In common imagination, "elementary particles" are often depicted as tiny "steel balls"—hard, impenetrable, and with distinct boundaries. However, experiments in modern physics have long refuted this naive image. In fact, elementary particles such as electrons, quarks, and even neutrinos are not "small hard spheres" but field structures with specific spatial scales that can penetrate each other. Understanding their "size" does not depend on geometric radius, but on the dynamical scale revealed by interactions—among which the Compton wavelength provides the most reliable ontological measure.

1. What is the "Size of Elementary Particles"?

When we say an object is "how large," we usually refer to the distance from one boundary to another. But this concept fails for elementary particles:

• They have no internal components (hence the term "elementary");

• They have no hard surface;

• They do not rebound like billiard balls in high-energy scattering.

So how to define their "size"? The answer comes from interactions:

The "effective size" of a particle is the characteristic spatial range where its field interacts significantly with the external environment.

This scale is precisely the Compton wavelength:

λ_C = h/(mc)

where h is the Planck constant, m is the rest mass of the particle, and c is the speed of light. It marks the length scale dominated by the combined effects of quantum and relativistic phenomena.

• For the electron: λ_C ≈ 2.43×10⁻¹² meters (2.43 picometers);

• For the proton (though not elementary): λ_C ≈ 1.32×10⁻¹⁵ meters;

• For the neutrino (with extremely small mass): λ_C can reach the nanometer or even micrometer scale—a surprising discovery from recent experiments.

2. Why Can Elementary Particles "Pass Through Each Other"?

Unlike atoms, elementary particles have no "hard core." An atom consists of a dense atomic nucleus (scale ~10⁻¹⁵ m) and a diffused electron cloud; α-particles are strongly deflected by the atomic nucleus at MeV energies (Rutherford scattering). However, elementary particles such as electrons and quarks:

• Are localized field excitations (e.g., vortex structures of the electromagnetic field or other fundamental fields);

• Have smoothly distributed charge and mass without abrupt boundaries;

• Interact through the superposition and coupling of fields, rather than physical collisions.

Thus, when two high-energy electrons collide:

• Their fields penetrate each other;

• Deflection occurs through momentum exchange (e.g., emission/absorption of virtual photons);

• The process is continuous without instantaneous impact, similar to two beams of light crossing paths.

This explains why electron scattering at colliders like the LHC exhibits a smooth differential cross-section even at TeV energies, rather than large-angle "rebounds"—they are not hard spheres.

3. Neutrino Experiments: Subverting the Perception That "Smaller Is Harder to Detect"

For a long time, neutrinos were thought to be "extremely small" point particles because they barely interact with matter. However, a groundbreaking experiment in early 2025 completely overturned this notion.

As reported in Nature on February 12, 2025, an international team of scientists from the United States, France, and Canada successfully measured the spatial extent of the electron neutrino for the first time through the BeEST experiment (Beryllium Electron-capture in Superconducting Tunnel Junctions).

Brief Description of Experimental Principle:

• Utilize the electron-capture decay of beryllium-7 nuclei: ⁷Be + e⁻ → ⁷Li + νₑ;

• Interaction between lithium-7 and the neutrino;

• Precisely measure the recoil energy of the lithium nucleus at extremely low temperatures using superconducting sensors;

• Deduce the spatial broadening of the neutrino wave packet through quantum mechanical correlations.

Striking Results:

• The wave packet size of the electron neutrino is at least 6.2 picometers (6.2 × 10⁻¹² m);

• It is over a thousand times larger than the proton (~0.84 femtometers) and even exceeds one-tenth of the Bohr radius of the entire hydrogen atom (approximately 53 picometers)!

This discovery confirms:

• Neutrinos can easily penetrate the Earth not because they are "small enough," but because they do not participate in strong or electromagnetic interactions.

• Their "large" spatial scale is precisely a reflection of the Compton wavelength as a low-mass particle—the smaller the mass, the larger λ_C.

This provides direct experimental evidence that "the Compton wavelength is the ontological scale."

4. Compton Wavelength: An Ontological Physical Scale

Within an ontological framework (e.g., the Global Approximation Interpretation (GAI) or classical field vortex models), the Compton wavelength should not be regarded as an abstract parameter, but rather as:

• The natural spatial extension of the particle as a physical entity;

• The characteristic range of interactions between its field structure and the vacuum;

• The origin scale of quantum behaviors (e.g., uncertainty, wave nature).

For example:

• The electron’s λ_C ~ 2.4 picometers means its charge is not concentrated at a point, but distributed in a "cloud" on the picometer scale;

• Due to its extremely small mass (< 1 eV/c²), the neutrino’s λ_C can reach the micrometer scale, which is consistent with its "ghostly penetrability"—large yet sparse, hence difficult to intercept.

This is fundamentally different from the "point particle" image: a point particle is a mathematical idealization, while the Compton scale is a physical reality.

5. Conclusion: The Paradigm Shift from "Point" to "Field Structure"

Elementary particles have no "hard core" and do not require "internal parts." They are stable excited states of fundamental fields, with a natural spatial scale determined by their mass—the Compton wavelength. They can pass through each other not because they "do not exist," but because they are fields, not solids.

The latest measurement of the neutrino’s size not only refreshes our understanding of the microcosm but also strongly supports the ontological physical image: particles are real, scaled, and understandable physical structures, not mysterious probabilistic symbols.

The future of physics lies not in smaller "points," but in clearer "fields."When we ask "how large is an electron," the answer is no longer "zero," but:"Its ontological scale is inscribed in the Compton wavelength."