to "dephase" (dephasing refers to the phenomenon that the states lose phase coherence; then the phases get randomized in interaction with a bath of other oscillators, which is referred to as "decoherence"), then "decohere" and "collapse" (or more precisely "register" and "reduce") the state into one of several eigenstates of the operator corresponding to the observable being measured. This measurement process is sometimes described as outside standard quantum-mechanical evolution and not calculable from Schrödinger's equation. Progress has, however, been made in studying this problem with two main calculation tools-one uses a time-independent Hamiltonian, while a rather more general approach proving that decoherence occurs under some generic conditions. The two general approaches to the study of wave-function collapse are as follows. The first approach, called the "consistent" or "decoherent"' histories approach, studies microscopic histories that diverge probabilistically and explains collapse as an event in our particular history. The other, referred to as the "environmental decoherence" approach studies the effect of the environment upon the quantum system, to explain wave-function decoherence which is produced by irreversible effects of various sorts. However, as we know, wave-function collapse is not related to thermal connection with the environment, rather, it is inherent to how measurements are performed by macroscopic apparata. In the "environmental decoherence" approach, one studies decoherence using a Markovian-approximated Master equation to study the time-evolution of the reduced density matrix (post dephasing) and obtains the long-time dependence of the off-diagonal elements of this matrix. The calculation in this paper studies the evolution of a quantum system starting with "dephasing" followed by the effects of the environment with some differences from prior analyses. We start from the Schrödinger equation for the state of the system, with a time-dependent Hamiltonian that reflects the actual microscopic interactions that are occurring. Then we systematically solve (exactly) for the time-evolved state, without invoking a Markovian approximation when writing out the effective time-evolution equation, i.e., keeping the evolution unitary until the end. This approach is useful, and it shows that the system wave-function will explicitly "un-collapse" if the measurement apparatus is sufficiently small. However, in the limit of a macroscopic system, this "dephasing" quickly leads to "decoherence"-collapse is a temporary state that will simply take extremely long (of the order of multiple universe lifetimes) to reverse. This has been attempted previously and our calculation is particularly simple and calculable. We make some connections to the work by Linden et al. while doing so. The calculation in this paper has interesting implications for the interpretation of the Wigner's friend experiment, as well as the Mott experiment, which is explored in "Connection to some general theoretical results" and "Recurrence times" (especially the enumerated points in "Recurrence times"). The upshot is that as long as Wigner's friend is macroscopically large (or uses a macroscopically large measuring instrument), no one needs to worry that Wigner would see something different from his friend. Indeed, Wigner's friend does not even need to be conscious during the measurement that she conducts. It also allows one to reasonably interpret some of the more recent thought experiments proposed. In particular, as a result of the mathematical analysis, the short-time behavior of a collapsing system, at least the one considered in this paper, is not exponential. Instead, it is the usual Fermi-golden rule result. The long-term behavior is, of course, still exponential. This is a second novel feature of the paper-we connect the short-term Fermi-golden rule (quadratic-in-time behavior) transition probability to the exponential long-time behavior of a collapsing wave-function in one continuous mathematical formulation.
Decoherence is a relatively recent concept in the field of quantum mechanics. Although the pioneers of the field must have understood that loss of phase coherence in quantum superpositions is the reason underlying the appearance of definite outcomes in the quantum measurement problem, the latter was not treated in terms of decoherence until sixty years after the formulation of quantum mechanics as described in a report by Joos and Zeh in 1983 [1]. However, soon after, the theory was developed in further detail, and experiments to measure the actual decoherence rates in various systems commenced. Today, decoherence is the main concern for another reason, i.e., the fact that superposition states must be maintained undisturbed in the quantum communication systems and decoherence presents a strong limitation for their practical application. Decoherence appears in open quantum systems, where the basic system under consideration interacts relatively strongly with an environment. Decoherence times may be as long as seconds for small atomic systems in extreme vacua, although below what is presently measurable (i.e., less than a fraction of a femtosecond) in most liquids and solids, where coupling to the surrounding molecules or atomic arrangements is strong. The relatively slow decoherence in well-isolated particle systems has been described in several recent articles on quantum optics, while the rapid decoherence in liquids and solids has not received this kind of attention. It is the purpose of the present review to fill this gap.
We attempt to clarify certain puzzles concerning state collapse and decoherence. In open quantum systems decoherence is shown to be a necessary consequence of the transfer of information to the outside; we prove an upper bound for the amount of coherence which can survive such a transfer. We claim that in large closed systems decoherence has never been observed, but we will show that it is usually harmless to assume its occurrence. An independent postulate of state collapse over and above Schroedinger's equation and the probability interpretation of quantum states, is shown to be redundant.
Quantum mechanics famously posits two distinct evolution rules for the state of a system: a deterministic, unitary time evolution under the Schr¨odinger equation, and a probabilistic “collapse” of the wavefunction upon measurement as dictated by the Born rule. The apparent inconsistency of these two dynamical laws – one continuous and one discontinuous – constitutes the quantum measurement problem. This foundational problem, which underlies the emergence of definite outcomes from quantum superpositions, has persisted since the theory’s inception. In this review, we present a comprehensive and rigorous examination of the measurement problem and survey the leading approaches that seek to resolve or circumvent it. We begin by formulating the measurement problem and its conceptual challenges. We then discuss in detail the major interpretations of quantum mechanics and theoretical frameworks addressing the problem: the Copenhagen interpretation, Everett’s many-worlds interpretation, de Broglie–Bohm pilot-wave theory, objective collapse models, the role of decoherence and environment-induced superselection, and epistemic approaches such as QBism. For each interpretation, we describe the core principles and mathematical formalism, assessing how (and whether) it attempts to solve the measurement problem. We also review modern developments and experiments relevant to quantum measurements, including tests of Bell inequalities, observations of decoherence and macroscopic superpositions, weak measurements and quantum eraser experiments, and thought experiments ‘a la Wigner’s friend. We highlight how these results inform the ongoing debate. Finally, we discuss open problems and challenges that remain in fully resolving the measurement problem.