The interaction of particles with the Higgs field is indeed related to the phenomenon of mass and the limitation on acceleration to the speed of light.
According to the prevailing theory in particle physics known as the Standard Model, particles acquire mass through their interactions with the Higgs field. The Higgs field permeates all of space, and particles such as quarks and electrons interact with this field, effectively acquiring mass. The Higgs field is associated with a particle called the Higgs boson, which was discovered at the Large Hadron Collider (LHC) in 2012.
Particles that have mass experience resistance to changes in their motion, which we refer to as inertia. As a particle accelerates, it requires an input of energy to increase its speed, and its inertia resists changes in that speed. As a particle with mass approaches the speed of light, its inertia becomes infinitely large, making it impossible to accelerate it to or beyond the speed of light within our current understanding of physics.
This limitation on the speed of particles with mass, such as electrons or protons, is a fundamental aspect of the theory of special relativity, proposed by Albert Einstein. Special relativity provides a framework for understanding the behavior of objects that move at high speeds, close to the speed of light. It establishes that the speed of light in a vacuum is a constant, and particles with mass cannot reach or exceed this speed.
In summary, the interaction of particles with the Higgs field is related to the origin of mass, and mass itself plays a role in limiting the acceleration of particles to the speed of light.