These detailed studies, using large numbers of quasar spectra, hint at a spatial variation of α at a level of ∼4σ ( 42 – 44 ). The apparent spatial signal was initially claimed to be caused by long-range wavelength distortions ( 45 ), but a more detailed analysis showed this to be incorrect ( 44 ). This apparently persistent spatial signal motivates further direct measurements, especially by extending the measurement redshift range.

The inputs needed for these theories come from a variety of different types of astronomical observations: high-precision observations of the instantaneous value of α(z i ) characterizing quasar spectra at various redshifts z i to test possible time variations, both local and nonlocal measurements of α ( x → ) at different positions in the universe ( 28 – 30 ) to search for spatial variation, the cosmic microwave background ( 31 , 32 ), the Oklo natural reactor ( 33 – 36 ), atomic clocks ( 7 , 37 , 38 ), compact objects in which the local gravitational potential may be different ( 39 , 40 ), or atomic line separations in white dwarf atmospheres ( 41 ).

Direct measurements of α are also important for testing dynamical dark energy models, since they help to constrain the dynamics of the underlying scalar field ( 11 ), and thus, dynamics can be constrained (through α) even at epochs where dark energy is still not dominating the universe. The possibility of doing these measurements deep into the matter era is particularly useful, since most other cosmological datasets (coming from type Ia supernovas, galaxy clustering, etc.) are limited to lower redshifts.

There are also interesting new problems that have been about extreme fine-tuning of quantum corrections in theories with variation of α by Donoghue ( 12 ) and Marsh ( 13 ). Accordingly, self-consistent theories of gravity and electromagnetism, which incorporate the fine-structure “constant” as a self-gravitating scalar field with self-consistent dynamics that couple to the geometry of spacetime, have been formulated in ( 14 – 20 ) and extended to the Weinberg-Salam theory in ( 21 , 22 ). They generalize Maxwell’s equations and general relativity in the way that Jordan-Brans-Dicke gravity theory ( 23 , 24 ) extends general relativity to include space or time variations of the Newtonian gravitational constant, G, by upgrading it to become a scalar field. This enables different constraints on a changing α(z) at different redshifts, z, to be coordinated; it supersedes the traditional approach ( 25 ) to constraining varying α by simply allowing α to become a variable in the physical laws for constant α. Further discussions relating spatial variations of α to inhomogeneous cosmological models can be found in ( 26 , 27 ).

The quest to determine whether the bare fine-structure constant, α, is a constant in space and time has received impetus from the recognition that there might be additional dimensions of space or that our constants are partly or wholly determined by symmetry breaking at ultrahigh energies in the very early universe. The first proposals for time variation in α by Stanyukovich ( 1 ), Teller ( 2 ), and Gamow ( 3 ) were motivated by the large-number coincidences noted by Dirac ( 4 , 5 ) but were quickly ruled out by observations ( 6 ). This has led to an extensive literature on varying constants that is reviewed in ( 7 – 11 ).

The quantity that we focus on here is the fine-structure constant, which can be expressed as α = e 2 /4πε 0 ħc, where e is the electron charge, ε 0 is the permittivity of free space, ħ is the reduced Planck constant, and c is the speed of light. The dimensionless quantity described by α is the ratio of the speed of an electron in the lowest-energy orbit of the Bohr-Sommerfeld atom to the speed of light. α may be considered to relate quantum mechanics (through ħ) to electromagnetism (through the remaining constants in the ratio).

What fundamental aspects of the universe give rise to the laws of Nature? Are the laws finely tuned from the outset, immutable in time and space, or do they vary in space or time such that our local patch of the universe is particularly suited to our own existence? We characterize the laws of Nature using the numerical values of the fundamental constants, for which increasingly precise and ever-distant measurements are accessible using quasar absorption spectra.

Observations and artificial intelligence algorithm

The relative wavelengths of absorption lines imprinted on the spectra of background quasars are sensitive to the fine-structure constant. Comparing quasar measurements with high-precision terrestrial experiments provides stringent constraints on any possible spacetime variations of the fine-structure constant, as predicted by some theoretical models (7, 11, 16, 46, 47). The quasar J1120+0641 (48) is of particular interest in this context because of its very high redshift. Its emission redshift is z = 7.085, corresponding to a look-back time of 12.96 billion years in standard ΛCDM (lambda cold dark matter) cosmology. J1120+0641 is one of the most luminous quasars known (49), enabling high spectral resolution at high signal-to-noise ratio. We make use of spectra obtained using the x-shooter spectrograph (50) on the European Southern Observatory’s Very Large Telescope (VLT), with nominal spectral resolution R = λ a λ = 7000 to 10,000 (51). The total integration time is 30 hours.

