The physical question is whether temporal topology produces a nonzero magnetic flux through an observable closed surface. This turns the original proposal into a constructive programme: derive the electromagnetic connection, its charge lattice, and the rule that permits or forbids isolated magnetic excitations.
What a magnetic monopole would mean
A magnetic monopole is an excitation carrying net magnetic charge: a closed surface surrounding it would enclose a nonzero outward magnetic flux. Cutting an ordinary bar magnet does not produce such an object; each piece retains two poles. In quantum theory, a monopole would also constrain the allowed electric charges. Dirac’s 1931 analysis established this connection by requiring consistent quantum phases around magnetic flux.
The existence of quantized electric charge does not logically require that an isolated monopole be accessible in every physical theory. The implication runs from an admissible monopole and consistent charged states to a quantization condition. The SMM/DTT question therefore has two parts: how a charge lattice emerges, and whether the source dynamics allows magnetic charge to survive as an outward, localized object.
The original temporal mechanism
In the proposal developed in Chapter III of Duality of Time, a spatial configuration is assembled through inner generation before it is encountered in outer time. The most elementary source contribution cannot be separated from the higher relations through which it becomes observable. The original article identifies that elementary role with magnetic structure and interprets the familiar interactions as different expressions of nested formation. Its explanation for the absence of free monopoles is consequently structural: the primordial contribution appears through completed couplings.
The six inner stages are dependent formation roles within one process; the seventh is outward completion. They are not six independent observer clocks or extra timelike coordinates. This permits a clear mathematical task: start with source transitions and retained phase relations, then derive the connection measured by charged probes on completed space. The order of construction matters because neither a surrounding sphere nor its magnetic flux exists as an observable before spatial relations have been supplied.
A concrete topological calculation
Suppose the completed electromagnetic description has a dimensionless U(1) connection a, normalized so a unit electric charge acquires the phase exp(i∮a). Its curvature is f = da. For a closed surface covered by compatible gauge patches, the first Chern number is
In a convention where g denotes total magnetic flux and ℏ = c = 1, this gives eg = 2πn. Stating the flux convention avoids a common ambiguity: different definitions of magnetic charge move factors of 4π between the charge and the field. The invariant content is the integer winding of the transition function between the gauge patches.
A periodic inner phase offers a possible origin for integer representation labels: U(θ)|n〉 = exp(inθ)|n〉 and U(2π) = I require integer n. That observation supplies a candidate charge lattice, but a map from the inner cycle to the outer connection is still needed. The quantum phase here uses ordinary i² = −1; the split-complex unit j² = +1 used for hyperbolic temporal geometry has a different algebraic role.
When source winding becomes a physical monopole
A useful source model would assign a phase or parallel-transport operator to each completed link. Products around small loops would define curvature. Summing oriented flux through the faces of a closed cell would then determine whether that cell contains magnetic charge. This is an operational prescription: it says which combinations of completed measurements test the proposal.
Two different outcomes are possible. The completion rule could force all closed-cell fluxes to cancel, despite nontrivial inner winding. Alternatively, it could admit defects whose uncancelled flux is an integer multiple of a basic unit. The first outcome implements a precise absence of isolated monopoles; the second predicts a monopole sector and calls for its energy, size, production rate, and stability. The ontology by itself does not select between them.
There is also a distinction between magnetic flux and electric charge. A particle can carry a nonzero U(1) representation label while the observable field has no magnetic source. A successful construction should compute both quantities, rather than assign them the same integer by convention.
Connecting the proposal to searches
The MoEDAL collaboration’s 2022 search examined magnetic monopoles produced through the Schwinger mechanism in heavy-ion collisions. Such searches constrain specified production mechanisms and charge ranges. They provide a concrete experimental comparison for a DTT model that admits outward magnetic excitations; they do not directly test an inner source role with no isolated magnetic flux.
If the model predicts a strict exclusion of isolated monopoles, a confirmed particle with reproducible nonzero magnetic flux would challenge that completion rule. If monopoles are permitted but heavy or short-lived, the useful comparison is a predicted event rate including detector acceptance. Explaining a null result by simply declaring the source inaccessible would leave no quantitative connection to the experiment.
The same distinction guides indirect tests. A proposed conversion between electromagnetic and gravitational responses requires a coupled action and an energy budget. The older dimensional analogy can motivate that action, but a force conversion law must specify conserved quantities and observable fields.
The calculation that would advance the model
The next substantial result would be an explicit source-to-connection theorem: a defined inner update generates compact electromagnetic phase, fixes the electric charge unit relative to other couplings, and determines the allowed closed-surface fluxes. It should identify which part follows from topology and which part follows from the source energy or completion constraint.
That result would strengthen the distinctive SMM idea that interactions are properties of generated geometry. It would connect an elementary source role to quantities a detector can measure, while explaining why a magnetic structure may be fundamental even when its isolated particle realization is absent.
Books, papers and further reading
- Duality of Time — Chapter III and Chapter V
The problem survey and the temporal postulate provide the original SMM/DTT interpretation.
- P. A. M. Dirac, Quantised singularities in the electromagnetic field (1931)
Published in Proceedings of the Royal Society A; the phase-consistency origin of electric–magnetic charge quantization.
- MoEDAL Collaboration, Search for magnetic monopoles produced via the Schwinger mechanism (2022)
Published in Nature 602, 63–67; a specific experimental production and detection test.