On the Magnetic Moment of Electron and its Significance for the Standard Model

^{Credit: IOP Publishing}  

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

The magnetic moment of an electron is essentially an inherent property that emerges from the particle’s charge and spin. Physicists know that elementary particles like electrons display two kinds of angular momentum: orbital and spin which collectively is known as the spin-orbit coupling. This collective dynamical behavior further gives rise to the magnetic dipole moment or simply the magnetic moment. In fact, the magnetic dipole moment can also appear separately as spin and orbital magnetic dipole moment.  

In general, the magnetic moment can be described as a representation of the strength of any magnetic source. Consider a classical representation of an electron. Due to the charge distribution of the electron, which is essentially rotating, there is a creation of a magnetic dipole or in other words, the electron behaves as a microscopic bar magnet which obviously brings us to the fact that it will show deflection when placed in an external magnetic field. 

Usually, physicists tend to measure certain physical quantities associated with a phenomenon with greater levels of accuracy to probe the phenomena more deeply and this helps them to continuously make changes in models and hence maintain the most updated one at a given moment in time. Following the same trend, physicists around the world have been trying to make measurements of the electron magnetic moment with greater levels of precision and a blended research team from Harvard and North-western University have recently made the most precise measurement ever of the same [1]. 

^{Measurements of the magnetic moment of an electron spinning in a magnetic field (B) can be used to test the standard model. Discrepancies between the experimental value and standard model predictions may reveal missing pieces in the model’s repertoire of particles or interactions. The image background represents a subset of the Feynman diagrams that theorists use to compute the electron’s g factor—which relates the particle’s magnetic moment to its angular momentum. Credit: APS/Carin Cain} 

The latest work supersedes the previous best result made in 2008 by a group led by physicist G. Gabrielse from North-western University [2], who also happens to be a co-author of the fresh study. The novel measured value that comes with a precision of 0.13 fractions of 1 trillion is an advancement by a factor of 2.2 times, which is quite a big achievement with respect to the empirical standards.  

An important parameter that is worth discussing here and which is quite relevant to the topic of discussion is the g-factor. The g-factor is essentially a dimensionless physical quantity that bridges two very important physical properties of a particle or even an atom as a whole (it can also be determined for different isotopes, for example, look at a previous RSF article in which I have described the work that led to one of the most accurate measurements of the g-factor for neon isotopes). These are magnetic moment and angular momentum. Paul Dirac’s work on relativistic quantum mechanics helped predict the g-factor for the electron as 2. However, later empirical tests by physicist Polykarp Kusch revealed that the g-factor is in fact greater than 2 by a small yet physically significant amount. This deviation called the anomalous magnetic moment was later explained by Julian Schwinger by invoking quantum field theoretic corrections in the calculation of the g-factor. It was found that the extra amount is chiefly due to the contributions of virtual photons, a major object of study in quantum electrodynamics (QED). 

As a result of the extra contribution to the g-factor, physicists have adopted g-2 as the anomalous magnetic moment. It is worth noting that the g-2 value for the muon (a particle like an electron but about 207 times heavier) led to a discrepancy as it was incoherent with the standard model. This is essentially an opportunity for other novel frameworks to come over and flourish, as the successful explanation by a different theory would mean the necessary modification of the standard model and uncovering of new physics. 

RSF in Perspective: 

The high precision in the measurement of the magnetic moment of electron is a boon to the physics community in two fundamental ways. First, it provides a great vindication of quantum electrodynamics and second it explicitly brings forward the current inconsistency within the standard model of particle physics as it fails to account for the muon g-2 value. Furthermore, as discussed by physicist Saïda Guellati-Khelifa in her article, the manipulation of the latest empirical value of the electron magnetic moment to justify the electron’s g-2 value is currently a hindrance as this would demand involvement of a very accurate value for the fine-structure constant, which is yet a paradox for the mainstream models. 

Among this chaos within the standard model, the work of physicist Nassim Haramein and other scientists at the Resonance Science Foundation comes forward quite remarkably. The experimental result concerning the electron magnetic moment is very important in the frame of the unified field model based on the generalized holographic approach. The latest measurements of the magnetic moment combined with the previous measurements of the electron g-factor can be compared with Nassim’s model and as well be derived in a first principles approach. All this would be much more elaborated upon in the upcoming new paper entitled “Scale Invariant Unification of Forces, Fields & Particles in a Quantum Vacuum Plasma”, which hopefully would be published very soon.  

It is also quite appealing to see that in the abstract of the new paper, it is explicitly mentioned that 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 would conceivably help unify all fundamental constants in a single unified framework. 

References 

[1] X. Fan et al, Measurement of the Electron Magnetic Moment, Physical Review Letters (2023). DOI: 10.1103/PhysRevLett.130.071801 

[2] G. Gabrielse et al, New Measurement of the Electron Magnetic Moment and the Fine Structure Constant, Physical Review Letters (2008). DOI: 10.1103/PhysRevLett.100.120801