The concept of supersymmetry (SUSY) is among the most intriguing ideas in physics, irrespective of whether it accurately represents reality. The Standard Model of elementary particles has evolved throughout the 20th century, based on initial insights into the quantum nature of light and matter. The discovery of numerous subatomic particles—including not just protons, neutrons, and electrons, but also quarks, neutrinos, and muons—alongside advancements in quantum field theory, has dramatically transformed our understanding of the universe.

Nearly a century ago, the positron—the antimatter equivalent of the electron—was not discovered through direct observation but was theorized to resolve a potential anomaly that could give the electron infinite self-energy. The eventual detection of the positron validated this theoretical proposition and marked the beginning of quantum field theory's impact on particle physics. To avoid a similar issue with the masses of particles in the Standard Model, a new symmetry can safeguard them from excessively high values. This symmetry is precisely what SUSY offers, which is why physicists find it challenging to abandon this theoretical construct, even in the absence of supporting evidence.

There’s a humorous analogy among physics educators regarding electric potential energy: likening it to a neighborhood drug dealer—because the first dose is free. The truth is that introducing a single point charge incurs no energy cost, regardless of its distance from the source. However, placing a second charge incurs energy costs as it must work against the electric field generated by the first charge.

Assuming the electron is not a point particle but a sphere with distributed charge, calculations suggest it could have a radius of approximately 2.9 femtometers—over three times larger than a proton. This is inconsistent with reality, as experimental limits from the Large Hadron Collider indicate the electron is over 10,000 times smaller.

Transitioning from classical to quantum mechanics, we recognize that electrons exhibit both point-like properties during interactions and wave-like behavior when propagating. This dual nature implies that not only are particles like electrons inherently quantum, but the fields they create—such as electric and magnetic fields—must also adhere to quantum mechanics and relativity. The Klein-Gordon equation, formulated in 1926, was the first attempt at a quantum-relativistic description of particles and fields, yet it was the Dirac equation, published two years later, that accurately accounted for particle spin.

Despite its elegance in describing the electron, the Dirac equation introduces negative energy solutions, implying that electrons have no defined lowest energy state and can theoretically transition to increasingly negative states. Dirac proposed the existence of an "anti-electron" to occupy these negative energy states—this particle, originally termed a "hole," is what we now know as the positron. Its discovery by Carl Anderson in 1932 confirmed this theory.

Revisiting the electron's self-energy, classical expectations suggest a finite size, which would imply a larger self-energy if compressed. However, quantum mechanics dictates that the electron be point-like, leading to infinite electrostatic energy as its radius approaches zero. Additionally, electrons possess intrinsic angular momentum, generating magnetic fields that further contribute to total energy, which also diverges. Ultimately, reconciling the electron's mass became increasingly complex.

The introduction of antimatter—recognizing that each matter particle has a corresponding opposite-charged counterpart—addresses the electron’s self-energy divergence. The quantum vacuum, rather than being empty, is filled with virtual states and fluctuates with particle-antiparticle pairs. Near an electron, these pairs become polarized, causing their electric fields to shield the electron and stabilize its mass.

Adding antimatter to the universe provides a coherent model of matter, allowing electrons to retain a relatively small observed mass. Fast-forward to today, and physicists face a similar challenge regarding the masses of fundamental particles. The Higgs mechanism, through symmetry breaking, generates mass for particles, including quarks and leptons. However, theoretical predictions of their masses often point toward the Planck mass, which is far greater than the measured values.

This significant disparity between predicted and observed masses is known as the hierarchy problem. It raises questions about why the masses of fundamental particles remain relatively low compared to the Planck mass, despite their coupling to the Higgs field. The unresolved nature of this problem makes SUSY particularly appealing, as it could potentially provide a resolution analogous to that offered by the positron for the electron's self-energy.

The concept behind SUSY suggests that for every Standard Model particle, there exists a supersymmetric partner that could effectively cancel its contributions to the Higgs boson's mass. For instance, the mass contributions from the top quark could be offset by its supersymmetric partner, a 'stop' or squark, while the Higgs boson’s self-coupling could be countered by its partner, the Higgsino.

Despite the allure of SUSY as a solution to the hierarchy problem, the lack of evidence from experiments, such as those conducted at the Large Hadron Collider, raises concerns. The search for these supersymmetric particles at energies relevant to their theoretical predictions has yielded no results, compelling physicists to consider alternative explanations.

Ultimately, while SUSY offers a fascinating potential solution to the hierarchy problem, the absence of experimental validation—despite extensive searches—challenges its viability. As Richard Feynman famously asserted, the beauty or complexity of a theory matters little if it fails to align with experimental findings.

Starts With A Bang is authored by Ethan Siegel, Ph.D., who has written Beyond The Galaxy, Treknology, and The Littlest Girl Goes Inside An Atom, among other works. Stay tuned for upcoming publications, including the Encyclopaedia Cosmologica.