A study on visualizing the solid angle Ω₂ and reorganizing electromagnetic quantities into a symmetric diagram.
The original aim of parity1997 was:
- to visualize the total solid angle of a sphere Ω₂, and
- to obtain a bird’s‑eye view of how electromagnetic quantities are positioned with respect to rational and unrational units.
This was a dimensional‑analysis exercise, not a modification of Maxwell’s equations.
During the analysis, it was found that by:
- explicitly including Ω₂ in dimensional expressions, and
- introducing the characteristic impedance of vacuum
$Z_P$ as a dimensional operator,
the major electromagnetic quantities fall naturally into a highly symmetric arrangement.
This symmetry was not the initial goal—it emerged unexpectedly and became the central educational result of the paper.
Figure 1 shows:
- electric and magnetic quantities
- arranged in parallel, symmetric positions
- connected through solid angle and impedance
- clarifying the structural relationships among
- field strengths (E, H)
- potentials (V, V_m)
- fluxes (Φ, Ψ)
- densities (B, D, ρ, j)
This diagram is the conceptual heart of parity1997.
Figure 2 provides the intuitive breakthrough:
- A viewpoint observes a current loop.
- The magnetic potential corresponds to the solid angle subtended by the loop.
- This makes Ω₂ a natural geometric quantity.
- It explains why magnetic potential and electric potential appear in symmetric positions in Figure 1.
This is the “Aha!” moment of the paper.
To avoid misunderstanding:
-
Eliminating ε₀ or μ₀ was not the purpose.
Their disappearance is a by‑product of rewriting dimensions using solid angle(Ω₂) and impedance($Z_P$ ). -
The system is not a reduction of MKSA.
MKSA is 4‑dimensional; the proposed MKSΩ₂$Z_P$ framework is 5‑dimensional.
It is a rearrangement, not a contraction. -
All formulas remain mathematically equivalent to SI.
Only the dimensional expression is rewritten.
Parity1997 provides:
- a clearer conceptual map of electromagnetic quantities
- a geometric interpretation of magnetic potential
- a symmetric arrangement that aids teaching and understanding
- a way to see electric and magnetic quantities as parallel structures
The diagrams—not the algebra—are the main contribution.
Original paper: parity1997 (1997).