The Compton-Schwarzschild correspondence from extended de Broglie relations

2017

J. Phys.: Conf. Ser.

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In the early-mid 20 th century Dirac and Zel'dovich were among the first scientists to suggest an intimate connection between cosmology and atomic physics. Though a revolutionary proposal for its time, Dirac's Large Number Hypothesis (1937) adopted a standard assumption of the day, namely, the non-existence of the cosmological constant term (Λ = 0). As a result, its implementation necessitated extreme violence to the theory of general relativity -something few physicists were prepared to sacrifice in favour of 'numerology' -requiring a time-dependent gravitational coupling of the form G(t) ∼ 1/t. Zel'dovich's insight (1968) was to realise that a small but nonzero cosmological term (Λ > 0) allowed the present day radius of the Universe to be identified with the de Sitter radius, rU l dS 1/ √ Λ, which removed the need for time-dependence in the fundamental couplings. Thus, he obtained the formula Λ m 6 G 2 / 4 , where m is a mass scale characterising the relative strengths of the gravitational and electromagnetic interactions, which he identified with the proton mass mp. In this paper, we review a number of recent arguments which, instead, suggest the identification m = me/αe, where me is the electron mass and αe = e 2 / c 1/137 is the usual fine structure constant. We note that these are of a physical nature and, therefore, represent an attempt to lift previous argumentsà la Dirac from the realm of numerology into the realm of empirical science. If valid, such arguments suggest an intimate connection, not only between the macroscopic and microscopic worlds, but, perhaps even more surprisingly, between the very essence of "dark" and "light" physics.

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Is there a connection between “dark” and “light” physics?

2017

J. Phys.: Conf. Ser.

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“…Though tentative, an identification of the form (109) in the super-Planck mass regime would provide a concrete realisation of the BHUP correspondence, but not one based on modified de Broglie relations applied to fixed-background states [81][82][83][84], or on the inclusion of gravitational torsion [87][88][89], as in previous approaches.…”

Section: B the Bhup Correspondencementioning

confidence: 99%

Generalised uncertainty relations from superpositions of geometries

Miller

Ganardi

et al. 2019

Class. Quantum Grav.

198

Phenomenological approaches to quantum gravity implement a minimum resolvable length-scale but do not link it to an underlying formalism describing geometric superpositions. Here, we introduce an intuitive approach in which points in the classical spatial background are delocalised, or 'smeared', giving rise to an entangled superposition of geometries. The model uses additional degrees of freedom to parameterise the superposed classical backgrounds. Our formalism contains both minimum length and minimum momentum resolutions and we naturally identify the former with the Planck length. In addition, we argue that the minimum momentum is determined by the de Sitter scale, and may be identified with the effects of dark energy in the form of a cosmological constant. Within the new formalism, we obtain both the generalised uncertainty principle (GUP) and extended uncertainty principle (EUP), which may be combined to give an uncertainty relation that is symmetric in position and momentum. Crucially, our approach does not imply a significant modification of the positionmomentum commutator, which remains proportional to the identity matrix. It therefore yields generalised uncertainty relations without violating the equivalence principle, in contradistinction to existing models based on nonlinear dispersion relations. Implications for cosmology and the black hole uncertainty principle correspondence are briefly discussed, and prospects for future work on the smeared-space model are outlined.

“…One way of obtaining a smooth transition between the Compton and Schwarzschild lines is to invoke some connection between the uncertainty principle on microscopic scales and black holes on macroscopic scales. This is termed the Black Hole Uncertainty Principle (BHUP) correspondence [10] and also the Compton-Schwarzschild correspondence when discussing an interpretation in terms of extended de Broglie relations [11]. It is manifested in a unified expression for the Compton wavelength and Schwarzschild radius.…”

Section: Introductionmentioning

confidence: 99%

Does Compton–Schwarzschild duality in higher dimensions exclude TeV quantum gravity?

Carr

2018

Int. J. Mod. Phys. D

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In three spatial dimensions, the Compton wavelength (R C ∝ M −1 ) and Schwarzschild radius (R S ∝ M ) are dual under the transformation M → M 2 P /M , where M P is the Planck mass. This suggests that there could be a fundamental link -termed the Black Hole Uncertainty Principle or Compton-Schwarzschild correspondence -between elementary particles with M < M P and black holes in the M > M P regime. In the presence of n extra dimensions, compactified on some scale R E exceeding the Planck length R P , one expects R S ∝ M 1/(1+n) for R P < R < R E , which breaks this duality. However, it may be restored in some circumstances because the effective Compton wavelength of a particle depends on the form of the (3 + n)-dimensional wavefunction. If this is spherically symmetric, then one still has R C ∝ M −1 , as in the 3-dimensional case. The effective Planck length is then increased and the Planck mass reduced, allowing the possibility of TeV quantum gravity and black hole production at the LHC. However, if the wave function of a particle is asymmetric and has a scale R E in the extra dimensions, then R C ∝ M −1/(1+n) , so that the duality between R C and R S is preserved. In this case, the effective Planck length is increased even more but the Planck mass is unchanged, so that TeV quantum gravity is precluded and black holes cannot be generated in collider experiments. Nevertheless, the extra dimensions could still have consequences for the detectability of black hole evaporations and the enhancement of pair-production at accelerators on scales below R E . Though phenomenologically general for higher-dimensional theories, our results are shown to be consistent with string theory via the minimum positional uncertainty derived from D-particle scattering amplitudes.