Modified Newtonian Dynamics as an Entropic Force


Under natural assumptions on the thermodynamic properties of space and time with the holo-graphic principle, we reproduce a MOND-like behaviour of gravity on particular scales of mass and length, where Newtonian gravity requires a modification or extension if no dark matter component is introduced in the description of gravitational phenomena. The result is directly obtained with the assumption that a fundamental constant of nature with dimensions of acceleration needs to be introduced into gravitational interactions. This in turn allows for modifications or extensions of the equipartion law and/or the holographic principle. In other words, MOND-like phenomenology can be reproduced when appropriate generalised concepts at the thermodynamical level of space and/or at the holographic principle are introduced. Thermodynamical modifications are reflected in extensions to the equipartition law which occur when the temperature of the system drops below a critical value, equals to Unruh’s temperature evaluated at the acceleration constant scale introduced for the description of the gravitational phenomena. Our calculations extend the ones by [1] in which Newtonian gravity is shown to be an emergent phenomenon, and together with it reinforces the idea that gravity at all scales is emergent.

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Carranza, D. and Mendoza, S. (2015) Modified Newtonian Dynamics as an Entropic Force. Journal of Modern Physics, 6, 786-793. doi: 10.4236/jmp.2015.66084.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Verlinde, E. (2011) Journal of High Energy Physics, 4, 29.
[2] Bekenstein, J.D. (1973) Physical Review D, 7, 2333-2346.
[3] Bekenstein, J.D. (1974) Physical Review D, 9, 3292-3300.
[4] Bardeen, J.M., Carter, B. and Hawking, S.W. (1973) Communications in Mathematical Physics, 31, 161-170.
[5] Hawking, S.W. (1974) Nature (London), 248, 30-31.
[6] Townsend, P.K. (1997) Black Holes. ArXiv General Relativity and Quantum Cosmology e-Prints.
[7] Padmanabhan, T. (2010) Reports on Progress in Physics, 73, Article ID: 046901.
[8] Jacobson, T. (1995) Physical Review Letters, 75, 1260-1263.
[9] Hernandez, X. and Jimenez, M.A. (2012) Astrophysical Journal, 750, 9.
[10] Hernandez, X., Jimenez, M.A. and Allen, C. (2012) European Physical Journal C, 72, 1884.
[11] Mastropietro, C. and Burkert, A. (2008) Monthly Notices of the Royal Astronomical Society, 389, 967-988.
[12] Lee, J. and Komatsu, E. (2010) The Astrophysical Journal, 718, 60-65.
[13] Thompson, R. and Nagamine, K. (2012) Monthly Notices of the Royal Astronomical Society, 419, 3560-3570.
[14] Moffat, J.W. and Toth, V.T. (2010) Can Modified Gravity (MOG) Explain the Speeding Bullet (Cluster)?
[15] Mendoza, S., Hernandez, X., Hidalgo, J.C. and Bernal, T. (2011) Monthly Notices of the Royal Astronomical Society, 411, 226-234.
[16] Milgrom, M. (1982) The Astrophysical Journal, 270, 371-389.
[17] Bernal, T., Capozziello, S., Hidalgo, J.C. and Mendoza, S. (2011) European Physical Journal C, 71, 1794.
[18] Carranza, D.A., Mendoza, S. and Torres, L.A. (2013) European Physical Journal C, 73, 2282.
[19] Mendoza, S., Bernal, T., Hernandez, X., Hidalgo, J.C. and Torres, L.A. (2013) Monthly Notices of the Royal Astronomical Society, 433, 1802-1812.
[20] Sheykhi, A. and Sarab, K.R. (2012) Journal of Cosmology and Astroparticle Physics, 2012, 12.
[21] Sedov, L.I. (1959) Similarity and Dimensional Methods in Mechanics. Academic Press, Waltham.
[22] Famaey, B. and McGaugh, S.S. (2012) Living Reviews in Relativity, 15, 10.
[23] Mendoza, S. (2011) Extending Cosmology: The Metric Approach.
[24] Mendoza, S. and Olmo, G. (2012) Living Reviews in Relativity, 15, 10.
[25] Will, C.M. (1992) Theory and Experiment in Gravitational Physics. Cambridge University Press, Cambridge.
[26] Pazy, E. and Argaman, N. (2012) Physical Review D, 85, Article ID: 104021.

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