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Empirically Derived Limit on Variations in the Fine-structure Constant

The physical constant alpha (α) has been described as one of the greatest mysteries of physics. Now, new measurements and analysis of spectra from Sun-like stars have produced the most precise astronomical test of alpha and hence potential locational variability in the strength of the electromagnetic interaction with charged particles. 

By: William Brown, scientist at the Resonance Science Foundation


How Constant are the Physical Constants of Nature?

Although the forces and physical constants of Nature have been measured and characterized to an astonishing level of precision, some big questions remain: what fundamental aspects of the universe give rise to the laws of Nature? Are the laws set from the beginning by some as-of-yet unidentified intrinsic and indelible relationship or mechanism, producing the seemingly fine-tuned physical parameters that give rise to organized matter and life? Are they 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 example, the fine-structure constant, α (pronounced alpha), sets the strength of the electromagnetic force. The strength of this force defines precisely how the electron interacts via the electromagnetic force and its behavior within and outside of the atom, and hence is a fundamental basis for the behavior and properties of matter. However, the Standard Model of particle physics provides no explanation for its value, which could potentially vary from place to place.

The quest to determine whether the strength of the electromagnetic interaction is constant in space and time has received impetus from the suggestion that there might be additional dimensions of space—measurements of variations in alpha could rule out these hyperdimensional models— or that the 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 subsequently ruled out by observations [6]. However, the question of the potential variability of this fundamental physical constant remains and further experiments and theoretical development are needed to understand this intrinsic property of the universe which has been called one of the greatest mysteries in physics (a remark attributed to the renowned physicist Richard Feynman). 

Measuring Starlight

To determine the potential variability of the fine-structure constant scientists are interested in taking measurements beyond the laboratory, to see for instance if there is variation in the strength of the electromagnetic interaction in different locales of the universe separated by large distances (what is called spatial variation). To this end, a team of astrophysicists have taken the measurement of α to an astronomical scale by measuring the wavelengths of stellar absorption lines and performing a systematic analysis to detect the amount of variation in the constant, if any. Using spectra of 17 nearby stars, with properties matched to the Sun, the research team measured and analyzed absorption lines that are sensitive to α, reporting their findings in the journal Science [7]. Because the absorption spectra of matter depend on how electrons move around in the orbitals of atoms, which is defined by the fine structure constant, any potential spatial variability in α can be determined by detailed measurements of the absorption lines of stars.  

By comparing the absorption spectra of the 17 nearby stars, the astrophysicists were able to set an upper limit of 50 parts per billion on variations of α between the stars. The results rule out substantial changes in α within the local region of the Milky Way, filling a gap between laboratory measurements done here a little closer to home, here on Earth, and previous studies that have measured absorption lines in some of the most distant regions (and times) of the universe using spectra of quasars billions of light-years away with light that was emitted almost 13 billion years ago.

Previous Indications of Spatiotemporal Variability of Alpha

Interestingly, although this most recent study shows consistency in the fine-structure constant within our local region of the galaxy, previous studies that examined the strength of electromagnetic interaction with charged particles in more distant locations and epochs have reported spatial and temporal variations in α. In 2004 researchers analyzed the isotopic ratios of fission products and secondary neutron absorption reactions that occurred in the Oklo uranium mine— a series of sites where a naturally sustained fission reaction occurred 2 billion years ago [8]. The researchers found shifts in the isotopic ratios of fission reaction products at the site that indicate a non-zero change in α over time, a temporal variability. The researchers concluded that based on the data, it is likely the fine-structure constant has changed by 45 parts per billion over the last 2 billion years.

Subsequently, in 2010 researchers announced the detection of spatial variation in α in what has come to be known as the Australian dipole. The researchers purported to have identified a dipole-like structure in the variation of the fine-structure constant across the observable universe. They used data on quasars obtained by the Very Large Telescope, combined with the previous data obtained by Webb at the Keck telescopes. The fine-structure constant appears to have been larger by 1 part in 100,000 in the direction of the southern hemisphere constellation Ara, 10 billion years ago. Similarly, the constant appeared to have been smaller by a similar fraction in the northern direction, 10 billion years ago. Then, in 2020, the team performed the same type of measurements this time using light from one of the most distant quasars known, which first started emitting light when the universe was only 0.8 billion years old (very young from cosmological standards). With the new more robust data verifing their previous findings of a dipole structure with spatial variation along a specific axis of the universe in the strength of the electromagnetic force [9].

A picture is thus emerging of the potential variability of the fine structure constant. All analysis so-far having indicated that in local regions and timeframes the strength of electromagnetic interaction is constant, while some analyses have indicated that it may vary spatially and temporally. Certainly, for the latter more testing and critical analysis needs to be done to verify the purported variability. Knowing whether the fine structure is constant over space and time will have significant implications for physics and our understanding of the universe. If it is found that there is variation in α over large distances and epochs, cosmological models will have to be adjusted to compensate for the rate of variability. And on a more speculative side, if the fine structure constant does naturally vary, then there is possibly a mechanism by which this variability takes place, and if there is a mechanism it can be understood and potentially engineered: could we then harness this mechanism to generate a change in the speed of light or the strength of EM interaction with elementary charge in a localized region?

