The measurement processes that are traditionally described within the realm of non-relativistic quantum mechanics are transcribed into the covariant framework of Cartan's space, the four-valued representation space of the restricted conformal group for special relativity. It is assumed at the outset that the non-relativistic quantum measurement mechanisms of state reductions as well as the definition of Born probabilities should remain unaltered when the passage to the covariant framework is worked out. The correlations between observations registered in different spacetime frames, concerning intermediate steps and outcomes of microscopic measurements, are attained through the implementation of the orthochronous proper Poincaré subgroup of an appropriate realization of SU(2,2). It will be seen that the settlement of such correlations strongly supports the view whereby the physical inner structure of the Schrödinger quantum mechanical picture may be described consistently within special relativity. The overall work likewise affords a fundamental background to the construction of covariant quantum computational gates whilst making it feasible to elaborate upon the predicted and observed formation of entangled states in processes of creation-annihilation pairs. In addition, it is suggested that the usually accepted non-locality feature of the old quantum mechanics should be reconsidered inside an actual relativistic formulation. The important question as to whether quantum computation should bear an invariant character is then raised.
The measurement processes that are traditionally described within the realm of non-relativistic quantum mechanics are transcribed into the covariant framework of Cartan's space, the four-valued representation space of the restricted conformal group for special relativity. It is assumed at the outset that the non-relativistic quantum measurement mechanisms of state reductions as well as the definition of Born probabilities should remain unaltered when the passage to the covariant framework is worked out. The correlations between observations registered in different spacetime frames, concerning intermediate steps and outcomes of microscopic measurements, are attained through the implementation of the orthochronous proper Poincaré subgroup of an appropriate realization of SU(2,2). It will be seen that the settlement of such correlations strongly supports the view whereby the physical inner structure of the Schrödinger quantum mechanical picture may be described consistently within special relativity. The overall work likewise affords a fundamental background to the construction of covariant quantum computational gates whilst making it feasible to elaborate upon the predicted and observed formation of entangled states in processes of creation-annihilation pairs. In addition, it is suggested that the usually accepted non-locality feature of the old quantum mechanics should be reconsidered inside an actual relativistic formulation. The important question as to whether quantum computation should bear an invariant character is then raised.
Abstract Quantum mechanics and relativity are two of the most successful theoretical frameworks in modern physics, yet their conceptual foundations remain difficult to reconcile at the deepest level. Quantum theory describes physical systems through states, observables, probabilities, measurement contexts, superposition, entanglement, and nonclassical correlations. Relativity describes physical processes through space-time structure, causal order, invariant physical law, observer-dependent decomposition of time and space, and constraints on signal propagation. This article examines the conceptual relationship between quantum measurement, relativistic causality, and space-time description. The purpose is not to present a mathematical unification but to analyze how the two frameworks organize physical explanation differently and where their interpretive tensions arise. Special attention is given to the measurement problem, the status of quantum states, the role of observers and reference frames, the meaning of locality, the distinction between correlation and causal influence, and the challenge of describing quantum processes without privileging a single global time. The article argues that many apparent conflicts between quantum theory and relativity result from importing classical intuitions into domains where they no longer apply. Quantum entanglement does not permit controllable faster-than-light communication, yet it challenges classical separability. Relativity forbids superluminal signaling, yet it does not require that all physically meaningful correlations be reducible to local classical properties. Measurement introduces another difficulty because standard quantum theory often describes state update in a way that appears instantaneous, while relativistic space-time does not provide a universal present. The discussion develops a conceptual framework in which quantum measurement is treated as a physical interaction, relativistic causality as a constraint on operational influence, and space-time description as an organizing structure for events rather than a simple background stage. This analysis is relevant for quantum field theory, quantum information, relativistic quantum foundations, and future approaches to quantum gravity.
