Built on

A. G. Riess, S. Casertano, W. Yuan, L. M. Macri, and D. Scolnic, Astrophys. J. 876
Original
1903
Earlier work this paper cites.
J. A. Helayël-Neto and A. D. A. M. Spallicci, Eur. Phys. J. C 79
Original
1904
Earlier work this paper cites.
S. Capozziello, R. D’Agostino, and O. Luongo, Int. J. Mod. Phys. D 28
Original
1904
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1939
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Similar

E. R. Williams, J. E. Faller, and H. A. Hill, Phys. Rev. Lett. 26
1971
Cited alongside, same era.
D. H. Kobe and V. C. Aguilera-Navarro, Phys. Rev. A 50
1994
Cited alongside, same era.
S. Capozziello, R. D’Agostino, and O. Luongo, Mon. Not. Roy. Astron. Soc. 494
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2003
Cited alongside, same era.
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Cited alongside, same era.
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Original
2005
Cited alongside, same era.
S. Capozziello, M. Benetti, and A. D. A. M. Spallicci, Found. Phys. 50

Then

A. Retinò, A. D. A. M. Spallicci, and A. Vaivads, Astropart. Phys. 82
Original
2016
Later among the works it cites.
L. Bonetti, J. Ellis, N. E. Mavromatos, A. S. Sakharov, E. K. Sarkisian-Grinbaum, and A. D. A. M. Spallicci, Phys. Lett. B 757
2016
Later among the works it cites.
M. J. Bentum, L. Bonetti, and A. D. A. M. Spallicci, Adv. Space Res. 59
Original
2017
Later among the works it cites.
M. Sahlén, The philosophy of cosmology (Cambridge University Press, Cambridge, 2017), chap. On probability and cosmology: inference beyond data?, p. 429, K. Chamcham, J. Silk, J. Barrow, S. Saunders (Eds.), eprint arXiv:1812.04149 [physics.hist-ph]
Original
2017
Later among the works it cites.
International Astronomical Union, Resolution B4 on a suggested renaming of the Hubble law , https://www.iau.org/news/pressreleases/detail/iau1812/ (2018), XXX General Assembly, August 2018, Wien

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2021

The Heisenberg limit at cosmological scales

Spallicci, Alessandro D. A. M., Benetti, Micol, Capozziello, Salvatore

Understand

For an observation time {equal to} the universe age, the Heisenberg principle fixes the value of the smallest measurable mass at $m_{\rm H}=1.35 \times 10^{-69}$ kg and prevents to probe the masslessness for any particle using a balance.

The corresponding reduced Compton length to $m_{\rm H}$ is $\lambdabar_{\rm H}$, and represents the length limit beyond which masslessness cannot be proved using a metre ruler.
In turns, $\lambdabar_{\rm H}$ is equated to the luminosity distance $d_{\rm H}$ which corresponds to a red shift $z_{\rm H}$.
When using the Concordance-Model parameters, we get $d_{\rm H} = 8.4$ Gpc and $z_{\rm H}=1.3$.

Built on

A. G. Riess, S. Casertano, W. Yuan, L. M. Macri, and D. Scolnic, Astrophys. J. 876
Original
1903
Earlier work this paper cites.
J. A. Helayël-Neto and A. D. A. M. Spallicci, Eur. Phys. J. C 79
Original
1904
Earlier work this paper cites.
S. Capozziello, R. D’Agostino, and O. Luongo, Int. J. Mod. Phys. D 28
Original
1904
Earlier work this paper cites.
N. Xing, H. Gao, J.-J. Wei, Z. Li, W. Wang, B. Zhang, X. Wu, and P. Mészáros, Astrophys. J. Lett. 882
Original
1907
Earlier work this paper cites.
L. de Broglie, J. Phys. et Radium 3
1922
Earlier work this paper cites.
L. de Broglie, Comptes Rendus Hebd. Séances Acad. Sci. Paris 177
1923
Earlier work this paper cites.
L. de Broglie, Recherches sur la théorie des quanta (Masson & C ie , Paris, 1924), Doctorate thesis (Dir. P. Langevin) Université de Paris, Sorbonne
1924
Earlier work this paper cites.
W. Heisenberg, Zeitschr. Phys. 43
1927
Earlier work this paper cites.
M. L. Humason, Proc. Nat. Ac. Sci. U.S.A. 15
1929
Earlier work this paper cites.
M. L. Humason, Astrophys. J. 74
1931
Earlier work this paper cites.
E. Hubble and M. L. Humason, Astrophys. J. 74
1931
Earlier work this paper cites.
L. de Broglie, Nouvelles Recherches sur la Lumière , vol. 411 of Actualités Scientifiques et Industrielles (Hermann & C ie , Paris, 1936)
1936
Earlier work this paper cites.
M. Fierz and W. Pauli, Proc. Roy. Soc. London A: Math. Phys. Sci. 173
1939
Earlier work this paper cites.
E. Schrödinger, Proc. Royal Irish Acad. A 49
1943
Earlier work this paper cites.
W. H. McCrea, Nat. 186
1960
Earlier work this paper cites.
L. E. Ballentine, Rev. Mod. Phys. 42
1970
Earlier work this paper cites.

