Negative signed numbers can represent a variety of concepts depending on the specific context in physics. Sometimes, their meaning is ambiguous, and in quantum equations, the physical interpretation of these quantities can be uniquely challenging. For example, the Dirac equation is well-known to have both positive and negative signed solutions. Today, physicists still debate the physical significance of the negative signed solutions. One way to confer meaning to these ambiguous negative signed quantities is to express them in an expanded dimensional canvas. But how might such a canvas be conceived?

Part 1 of this paper sketches a new approach showing considerable promise. The fundamental symmetry of positivity and negativity seem to be built into the very fabric of the universe at subatomic scales. In consonance with Rowlands’ concept of totality zero, these fundamental symmetries can be shown to naturally admit an alternative explanation for conceptualising the shape and content of space at subatomic scales. The approach posited is that a recursive pseudo Riemannian cobordism (PRC) of manifolds can describe the shape of space using an expanded nD + 1 space coordinate system. The advantage of this system is that it confers physicality on abstract nD mathematical spaces that are conventionally assumed to map the structure of reality. The revised shape of space admits physical content consistent with experimental findings in an altogether different way. The physical system of two surfaces connected by a small, variable length, recursive dimension, constitutes a recursive cobordism, a modification of the one conceptualised by P. Yodzis. 

The new frame of thinking distinguishes between the content of space – light and matter – and the shape of space in which that content exists. Two elementary particles – analogous to the photon and electron - are described as embedded deterministic objects in this space. 

By adding a small, variable length +1 dimension that runs perpendicular to every direction in nD space, the emergent nD + 1 space physical system allows us to account for the ubiquitous negative signed quantities that emerge in certain quantum equations. It also admits a qualitative, deterministic expression of Maxwell’s equations, the Schrödinger equation and the Dirac equation.

This naturally leads to a deeper understanding of Rowlands' fundamental parameters of space, time, mass and charge, and delivers new insight into our understanding of condensed matter physics. Most tellingly, the approach opens the way to conceptualising subatomic particles, such as photons and electrons, as real physical objects existing in 3D + 1 space rather than appearing as statistical probabilities in abstract 3D space.

Negative signed numbers can represent a variety of concepts depending on the specific context in physics. Sometimes, their meaning is ambiguous, and in quantum equations, the physical interpretation of these quantities can be uniquely challenging. One way to confer meaning to these ambiguous negative signed quantities is to express them in an expanded dimensional canvas. 

In Part 1, a new approach showing considerable promise was introduced. Part 2 of this paper extends this approach. It was noted that positive and negative signed quantities seem to be built into the very fabric of the universe at subatomic scales. In consonance with Rowlands’ concept of totality zero, certain fundamental symmetries were shown to naturally admit an alternative explanation for conceptualising the shape and content of space at subatomic scales. The new approach posited that a pseudo Riemannian cobordism (PRC) of manifolds can describe the shape of space using an expanded nD + 1 space coordinate system. The advantage of this system is that it confers physicality on an otherwise abstract mathematical space. The revised shape of space admits physical content consistent with experimental findings in an altogether different way. Two particles – the fundamental particle of light analogous to the photon and the fundamental particle of matter, analogous to the electron, were described. 

In Part 2, the structure and dynamics of two additional particles analogous to the proton and neutron will be described in a PRC. The topology of these particles provides compelling answers to certain questions that have long eluded quantum theorists. In particular, the structure and dynamics of particles analogous to quarks and their force carrying gluons can be described deterministically, and this offers significant advantages. The elusive reasoning that gives rise to the strong interaction, the property of confinement, and the origin of fractional colour charges can all be seen as inevitable consequences of the new understanding. This completes the cobordism manifold picture of subatomic particles that constitute the atom.

This new approach opens the way to reconceptualising protons and neutrons as real physical objects existing in 3D + 1 space rather than appearing as statistical excitations associated with an infinitely extensive quantum field in 3D space. This naturally leads to a deeper understanding of subatomic reality, the fundamental parameters of space, time, mass and charge, and delivers new insight into our understanding of condensed matter physics.