Abstract The phase space of a relativistic system can be identified with the future tube of complexified Minkowski space. As well as a complex structure and a symplectic structure, the future tube, seen as an eight-dimensional real manifold, is endowed with a natural positive-definite Riemannian metric that accommodates the underlying geometry of the indefinite Minkowski space metric, together with its symmetry group. A unitary representation of the 15-parameter group of conformal transformations can then be constructed that acts upon the Hilbert space of square-integrable holomorphic functions on the future tube. These structures are enough to allow one to put forward a quantum theory of phase-space events. In particular, a theory of quantum measurement can be formulated in a relativistic setting, based on the use of positive operator valued measures, for the detection of phase-space events, hence allowing one to assign probabilities to the outcomes of joint space-time and four-momentum measurements in a manifestly covariant framework. This leads to a localization theorem for phase-space events in relativistic quantum theory, determined by the associated Compton wavelength.
A mathematical framework that unifies the standard formalisms of special relativity and quantum mechanics is proposed. For this a Hilbert space H of functions of four variables x,t furnished with an additional indefinite inner product invariant under Poincaré transformations is introduced. For a class of functions in H that are well localized in the time variable, the usual formalism of nonrelativistic quantum mechanics is derived. In particular, the interference in time for these functions is suppressed; a motion in H becomes the usual Schrödinger evolution with t as a parameter. The relativistic invariance of the construction is proved. The usual theory of relativity on Minkowski space-time is shown to be “isometrically and equivariantly embedded” into H. That is, classical space-time is isometrically embedded into H, Poincaré transformations have unique extensions to isomorphisms of H, and the embedding commutes with Poincaré transformations.
We have recently introduced a realistic, covariant, interpretation for the reduction process in relativistic quantum mechanics. The basic problem for a covariant description is the dependence of the states on the frame within which collapse takes place. A suitable use of the causal structure of the devices involved in the measurement process allowed us to introduce a covariant notion for the collapse of quantum states. However, a fully consistent description in the relativistic domain requires the extension of the interpretation to quantum fields. The extension is far from straightforward. Besides the obvious difficulty of dealing with the infinite degrees of freedom of the field theory, one has to analyze the restrictions imposed by causality concerning the allowed operations in a measurement process. In this paper we address these issues. We shall show that, in the case of partial causally connected measurements, our description allows us to include a wider class of causal operations than the one resulting from the standard way for computing conditional probabilities. This alternative description could be experimentally tested. A verification of this proposal would give a stronger support to the realistic interpretations of the states in quantum mechanics. 1
Ultimately, any explanation of quantum measurement must be extendable to relativistic quantum mechanics (RQM), since many precisely confirmed experimental results follow from quantum field theory (QFT), which is based on RQM. Certainly, the traditional "collapse" postulate for quantum measurement is problematic in a relativistic context, at the very least because, as usually formulated, it violates the relativity of simultaneity. The present paper addresses this with a relativistic model of measurement in which the state of the universe is decomposed into decoherent histories of measurements recorded within it. The approach is essentially Everettian, in the sense that it uses the unmodified, unitary quantum formalism of RQM. But it addresses the difficulty with typical "many worlds" interpretations on how to even define probabilities over different possible ``worlds''. To do this, Zurek's concept of envariance is generalized to the context of relativistic spacetime, giving an objective definition of the probability of any one of the quantum histories, consistent with Born's rule. It is then shown that the statistics of any repeated experiment within the universe also tend to follow the Born rule as the number of repetitions increases. The wave functions that we actually use for such experiments are local reductions of very coarse-grained superpositions of universal eigenstates, and their "collapse" can be re-interpreted as simply an update based on additional incremental knowledge gained from a measurement about the "real" eigenstate of our universe.
We have recently introduced a realistic, covariant, interpretation for the reduction process in relativistic quantum mechanics. The basic problem for a covariant description is the dependence of the states on the frame within which collapse takes place. A suitable use of the causal structure of the devices involved in the measurement process allowed us to introduce a covariant notion for the collapse of quantum states. However, a fully consistent description in the relativistic domain requires the extension of the interpretation to quantum fields. The extension is far from straightforward. Besides the obvious difficulty of dealing with the infinite degrees of freedom of the field theory, one has to analyse the restrictions imposed by causality concerning the allowed operations in a measurement process. In this paper we address these issues. We shall show that, in the case of partial causally connected measurements, our description allows us to include a wider class of causal operations than the one resulting from the standard way of computing conditional probabilities. This alternative description could be experimentally tested. A verification of this proposal would give stronger support to the realistic interpretations of the states in quantum mechanics.