Derivation of the deformed Heisenberg algebra from discrete spacetime
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Bibliographic record
Abstract
Abstract Although the deformation of the Heisenberg algebra by a minimal length has become a central tool in quantum gravity phenomenology, it has never been rigorously obtained and is often derived using heuristic reasoning. In this study, we move beyond the heuristic derivation of the deformed Heisenberg algebra and explicitly derive it using a model of discrete spacetime, which is motivated by quantum gravity. Initially, we investigate the effects of the leading order Planckian lattice corrections and demonstrate that they precisely match those suggested by the heuristic arguments commonly used in quantum gravity phenomenology. Furthermore, we rigorously obtain deformations from the higher-order Planckian lattice corrections. In contrast to the leading-order corrections, these higher-order corrections are model dependent. We select a specific model that breaks the rotational symmetry, as the importance of such rotational symmetry breaking lies in the relationship between CMB anisotropies and quantum gravitational effects. Based on the mathematical similarity of the Planckian lattice used here with the graphene lattice, we propose that graphene can serve as an analogue system for the study of quantum gravity. Finally, we examine the deformation of the covariant form of the Heisenberg algebra using a four-dimensional Euclidean lattice.
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Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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