Indistinguishable elements in the origins of quantum statistics. The case of Fermi–Dirac statistics

In this paper, we deal with the historical origins of Fermi–Dirac statistics, focusing on the contribution by Enrico Fermi of 1926. We argue that this statistics, as opposed to that of Bose–Einstein, has been somewhat overlooked in the usual accounts of the old quantum theory. Our main objective is to offer a critical analysis of Fermi’s seminal paper and its immediate impact. Secondly, we are also interested in assessing the status of the particle concept in the years 1926–1927, especially regarding the germ of quantum indistinguishability. We will see, for example, that the first applications of the Fermi–Dirac statistics to the study of metals or stellar matter had a technical nature, and that their main instigators barely touched upon interpretative matters. Finally, we will discuss the reflections and remarks made in these respects in two famous events in physics of 1927, the Como conference and the fifth Solvay congress.

“Two bits less” after quantum-information conservation and their interpretation as “distinguishability / indistinguishability” and “classical / quantum”

The paper investigates the understanding of quantum indistinguishability afterquantum information in comparison with the “classical” quantum mechanics based on theseparable complex Hilbert space. The two oppositions, correspondingly “distinguishability/ indistinguishability” and “classical / quantum”, available implicitly in the concept of quantumindistinguishability can be interpreted as two “missing” bits of classical information, whichare to be added after teleportation of quantum information to be restored the initial stateunambiguously. That new understanding of quantum indistinguishability is linked to thedistinction of classical (Maxwell-Boltzmann) versus quantum (either Fermi-Dirac orBose-Einstein) statistics. The latter can be generalized to classes of wave functions (“empty” qubits) and represented exhaustively in Hilbert arithmetic therefore connectible to the foundations of mathematics, more precisely, to the interrelations of propositional logic and set theory sharing the structure of Boolean algebra and two anti-isometric copies of Peano arithmetic.

A Non-Spatial Reality

It is generally assumed, and usually taken for granted, that reality is fully contained in space. However, when taking a closer look at the strange behavior of the entities of the micro-world, we are forced to abandon such a prejudice and recognize that space is just a temporary crystallization of a small theatre for reality, where the material entities can take a place and meet with each other. More precisely, phenomena like quantum entanglement, quantum interference effects and quantum indistinguishability, when analyzed attentively, tell us that there is much more in our physical reality than what meets our three-dimensional human eyes. But if the building blocks of our physical reality are non-spatial, what does it mean? Can we understand what the nature of a non-spatial entity is? And if so, what are the consequences for our view of the world in which we live and evolve as a species? This article was written having in mind one of the objectives of the Center Leo Apostel for Interdisciplinary Studies, that of a broad dissemination of scientific knowledge. Hence, it addresses a transversal audience of readers, both academic and nonacademic, hoping to stimulate in this way the interdisciplinary dialogue about foundational issues in science.

Tuning the quantumness of simple Bose systems: A universal phase diagram

We present a comprehensive theoretical study of the phase diagram of a system of many Bose particles interacting with a two-body central potential of the so-called Lennard-Jones form. First-principles path-integral computations are carried out, providing essentially exact numerical results on the thermodynamic properties. The theoretical model used here provides a realistic and remarkably general framework for describing simple Bose systems ranging from crystals to normal fluids to superfluids and gases. The interplay between particle interactions on the one hand and quantum indistinguishability and delocalization on the other hand is characterized by a single quantumness parameter, which can be tuned to engineer and explore different regimes. Taking advantage of the rare combination of the versatility of the many-body Hamiltonian and the possibility for exact computations, we systematically investigate the phases of the systems as a function of pressure (P) and temperature (T), as well as the quantumness parameter. We show how the topology of the phase diagram evolves from the known case of4He, as the system is made more (and less) quantum, and compare our predictions with available results from mean-field theory. Possible realization and observation of the phases and physical regimes predicted here are discussed in various experimental systems, including hypothetical muonic matter.

Quantum indistinguishability in chemical reactions

Quantum indistinguishability plays a crucial role in many low-energy physical phenomena, from quantum fluids to molecular spectroscopy. It is, however, typically ignored in most high-temperature processes, particularly for ionic coordinates, implicitly assumed to be distinguishable, incoherent, and thus well approximated classically. We explore enzymatic chemical reactions involving small symmetric molecules and argue that in many situations a full quantum treatment of collective nuclear degrees of freedom is essential. Supported by several physical arguments, we conjecture a “quantum dynamical selection” (QDS) rule for small symmetric molecules that precludes chemical processes that involve direct transitions from orbitally nonsymmetric molecular states. As we propose and discuss, the implications of the QDS rule include (i) a differential chemical reactivity of para- and orthohydrogen, (ii) a mechanism for inducing intermolecular quantum entanglement of nuclear spins, (iii) a mass-independent isotope fractionation mechanism, (iv) an explanation of the enhanced chemical activity of “reactive oxygen species”, (v) illuminating the importance of ortho-water molecules in modulating the quantum dynamics of liquid water, and (vi) providing the critical quantum-to-biochemical linkage in the nuclear spin model of the (putative) quantum brain, among others.