Naive attempts to put together relativity and quantum measurements lead to signaling between space-like separated regions. In QFT, these are known as impossible measurements . We show that the same problem arises in non-relativistic quantum physics, where joint nonlocal measurements (i.e., between systems kept spatially separated) in general lead to signaling, while one would expect no-signaling (based for instance on the principle of no-nonphysical communication ). This raises the question: Which nonlocal quantum measurements are physically possible? We review and develop further a non-relativistic quantum information approach developed independently of the impossible measurements in QFT, and show that these two have been addressing virtually the same problem. The non-relativistic solution shows that all nonlocal measurements are localizable (i.e., they can be carried out at a distance without violating no-signaling) but they (i) may require arbitrarily large entangled resources and (ii) cannot in general be ideal , i.e., are not immediately reproducible. These considerations could help guide the development of a complete theory of measurement in QFT.
Naive attempts to put together relativity and quantum measurements lead to signaling between space-like separated regions. In QFT, these are known as impossible measurements . We show that the same problem arises in non-relativistic quantum physics, where joint nonlocal measurements (i.e., between systems kept spatially separated) in general lead to signaling, while one would expect no-signaling (based for instance on the principle of no-nonphysical communication ). This raises the question: Which nonlocal quantum measurements are physically possible? We review and develop further a non-relativistic quantum information approach developed independently of the impossible measurements in QFT, and show that these two have been addressing virtually the same problem. The non-relativistic solution shows that all nonlocal measurements are localizable (i.e., they can be carried out at a distance without violating no-signaling) but they (i) may require arbitrarily large entangled resources and (ii) cannot in general be ideal , i.e., are not immediately reproducible. These considerations could help guide the development of a complete theory of measurement in QFT.
Abstract Arguments by Sorkin (Impossible measurements on quantum fields. In: Directions in general relativity: proceedings of the 1993 International Symposium, Maryland, vol 2, pp 293–305, 1993) and Borsten et al. (Phys Rev D 104(2), 2021. https://doi.org/10.1103/PhysRevD.104.025012 ) establish that a natural extension of quantum measurement theory from non-relativistic quantum mechanics to relativistic quantum theory leads to the unacceptable consequence that expectation values in one region depend on which unitary operation is performed in a spacelike separated region. Sorkin [1] labels such scenarios ‘impossible measurements’. We explicitly present these arguments as a no-go result with the logical form of a reductio argument and investigate the consequences for measurement in quantum field theory (QFT). Sorkin-type impossible measurement scenarios clearly illustrate the moral that Microcausality is not by itself sufficient to rule out superluminal signalling in relativistic quantum theories that use Lüders’ rule. We review three different approaches to formulating an account of measurement for QFT and analyze their responses to the ‘impossible measurements’ problem. Two of the approaches are: a measurement theory based on detector models proposed in Polo-Gómez et al. (Phys Rev D, 2022. https://doi.org/10.1103/physrevd.105.065003 ) and a measurement framework for algebraic QFT proposed in Fewster and Verch (Commun Math Phys 378(2):851–889, 2020). Of particular interest for foundations of QFT is that they share common features that may hold general morals about how to represent measurement in QFT. These morals are about the role that dynamics plays in eliminating ‘impossible measurements’, the abandonment of the operational interpretation of local algebras A(O) A ( O ) as representing possible operations carried out in region O , and the interpretation of state update rules. Finally, we examine the form that the ‘impossible measurements’ problem takes in histories-based approaches and we discuss the remaining challenges.
