Superdeterminism has received a recent surge of attention in the foundations community. A particular superdeterministic proposal, named Invariant-set theory, appears to bring ideas from several diverse fields (eg. number theory, chaos theory etc.) to quantum foundations and provides a novel justification for the choice of initial conditions in terms of state-space geometry. However, the lack of a concrete hidden-variable model makes it difficult to evaluate the proposal from a foundational perspective.
In this talk, I will critically analyse this superdeterministic proposal in three steps. First, I will show how to build a hidden-variable model based on the proposal's ideas. Second, I will analyse the properties of the model and show that several arguments that appear to work in the proposal (on counter-factual measurements, non-commutativity etc.) fail when considered in the model. Further, the model is not only superdeterministic but also nonlocal, $\psi$-ontic and contains redundant information in its bit-string. Third, I will discuss the accuracy of the model in representing the proposal. I will consider the arguments put forward to claim inaccuracy and show that they are incorrect. My results lend further support to the view that superdeterminism is unlikely to solve the puzzle posed by the Bell correlations.
Based on the papers:
1. I. Sen. "Analysis of the superdeterministic Invariant-set theory in a hidden-variable setting." Proc. R. Soc. A 478.2259 (2022): 20210667.
2. I. Sen. "Reply to superdeterminists on the hidden-variable formulation of Invariant-set theory." arXiv:2109.11109 (2021).
In the first part of my talk, I present the effective-field theory (EFT)-based cosmological full-shape analysis of the anisotropic power spectrum of eBOSS quasars. We perform extensive tests of our pipeline on simulations, paying particular attention to the modeling of observational systematics. Assuming the minimal ΛCDM model, we find the Hubble constant H0 = (66.7 ± 3.2) km/s/Mpc, the matter density fraction Ωm = 0.32 ± 0.03, and the late-time mass fluctuation amplitude σ8 = 0.95 ± 0.08. These measurements are fully consistent with the Planck cosmic microwave background results. Our work paves the way for systematic full-shape analyses of quasar samples from future surveys like DESI. I also present the cosmological constraints from the full-shape BOSS+eBOSS data in various extensions of the ΛCDM model, such as massive neutrinos, dynamical dark energy and spatial curvature.
In the second part, I study the one-point probability distribution function (PDF) for matter density averaged over spherical cells. The leading part to the PDF is defined by the dynamics of the spherical collapse whereas the next-to-leading part comes from the integration over fluctuations around the saddle-point solution. The latter calculation receives sizable contributions from unphysical short modes and must be renormalized. We propose a new approach to renormalization by modeling the effective stress-energy tensor for short perturbations. The model contains three free parameters which can be related to the counterterms in the one-loop matter power spectrum and bispectrum. We demonstrate that this relation can be used to impose priors in fitting the model to the PDF data. We confront the model with the results of high-resolution N-body simulations and find excellent agreement for cell radii r≥10 Mpc/h at all redshifts up to z=0.
