The hierarchy problem

Two related meanings of hierarchy

Gravity is extremely weak in interactions between elementary particles at laboratory energies. In units with ℏ = c = 1, its dimensionless strength at energy E is α_G(E) = GE² = (E/M_Pl)², using the unreduced Planck mass M_Pl = G^−1/2. A large separation between E and M_Pl therefore produces a very small gravitational coupling.

The Higgs hierarchy question is more specific: why does the electroweak scale remain small when a theory contains much heavier degrees of freedom coupled to the Higgs? Those degrees of freedom can shift the Higgs mass parameter. Explaining the numerical separation and protecting it against such shifts are connected tasks. Stephen Martin’s field-theory treatment sets out this sensitivity and the symmetry-based cancellation used in supersymmetric models.

The original proposal: a larger complementary symmetry

The original hierarchy article treats the weakness of gravity as a feature of the dimensional and temporal organization of interactions. It places the physical world within a broader account that also contains psychical and spiritual realms, described as evolving in complementary or conjugate temporal directions. In that interpretation, the full structure possesses a symmetry that is only partly visible in ordinary physical observations. The hierarchy, apparent matter asymmetries and missing partners are connected to this restricted view of a larger whole.

The proposal is developed through the complementary-world discussion and the account of eternal symmetry in Chapters VI and VII of Duality of Time. Its central physical idea is that a large source symmetry can coexist with unequal outward interactions because different sectors project differently into completed records. The terms for the additional realms belong to the author’s wider interpretation. A quantitative hierarchy model translates their proposed complementarity into specified state sectors, transformations and couplings. The six inner stages remain dependent generative roles; their ordering does not itself add six laboratory time coordinates.

Making a weak outward coupling from a shared source

One concrete candidate is to divide a source carrier into a visible sector and a complementary sector. Let P select the part available to ordinary measurements, and let a source interaction connect normalized states |s⟩ and |r⟩. A small overlap can give a weak effective interaction even if the underlying source coefficient g_* is substantial:

g_eff = g_* ⟨r|P|s⟩ = εg_*.

This equation turns the language of partial expression into an explicit matrix element. If the source symmetry makes the sectors exactly orthogonal, ε vanishes. A small, specified breaking of that symmetry can then generate ε. The construction becomes predictive when its representation and breaking rule determine the overlap, rather than inserting a small number as an independent fit.

Protection is a further benefit of a symmetry that forbids the coupling in the ε = 0 limit. Corrections involving that connection must carry the same symmetry-breaking factors. This provides a route by which the larger source organization can both create a hierarchy and preserve it.

A worked heavy-sector estimate

Consider an illustrative scalar sector containing a light Higgs field H and a heavy field X of mass M. Specify the portal coefficient λ_HX = ε²g², as would be appropriate if the selected completion rule supplies two suppressed connections. A heavy loop then gives a threshold correction of characteristic size

|δm_H²| ∼ ε²g²M²/(16π²).

The numerical factor and logarithms depend on the actual fields and matching prescription; the displayed equation isolates the scale dependence. Requiring this contribution to be no larger than a chosen light scale m_h² gives εg ≲ 4πm_h/M. Thus a sector that is vastly heavier must communicate correspondingly weakly, unless an additional cancellation operates.

This is a proposed realization of the original complementary-sector idea, rather than a value derived in the original article. Its strength is that a finite source model can calculate ε and test the inequality. Other heavy sectors, including gravity, must be included in the complete matching calculation.

What the larger symmetry should accomplish

There are two useful implementation routes. A selection symmetry can suppress all allowed connections to a heavy sector. Alternatively, a symmetry can relate different contributions so that their large parts cancel. In the latter route, matching masses is insufficient: the interaction vertices and multiplicities must obey the same relation. Otherwise the cancellation disappears when another process is considered.

The distinction matters for the original proposal about hidden partners. A partner that contributes to a physical cancellation has a precise mathematical role in the effective theory, even if ordinary detectors cannot produce it. Its influence must follow from the source dynamics and observable reduction. Merely assigning it a complementary temporal label does not supply the required relation among amplitudes.

For SMM/DTT, the promising organizing principle is one joint source law that fixes both visible and complementary responses. The hierarchy then becomes a statement about that law’s protected small eigenvalues or matrix elements, with consequences across several physical processes.

How to develop and test the proposal

Begin with a source action, a representation of its symmetry, and a physical readout. Calculate the light spectrum and every heavy contribution to its mass parameters. Vary the resolution scale and check whether the light scale remains stable without repeatedly readjusting unrelated constants. This establishes how the hierarchy survives the passage from inner description to outward field theory.

The same calculation should identify measurable remnants: modified Higgs interactions, additional effective operators, new resonances if accessible, or a relation between gravitational normalization and matter response. A model that fixes one suppression factor in several independent observables is much more informative than one that fits each quantity separately.

The original symmetry idea consequently suggests a focused research question: can the complementary source sectors select the observed weak communication and protect the electroweak scale through one calculable mechanism? An explicit spectrum and threshold calculation would answer that question directly.

Books, papers and further reading

1. Mohamed Haj Yousef — Duality of Time

   Chapter III: hierarchy proposal; Chapter VI, Consciousness and the Three Orthogonal Worlds; Chapter VII, Alchemy and Eternal Symmetry. Native edition and contents record.

2. Mohamed Haj Yousef — Ultimate Symmetry

   Native record of Volume III and its normal, super, hyper and ultimate symmetry chapters.

3. Stephen P. Martin — A Supersymmetry Primer

   Version 7, Section 1: Higgs sensitivity to heavy physics and the role of symmetry in radiative cancellations.