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arXiv:2602.14175

Quantum field theory measurements for relativistic particles

Nadia Koliopoulou, Charis Anastopoulos, Ntina Savvidou

quant-phhep-thSubmitted Feb 15, 2026• Announced Feb 17, 2026• 0 citations• Revised Jul 17, 2026 (v2)
v1 · Feb 15, 2026v2 · Jul 17, 2026
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Abstract

The formulation of a consistent measurement theory for relativistic quantum fields has become a problem of growing foundational and practical significance. Standard non-relativistic measurement models fail to incorporate the essential relativistic principles of locality, causality, and Lorentz covariance, and are therefore inadequate for quantum field theoretic settings. While most existing work focuses on scalar fields, realistic particles possess spin, polarization, and internal degrees of freedom that introduce new conceptual and operational challenges. To this end, we employ the Quantum Temporal Probabilities (QTP) framework for relativistic measurements to describe electromagnetic, Dirac, and internally structured scalar fields. Our results include probabilities for the time-of-arrival that take spin/polarization into account, generalized photodetection formulas beyond Glauber's theory, an unambiguous derivation of the particle oscillation formula together with its limitations, and a first-principles analysis of relativistic qudits.

Comments
29 pages. latex, 1 figure. Added details and explanations. To appear in PRD

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The formulation of a consistent measurement theory for relativistic quantum fields has become a problem of growing foundational and practical significance. Standard non-relativistic measurement models fail to incorporate the essential relativistic principles of locality, causality, and Lorentz covariance, and are therefore inadequate for quantum field theoretic settings. While most existing work focuses on scalar fields, realistic particles possess spin, polarization, and internal degrees of freedom that introduce new conceptual and operational challenges. To this end, we employ the Quantum Temporal Probabilities (QTP) framework for relativistic measurements to describe electromagnetic, Dirac, and internally structured scalar fields. Our results include probabilities for the time-of-arrival that take spin/polarization into account, generalized photodetection formulas beyond Glauber's theory, an unambiguous derivation of the particle oscillation formula together with its limitations, and a first-principles analysis of relativistic qudits.
This is the second paper on a new formalism for relativistic quantum measurements. Here, we construct a fully relativistic model for detectors that takes into account the detector's state of motion, intrinsics dynamics, initial states and couplings to the measured field. The dual classical/quantum description of the detector is implemented by using a master-equation type of approximation for the coarse-grained pointer variables. Then we identify the probabilities that correspond to ideal measurements, i.e., measurements that are largely insensitive to modeling details of the apparatus. The Unruh-Dewitt and Glauber detectors are recovered at the appropriate limits. We employ our results to models of particle detection, photodetection and relativistic spin measurements, and we derive an ideal distribution for relativistic time-of-arrival probabilities.
Constructing observables that describe the localization of relativistic particles is an important foundational problem in relativistic quantum field theory (QFT). The description of localization in terms of single-time observables leads to conflict with the requirement of causality. In this paper, we describe particle localization in terms of time-of-arrival observables, defined in terms of the interaction between a quantum field and a measuring apparatus. The resulting probabilities are linear functionals of QFT correlation functions. Specializing to the case of a scalar field, we identify several time-of-arrival observables differing on the way that the apparatus localizes particle-detection records. Maximum localization is obtained for a unique observable that is related to the Newton-Wigner position operator. Finally, we define a measure of localizability for relativistic particles in terms of a novel time-energy uncertainty relation for the variance of the time of arrival.
Abstract The conceptual unification of quantum mechanics and relativity remains one of the central challenges of modern theoretical physics. While quantum theory successfully describes microscopic phenomena through probabilistic wave dynamics and field quantization, relativity establishes the geometric structure of space-time and the causal organization of physical events. Despite extensive progress in quantum field theory and relativistic quantum frameworks, foundational tensions persist regarding locality, causality, and coherence. This study presents a conceptual and structural analysis of quantum field coherence within relativistic space-time. Rather than focusing on specific unification proposals, we examine the compatibility conditions between quantum coherence, relativistic causality, and space-time structure. Particular attention is given to field-based interpretations of quantum states, entanglement propagation limits, and covariance requirements. The analysis synthesizes perspectives from relativistic quantum field theory, conceptual foundations of quantum measurement, and geometric interpretations of space-time. We argue that coherence phenomena can be understood as structurally constrained by relativistic causal order, without requiring violation of space-time locality. The aim of this article is to clarify foundational relationships between quantum coherence and relativistic structure through a conceptual framework that integrates field-theoretic and geometric viewpoints.
Proposed quantum experiments in deep space will be able to explore quantum information issues in regimes where relativistic effects are important. In this essay, we argue that a proper extension of quantum information theory into the relativistic domain requires the expression of all informational notions in terms of quantum field theoretic (QFT) concepts. This task requires a working and practicable theory of QFT measurements. We present the foundational problems in constructing such a theory, especially in relation to longstanding causality and locality issues in the foundations of QFT. Finally, we present the ongoing Quantum Temporal Probabilities program for constructing a measurement theory that (i) works, in principle, for any QFT, (ii) allows for a first- principles investigation of all relevant issues of causality and locality, and (iii) it can be directly applied to experiments of current interest.
We analyze time-of-arrival probability distributions for relativistic particles in the context of quantum field theory (QFT). We show that QFT leads to a unique prediction, modulo post-selection that incorporates properties of the apparatus into the initial state. We also show that an experimental distinction of different probability assignments is possible especially in near-field measurements. We also analyze causality in relativistic measurements. We consider a quantum state obtained by a spacetime-localized operation on the vacuum, and we show that detection probabilities are typically characterized by small transient non-causal terms. We explain that these terms originate from Feynman propagation of the initial operation, because the Feynman propagator does not vanish outside the light cone. We discuss possible ways to restore causality, and we argue that this may not be possible in measurement models that involve switching the field–apparatus coupling on and off.
The topic of measurement in relativistic quantum field theory is addressed in this article. Some of the long standing problems of this subject are highlighted, including the incompatibility of an instantaneous ``collapse of the wavefunction'' with relativity of simultaneity, and the difficulty of maintaining causality in the rules for measurement highlighted by ``impossible measurement'' scenarios. Thereafter, the issue is considered from the perspective of mathematical physics. To this end, quantum field theory is described in a model-independent, operator algebraic setting, on generic Lorentzian spacetime manifolds. The process of measurement is modelled by a localized dynamical coupling between a quantum field called the ``system'', and another quantum field, called the ``probe''. The result of the dynamical coupling is a scattering map, whereby measurements carried out on the probe can be interpreted as measurements of induced observables on the system. The localization of the dynamical coupling allows it to derive causal relations for the induced observables. It will be discussed how this approach leads to the concept of selective or non-selective system state updates conditioned on the result of probe measurements, which in turn allows it to obtain conditional probabilities for consecutive probe measurements consistent with relativistic causality and general covariance, without the need for a physical collapse of the wavefunction. In particular, the problem of impossible measurements is resolved. Finally, there is a brief discussion of accelerated detectors and other related work.