Similar

E. R. Williams, J. E. Faller, and H. A. Hill, Phys. Rev. Lett. 26
1971
Cited alongside, same era.
D. H. Kobe and V. C. Aguilera-Navarro, Phys. Rev. A 50
1994
Cited alongside, same era.
S. Capozziello, R. D’Agostino, and O. Luongo, Mon. Not. Roy. Astron. Soc. 494
Original
2003
Cited alongside, same era.
S. R. Choudury, G. C. Joshi, S. Mahajan, and B. H. J. McKellar, Astropart. Phys. 21
2004
Cited alongside, same era.
M. Moussa, H. Shababi, A. Rahaman, and U. Kumar Dey, Phys. Lett. B. 820
Original
2005
Cited alongside, same era.
S. Capozziello, M. Benetti, and A. D. A. M. Spallicci, Found. Phys. 50

Then

A. Retinò, A. D. A. M. Spallicci, and A. Vaivads, Astropart. Phys. 82
Original
2016
Later among the works it cites.
L. Bonetti, J. Ellis, N. E. Mavromatos, A. S. Sakharov, E. K. Sarkisian-Grinbaum, and A. D. A. M. Spallicci, Phys. Lett. B 757
2016
Later among the works it cites.
M. J. Bentum, L. Bonetti, and A. D. A. M. Spallicci, Adv. Space Res. 59
Original
2017
Later among the works it cites.
M. Sahlén, The philosophy of cosmology (Cambridge University Press, Cambridge, 2017), chap. On probability and cosmology: inference beyond data?, p. 429, K. Chamcham, J. Silk, J. Barrow, S. Saunders (Eds.), eprint arXiv:1812.04149 [physics.hist-ph]
Original
2017
Later among the works it cites.
International Astronomical Union, Resolution B4 on a suggested renaming of the Hubble law , https://www.iau.org/news/pressreleases/detail/iau1812/ (2018), XXX General Assembly, August 2018, Wien

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Original

2007

Cited alongside, same era.

W. Yang, E. Di Valentino, S. Pan, and O. Mena, Phys. Dark En. 31

Original

2007

Cited alongside, same era.

P. Busch, T. Heinonen, and P. Lahti, Phys. Rep. 452

2007

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E. Di Valentino, L. A. Anchordoqui, Ö. Akarsu, Y. Ali-Haimoud, L. Amendola, N. Arendse, M. Asgari, M. Ballardini, S. Basilakos, E. Battistelli, et al., Astropart. Phys. 131

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2008

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P. Busch, Time in quantum mechanics (Springer-Verlag, Berlin, 2008), chap. The energy-time uncertainty relation, p. 73, Lecture Notes in Physics n. 734, J. G. Muga, R. Sala Mayato, I. L. Egusquiza (Eds.), eprint arXiv:quant-ph/0105049

2008

Cited alongside, same era.

A. Scharff Goldhaber and M. M. Nieto, Rev. Mod. Phys. 82

2010

Cited alongside, same era.

R. Amanullah, C. Lidman, D. Rubin, G. Aldering, P. Astier, K. Barbary, M. S. Burns, A. Conley, K. S. Dawson, S. E. Deustua, et al., Astrophys. J. 716

Original

2010

Cited alongside, same era.

2018

Later among the works it cites.

L. Bonetti, L. R. dos Santos Filho, J. A. Helayël-Neto, and A. D. A. M. Spallicci, Eur. Phys. J. C 78