dorsal/arxiv
View SchemaInvariants of Elementary Observations
| Authors | Johann Summhammer |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0008098 |
| URL | https://arxiv.org/abs/quant-ph/0008098 |
Abstract
As physics searches for invariants in observations, this paper looks for invariants of probabilistic observation without assuming physical structure. Structure emerges from the basic assumption of science that new information shall lead to more accurate knowledge of the invariants. This leads to statistically unique random variables for expressing observed information: Complex probability amplitudes. Predictions are also just random variables computed from observed data, and must become more accurate with more observations as input. This singles out the quantum mechanical superposition principle. The external conditions of a probabilistic experiment can themselves be monitored at the most detailed level, resulting in observation of coicidence probabilities. The invariants of any multi-coincidence experiment are the same as those of a one-event experiment with the same number of possible outcomes. An observable probability turns out to be controllable by two independent experimental conditions, naturally parametrized as a direction in a 3-dimensional space. In summary, the probabilistic paradigm itself defines a unique method of forming concepts and making predictions. The method appears irrefutable within probability, because, whenever a prediction turns out wrong the existence of an as yet unmonitored condition is postulated, and a formal way to incoroporate it is shown. The Hilbert space formalism of quantum theory seems to be isomorphic to this method.
{
"annotation_id": "b268777d-bdc3-4c27-8770-3d5a2c497555",
"date_created": "2026-03-02T18:01:39.100000Z",
"date_modified": "2026-03-02T18:01:39.100000Z",
"file_hash": "9307ee76a043553633d50ea81c7dff6a541b33687fa90921ee1ad2960aa000e9",
"private": false,
"record": {
"abstract": "As physics searches for invariants in observations, this paper looks for\ninvariants of probabilistic observation without assuming physical structure.\nStructure emerges from the basic assumption of science that new information\nshall lead to more accurate knowledge of the invariants. This leads to\nstatistically unique random variables for expressing observed information:\nComplex probability amplitudes. Predictions are also just random variables\ncomputed from observed data, and must become more accurate with more\nobservations as input. This singles out the quantum mechanical superposition\nprinciple. The external conditions of a probabilistic experiment can themselves\nbe monitored at the most detailed level, resulting in observation of coicidence\nprobabilities. The invariants of any multi-coincidence experiment are the same\nas those of a one-event experiment with the same number of possible outcomes.\nAn observable probability turns out to be controllable by two independent\nexperimental conditions, naturally parametrized as a direction in a\n3-dimensional space. In summary, the probabilistic paradigm itself defines a\nunique method of forming concepts and making predictions. The method appears\nirrefutable within probability, because, whenever a prediction turns out wrong\nthe existence of an as yet unmonitored condition is postulated, and a formal\nway to incoroporate it is shown. The Hilbert space formalism of quantum theory\nseems to be isomorphic to this method.",
"arxiv_id": "quant-ph/0008098",
"authors": [
"Johann Summhammer"
],
"categories": [
"quant-ph"
],
"title": "Invariants of Elementary Observations",
"url": "https://arxiv.org/abs/quant-ph/0008098"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "1c066c4e-276d-45b7-a16f-d2e78206bfba",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}