Let's talk about varying G

Abstract

It is possible that fundamental constants may not be constant at all. There is a generally accepted view that one can only talk about variations of dimensionless quantities, such as the fine structure constant ${\alpha }_{\mathrm{e}}\equiv e^2/4\pi {\epsilon }_0\hslash c$. However, constraints on the strength of gravity tend to focus on G itself, which is problematic. We stress that G needs to be multiplied by the square of a mass, and hence, for example, one should be constraining ${\alpha }_{\mathrm{g}}\equiv G{m}_{\mathrm{p}}^2/\hslash c$, where $m_{\mathrm{p}}$ is the proton mass. Failure to focus on such dimensionless quantities makes it difficult to interpret the physical dependence of constraints on the variation of G in many published studies. A thought experiment involving talking to observers in another universe about the values of physical constants may be useful for distinguishing what is genuinely measurable from what is merely part of our particular system of units.

6 pages, Gravity Research Foundation essay

References in corpus (4)

• Primordial Nucleosynthesis: from precision cosmology to fundamental physics
• Revision of VLT/UVES constraints on a varying fine-structure constant
• From Cavendish to PLANCK: Constraining Newton's Gravitational Constant with CMB Temperature and Polarization Anisotropy
• Constraints on time variation of fine structure constant from WMAP-3yr data