It is one of the most fundamental yet counter-intuitive concepts in physics: "Mass."
In modern particle physics (the Standard Model), it is explained that "the universe is filled with an invisible, syrup-like field called the Higgs field, and the 'resistance' particles feel when moving through it is the true nature of mass."
However, this explanation fails to answer one fatal question:
"Why is the electron heavy, while the neutrino is extremely light (effectively massless)?"
"Why, among particles that mediate forces, is the photon massless while the Z boson is enormously heavy?"
The Standard Model treats this as mere parameter-fitting, asserting that "each particle simply has a different coupling parameter with the Higgs field."
However, the Intergeometric Theory has completely uncovered the true nature of mass.
Mass is not an unknown parameter. It is simply the "collision with the particle's own wave (geometric phase interference)" that occurs when a particle moves through space.
1. Electrons "Collide", Neutrinos "Slip Through"
All elementary particles possess the properties of "waves." In this theory, we define elementary particles not as mere points, but as geometric entities possessing a "front wave" and a "back wave" relative to the direction of observation.
What happens when a particle moves (propagates) through space?
The particle's "current back part" and "past front part" end up overlapping at the same spatial coordinates. At this moment, wave interference (superposition) occurs.
[ The Case of the Electron ]
For an electron, the front wave and back wave are "in phase" (e.g., plus and plus).
If it moves through space in this state, the in-phase waves overlap, generating a intense self-interference where the waves attempt to cancel out (annihilate) each other.
Because the universe works to maintain "existence probability (wave amplitude)," it compensates for this potential annihilation by drawing energy from the background Higgs field to maintain a geometric "standing wave."
This "energy compensation to prevent wave cancellation" is the true identity of mass.
[ The Case of the Neutrino ]
Conversely, for a neutrino, the front wave and back wave are "out of phase" (e.g., plus and minus).
Even if the waves overlap due to movement, because they are out of phase, they pass symmetrically through each other, causing absolutely no self-interference (wave cancellation).
Since no interference occurs, no energy compensation from the Higgs field is required. Therefore, the (bare) mass of the neutrino is geometrically "strictly zero."
(Note: The infinitesimally small mass that actual neutrinos possess is due to self-energy in the internal space, which will be explained on another occasion.)
2. Photons are "Perpendicular", Z Bosons are "Head-On Collisions"
Once we understand that the condition for generating mass is "wave interference in the direction of propagation," the bizarre mass differences among the force-mediating particles (bosons) can be explained smoothly, as if by magic.
The mass of the "Photon (γ)", which mediates the electromagnetic force, is zero.
This is because a photon is an electromagnetic wave; it is a "transverse wave (plane wave)" oscillating perpendicular to the direction of propagation. Since there is no wave component in the direction of propagation, self-interference upon movement is zero. Hence, the mass( \(M_\gamma\) ) is zero.
\[M_\gamma=M_z\cos{90^\circ}=0\]
On the other hand, the "Z boson," which mediates the weak force, possesses a mass( \(M_Z\)) heavier than an iron nucleus.
This is because, opposite to the photon, the Z boson is a "longitudinal wave (plane wave)" possessing components exclusively in the particle's direction of propagation. Because the wave faces directly into the direction of movement, it causes a head-on collision (maximum interference) with itself, making it tremendously heavy.
3. Why is the W Boson Slightly Lighter than the Z Boson?
Finally, let's look at the mass of the "W boson," the sibling of the Z boson (another particle that mediates the weak force).
The W boson is a weak force particle like the Z boson, but experiments show it is slightly (about 10%) lighter than the Z boson.
Modern physics treats this mass tilt as a mysterious parameter called the "Weak mixing angle (Weinberg angle)," but with this theory, it is self-evident just by looking at the geometry.
As shown in Figure 2, the photon and Z boson are flat "plane waves." However, the W boson, which carries a positive or negative electric charge, possesses the properties of a "spherical wave" expanding in all directions.
The wave front of the spherical W boson does not face directly forward relative to the direction of propagation like the Z boson; geometrically, it overlaps with a "slight tilt."
Because the wave is slightly tilted relative to the direction of propagation, the degree of interference is slightly less than that of the head-on colliding Z boson, and its mass( \(M_W\) ) is correspondingly lighter.
(Note: Calculating the overlap between this spherical wave and the plane wave yields a value that perfectly matches the experimental value of the weak mixing angle down to the final digit.)
\[M_W=M_z\cos{\theta_W}\]
Conclusion: Mass Was the "Direction of the Wave"
The differences in the masses of elementary particles were not arbitrary parameters decided by God.
They were determined by pure geometry: the "direction of the wave (whether it is parallel, perpendicular, or tilted relative to the direction of propagation)" as the particle moves through space.
Once we understand that the true nature of mass is "interference with oneself," we are ready to solve the universe's greatest mystery.
Next time, armed with this geometry of "direction," we will uncover the true identity of the unobservable cosmic ghost: "Dark Matter."
