We prove that superdeterministic models of quantum mechanics are conspiratorial in a mathematically well-defined sense, by further development of the ideas presented in a previous article A . We consider a Bell scenario where, in each run and at each wing, the experimenter chooses one of N devices to determine the local measurement setting. We prove, without assuming any features of quantum statistics, that superdeterministic models of this scenario must have a finely tuned distribution of hidden variables. Specifically, fine-tuning is required so that the measurement statistics depend on the measurement settings but not on the details of how the settings are chosen. We quantify this as the overhead fine-tuning F of the model, and show that F  > 0 (corresponding to ‘fine-tuned’) for any N  > 1. The notion of fine-tuning assumes that arbitrary (‘non-equilibrium’) hidden-variables distributions are possible in principle. We also show how to quantify superdeterministic conspiracy without using non-equilibrium. This second approach is based on the fact that superdeterministic correlations can mimic actual signalling. We argue that an analogous situation occurs in equilibrium where, for every run, the devices that the hidden variables are correlated with are coincidentally the same as the devices in fact used. This results in extremely large superdeterministic correlations, which we quantify as a drop of an appropriately defined formal entropy. Non-local and retrocausal models turn out to be non-conspiratorial according to both approaches.

This is the first of two papers that attempt to comprehensively analyse superdeterministic hidden-variables models of Bell correlations. We first give an overview of superdeterminism and discuss various criticisms of it raised in the literature. We argue that the most common criticism, the violation of ‘free-will’, is incorrect. We take up Bell’s intuitive criticism that these models are ‘conspiratorial’. To develop this further, we introduce non-equilibrium extensions of superdeterministic models. We show that the measurement statistics of these extended models depend on the physical system used to determine the measurement settings. This suggests a fine-tuning in order to eliminate this dependence from experimental observation. We also study the signalling properties of these extended models. We show that although they generally violate the formal no-signalling constraints, this violation cannot be equated to an actual signal. We therefore suggest that the so-called no-signalling constraints be more appropriately named the marginal-independence constraints. We discuss the mechanism by which marginal-independence is violated in superdeterministic models. Lastly, we consider a hypothetical scenario where two experimenters use the apparent-signalling of a superdeterministic model to communicate with each other. This scenario suggests another conspiratorial feature peculiar to superdeterminism. These suggestions are quantitatively developed in the second paper.

No abstract

The present study was aimed at exploring the effect of soil application of different concentrations of orthophosphate (P) (0, 10, 20, 30, and 40 mg kg−1) on rice agronomic and yield parameters, arsenic (As) species accumulation, and polyphenol levels in the grain of rice grown under As spiked soil (10 mg kg−1). The contents of As species (As(V), As (III), MMA and DMA) and polyphenols in rice grain samples were estimated using LC-ICP-MS and LC-MS/MS, respectively. P treatments significantly reduced the toxic effects of As on agronomic parameters such as root weight and length, shoot and spike length, straw, and grain yield. Among the treatments studied, only the treatment of 30 mg kg−1 P helps to decrease the elevated levels of As (V), As (III), and DMA in rice grains due to As application. The study revealed that 30 mg kg−1 was the optimal P application amount to minimize AS accumulation in rice grains and As-linked toxicity on agronomic parameters and chlorophyll biosynthesis. Furthermore, the levels of trans-ferulic acid, chlorogenic acid, caffeic acid, and apigenin-7-glucoside increased in response to accumulation of As in the rice grain. In conclusion, the precise use of phosphorus may help to mitigate arsenic linked phytotoxicity and enhance the food safety aspect of rice grain.

The possibility of using retrocausality to obtain a fundamentally relativistic account of the Bell correlations has gained increasing recognition in recent years. It is not known, however, the extent to which these models can make use of their relativistic properties to account for relativistic effects on entangled systems. We consider here a hypothetical relativistic Bell experiment, where one wing of the experiment is located in a lab on Earth, whereas the other wing is located inside a relativistic rocket, initially grounded adjacent to the lab. The Stern-Gerlach magnets in both the wings are turned on simultaneously as the rocket lifts off into orbit, and turned off when the rocket returns after a certain duration to its original spot. We show that the retrocausal Brans model (Found. Phys, 49(2), 2019) can be easily generalised to analyse this setup, and that it predicts less separation of eigenpackets in the rocket compared to the stationary lab. This causes the particle distribution patterns on the photographic plates to differ between the wings -an experimentally testable prediction of the model. We argue that the description of the experiment and the verification of this prediction using quantum field theory is a challenging task, in contrast to the ease of handling in the retrocausal Brans model. We mention the implications of our hypothetical experiment for hidden variable models in general.