Resonance Science Foundation In-Perspective

Some of the physical constants of nature that are most central to physics are empirically derived values, which means they are known only from measurement. With constants such as alpha, there is no model that predicts what its precise value should be—there is no prediction based on a first principle of theoretical tenets alone. This shows that our understanding of the fundamentals of nature is incomplete (at best) and leads to significant challenges such as the fine-tuning problem.

Since the Standard Model has no theoretical basis to explain the physical constants and what their respective values should be based on first principles, their values are largely perplexing to scientists. Since the constants could have conceivably any value, the question arises “why the specific values that we measure”? The situation becomes problematic when it is considered that even relatively small deviations in the values of some of the physical constants would result in a universe with properties very different from ours. In most cases, with even small deviations— for instance in the fine-structure constant— electrons would fly into or away from protons and even the simplest atom would not be able to form. Obviously, such a universe would not be able to form that most precious arrangement of organized matter, the living system. Hence, we have a fine-tuning “problem”: why are the physical constants seemingly “tuned” to the optimal values that allow complex matter and life to form?

The so-called problem of “fine-tuning” evaporates as soon as we have a theory that explains from first principles the constants and their precise values. At that point, it is understood from theoretical tenets why the physical constants have the precise values that are observed and why they don’t manifest with any other of a potentially endless range of values.

Excitingly, we now have just such a first principles theory, as physicists Nassim Haramein and Olivier Alirol have discovered a scaling coefficient from the Planck scale to the cosmological scale that produces a precise periodic fit to organized matter and a direct correlation between the forces coupling constants and the holographic ratio ΙΈ (described in previous work [8, 9, 10]). With the discovery of their scaling law there is now a geometric interpretation of the fine structure constant and the proton to the electron mass ratio. This is a significant advancement in understanding that most elusive and perplexing of the physical constants, α. Haramein & Olivier validate their exact first principle computed value of α to 10-13 digits of accuracy by predicting the electron g-factor ge, further exemplifying the analytical power of understanding the physical constants of nature from a fundamental theoretical basis versus simply knowing the values from experimental derivation.

With Haramein’s first principles unification theory, we will no longer have to speculate on whether the fine-structure constant may or may not vary in time and / or space, as we can utilize the fundamental understanding of the nature of this physical constant to predict that it will have low variance over spatial distances, and then experiments such as that performed by Murphy et al. will serve to verify theory and not just further extend our measurements and empirical understanding of α—we will be testing our understanding of nature at the most fundamental of levels. Haramein’s breakthrough research opens the way to the unification of all particles, fundamental constants and forces in a unified theoretical framework based on a fractalization of spacetime defined by an entropic principle related to the surface-to-volume holographic ratio Φ.


[1] K. P. Stanyukovich, Possible changes in the gravitational constant. Sov. Phys. Dokl. 7, 1150 (1963).

[2] E. Teller, On the change of physical constants. Phys. Rev. 73, 801–802 (1948).

[3] G. Gamow, Electricity, gravity, and cosmology. Phys. Rev. Lett. 19, 759–761 (1967).

[4] P. A. M. Dirac, The cosmological constants. Nature 139, 323 (1937).

[5] J. D. Barrow, F. J. Tipler, The Anthropic Cosmological Principle (Clarendon Press, 1986). Google Scholar

[6] F. J. Dyson, Time variation of the charge of the proton. Phys. Rev. Lett. 19, 1291–1293 (1967).

[7] M. T. Murphy et al., “A limit on variations in the fine-structure constant from spectra of nearby Sun-like stars,” Science, vol. 378, no. 6620, pp. 634–636, Nov. 2022, doi: 10.1126/science.abi9232

[8] S. K. Lamoreaux and J. R. Torgerson, “Neutron moderation in the Oklo natural reactor and the time variation of α”, Phys. Rev. D, vol. 69, no. 12, p. 121701, Jun. 2004, doi: 10.1103/PhysRevD.69.121701

[9] M. R. Wilczynska et al., “Four direct measurements of the fine-structure constant 13 billion years ago,” Science Advances, vol. 6, no. 17, p. eaay9672, Apr. 2020, doi: 10.1126/sciadv.aay9672

[10] Haramein, N., Quantum Gravity and the Holographic Mass, Quantum, Physical Review & Research International, ISSN: 2231-1815, Page 270-292, (2012).

[11] Val baker, A.K.F, Haramein, N. and Alirol, O., The Electron and the Holographic Mass SolutionPhysics Essays, Vol 32, Pages 255-262, (2019).

[12] Haramein, N & Val Baker, A. K. F., Resolving the Vacuum Catastrophe: A Generalized Holographic Approach, Journal of High Energy Physics, Gravitation and Cosmology, Vol.05 No.02(2019), Article ID:91083, 13 pages, (2019).



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