What is the Fine-Structure Constant and How Do Physicists Compute it?

^{By Amal Pushp, Affiliate Physicist at the Resonance Science Foundation} 

The fine structure constant, also called the Sommerfeld constant or electromagnetic coupling constant, is one of the fundamental physical constants that characterizes the strength of the electromagnetic interaction between charged atomic particles. The name of this constant was coined by physicist Arnold Sommerfeld who extended Bohr’s atomic model with the motivation of explaining the fine structure lines observed in the hydrogen spectra, which the previous models had failed to explain satisfactorily.   

Physical constants are generally of two types: one which has a proper unit associated with them and others that are dimensionless. The fine-structure constant is of the latter type, it is dimensionless and is represented by a number. Various probes have determined this number to be close to about 1/137.  

Physicists have estimated that the values of fundamental constants are fine-tuned. In this regard, the fine structure constant is no different. Any minor deviation in its numerical value would have resulted in a universe, way different than it currently is. To be explicit about the consequences it could have posed: atomic size would have been altered, stellar systems and their processes would have worked quite differently than it does, and possibly there would have been no intelligent life present.  

However, there is a plot twist awaiting. There are pieces of evidence that indicate the fine-structure constant is not a constant at all but has varying values! Although the concept poses challenges to our preconceived notions about the universe, it does solve some important questions of astrophysical interest. 

Coming to the measurement techniques, there are various methods to measure the fine structure constant. Quantum field theoretic approaches like QED allow measurement of the constant using the quantum Hall effect or by using the anomalous magnetic moment of the electron. Some other methods include atom interferometry and Josephson effects [1]. A common notion in all the conventional methods is that in order to estimate an accurate value of the fine structure constant, various other physical quantities associated with it have to be measured as well because each method would give a different definition for the fine structure constant. In other words, they are indirect techniques. 

However, recently physicists at TU Wien have performed an experiment in which they have revealed the value of the fine structure constant directly! The research was published in the journal Applied Physics Letters [2]. To describe the experiment briefly, it involves a laser beam incident on a special thin film that can change the direction of polarization of light. Andrei Pimenov, a co-author of the study explains: "A material rotating the polarization of a laser beam is, by itself, nothing unusual. Different materials can do this; the thicker the material layer, the more the polarization of the laser is rotated. But we are dealing with a completely different effect here. In our case, the polarization is not rotated continuously—it jumps.” 

When the researchers calculated the size of this quantum jump, they found that the quantum of the angular change was exactly equal to the fine structure constant. Thus, by displaying a quantum of rotation, the fine structure constant is directly observable as an angle. 

^{The Figure shows a schematic of the experimental setup employed. A light source (left) sends a beam of light through a special material, which changes the direction of polarization—by an angle that is given by the fine structure constant. Credit: Tatiana Lysenko / TU Wien} 

RSF in Perspective: 

The fine structure constant is one of the important parameters of our universe as it describes the strength of one of the four fundamental forces that comprise our universe. Interestingly, it is also a chief feature of physicist Nassim Haramein’s unified field theory. In the new paper entitled “Scale Invariant Unification of Forces, Fields & Particles in a Quantum Vacuum Plasma”, Haramein et al. devise a scaling law that helps formulate a geometric interpretation of the fine structure constant. Moreover, an exact solution for the fine structure constant is presented as well. This in combination with other features help unify all fundamental constants in a single systematic framework. Stay tuned for more details as the new paper will be out soon! 

References  

[1] H Müller, et al "Atom‐interferometry measurement of the fine structure constant".  Annalen der Physik (2019). doi:10.1002/andp.201800346nj.  

[2] Alexey Shuvaev et al, Universal rotation gauge via quantum anomalous Hall effect, Applied Physics Letters (2022). DOI: 10.1063/5.0105159