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CRC Press eBooks

Identical Particles

Jonathan Allday

Published Mar 3, 2009• 0 citations
Publisher

Abstract

Although atoms are very complicated objects, there are certain situations in which they can be treated as simple lumps of matter. eir internal structure has no relevance to the details of what is happening. is sort of situation is exempli ed by experiments in which atoms are deliberately smashed into one another. Such experiments provide an ideal starting place for a study of the quantum physics of identical particles.

DOI
10.1201/9781584887041-14

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Although atoms are very complicated objects, there are certain situations in which they can be treated as simple lumps of matter. eir internal structure has no relevance to the details of what is happening. is sort of situation is exempli ed by experiments in which atoms are deliberately smashed into one another. Such experiments provide an ideal starting place for a study of the quantum physics of identical particles.
An atom consists of a nucleus, containing protons and neutrons, with various electrons swarming around the outskirts. The electrons are held in the vicinity of the nucleus as they are negatively charged and hence attracted by the positively charged protons. Although atoms are complicated objects, there are certain situations where they can be treated as simple lumps of matter. Their internal structure has no relevance to the details of what is happening. This sort of situation is exemplified by experiments in which atoms are deliberately smashed into one another at comparatively low energy and as such provide an ideal start in a study of the quantum physics of identical particles. When we are dealing with atoms, there is something more to being ‘identical’ than we can appreciate with larger-scale objects. Atoms of the same type are really identical, measurably identical if you like, which can make a considerable difference in some physically important situations.
A long-form meditation on how physics came to mistake debris for truth. This document argues that atoms, particles, and the so‑called building blocks of reality are not objects but expressions of deeper geometry — and that smashing expressions to understand geometry is a category error. It traces the historical path that led physics into the collider mindset, examines the blind spots of legacy mathematics, and maps the difference between studying collapse and studying structure. The reader should approach this text slowly, as if walking through a garden of ideas rather than a technical manual. Each section is a stone placed deliberately: some are conceptual, some are analogical, some are mathematical, some are philosophical. Together they form a path that leads from object‑based ontology to geometric understanding. This is not a physics paper in the traditional sense. It is a critique of how physics thinks. It is a reframing of matter as geometry behaving. It is an invitation to stop hitting the hammer and start studying the hand that made it. v2 in pdf for ease of reading KEYWORDS AND SUBJECTSSubstrate-first physics; geometric ontology; field geometry; atom as expression; debris epistemology; collider mindset; catastrophic failure states; hammer paradox; object-based ontology; symmetry limitations; constraint-driven expression; emergence from fields; stability vs collapse; reaction vs revelation; fragment non-fundamentality; wormhole of specifics; Standard Model critique; mathematical self-reference; geometry–expression–behaviour chain; non-destructive physics; epistemology of destruction; geometric turn; contextual particle identity; quantum interpretation reframing; collapse artefacts; field excitation; geometric indeterminacy; constraint mapping; stability modelling; non-object ontology; physics philosophy; matter as geometry behaving. And somewhere in the background of all this geometry, epistemology, and hammer smashing, the tune of the evening kept looping: “War — Why Can’t We Be Friends.” It was ridiculous and perfect. A song about not fighting, playing while I wrote a paper about physics punching atoms in the face to understand them. The timing was stupidly poetic. Every time the chorus hit, it felt like the universe itself was leaning over and saying, “See? Even the soundtrack gets the joke.” - Matt 🦆🦆🦆 🦢✨ 🐤💛 🦆🎶 🪿😎 🦆➡️🧠 🐥🌊 🦆🤝🦆 Contact: For enquiries or research questions related to this work, email matthewcarlo.research@gmail.com
In this article, we discuss some questions about the nature of elementary particles treated by quantum mechanics, in particular related to the concepts of identity and individuality of these particles. We started briefly exposing the philosophical and formal concepts of the identity and individuality, and then show how these notions are problematic when applied to elementary particles such as electrons, protons and neutrons. In particular, we emphasize that both philosophy, logic and set theory (and thus the mathematics) admit the usual assumption that things have a ‘type’ of identity and individuality (i.e., are individuals), in the sense that objects which have all the same properties are the same object (are equal). Nevertheless, we show that in the quantum universe is possible to find objects that share all their properties, but are not just one, constituting in something like “nonindividuals” (thesis defended by many physicists and philosophers of science). In sequence, we show how classical mathematics — which, as we said, assumes an individuality to your entities — handle this situation, in particular admitting assumptions external to the physical theories. To avoid this procedure, and look for a formalism more ‘natural’ and appropriate to work with these quantum characteristics, we suggest the use of a non-classical set theory called the quasi-set theory, based on a non-reflective logics, which admits objects devoid of identity and individuality ab initio. Finally, we show another application of this theory: the search to a quasi-set mathematical structure that describes the ‘behaviour’ of non-relativistic quantum theory, and discuss some advantages of this ‘quasi-structure’ to a classical one.
I consider the "Quantum Bayesian" view of quantum theory as expounded in a 2006 paper of Caves, Fuchs, and Schack. I argue that one can accept a generally personalist, decision-theoretic view of probability, including probability as manifested in quantum physics, while nevertheless accepting that in some situations, including some in quantum physics, probabilities may in a useful sense be thought of as objectively correct. This includes situations in which the ascription of a quantum state should be thought of as objectively correct. I argue that this does not cause any prima facie objectionable sort of action at a distance, though it may involve adopting the attitude that certain dispositional properties of things are not "localized" at those things. Whether this insouciant view of nonlocality and objectivity can survive more detailed analysis is a matter for further investigation.