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Gravity at Small Distances

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Gravity, Strings and Particles

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Abstract

Among all fundamental forces of Nature, gravity is probably the one we think we know better—if only because it is the one which has always influenced our experience and our way of life, since the beginning of the human history.

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Notes

  1. 1.

    For those who are expert of physics it will be clear that I am referring to the quantum “loop” corrections, described by a series of Feynman graphs of increasing accuracy and complexity.

  2. 2.

    The interested reader can find a description of such experiments in the review paper by Adelberger et al. [4].

  3. 3.

    It was a paper by Fischbach et al. [5].

  4. 4.

    At least, to the best of our present knowledge.

  5. 5.

    See for instance the paper by Barbieri and Cecotti [6].

  6. 6.

    In the case of the Bose–Einstein statistics there is no limit to the number of particles that can occupy the same quantum state. In the case of the Fermi–Dirac statistic, on the contrary, two or more particles cannot occupy the same quantum state (according to the so-called Pauli exclusion principle).

  7. 7.

    The search of supersymmetric particles is one of the main goals of the experiments performed using the powerful accelerator LHC at the CERN laboratories in Geneva. At the time of writing (March 2013), however, no positive result has yet been reported.

  8. 8.

    The existence of these particles was theoretically predicted by S. Glashow, S. Weinberg, and A. Salam. The final experimental confirmation is due to C. Rubbia and S. van de Meer. All these physicists have been subsequently awarded the Nobel Prize in Physics.

  9. 9.

    More precisely, the graviphoton is coupled to the so-called hypercharge, defined by adding to the baryonic charge other elementary charges characterizing the different species of quarks (which are the elementary components of protons and neutrons). Such additional charges, however, are vanishing for the typical atomic nuclei of ordinary matter.

  10. 10.

    For a consistent supersymmetric model, in fact, all particles belonging to the same multiplet should be characterized by the same mass. Hence, in the exact supersymmetric regime, the mass of the graviphoton should be the same as the graviton mass (which is zero). When supersymmetry is broken, on the contrary, a mass difference is generated even among the particles of the same multiplet.

  11. 11.

    See for instance an old paper I wrote in 1989 [7].

  12. 12.

    I have discussed this possibility in a paper written in 2001 [8].

  13. 13.

    A scalar particle is represented by a mathematical function that has only one component, which is left invariant under a general change of coordinates. A vector particle, instead, is represented by a function with many components, transforming as the components of a vector under a coordinate transformation.

  14. 14.

    See in particular a paper by Taylor and Veneziano [9].

  15. 15.

    If the dilaton mass is larger than this limit then the dilaton lifetime becomes smaller than present age of the Universe. All the dilatons copiously produced immediately after the Big Bang thus decay (into photons) before reaching the present epoch, and there is today no relic dilaton background waiting for a possible detection.

  16. 16.

    The possible existence of a cosmic background of relic dilatons was first suggested and studied by Gasperini and Veneziano (see, e.g., [10]).

  17. 17.

    See for instance the paper by Khoury and Weltman [11].

  18. 18.

    See the paper by Sundrum [12].

  19. 19.

    Usually the infinities appearing in the quantum regime can be eliminated by applying the so-called “renormalization” procedure. In the case of general relativity such a procedure does not work.

  20. 20.

    In fact, as already mentioned in Chap. 1, the Heisenberg principle tells us that, in a quantum context, the energy exchanges are inversely proportional to the involved distances.

  21. 21.

    The search for new additional spatial dimensions is one of the main goals of the big accelerator LHC at the CERN laboratories, near Geneva. At the time of writing (March 2013) no positive result has yet been reported. A final absence of signals would imply that the additional dimensions, if present, may become visible only at energies higher than the maximum values accessible to LHC (i.e., about 14 TeV).

  22. 22.

    The gauge symmetry is a property ensuring that the electric and magnetic fields remain unchanged under suitable transformations of the electromagnetic potential.

  23. 23.

    Two (or more) symmetry transformations are called Abelian if they give the same result regardless of the order in which they are performed. Otherwise they are called “non-Abelian.”

  24. 24.

    See for instance the paper by Arkani Hamed et al. [14], and the paper by Antoniadis [15].

  25. 25.

    Presented in a famous paper by Randall and Sundrum [16].

  26. 26.

    In the case of the Kaluza–Klein models, instead, the mass spectrum is discrete (see Sect. 2.3.1).

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  1. Dipartimento di Fisica, Università di Bari, Bari, Italy

    Maurizio Gasperini

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  1. Maurizio Gasperini
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Gasperini, M. (2014). Gravity at Small Distances. In: Gravity, Strings and Particles. Springer, Cham. https://doi.org/10.1007/978-3-319-00599-7_2

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