FINDING: Quantum tunneling is a wave-mechanical transmission through classically forbidden barriers, governed by exponential decay of the wavefunction; "impossible" measurements in QFT are possible but non-ideal, revealing fundamental limits on joint nonlocal observables. | MATH: Transmission coefficient T≈e−2κL, where κ=2m(V0−E)/ℏ for a rectangular barrier of height V0, width L. For arbitrary barriers, WKB: T≈exp(−ℏ2∫x1x22m(V(x)−E)dx). The QFT "impossible measurement" result (arXiv:2311.13644) shows that nonlocal joint measurements violate causality unless they are non-ideal — mathematically, the measurement map is not a completely positive trace-preserving (CPTP) map on the joint algebra; it requires a non-unital, non-CP extension, with the deviation quantified by a signaling parameter ϵ>0. | CONNECTION: The exponential decay e−2κL is a pure exponen Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
It is by now well recognized that the naive application of the projection postulate on composite quantum systems can induce signalling between their constituent components, indicative of a breakdown of causality in a relativistic spacetime context. Here we introduce a necessary and sufficient condition for an ideal measurement of an observable to be nonsignalling. As well as being particularly simple, it generalizes previous no-signalling conditions in that it allows for degeneracies and can be applied to all bounded self-adjoint operators. The condition is used to establish that arbitrary sums of local observables will not signal, in accordance with our expectations from relativistic quantum field theory. On the other hand, it is shown that the measurement of the tensor product of commuting local observables, for example bipartite operators of the form $A\ensuremath{\bigotimes}B$, can in fact signal, contrary to the widely held belief that such measurements are always locally realizable. The implications for the notion of measurement in relativistic quantum field theory are addressed; it appears that the most straightforward application of the standard quantum formalism generically leads to violations of causality. We conclude that either the class of observables that can be measured should be restricted and/or that the naive translation of the measurement framework of quantum theory, in particular the projection postulate, to quantum field theory should be reevaluated.
FINDING: Quantum tunneling is a wave-mechanical penetration of finite potential barriers, with a transmission coefficient governed by exponential decay of the wavefunction inside the barrier; "impossible" relativistic measurements are shown to be possible but non-ideal, revealing a fundamental tension between QFT and measurement theory. MATH: - Transmission coefficient T≈e−2κL, where κ=2m(V0−E)/ℏ (rectangular barrier, E<V0). - For a general barrier V(x): T≈exp[−ℏ2∫x1x22m(V(x)−E)dx] (WKB approximation). - Reflection coefficient R=1−T (unitarity). - In QFT impossibility: signaling between spacelike-separated regions is avoided only if measurement operators commute — the paper (arXiv:2311.13644) shows nonlocal joint measurements in non-relativistic QM produce the same paradox, implying a constraint on measurement algebra: \( [\hat{O}_A, \hat{O}_ Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
FINDING: Quantum tunneling is a well-established wave-mechanical phenomenon; the "impossible measurements" problem in QFT is shown to be non-relativistic in origin, not a relativistic artifact. | MATH: Tunneling transmission coefficient T≈e−2κL, where κ=2m(V0−E)/ℏ; for a rectangular barrier, T=[1+4E(V0−E)V02sinh2(κL)]−1. The QFT impossibility result (arXiv:2311.13644) shows nonlocal joint measurements violate causality even in non-relativistic QM — the mathematical structure is the commutator [A,B]=0 for spacelike-separated operators, with signaling bounded by the Lieb-Robinson-type bound ∥[OA(t),OB]∥≤Ce−(d−vt)/ξ. | CONNECTION: The exponential decay in tunneling e−2κL mirrors the golden-ratio-related decay constant in Fibonacci-like recursive barrier stacks — for periodic barriers, the band structure yields transmission peaks at kL=nπ, and the critical coupli Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Quantum tunneling is transmission through a classically forbidden region, governed by exponential decay of the wavefunction, and in quantum field theory, the supposedly impossible nonlocal measurements are realizable only as non-ideal operations, revealing a hard limit on joint observables. That is the finding in one sentence. The context is this: for decades, we have treated tunneling as textbook quantum mechanics, and nonlocal measurements as either forbidden or trivial. But the two problems meet at a deeper junction. In relativistic QFT, the algebra of observables in spacelike-separated regions is a type III von Neumann factor. That means there is no tensor product decomposition into local subsystems, and ideal joint measurements across such regions are not just difficult — they are mathematically inconsistent with causality. The recent result, archived as arXiv:2311.13644, makes this precise. Here is the mechanism, at a level you can check. For a rectangular barrier, the transmis Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com