The proton, the fundamental building block of atomic nuclei, stands as a perfect example of modern physics’ greatest theoretical crisis. A composite particle with clearly measurable internal structure has been forced into the mathematical framework of point particles—a disconnect between theory and reality that exposes the fundamental flaws of contemporary particle physics.
Undeniable Internal Structure
Modern experiments have unequivocally confirmed the proton’s complex internal structure:
Deep inelastic scattering (DIS) has directly "seen" the quarks inside the proton. When high-energy electrons collide with protons, the scattering patterns clearly reveal three point-like scattering centers—the existence of quarks. Structure function measurements have precisely mapped the momentum distribution within the proton, and the breakdown of Bjorken scaling has proven the presence of multiple interacting degrees of freedom internally.
The success of lattice Quantum Chromodynamics (QCD) calculations is even more striking. This ab initio computational method can:
Charge radius measurements provide another irrefutable proof. The proton’s charge radius is approximately 0.84 femtometers (fm), and surprisingly, the electrically neutral neutron possesses a negative mean-square charge radius—an observation that can only be explained by the specific distribution of positive and negative charges within it.
Theoretical Schizophrenia
Faced with such overwhelming evidence, the theoretical physics community has exhibited a perplexing double standard:
When studying the proton’s interior, physicists meticulously calculate quark color charges, spins, and orbital angular momentum, use complex QCD theory to describe gluon exchange, and employ supercomputers for lattice simulations. However, once shifting to nuclear physics calculations, these same physicists suddenly pretend the proton is a structureless point, using so-called "effective field theories" to mask this fundamental contradiction and constantly introducing new phenomenological parameters to bridge the gap between theory and experiment.
This approach is as absurd as analyzing the mechanics of a building with known complex internal structure by treating it as a point mass, then expressing "surprise" when predictions fail.
Complete Collapse of Predictive Power
The failure of the point-particle model is laid bare in two critical issues:
The Spin Crisis
According to the simple quark model, the proton’s spin of 1/2 should be entirely derived from its three valence quarks. Yet the results of the EMC experiment shocked the entire physics community: quark spins contribute only about 30% of the proton’s total spin. Where does the remaining 70% come from?
Standard theory has proposed a series of ad hoc explanations: perhaps from gluon spin, perhaps from orbital angular momentum, or perhaps from mysterious "sea quarks." But these are merely patches, none of which can provide quantitative predictions from first principles. The real problem lies in the point-particle framework’s treatment of spin as a "fundamental" quantum number, while the proton’s spin is clearly a collective effect.
Failed Calculations of the Anomalous Magnetic Moment
Even more embarrassing is the issue of the g-factor. Dirac theory predicts that all spin-1/2 point particles should have g = 2. Yet experimental results show:
Lattice QCD can calculate the proton mass with 2% precision and compute the charge radius, but it cannot predict the g-factor. Why? Because the magnetic moment directly reflects the dynamic characteristics of internal current distribution—a spatial structure that the point-particle framework is fundamentally unable to describe.
The Compton Wavelength: The Neglected Key
The proton’s Compton wavelength λ_C ≈ 0.21 fm precisely defines its characteristic physical scale. This is no coincidence, but a profound physical principle: at this scale, quantum and relativistic effects become equally significant, and all of the particle’s fundamental properties—mass, spin, magnetic moment—are mutually coupled and inseparable.
When the probing scale approaches the Compton wavelength, the point-particle approximation fails in principle. This is why calculations involving magnetic moments and spin always fail—they are inherently properties of extended structures.
Why Insist on a Failed Model?
Given the point-particle model’s fundamental flaws, why does the physics community persist in using it?
Mathematical convenience is the most immediate reason. The mathematical treatment of point particles is relatively simple, leveraging well-established quantum field theory tools. Once extended structure is considered, computational complexity increases drastically.
Historical inertia also plays a significant role. From atoms to atomic nuclei to nucleons, physics has consistently used point models, masking problems with "effective theories" at each layer. This mental inertia has become deeply entrenched.
A deeper reason is the theoretical vacuum. No complete theoretical framework for extended particles has yet been established. Abandoning point particles would mean rebuilding the entire mathematical foundation of particle physics—a prospect most physicists are unwilling to confront.
The Necessity of a Paradigm Shift
The proton’s example clearly demonstrates that what we need is not more patches and corrections, but a fundamental transformation of conceptual foundations:
We must acknowledge that all particles possess a physical scale defined by their Compton wavelength. At this scale, the particle’s fundamental properties are not independent labels, but different manifestations of internal field structure: spin originates from the angular momentum of internal electromagnetic fields, magnetic moments from internal current distributions, and mass from the localization of field energy.
The success of lattice QCD precisely proves the failure of the point-particle framework. It reveals the true physical picture: the proton is an extended object with rich internal structure, and all its properties stem from the dynamics of this structure. Continuing to adhere to the point-particle model is as absurd as insisting that organisms are homogeneous colloids after observing cellular structure.
As a paradigm, the proton exposes modern physics’ deepest crisis: when mathematical convenience conflicts with physical reality, we have chosen the former. The cost of this choice is the loss of predictive power, entanglement in endless parameter fitting, and ultimately a departure from physics’ original mission of pursuing unification and simplicity. True progress requires courage—acknowledging mistakes, abandoning dogma, and rebuilding a new theory based on physical reality.