Built on

L. Perivolaropoulos and L. Kazantzidis, Hints of modified gravity in cosmos and in the lab?
Original
1904
Earlier work this paper cites.
M. J. Lake, A Solution to the Soccer Ball Problem for Generalized Uncertainty Relations
Original
1912
Earlier work this paper cites.
M. J. Lake, M. Miller and S. D. Liang, Generalised uncertainty relations for angular momentum and spin in quantum geometry
Original
1912
Earlier work this paper cites.
L. D. Landau and E. M. Lifshitz, Mechanics
1960
Earlier work this paper cites.
C. Bambi and F. R. Urban, Natural extension of the Generalised Uncertainty Principle
Original
1965
Earlier work this paper cites.
T. Padmanabhan, Physical significance of the Planck length
1985
Earlier work this paper cites.
J. Madore, Fuzzy physics
1992
Earlier work this paper cites.
C. J. Isham, Lectures on Quantum Theory: Mathematical and Structural Foundations
1995
Earlier work this paper cites.
S. Weinberg, The Quantum theory of fields. Vol. 1: Foundations
1995
Earlier work this paper cites.
L. J. Garay, Quantum gravity and minimum length
1995
Earlier work this paper cites.
S. Doplicher, K. Fredenhagen and J. E. Roberts, The Quantum structure of space-time at the Planck scale and quantum fields
1995
Earlier work this paper cites.
A. Kempf, G. Mangano and R. B. Mann, Hilbert space representation of the minimal length uncertainty relation
1995
Earlier work this paper cites.

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Then

M. Bishop, J. Contreras, J. Lee and D. Singleton, Reconciling a quantum gravity minimal length with lack of photon dispersion
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R. Gambini and J. Pullin, A First Course in Loop Quantum Gravity
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P. Nicolini and B. Niedner, Hausdorff dimension of a particle path in a quantum manifold
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2020

Why space could be quantised on a different scale to matter

Lake, Matthew J.

Understand

The scale of quantum mechanical effects in matter is set by Planck's constant, $\hbar$.

This represents the quantisation scale for material objects.
In this article, we present a simple argument why the quantisation scale for space, and hence for gravity, may not be equal to $\hbar$.
Indeed, assuming a single quantisation scale for both matter and geometry leads to the `worst prediction in physics', namely, the huge difference between the observed and predicted vacuum energies.

Built on

L. Perivolaropoulos and L. Kazantzidis, Hints of modified gravity in cosmos and in the lab?
Original
1904
Earlier work this paper cites.
M. J. Lake, A Solution to the Soccer Ball Problem for Generalized Uncertainty Relations
Original
1912
Earlier work this paper cites.
M. J. Lake, M. Miller and S. D. Liang, Generalised uncertainty relations for angular momentum and spin in quantum geometry
Original
1912
Earlier work this paper cites.
L. D. Landau and E. M. Lifshitz, Mechanics
1960
Earlier work this paper cites.
C. Bambi and F. R. Urban, Natural extension of the Generalised Uncertainty Principle
Original
1965
Earlier work this paper cites.
T. Padmanabhan, Physical significance of the Planck length
1985
Earlier work this paper cites.
J. Madore, Fuzzy physics
1992
Earlier work this paper cites.
C. J. Isham, Lectures on Quantum Theory: Mathematical and Structural Foundations
1995
Earlier work this paper cites.
S. Weinberg, The Quantum theory of fields. Vol. 1: Foundations
1995
Earlier work this paper cites.
L. J. Garay, Quantum gravity and minimum length
1995
Earlier work this paper cites.
S. Doplicher, K. Fredenhagen and J. E. Roberts, The Quantum structure of space-time at the Planck scale and quantum fields
1995
Earlier work this paper cites.
A. Kempf, G. Mangano and R. B. Mann, Hilbert space representation of the minimal length uncertainty relation
1995
Earlier work this paper cites.

Similar

R. Penrose, On gravity’s role in quantum state reduction
1996
Cited alongside, same era.
T. Frankel, The geometry of physics: An introduction
1997
Cited alongside, same era.
R. J. Adler and D. I. Santiago, On gravity and the uncertainty principle
1999
Cited alongside, same era.
F. Scardigli, Generalized uncertainty principle in quantum gravity from micro - black hole Gedanken experiment
1999
Cited alongside, same era.
A. I. M. Rae, Quantum Mechanics
2002
Cited alongside, same era.
A. Krishak and S. Desai, Model Comparison tests of modified gravity from the Eöt-Wash experiment
Original
2003
Cited alongside, same era.

Then

M. Bishop, J. Contreras, J. Lee and D. Singleton, Reconciling a quantum gravity minimal length with lack of photon dispersion
Original
2009
Later among the works it cites.
R. Gambini and J. Pullin, A First Course in Loop Quantum Gravity
2011
Later among the works it cites.
P. Nicolini and B. Niedner, Hausdorff dimension of a particle path in a quantum manifold
Original
2011
Later among the works it cites.
J. Martin, Everything You Always Wanted To Know About The Cosmological Constant Problem (But Were Afraid To Ask)
Original
2012
Later among the works it cites.
S. Hossenfelder, Minimal Length Scale Scenarios for Quantum Gravity
Original
2013
Later among the works it cites.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

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M. A. Pinsky, Introduction to Fourier analysis and wavelets

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M. J. Lake, A New Approach to Generalised Uncertainty Relations

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2008

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See https://www.pbs.org/wgbh/nova/article/are-space-and-time-discrete-or-continuous/, and references therein, for interesting discussions of this point

Cited in the paper.

A. N. Tawfik and A. M. Diab, Generalized Uncertainty Principle: Approaches and Applications

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2014

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P. Burikham, K. Cheamsawat, T. Harko and M. J. Lake, The minimum mass of a spherically symmetric object in D D -dimensions, and its implications for the mass hierarchy problem

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N. Aghanim et al

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2018