Since more than two centuries physics knows two categories of super-tiny objects that instruments cannot observe separately, but that obviously occur in huge quantities. If these super-tiny objects form coherent sets, then these sets constitute the objects that we currently consider as fundamental to quantum physics.
The super-tiny objects are solutions of homogeneous second order partial differential equations. One of these equations is the well-known wave equation. Solutions of differential equations do not occur spontaneously. A suitable actuator generates them. For example, waves require a periodic harmonic actuator. One-shot actuators cause the objects that are subject of this blog chapter. They are shock fronts, and they only occur in odd numbers of participating dimensions. I have given them names. I call the one-dimensional shock fronts warps, and I call the spherical shock fronts clamps.
During travel, warps keep their shape and their amplitude. Thus, they can travel huge distances without losing their integrity. In contrast, clamps keep their shape in the direction of travel, but their amplitude diminishes as 1/r with distance r from the trigger point. They integrate into the Green’s function of the carrier field. Since shock fronts travel at high speed, the clamps quickly fade away. But in the mean time, the clamps cause a tiny temporary deformation of the carrier. So, clamps can be considered to be massive objects, and therefore, clamps carry a standard bit of mass. Only recurrently regenerated coherent and dense swarms of isotropic three-dimensional one-shot triggers can cause a significant and persistent deformation of the carrier field.
A stochastic process that generates the hop landing locations of a point-like particle and that owns a characteristic function which ensures the coherence of the resulting hop landing location swarm can achieve a significant and persistant deformation of the carrier field that instruments can perceive. The hop landing represents an artifact on which the carrier field reacts with a clamp. The characteristic function equals the Fourier transform of the location density distribution of the generated swarm and acts as a displacement generator for the swarm. Consequently, at first approximation, the swarm moves as a single (coherent) object. The location density distribution equals the squared modulus of the wavefunction of the particle. The swarm causes a deformation of the carrier that equals the convolution of the Green’s function of the carrier field and the location density distribution of the swarm.
For example, if the stochastic process produces a Gaussian hop landing location distribution, then the deformation of the carrier field is described by ERF(r)/r. This descriptor is a perfectly smooth function that already at a short distance behaves as 1/r. This indicates that the gravitation potential of elementary particles is not afflicted by singularities.
The described particle is an elementary module and exists in multiple types. Together these elementary modules generate all other modules. Thus clamps play the role that the Higgs boson is claimed to perform. However, the LHC can impossibly observe separate clamps. The LHC can certainly observe the resulting elementary modules. The description shows that quantum physics simply unifies with gravitation.
No instrument can detect warps in isolation. However, if an actuator emits them equidistant in strings, then the string will feature a frequency. If independent of this frequency, the duration of the emission is constant, then the warp string can obey the Einstein-Planck relation E=h v. This means that each warp carries a standard bit of energy. Thus such warp strings implement the functionality of photons.
EM waves can never cross the huge distances through nearly free space that warp strings can.
How can physics ignore these super-tiny objects for more than two centuries while these super-tiny objects obviously play such an important role?
Quaternionic differential calculus offers TWO homogeneous second order partial differential equations. One of them is similar to the wave equation. The other is better suited for describing warps because it enables the attachment of polarization to warp strings.