# Weekly Papers on Quantum Foundations (29)

The Relativity Principle at the Foundation of Quantum Mechanics. (arXiv:2107.06942v1 [quant-ph])

Quantum information theorists have created axiomatic reconstructions of quantum mechanics (QM) that are very successful at identifying precisely what distinguishes quantum probability theory from classical and more general probability theories in terms of information-theoretic principles. Herein, we show how two such principles, i.e., “Existence of an Information Unit” and “Continuous Reversibility,” map to the relativity principle as it pertains to the invariant measurement of Planck’s constant h for Stern-Gerlach (SG) spin measurements in spacetime in exact analogy to the relativity principle as it pertains to the invariant measurement of the speed of light c for special relativity (SR). Essentially, quantum information theorists have extended Einstein’s use of the relativity principle from the boost invariance of measurements of c to include the SO(3) invariance of measurements of h between different reference frames of mutually complementary spin measurements via the principle of “Information Invariance & Continuity.” Consequently, the “average-only” conservation represented by the Bell states that is responsible for the Tsirelson bound and the exclusion of the no-signalling, “superquantum” Popescu-Rohrlich joint probabilities is understood to result from conservation per Information Invariance & Continuity between different reference frames of mutually complementary measurements, and this maps to conservation per the relativity principle in spacetime. Thus, the axiomatic reconstructions of QM have succeeded in producing a principle account of QM that is every bit as robust as the postulates of SR, revealing a still broader role for the relativity principle in the foundations of physics.

Strong light-matter interaction effects on molecular ensembles. (arXiv:2107.07032v1 [physics.chem-ph])

Despite the potential paradigm breaking capability of microcavities to control chemical processes, the extent to which photonic devices change properties of molecular materials is still unclear, in part due to challenges in modeling hybrid light-matter excitations delocalized over many length scales. We overcome these challenges for a photonic wire under strong coupling with a molecular ensemble. Our simulations provide a detailed picture of the effect of photonic wires on spectral and transport properties of a disordered molecular material. We find stronger changes to the probed molecular observables when the cavity is redshifted relative to the molecules and energetic disorder is weak. These trends are expected to hold also in higher-dimensional cavities, but are not captured with theories that only include a single cavity-mode. Therefore, our results raise important issues for future experiments and model building focused on unraveling new ways to manipulate chemistry with optical cavities.

The Quantum Mechanics Swampland. (arXiv:2012.11606v2 [hep-th] UPDATED)

We investigate non-relativistic quantum mechanical potentials between fermions generated by various classes of QFT operators and evaluate their singularity structure. These potentials can be generated either by four-fermion operators or by the exchange of a scalar or vector mediator coupled via renormalizable or non-renormalizable operators. In the non-relativistic regime, solving the Schr\”odinger equation with these potentials provides an accurate description of the scattering process. This procedure requires providing a set of boundary conditions. We first recapitulate the procedure for setting the boundary conditions by matching the first Born approximation in quantum mechanics to the tree-level QFT approximation. Using this procedure, we show that the potentials are nonsingular, despite the presence of terms proportional to $r^{-3}$ and $\nabla_{i}\nabla_{j}\delta^{3}(\vec{r})$. This surprising feature leads us to propose the \emph{Quantum Mechanics Swampland}, in which the Landscape consists of non-relativistic quantum mechanical potentials that can be UV completed to a QFT, and the Swampland consists of pathological potentials which cannot. We identify preliminary criteria for distinguishing potentials which reside in the Landscape from those that reside in the Swampland. We also consider extensions to potentials in higher dimensions and find that Coulomb potentials are nonsingular in an arbitrary number of spacetime dimensions.

Give quantum mechanics a chance: use relativistic quantum mechanics to analyze measurement!. (arXiv:2106.07538v2 [quant-ph] UPDATED)

Authors: Karl-Erik Eriksson

At the time of publication of H. Everett’s Relative-State Formulation (1957) and DeWitt’s Many-Worlds Interpretation (1970), quantum mechanics was available in a more modern and adequate version than the one used by these authors. We show that with the more modern quantum theory, quantum measurement could have been analyzed along more conventional lines in a one-world cosmology. Bell criticized the Everett-DeWitt theory quite sharply in 1987 but this seems not to have affected the acceptance of the old quantum mechanics as the framework for analysis of measurement.

Analysis of the superdeterministic Invariant-set theory in a hidden-variable setting. (arXiv:2107.04761v2 [quant-ph] UPDATED)

Authors: Indrajit Sen

A recent proposal for a superdeterministic account of quantum mechanics, named Invariant-set theory, appears to bring ideas from several diverse fields like chaos theory, number theory and dynamical systems to quantum foundations. However, a clear cut hidden-variable model has not been developed, which makes it difficult to assess the proposal from a quantum foundational perspective. In this article, we first build a hidden-variable model based on the proposal, and then critically analyse several aspects of the proposal using the model. We show that several arguments related to counter-factual measurements, nonlocality, non-commutativity of quantum observables, measurement independence etcetera that appear to work in the proposal fail when considered in our model. We further show that our model is not only superdeterministic but also nonlocal, with an ontic quantum state. Lastly, we apply the analysis developed in a previous work (Proc. R. Soc. A, 476(2243):20200214, 2020) to illustrate the issue of superdeterministic conspiracy in the model. Our results lend further support to the view that superdeterminism is unlikely to solve the puzzle posed by the Bell correlations.

Universal signature of quantum entanglement across cosmological distances. (arXiv:2107.06910v1 [hep-th])

Although the paradigm of inflation has been extensively studied to demonstrate how macroscopic inhomogeneities in our universe originate from quantum fluctuations, most of the established literature ignores the crucial role that entanglement between the modes of the fluctuating field plays in its observable predictions. In this paper, we import techniques from quantum information theory to reveal hitherto undiscovered predictions for inflation which, in turn, signals how quantum entanglement across cosmological scales can affect large scale structure. Our key insight is that observable long-wavelength modes must be part of an open quantum system, so that the quantum fluctuations can decohere in the presence of an environment of short-wavelength modes. By assuming the simplest model of single-field inflation, and considering the leading order interaction term from the gravitational action, we derive a universal lower bound on the observable effect of such inescapable entanglement.

On the re-interpretation of Wheeler-DeWitt equation. (arXiv:1910.13217v2 [gr-qc] UPDATED)

Authors: Avadhut V. Purohit

I have shown that the field defined by the Wheeler-DeWitt equation for pure gravity is not a standard gravitational field. This field has some features that are common to the matter fields. The re-interpretation leads to the geometrization of quantum theory..

Creativity and Modelling the Measurement Process of the Higgs self-coupling at the LHC and HL-LHC

Ritson, Sophie (2021) Creativity and Modelling the Measurement Process of the Higgs self-coupling at the LHC and HL-LHC. [Preprint]

A reply to Rovelli’s response to our “Assessing Relational Quantum Mechanics”

Muciño, Ricardo and Okon, Elias and Sudarsky, Daniel (2021) A reply to Rovelli’s response to our “Assessing Relational Quantum Mechanics”. [Preprint]