Newton's Understanding of Mass

To grasp the confusion surrounding mass, we must first look at Newton's original definition:

“The quantity of matter is that which arises conjointly from its density and magnitude. A body twice as dense in double the space is quadruple in quantity. This quantity I designate by the name of body or of mass.”

From Newton’s "Principia"

This definition links mass to density, suggesting that mass equals density multiplied by volume. While this explanation might seem straightforward, it prompts deeper questions about what we mean by terms like “quantity of matter.” Does this refer to the number of atoms? Although atoms were not directly observed in Newton's time, many scientists—including Newton himself—held Atomism as a philosophical belief.

Newton further elaborates:

“The least of bodies (atoms) are extended, impenetrable, and endowed with their proper inertia.”

Thus, he viewed matter as composed of atoms that possess inertia, and he equated the "quantity" of matter—density times volume—with mass. However, this definition is somewhat ambiguous and can be seen as circular. While mass is certainly related to the atoms that comprise an object, it remains unclear whether this quantity pertains to size, shape, or even the number of atoms. Critics argue that since density is defined as mass divided by volume, using density to define mass creates a tautology.

Newton asserted that a body's inertia correlates with its mass. Some interpret this to mean that mass equals inertia, but this is misleading since inertia is not explicitly mentioned in his definition; they are merely related concepts. Thus, while Newton's definition is foundational, it lacks clarity and precision.

Euler's Contribution to Mass

Leonhard Euler later defined mass as the measure of inertia within an object. For instance, if a ball can be divided into five equal parts, Euler would assert that the mass is five units, as it reflects the total inertia. Despite its apparent soundness, this definition raises further questions about the nature of inertia itself.

Euler characterized inertia as the resistance to a force. In simple terms, if it takes more force to accelerate an object, it has greater inertia. While this explanation is intuitive, it lacks the mathematical rigor found in Newton’s formulations, particularly concerning the definition of “force.” Euler’s conceptual approach has been criticized for being overly abstract and lacking the logical consistency needed for a comprehensive definition of mass.

Einstein's Perspective

As physics evolved, two prevailing interpretations of mass emerged: the “amount of matter” (Newton's view) and the “amount of inertia” (Euler's perspective). Despite being a critical component in the equations of motion, the concept of mass remained poorly defined.

As new particles were discovered, a clear definition of mass became increasingly vital. This is where Einstein’s famous equation, E=mc², enters the conversation. Using natural units, the mass equation expands to m = sqrt(E² - p²), which is utilized in particle collider experiments. While this offers a functional approach to measuring mass, it does not satisfactorily define what mass actually is.

This definition inadvertently trivializes the energy-mass relationship since it was previously derived using mass. Furthermore, the equation for momentum—mass times velocity—could lead to tautological definitions, as it hinges on the concept of mass itself. Although Einstein's formula is effective for measurement, it falls short as a definitive explanation.

The Role of the Higgs Mechanism

The Higgs Mechanism may provide new insights into the nature of mass. It posits that mass is a mathematical quantity that emerges from spontaneous symmetry breaking within the Higgs field. Essentially, the interaction strength between the Higgs field and another field determines a particle's mass. This perspective offers an elegant definition of mass as a mathematical construct that reflects interaction strength.

However, this does not resolve the overarching question of what mass represents in classical mechanics. Quantum Field Theory does not apply at macroscopic scales, rendering the Higgs definition problematic when discussing everyday mass concepts.

Is the Confusion Over Mass a Major Issue?

So, where does this leave us? Is the ambiguity surrounding mass a pressing concern for physicists? The answer is both yes and no. While treating mass as a mere parameter allows for accurate calculations in theoretical frameworks, it does not provide a true understanding of its essence.

Physics can be likened to observing nature; we can analyze how leaves fall or how branches sway, but these observations do not define the tree itself. Addressing the deeper questions about mass requires further contemplation. Perhaps one day, we will fully comprehend the enigma of mass. For now, we can perform calculations while acknowledging that the fundamental nature of mass remains elusive.

For those interested in delving deeper into the Higgs Mechanism, visit my channel, Fermion Physics, where I explore gauge theory—an essential aspect of the Higgs Mechanism. Until next time! :)

The first video, "You Probably Don't Know Why You Really Have Mass," discusses the common misconceptions about mass and its underlying principles.

The second video, "What You Never Learned About Mass," uncovers the complexities of mass and its significance in physics.