Conjugate matter and the velocity gate on The Broken-Born program

The velocity gate

Mon, 01 Jan 0001 00:00:00 +0000

The velocity gate is a factor in the self-interaction of conjugate matter χ that turns the interaction off between two particles that approach each other with a large relative velocity. For an ordinary force carried through position space, the scattering amplitude depends on how much momentum the two particles exchange; the gate makes it depend also on the momentum with which they approach, a variable that, according to the checkpoint, no carrier local in position produces. In signal terms, an ordinary contact force acts where two waveforms overlap, and the gate acts only where their spectra overlap as well. The program first postulated the gate as a Gaussian, then derived its mechanism from exchange of the momentum graviton X between conjugate particles. The mechanism stands as a structural derivation; the exact shape of the cutoff is open. The gate is what lets conjugate matter scatter off itself in dwarf galaxies, where dark matter moves slowly, and not in galaxy clusters, where it moves fast.

Dual stress T̃

Mon, 01 Jan 0001 00:00:00 +0000

The dual stress, written T̃, is the quantity through which matter couples to the momentum graviton X, in the way the stress-energy tensor is the quantity through which matter couples to the ordinary graviton. Stress-energy is built from derivatives of a matter field along spacetime and describes how energy and momentum are distributed in position; the dual stress is built from derivatives along the momentum directions and so reflects how the field is structured across momentum, the spectrum side of the same field. Exchange of X between the dual stresses of two particles of conjugate matter produces the velocity gate. The calc notes define the dual stress in words and give no formula for it. Why it is strong for conjugate matter and weak for ordinary matter is an open problem.

The gate mechanism: X exchange over fiber overlap

Mon, 01 Jan 0001 00:00:00 +0000

The gate mechanism is the program’s derivation of the velocity gate: two particles of conjugate matter interact by exchanging the massive momentum graviton X, and they can do so only where their wavepackets overlap in momentum space. A conjugate quantum has a finite width μ along the momentum directions, as an atomic nucleus has a finite radius in space. A nucleus’s size cuts off its scattering at large momentum transfer; the χ quantum’s momentum width cuts off its interaction at large relative momentum, which is the same construction with position and momentum exchanged. Because X is heavy, its exchange acts as a contact interaction, and the overlap of the two wavepackets supplies the gate. The derivation is structural: it fixes what the interaction depends on, but the exact shape of the cutoff depends on a propagator and a profile that no document has computed.

The gated scattering law σ_T(v)

Mon, 01 Jan 0001 00:00:00 +0000

The gated scattering law gives the momentum-transfer cross-section σ_T of conjugate matter, the measure of how strongly its particles scatter off one another, as a function of the relative velocity v of a colliding pair. Because the velocity gate turns the interaction off at large relative velocity, self-scattering is strong in dwarf galaxies, where dark matter moves at tens of kilometres per second, and absent in galaxy clusters, where it moves at thousands; between the two, σ_T bends down at a knee near the gate velocity v*. Below the knee the scattering goes equally in all directions, unlike the forward-peaked scattering of the usual models with a light force carrier. The lab notebook first derived a sharp exponential cliff at v*; once the gate’s mechanism was found, the program kept only the knee, and the shape of its tail became an open question that observations could answer.

The scattering benchmark

Mon, 01 Jan 0001 00:00:00 +0000

The scattering benchmark is the set of numbers obtained by requiring the self-scattering of conjugate matter to produce the flat central cores observed in dwarf galaxies. Fitting the cores fixes the cross-section per unit mass at low velocity; with an assumed mass for the carrier of the momentum transfer, that fixes the mass of a χ particle at about 70 MeV for a coupling of order one. The checkpoint keeps only this mass relation. The other benchmark numbers, among them the prediction that galaxy clusters show no self-interaction at any sensitivity, appear only in the lab notebook, rest on a Gaussian gate tail that is now an open question, and have never been checked by machine. The benchmark also fixes the coupling that the program’s Debt-3 calculation used to rule out collective clumping of χ particles.

Open: the gate shape (OP4)

Mon, 01 Jan 0001 00:00:00 +0000

The gate shape is the exact form of the function F that turns off the self-interaction of conjugate matter at large relative velocity. A Gaussian F falls off faster than any power of the velocity; a rational F, a ratio of polynomials, falls off as a power law. Which one holds depends on how the momentum graviton X propagates along the momentum directions of phase space, and on the profile of a single conjugate quantum along those directions; neither has been computed. The question is open, and it is observable: the tail of the knee in the self-interaction cross-section is the same function. The checkpoint counts the tail, not yet forced by any derivation, among the program’s risks of degeneration.

Open: the dual-stress enhancement (OP5)

Mon, 01 Jan 0001 00:00:00 +0000

The dual-stress enhancement is the unexplained gap between how strongly conjugate matter scatters off itself and how weakly ordinary matter couples to the same carrier. In the program both kinds of matter couple to the momentum graviton X: conjugate matter through its dual stress, ordinary matter through the spacetime metric. Fitting the flat cores of dwarf galaxies needs a self-scattering cross-section that the checkpoint calls nuclear-scale, while ordinary matter must feel X only at gravitational strength. Something must make conjugate matter’s coupling far more effective than ordinary matter’s; what it is, and by how much, has not been worked out. The checkpoint calls it the main open quantitative item of the conjugate sector.