A balanced source can contain unequal sector populations, but symmetry alone does not choose their sign or size. A predictive theory must derive which states populate the observed sector, how a baryon asymmetry is generated or transferred, and why subsequent reactions do not erase it.
The quantity a cosmological model must explain
Baryon asymmetry is a signed excess of baryons over antibaryons. A convenient observable is ηB = (nB − nB̄)/nγ, where nγ is the photon density. Standard cosmological analyses require a small positive value, of order six parts in ten billion. The baryon density inferred from the Planck cosmological-parameter analysis supplies an important quantitative benchmark when translated within that cosmological model.
The task includes more than explaining why most surviving ordinary matter is baryonic. A theory must explain the small signed abundance after pair annihilation, the thermal and expansion history that preserves it, and the relation between visible matter and any proposed complementary sector. Equal total source charge can be compatible with a visible excess, but only if the distribution and interactions of the sectors are specified.
The original SMM/DTT proposal
The original article, drawing on Chapter II of Ultimate Symmetry, associates matter and a complementary incorporeal sector with differently oriented temporal development. Re-creation is described as a repeated passage between primordial source configurations and their differentiated manifestations. In that ontology, an apparent imbalance in one outward description need not mean that the full source structure lacks a complementary relation.
A physical development of this idea should distinguish the broad metaphysical interpretation from the particle quantum numbers that enter a detector or a cosmological calculation. The proposed complementary sector needs its own state space, energy, charges and coupling to the observed sector. Laboratory antiparticles remain excitations of the same measured fields; they are not automatically identical to every hidden or oppositely oriented source state.
The six nested inner stages organize formation within the source, and the seventh is outward completion. Temporal orientation can affect which records become available, but it is not a collection of independent time axes in which missing particles can be placed without a dynamical account.
A globally balanced state with a visible bias
Consider a simple model with visible and hidden baryon-number operators. A normalized source state could have the form
Every term has total baryon number zero. Nevertheless, the visible expectation is 〈Bv〉 = 2p − 1, while the hidden expectation is its negative. This gives a precise example of sector asymmetry with global conservation. It also exposes the essential selection problem: a source symmetry that fixes p = 1/2 gives zero average visible asymmetry.
For N such formation events and Nγ final photons, a simple independent-event estimate would give ηB = N(2p − 1)/Nγ, before including further reactions. The observed small number therefore depends on a calculated bias and on the abundance history. Neither the existence of two orientations nor global charge balance fixes it. A symmetry-breaking state, a biased transition amplitude, or a specified boundary condition must do that work.
Translate temporal selection into rates
Sakharov’s baryogenesis argument identifies the familiar requirements for generating an asymmetry from a symmetric initial state in the usual local, CPT-invariant setting: baryon-number-changing processes, C and CP asymmetry, and departure from thermal equilibrium. A temporal model should show how its source operations implement the relevant ingredients or state precisely which premise is changed.
For a homogeneous expanding description, a useful effective equation is
Here nΔB is the net visible baryon density, SB the signed production or transfer rate, Γw the washout rate, and H the expansion rate. A common source update should determine SB from its amplitudes and physical clock. If total baryon number is conserved across sectors, the hidden-sector collision term must be −SB + ΓwnΔB. It balances the entire visible collision term, including any visible washout that represents transfer to hidden states. This is a concrete conservation law rather than an appeal to unobserved compensation.
Preserving the asymmetry and accounting for energy
After production, the asymmetry can survive only if processes that erase it become sufficiently ineffective. A source construction that generates a bias at every completion but immediately re-equilibrates it may leave no cosmological signal. Calculating the competition among generation, transfer, annihilation and expansion is therefore part of the mechanism.
The complementary sector also has a stress-energy contribution. Opposite baryon number does not imply negative energy, and equal positive energies do not cancel gravitationally. A hidden compensation scheme must calculate its energy density and interaction history. These determine effects on cosmic expansion, structure formation and the radiation budget even if direct electromagnetic detection is suppressed.
One promising distinction is between a symmetry of the source law and a symmetry of the selected state. A law can treat the two sectors equally while a particular cosmological solution populates them differently. The source must then explain the selection or characterize a genuine degeneracy, including whether the observed sign is predicted or an initial-condition choice.
A concrete route to a new result
The next useful model would define a sector-exchange operation, a baryon-number observable and source transitions that produce a calculable CP-sensitive interference term. It would evolve those transitions through a thermal history and compute ηB, the compensating abundance and any residual portal interaction together. Introducing a free tiny bias solely to match ηB would leave the central question untouched.
Such a construction could yield correlated predictions: a relation between visible and hidden abundance, a neutrino-sector phase connected to the source of the asymmetry, a freeze-out scale, or a measurable baryon-number-violating process. The original temporal-sector proposal becomes physically distinctive when the same mechanism fixes several of these quantities and remains consistent with laboratory antimatter and cosmological energy accounting.
Books, papers and further reading
- Ultimate Symmetry — Chapter II, temporal-sector interpretation
Original SMM/DTT discussion of complementary sectors and differentiated source configurations.
- Duality of Time — Chapter V, temporal postulate
The underlying distinction between inner generation and outward observation.
- A. D. Sakharov, Violation of CP invariance, C asymmetry, and baryon asymmetry of the universe
The original 1967 proposal, reprinted in Soviet Physics Uspekhi 34, 392–393 (1991); conditions for dynamical baryogenesis.
- Planck Collaboration, Planck 2018 results. VI. Cosmological parameters (2020)
Published in Astronomy & Astrophysics 641, A6; baryon abundance within a specified cosmological model.