# Varying fundamental constants

The presumed constant nature of fundamental physical quantities such as the fine structure constant,

$\alpha \equiv \frac{e^2}{(4 \pi \epsilon_0) \hbar c} \approx \frac{1}{137.036}$

and the proton-to-electron mass ratio,

$\mu\equiv \frac{m_{\rm p}}{m_{\rm e}} \approx 1836.153$

have recently come under experimental scrutiny. These dimensionless quantities are essentially coupling constants. $\alpha$ determines the strength of the electromagnetic force and consequently the strength of interaction between charged particles and light; $\mu$ is sensitive to the strength of the strong force.

The Standard Model of particle physics relies on precise experimental measurement of coupling constants and does not predict or guarantee their constancy. Positive detection of variation of fundamental constants may help uncover yet undiscovered physical processes, which would require a more fundamental theory, perhaps one unifying the four known physical interactions.

Two different approaches that offer model-independent and precise constraints on potential variation of fundamental constants are lab-based atomic clock experiments and quasar (QSO) absorption line observations.

Lab-based studies provide stringent bounds for both $\alpha$ and $\mu$ variation. However, Earth-based laboratory experiments are limited to local time and spatial scales, while QSO-based studies allow one to probe for variation at cosmological scales, limited only by the detection capacities of the current generation of optical and radio telescopes.

Cosmological constraints of $\alpha$ variation are expressed in terms of

$\frac{\Delta\alpha}{\alpha} = \frac{\alpha_z - \alpha_{\rm lab}}{\alpha_{\rm lab}},$

where $\alpha_z$ is the measured $\alpha$ value at redshift $z$, and $\alpha_{\rm lab}$ is the local lab-measured value. In the same way $\mu$ variation is expressed as $\Delta\mu/\mu$.

To constrain the potential variation of $\alpha$ I apply the method introduced by Webb et al. (1999) and Dzuba et al. (1999) to spectroscopic data observed using HIRES and UVES spectrographs on the Keck and VLT telescopes respectively. The method uses redshifted absorption lines arising from transitions in different atoms/ions within a single QSO absorption system (such as Mg II, Fe II, Si II).

It is the relative velocities of these transitions which constrain changes $\alpha$ variation. As $\alpha$ changes, one can expect to observe a fine velocity shift in a given transition defined by the rest-frequency in the laboratory and a sensitivity coefficient which determines the magnitude and sign of the shift.

I construct multi-component Voigt profiles to model the velocity structure of the observed absorption ‘clouds’. These are fit to the observed data (using VPFIT) and simultaneous $\chi^2$ minimisation analysis is used to obtain a constraint for the absorber.

Combinations of greater numbers of transitions and greater varieties in coefficients result in stronger constraints. Because $\alpha$ variation would manifests itself as differential velocity shifts in absorption lines, it can be a parameter of the model fit to the data.

I use a similar method established by Varshalovich & Levshakov (1993) to constrain $\mu$ variation using molecular absorption lines in Malec et al. (2010). The success of these methods is strongly reliant on the wavelength calibration, therefore a large part of my research involves state of the art data reduction and detailed systematic error analysis.

The field of varying fundamental constants is currently addressing the unexpected and compelling results of Murphy et al. (2004) and Webb & King et al. (2011), who present evidence for temporal and spatial $\alpha$ variation. Given the extraordinary nature of the claims made, these results require independent confirmation or refutation.

My current work aims to confirm or refute the results by using a unique sample of spectra of rare ‘metal-strong’ Zn/Cr II systems. The constraint will be independent of — and qualitatively very different in nature to — previous and most (if not all) other future $\alpha$ constraints. You can expect results very soon…

For $\mu$, no evidence for variation has been found thus far (e.g. Ubachs et al., 2011; King et al., 2011; Malec et al., 2010; Thompson et al., 2009). However, because of the relatively small number of absorbers suitable for this study, this has not yet been fully ruled out.

For a selection of my publications see Publications.