Alexandre Harvey Tremblay

We present a novel approach to quantum theory construction that involves maximizing the Shannon entropy of quantum measurements relative to their initial preparation. By constraining the maximization problem with a phase that vanish under measurements, we obtain quantum mechanics (vanishing U(1)-valued phase), relativistic quantum mechanics (vanishing Spin^c(3,1)-valued phase), and quantum gravity (also a vanishing Spin^c(3,1)-valued phase, but with a non-vanishing dilation part). The first two cases are equivalent to established theory, whereas the later case yields a quantum theory of accelerated reference frames, in which a quantized version of the Einstein field equation lives. Specifically, the spacetime interval is promoted to an observable, effectively building the metric tensor from the underlying quantum structure. Moreover, the SU(3)xSU(2)xU(1) gauge symmetries of the Standard Model arise naturally without additional assumptions. Finally, the solution is consistent only with 3+1 spacetime dimensions, as it encounters obstructions in all other dimensional configurations. This framework integrates quantum mechanics, relativistic quantum mechanics, quantum gravity, spacetime dimensionality, and particle physics gauge symmetries from a simple entropy maximization problem constrained by a vanishing phase.

This work presents a novel formulation of quantum mechanics as the solution to an entropy maximization problem constrained by empirical measurement outcomes. By treating the complete set of possible measurement outcomes as an optimization constraint, our entropy maximization problem derives the axioms of quantum mechanics as theorems, demonstrating that the theory's mathematical structure is the least biased probability measure consistent with the observed data. This approach reduces the foundation of quantum mechanics to a single axiom, the measurement constraint, from which the full theory emerges through entropy maximization. In contrast to the conventional axiomatic approach, the framework grounds the axioms directly in empirical data, substantially restricting the interpretational landscape ruling out interpretations inconsistent with this empirical foundation.

In the RNA World hypothesis, it is generally assumed that self-replicating RNA emerged from a primordial soup of amino acids approximately 500 million years before the advent of life on Earth. Recently, prebiotic molecules such as glycolaldehyde and amino acetonitrile have been discovered in abundance in nebulae like Sagittarius B2. This paper proposes that icy grains within these nebulae could act as primordial soups and explores the implications of this hypothesis. It is argued that the sheer abundance of these grains in a typical nebula makes their collective volume astronomically greater than Earth’s primitive oceans, thus favouring the likelihood of an RNA self-replicator emerging within this environment based on volume arguments. The likelihood of naturally producing the first self-replicator may be significantly lower than previously envisioned, necessitating the contribution of a larger primordial soup spread across a nebula and functioning for billions of years before the emergence of life on Earth. According to this model, Earth could have been seeded by panspermia following the emergence of a self-replicator on nearby icy interstellar dust. Finally, we discuss the Fermi paradox in the context of this model.