The x-shooter instrument provides a broad spectral wavelength coverage. This maximizes the discovery probability of absorption systems along the sightline, enabling the identification of potential coincidences (i.e., blends) between absorption species at different redshifts, an essential step in making a reliable measurement of α. In all, 11 absorption systems are detected (Table 1). Desirable characteristics of an absorption system are a selection of transitions with different sensitivities to a change in α and a velocity structure in the absorbing medium that is as simple as possible.

Table 1 Absorption systems and transitions identified in the x - shooter spectrum of the z em = 7.084 quasar J1120+0641. Absorption redshifts are listed in column 1. Transitions present in each absorption system are listed in column 2.The four absorption systems and transitions used to measure Δα/α are indicated in bold. View this table:

Of the 11 absorption systems identified along the J1120+0641 sightline, 4 are found to be suitable for a measurement of α, at redshifts z abs = 7.059,6.171,5.951, and 5.507. The atomic transitions used to measure α in these four systems are highlighted in Table 1. The highest-redshift system has, of the four, the least sensitivity to varying α. No other direct quasar absorption α measurements have previously been made at such high redshift. Before the measurements described in this paper, the highest-redshift quasar absorption direct measurement of α was at z = 4.1798 (52). Voigt profile models for each of the four absorption systems were automatically constructed using a genetic algorithm, gvpfit, which requires no human decision-making beyond initial setup parameters (53). The genetic part of the procedure controls the evolution of the model development. vpfit (54) is called multiple times within each generation to refine the model, which then becomes the parent for subsequent generations. Absorption model complexity increases with each generation. A description of gvpfit can be found in (53), where it was used for the analysis of an absorption system at z abs = 1.839 toward the quasar J110325−264515. That particular system had previously been analyzed by several groups and so provided important comparative information between gvpfit and previous methods. Further assessments of gvpfit’s performance are given in (55). The procedure outperforms human interactive methods in that it gives objective, reproducible, robust results and introduces no additional systematic uncertainties. The method is computationally demanding, requiring supercomputers. New procedures have been introduced for the analysis in this paper, beyond those described in (53), and so are described here.

The analysis of each of the four absorption systems took place in four stages. Throughout, Δα/α is kept as a free-fitting parameter, making use of the Many-Multiplet Method (28, 38). In stage 1, we imposed the requirement that all velocity components are present in all species being fitted, irrespective of line strength. Without this requirement, an absorbing component in one species might fall below the detection threshold determined by the spectral data quality, but not in another. This requirement was only applied in the first stage because it was found in practice to help model stability by discouraging the fitting procedure from finding a model with physically implausible cloud parameters in one or more components. By “physically implausible,” we mean either large linewidth, i.e., a Voigt profile b parameter of tens of kilometers per second, or an improbably high column density. The requirement is dropped subsequently. gvpfit was allowed to evolve (that is, the complexity of the model was allowed to increase) for the number of generations required to pass through a minimum value of the corrected Akaike Information Criterion statistic (AICc) (56, 57). The model resulting from this first stage of the analysis is the model at which AICc is at a minimum and is already quite good but is not final.

In stage 2, we use the model from stage 1 as the parent model input to gvpfit but now drop the requirement that all velocity components are present. The other requirements from stage 1 were carried over to stage 2. At this stage, one further increase in model complexity is introduced. Although the spectral continuum model was derived before the line fitting process, we allow for residual uncertainties in continuum estimation where needed by including additional free parameters allowing the local continuum for each region to vary using a simple linear correction as described in the vpfit manual (http://www.ast.cam.ac.uk/~rfc/vpfit11.1.pdf). The minimum AICc model from this stage is again taken as the parent model for the next stage.

In stage 3, we check to see whether any interloping absorption lines from other redshift systems may be present within any of the spectral regions used to measure α. When interloper parameters are introduced, degeneracy can occur with other parameters associated with the metal lines used to measure α. To avoid this problem, all previous parameters are temporarily fixed, and gvpfit is used in a first pass to identify places in the data where the current model is inadequate. Interlopers, modeled as unidentified atomic species, are added automatically by gvpfit to improve the current fit.

In stage 4, the model resulting from this third stage is used as the input model for the fourth and final part of the process, which entails running gvpfit again but this time with all parameters free to vary (subject to the physical constraint that all b parameters are tied, and all redshifts of corresponding absorbing components are tied, as was the case throughout all stages).