The fundamental constants and their variation: observational status and theoretical motivations

TL;DR

This paper surveys observational and experimental bounds on the possible time or space variation of fundamental constants, emphasizing dimensionless combinations such as $\alpha_{EM}$ and $\mu$ and detailing how metrology, atomic/nuclear physics, and cosmology contribute constraints. It discusses geological, laboratory, astrophysical, and cosmological probes, highlighting robust bounds from Oklo, atomic clocks, CMB, and BBN, while noting tensions and model dependencies in high-redshift claims. The work surveys theoretical motivations from Dirac’s hypotheses, grand unification, Kaluza–Klein, and string theories, focusing on how extra dimensions and scalar fields (dilaton/quintessence) could drive variations and episteme tests such as equivalence-principle constraints. The paper concludes that while some high-sensitivity results hint at possible variations, these are contingent on model assumptions and systematics, and a coherent, cross-validated interpretation requires integrating local tests with cosmological data and unified theories. It emphasizes the deep connections between fundamental physics, metrology, gravity, and cosmology, and notes that future measurements (e.g., from Planck, ACES, MICROSCOPE, STEP) will be crucial to confirm or refute potential variations and to illuminate the physics of extra dimensions and scalar fields.

Abstract

This article describes the various experimental bounds on the variation of the fundamental constants of nature. After a discussion on the role of fundamental constants, of their definition and link with metrology, the various constraints on the variation of the fine structure constant, the gravitational, weak and strong interactions couplings and the electron to proton mass ratio are reviewed. This review aims (1) to provide the basics of each measurement, (2) to show as clearly as possible why it constrains a given constant and (3) to point out the underlying hypotheses. Such an investigation is of importance to compare the different results, particularly in view of understanding the recent claims of the detections of a variation of the fine structure constant and of the electron to proton mass ratio in quasar absorption spectra. The theoretical models leading to the prediction of such variation are also reviewed, including Kaluza-Klein theories, string theories and other alternative theories and cosmological implications of these results are discussed. The links with the tests of general relativity are emphasized.

Figures (7)

• Figure 1: The cube of physical theories as presented by Okun (1991). At the origin stands the part of Newtonian mechanics (NM) that does not take gravity into account. NG, QM and SR then stand for Newtonian gravity, quantum mechanics and special relativity which respectively introduce the effect of one of the constants. Special relativity 'merges' respectively with quantum mechanics and Newtonian gravity to give quantum field theory (QFT) and general relativity (GR). Bringing quantum mechanics and Newtonian gravity together leads to non-relativistic quantum gravity and all theories together give the theory of everything (TOE). [From Okun (1991)].
• Figure 2: Sketch of the experimental and theoretical chain leading to the determination of the electron mass. Note that, as expected, the determination of $\alpha_{_{\rm EM}}$ requires no dimensional input. [From Mohr and Taylor (2001)].
• Figure 3: The standard orbital parameters. $a$ and $b$ is the semi-major and semi-minor axis, $c=ae$ the focal distance, $p$ the semi-latus rectum, $\theta$ the true anomaly. $F$ is the focus, $A$ and $B$ the periastron and apoastron (see e.g. Murray and Dermott, 2000). It is easy to check that $b^2=a^2(1-e^2)$ and that $p=a(1-e^2)$ and one defines the frequency or mean motion as $n=2\pi/P$ where $P$ is the period.
• Figure 4: Hyperfine structure of the $n=1$ level of the hydrogen atom. The fine structure Hamiltonian induces a shift of $-m_{\rm e}c^2\alpha_{_{\rm EM}}^4/8$ of the level $1s$. $J$ can only take the value $+1/2$. The hyperfine Hamiltonian (\ref{['hfH']}) induces a splitting of the level $1s_{1/2}$ into the two hyperfine levels $F=0$ and $F=+1$. The transition between these two levels corresponds to the 21 cm ray with $Ah^2=1,420,405,751.768\pm0.001$ Hz and is of first importance in astronomy.
• Figure 5: The correction function $F_{_{\rm rel}}$. [From Prestage et al. (1995)].