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A contextual Planck parameter and the classical limit in quantum cosmology
General Relativity and Quantum Cosmology · Submitted 29 Jun 2020
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim With this criterion, the classical limit is expected, not for regions larger than the Planck length, $l_{P}$, but for those larger than $l_{Q}=(l_{P}^{2}H^{-1})^{1/3}$, where $H$ is the Hubble parameter.
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We propose that whatever quantity controls the Heisenberg uncertainty relations (for a given complementary pair of observables) it should be identified with an effective Planck parameter. With this definition it is not difficult to find examples where the Planck parameter depends on the region under study, varies in time, and even depends on which pair of observables one focuses on. In quantum cosmology the effective Planck parameter depends on the size of the comoving region under study, and so depends on that chosen region and on time. With this criterion, the classical limit is expected, not for regions larger than the Planck length, $l_{P}$, but for those larger than $l_{Q}=(l_{P}^{2}H^{-1})^{1/3}$, where $H$ is the Hubble parameter. In theories where the cosmological constant is dynamical, it is possible for the latter to remain quantum even in contexts where everything else is deemed classical. These results are derived from standard quantization methods, but we also include more speculative cases where ad hoc Planck parameters scale differently with the length scale under observation. Even more speculatively, we examine the possibility that similar complementary concepts affect thermodynamical variables, such as the temperature and the entropy of a black hole.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We propose that whatever quantity controls the Heisenberg uncertainty relations (for a given complementary pair of observables) it should be identified with an effective Planck parameter. | contribution 0.96 | 0.55 | 0.18 | hedged possibility 0.44 |
| s1 | With this definition it is not difficult to find examples where the Planck parameter depends on the region under study, varies in time, and even depends on which pair of observables one focuses on. | result 0.45 | 0.73 | 0.08 | asserted 0.84 |
| s2 | In quantum cosmology the effective Planck parameter depends on the size of the comoving region under study, and so depends on that chosen region and on time. | result 0.84 | 0.62 | 0.13 | asserted 1.00 |
| s3 | With this criterion, the classical limit is expected, not for regions larger than the Planck length, $l_{P}$, but for those larger than $l_{Q}=(l_{P}^{2}H^{-1})^{1/3}$, where $H$ is the Hubble parameter. | result 0.72 | 0.72 | 0.62 | hedged possibility 0.67 |
| s4 | In theories where the cosmological constant is dynamical, it is possible for the latter to remain quantum even in contexts where everything else is deemed classical. | result 0.54 | 0.45 | 0.08 | hedged possibility 0.98 |
| s5 | These results are derived from standard quantization methods, but we also include more speculative cases where ad hoc Planck parameters scale differently with the length scale under observation. | method 0.84 | 0.90 | 0.06 | asserted 0.87 |
| s6 | Even more speculatively, we examine the possibility that similar complementary concepts affect thermodynamical variables, such as the temperature and the entropy of a black hole. | contribution 0.68 | 0.74 | 0.03 | speculative 0.95 |
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Original abstract
We propose that whatever quantity controls the Heisenberg uncertainty relations (for a given complementary pair of observables) it should be identified with an effective Planck parameter. With this definition it is not difficult to find examples where the Planck parameter depends on the region under study, varies in time, and even depends on which pair of observables one focuses on. In quantum cosmology the effective Planck parameter depends on the size of the comoving region under study, and so depends on that chosen region and on time. With this criterion, the classical limit is expected, not for regions larger than the Planck length, $l_{P}$, but for those larger than $l_{Q}=(l_{P}^{2}H^{-1})^{1/3}$, where $H$ is the Hubble parameter. In theories where the cosmological constant is dynamical, it is possible for the latter to remain quantum even in contexts where everything else is deemed classical. These results are derived from standard quantization methods, but we also include more speculative cases where ad hoc Planck parameters scale differently with the length scale under observation. Even more speculatively, we examine the possibility that similar complementary concepts affect thermodynamical variables, such as the temperature and the entropy of a black hole.
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References
How the literature uses it
8 arXiv papers cite this in 10 sentences
Papers citing it · 8 sentences without a confident label
Cites it as background 2 papers
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For a physical interpretation of such an effective Planck's constant, see [ref] .
Lorentzian quantum cosmology with torsion · Inflationary scenario · 0.80
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Finally, Barrow entropy has been studied in the black-hole context in [ref] .
Big Bang Nucleosynthesis constraints on Barrow entropy · Introduction · 1.00
What it cites · 4 sentences without a confident label
Compares with 1 paper
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Whilst our result is more general (it does not depend on the concrete dynamics) the work of [ref] , precisely for being less general, is more concrete, and even derives wave functions for the Universe incorporating this scale.]
A Mesoscopic Quantum Gravity Effect · Planck's parameter in standard quantum cosmology · 0.98
Cites as background 1 paper
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The true hallmark of quantum behaviour is the impossibility of jointly measuring complementary observables, usually (but not always) resulting from their non-commutativity and associated Heisenberg uncertainty relations [ref] .
No Return to Classical Reality · Introduction · 0.86
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