dorsal/arxiv
View SchemaMaximum predictive power and the superposition principle
| Authors | Johann Summhammer |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9910039 |
| URL | https://arxiv.org/abs/quant-ph/9910039 |
Abstract
Recently, there has been a discussion on the origin of the quantum probability rules (Deutsch quant-ph/9906015, Polley quant-ph/9906124, Barnum et al. quant-ph/9907024, Finkelstein quant-ph/9907004). This contribution, which is a slightly reformulated version of a paper published in Int.J.Theor.Phys. 33, 171 (1994), points out the follwoing: To an experimenter the world is a persistent stream of discrete data. All that is certain is that with each observation he/she knows more than before, simply because he/she can now answer the question "Which of the possible outcomes have you just registered?", while this was not possible before the observation. One can ask whether this relentless increase of information entails a specific structure. In particular, how must different observations be related in order to ensure that predictions become ever more accurate, the more past observations serve as input? This leads to the quantum rule for adding the complex square roots of probabilities, and not to adding the probabilities themselves, as classical probability would have it.
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"abstract": "Recently, there has been a discussion on the origin of the quantum\nprobability rules (Deutsch quant-ph/9906015, Polley quant-ph/9906124, Barnum et\nal. quant-ph/9907024, Finkelstein quant-ph/9907004). This contribution, which\nis a slightly reformulated version of a paper published in Int.J.Theor.Phys.\n33, 171 (1994), points out the follwoing: To an experimenter the world is a\npersistent stream of discrete data. All that is certain is that with each\nobservation he/she knows more than before, simply because he/she can now answer\nthe question \"Which of the possible outcomes have you just registered?\", while\nthis was not possible before the observation. One can ask whether this\nrelentless increase of information entails a specific structure. In particular,\nhow must different observations be related in order to ensure that predictions\nbecome ever more accurate, the more past observations serve as input? This\nleads to the quantum rule for adding the complex square roots of probabilities,\nand not to adding the probabilities themselves, as classical probability would\nhave it.",
"arxiv_id": "quant-ph/9910039",
"authors": [
"Johann Summhammer"
],
"categories": [
"quant-ph"
],
"title": "Maximum predictive power and the superposition principle",
"url": "https://arxiv.org/abs/quant-ph/9910039"
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