“`html
Quantum mechanics carries a reputation that precedes it. Almost everyone who has encountered the quantum domain, whether in a physics lecture, a laboratory, or in accessible science literature, is often left pondering something akin to, “Now, that is truly bizarre.” For some, this translates to bizarre and marvelous. For others, it resembles bizarre and unsettling.
Chip Sebens, a philosophy professor at Caltech who poses foundational inquiries regarding physics, is decidedly in the latter group. “Philosophers of physics typically become very exasperated when individuals simply say, ‘Alright, here’s quantum mechanics. It’s going to be odd. Don’t stress. You can make accurate predictions with it. You don’t have to try to understand it deeply, just learn to utilize it.’ That kind of sentiment drives me up the wall,” Sebens remarks.
One notably odd and disconcerting field within physics for individuals like Sebens is quantum field theory. Quantum field theory extends beyond quantum mechanics, integrating the special theory of relativity and permitting the number of particles to fluctuate over time (for instance, when an electron and positron annihilate one another, generating two photons). The classical physics’ electromagnetic field is supplanted by a quantum field that undulates and moves to create the manifestation of quantum particles, photons. Alternatively, one might argue that reality comprises swarms of quantum particles that occasionally resemble fields. A central query that Sebens continues to explore in his research is whether the fields or the particles are more essential to nature. It’s akin to asking whether, when you zoom in on the water in a glass, it maintains the appearance of a fluid or reveals itself as composed of molecules. In this scenario, scientists are aware that the molecules are more fundamental than the fluid, yet in the physics domain, Sebens clarifies, “there is contention as to whether quantum field theory ultimately represents a theory of particles or fields.”
“Since I began delving into quantum field theory, I have found it confusing in numerous respects and have been attempting to comprehend precisely what it conveys about the universe,” Sebens states. “Philosophers of physics have been preoccupied with conventional quantum mechanics for quite a while, and the enigmas only intensify regarding quantum field theory.”
Quantum field theory is remarkable in the predictions it can make about phenomena that are subsequently verified in the laboratory. However, the method it employs to achieve these successful predictions is, in Sebens’s words, “a significant amount of work. These are highly intricate, laborious calculations that cannot be manually executed and must be performed by computers. As a philosopher, I aspire to uncover what lies at the foundation of the theory. We possess these equations that function well, but truly understanding the essence of the theory is far from straightforward.”
Thus, Sebens embarked on a quest to discover an alternative, potentially simpler, route to one successful prediction of quantum field theory: the magnetic strength, or moment, of the electron. “The electron is a negatively charged particle, but it also behaves like a miniature bar magnet with a north and south pole,” Sebens describes. “The magnetic moment of the electron quantifies how robust a magnet it is.”
Quantum field theory determines this value “with extreme precision to numerous decimal places,” Sebens states, yet the method it employs to achieve this remains unclear. Sebens tackled the dilemma by reverting to classical physics—the physics that usually describes larger entities in our universe, such as cannonballs and power lines. Specifically, he modeled the electron using a classical field (like the electromagnetic field) known as the Dirac field and computed the value of the electron’s magnetic moment utilizing the Dirac equation, named after British physicist Paul Dirac. “The Dirac equation is conventionally regarded as part of a quantum theory, where it dictates how a wave function, represented by the symbol ψ (psi), evolves over time. But you can interpret the Dirac equation differently,” Sebens points out, “not as an equation dictating a quantum wave function ψ but as one governing a classical field ψ. Wave functions provide probabilities for various events occurring upon measurement. A classical field, in contrast, does not operate in that manner. It depicts a distribution of different occurrences in various locations simultaneously.”
The conventional method of calculating the electron’s magnetic moment using the Dirac equation results in a value known as the Bohr magneton, named after the Danish physicist Niels Bohr. Regrettably, this computed value falls somewhat short of the experimentally determined value for the electron’s magnetic moment, which is slightly more robust. Quantum field theory, conversely, arrives at a significantly more accurate value, somehow factoring in the additional, or “anomalous,” magnetic moment overlooked by the Dirac equation.
At the onset of this project, Sebens hoped that by implementing key corrections to the calculations that yield the Bohr magneton estimate, he might uncover another avenue to the precise prediction of the electron’s magnetic moment currently attained through quantum field theory, or at least a more reliable estimate. “Upon closer examination of what can be achieved with the Dirac equation, it turns out that you can actually do a bit more without transitioning to quantum field theory,” Sebens notes.
In particular, Sebens refined the calculation of the electron’s magnetic moment derived from the Dirac equation to consider two phenomena impacting electrons that have long been incorporated into quantum field theory calculations: self-interaction, where an electron interacts with its own electromagnetic field, and mass renormalization, a method of adjusting the electron’s mass to account for the electromagnetic field that envelops it.
“What I discovered is that if you allow the electron to self-interact, then it possesses a magnetic strength that varies according to the electron’s state,” Sebens states. “If the electron is distributed or uneven, this state alters the magnetic strength.”
Sebens’s endeavor resulted in an intriguing conclusion, although not necessarily the one he anticipated. By amending the basic derivation from the Dirac equation to incorporate self-interaction and mass renormalization, he did indeed establish a new method for calculating the electron’s magnetic moment. However, this alternative approach to the electron’s magnetic moment calculation does not yield the fixed value predicted by quantum field theory. Rather, it produces a fluctuating value dependent on the electron’s state.
“The project that lies ahead is to elucidate why a particular magnetic moment exists in quantum field theory when the magnetic moment, contextualized through the Dirac equation, fluctuates based on the state of the electron,” Sebens explains. “How does quantum field theory determine what is a state-dependent magnetic moment when calculated from the classical Dirac field?”
Sebens’s response? “At least for the time being, I’m uncertain about how the trick operates. As a philosopher, my goal is to meticulously contemplate the foundations of these theories. Occasionally, I envision what it would be like if philosophers collaborated with physicists at an ancient excavation site, unearthing the remnants of a vast underground temple. A typical physicist might rush ahead with power tools to delve deeper and unearth new artifacts, always hurrying into the next dirt-laden chamber filled with treasures. A philosopher might instead pause to attempt to clean the remaining grime off a magnificent statue.”
Sebens’s study is featured in the journal Foundations of Physics under the title “How Anomalous is the Electron’s Magnetic Moment?”
“`