The research program on The Broken-Born program

Born's question

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

Born’s question asks why physics singles out position when quantum kinematics treats position and momentum as equals. A quantum particle can be described by a wavefunction of its position or by a wavefunction of its momentum. The Fourier transform, the operation that turns a sound’s waveform into its spectrum, converts either description into the other exactly, and exchanging the two variables, with one change of sign, leaves the rules of quantum kinematics unchanged. The laws of motion do not share this evenness: atoms are small in space rather than in speed, forces fall off with distance rather than with difference in velocity, and general relativity curves space-time while leaving the space of momenta flat. Max Born raised the question in 1938. The Broken-Born program is one proposed answer: the symmetry is exact in the laws and broken by the vacuum.

The hard core: spontaneously broken Born reciprocity

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

The hard core is the assumption the Broken-Born program keeps fixed while its other claims are tested and revised: Born reciprocity, the quarter-turn (x, p) → (p, −x) of quantum phase space (the space of positions and momenta taken together), is an exact symmetry of the laws, and the vacuum, the universe’s lowest-energy state, breaks it spontaneously. Only one structure of phase space is fixed in advance, the symplectic form ω, which encodes the constancy of Planck’s constant. The neutral metric η, the structure that marks which directions count as position, belongs to the vacuum state rather than to the laws, and it is the order parameter that distinguishes our vacuum from its mirror image. A cooled magnet is the standard picture: the laws governing its atoms single out no direction, but its magnetized state points in one. Checkpoint #11 v2.2 records the hard core as intact and sharpened twice by corrections that later derivations forced. The toy models, two small field theories built to test the idea, added two qualifications: a definite polarization, that is, a definite choice of which directions count as position, needs an extra potential, and the breaking has physical effect only once matter couples to the sign of the order parameter.

The conjugate universe: one state, two descriptions

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

In the current program the conjugate universe is a second description of our universe rather than a second world: the description of the one physical state in momentum variables, related to the ordinary description as a sound’s spectrum is related to its waveform. It began as one of the program’s founding suppositions, a second universe organized around momentum and existing alongside ours. Two derived relations turned it into a second description. The constancy of Planck’s constant fixes the size of a cell of phase space, so as our universe expands its momentum-space description contracts by the same factor; and a derived translation rule says how energy described on the momentum side acts on our expansion. The two descriptions are synchronized rather than causally linked, so an event in one is the same event read in the other, which is how the program reads its predicted far-future halt and reversal of our expansion as a bounce of the conjugate universe. The idea that observers might live in the momentum description appears only in the popular articles and has no status in the program.

Founding suppositions and their fates

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

The founding suppositions are the eleven ideas P.R. brought to the program at its start. Appendix A of the checkpoint (#11) lists each with the fate the later work gave it. One became the program’s hard core. Others survived in changed form: the conjugate universe became a second description of one state, conjugate matter became a dark-matter candidate that clusters in space like any other, and the idea that momentum space has its own gravity became a heavy, hidden field. One was promoted to a theorem, one split into a dead half and a living half, one was already established physics, and two died, including the founding image of dark matter clumping in velocity rather than in space. The audit is the record of which parts of the starting picture the calculations kept.

The 'framework does no work' critique

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

“The framework does no work” is the referees’ objection that the program’s phase-space framework, Born reciprocity included, contributed nothing to the results of its dark-matter proposal. It was stated most fully in the third review round, against the withdrawn manuscript #14, which proposed superheavy monopoles of a hidden gauge sector. The referee found that every number in it came from standard hidden-sector physics plus one choice of coupling, which the framework motivated but did not fix. The objection shaped what came next. The program retired the candidate rather than claim a version of it that did not depend on the framework, and it made its next task an explicit model: an action in which reciprocity is a genuine symmetry that the vacuum breaks. The toy models meet the referees’ wording of that demand, but by the program’s assessment they answer the objection only in part, because the locality of ordinary matter in position still enters through an assumed coupling rather than following from the vacuum.

Assessment: a live research program

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

The assessment is the checkpoint’s own judgement of where the program stands, written in the terms of Imre Lakatos’s account of research programmes: a hard core that is kept fixed, auxiliary claims that may be revised, and the question of whether the program keeps producing new predictions (progressive) or only accommodates its failures (degenerating). Checkpoint #11 v2.2 finds the hard core intact and sharpened twice by corrections that later derivations forced. It lists the signs of progress and the risks of degeneration side by side, it names three predictions that observations could falsify soon, and it notes that the current dark-energy data already lean against one of them. Its verdict is that this is a live research program, and that the word “theory” waits on three open problems.