dorsal/arxiv
View SchemaFoundations of quantum physics: a general realistic and operational approach
| Authors | Diederik Aerts |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0105109 |
| URL | https://arxiv.org/abs/quant-ph/0105109 |
| Journal | International Journal of Theoretical Physics, 38, 1999, 289 |
Abstract
We present a general formalism with the aim of describing the situation of an entity, how it is, how it reacts to experiments, how we can make statistics with it, and how it changes under the influence of the rest of the universe. Therefore we base our formalism on the following basic notions: (1) the states of the entity; they describe the modes of being of the entity, (2) the experiments that can be performed on the entity; they describe how we act upon and collect knowledge about the entity, (3) the probabilities; they describe our repeated experiments and the statistics of these repeated experiments, (4) the symmetries; they describe the interactions of the entity with the external world without being experimented upon. Starting from these basic notions we formulate the necessary derived notions: mixed states, mixed experiments and events, an eigen closure structure describing the properties of the entity, an ortho closure structure introducing an orthocomplementation, outcome determination, experiment determination, state determination and atomicity giving rise to some of the topological separation axioms for the closures. We define the notion of sub entity in a general way and identify the morphisms of our structure. We study specific examples in detail in the light of this formalism: a classical deterministic entity and a quantum entity described by the standard quantum mechanical formalism. We present a possible solution to the problem of the description of sub entities within the standard quantum mechanical procedure using the tensor product of the Hilbert spaces, by introducing a new completed quantum mechanics in Hilbert space, were new 'pure' states are introduced, not represented by rays of the Hilbert space.
{
"annotation_id": "c859ddd8-31e6-4fa9-91a6-a998359109cf",
"date_created": "2026-03-02T18:01:44.798000Z",
"date_modified": "2026-03-02T18:01:44.798000Z",
"file_hash": "efc26af0b2c5ad6703c1c9f5fa4cde0dfb9332c80ba515d099a8fb6b847f91e0",
"private": false,
"record": {
"abstract": "We present a general formalism with the aim of describing the situation of an\nentity, how it is, how it reacts to experiments, how we can make statistics\nwith it, and how it changes under the influence of the rest of the universe.\nTherefore we base our formalism on the following basic notions: (1) the states\nof the entity; they describe the modes of being of the entity, (2) the\nexperiments that can be performed on the entity; they describe how we act upon\nand collect knowledge about the entity, (3) the probabilities; they describe\nour repeated experiments and the statistics of these repeated experiments, (4)\nthe symmetries; they describe the interactions of the entity with the external\nworld without being experimented upon. Starting from these basic notions we\nformulate the necessary derived notions: mixed states, mixed experiments and\nevents, an eigen closure structure describing the properties of the entity, an\northo closure structure introducing an orthocomplementation, outcome\ndetermination, experiment determination, state determination and atomicity\ngiving rise to some of the topological separation axioms for the closures. We\ndefine the notion of sub entity in a general way and identify the morphisms of\nour structure. We study specific examples in detail in the light of this\nformalism: a classical deterministic entity and a quantum entity described by\nthe standard quantum mechanical formalism. We present a possible solution to\nthe problem of the description of sub entities within the standard quantum\nmechanical procedure using the tensor product of the Hilbert spaces, by\nintroducing a new completed quantum mechanics in Hilbert space, were new \u0027pure\u0027\nstates are introduced, not represented by rays of the Hilbert space.",
"arxiv_id": "quant-ph/0105109",
"authors": [
"Diederik Aerts"
],
"categories": [
"quant-ph"
],
"journal_ref": "International Journal of Theoretical Physics, 38, 1999, 289",
"title": "Foundations of quantum physics: a general realistic and operational approach",
"url": "https://arxiv.org/abs/quant-ph/0105109"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "ab41e415-eee7-44ca-89ba-f83c5f2bb4ff",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}