Redshift without loss

Any account of redshift must face a firm rule of wave physics. In a medium that does not change over time, a wave's frequency cannot change along its path. Its wavelength can change, as it does when light slows inside a glass lens, but its frequency cannot.

That rule excludes an energy toll paid by light in flight. Lowering the frequency on the way would mean destroying crests, which means absorbing or scattering the light, and scattering would blur distant galaxies, which stay sharp. The measurements agree: the Tolman surface brightness data rule out the simplest "tired light" model at more than 10 standard deviations, and the light curves of distant supernovae unfold more slowly by 1 + z, within the precision of the measurements.

RSI's answer keeps the rule. Free light keeps its frequency in flight, because the speed of waves in the medium is unchanged; what changes over time is the tightness of the medium's folding, and with it the size and rhythm of every knot. Redshift is the ratio between the rhythm of matter when the light left and the rhythm of matter now.

Because that comparison applies to everything carried on the light, a supernova's rise and fall stretches by the same 1 + z as its waves, as observed. A lens raises no puzzle at all: light slows inside it and leaves at its original frequency, and on a cosmic journey it likewise loses nothing.

The idea has a mathematical precedent. Christof Wetterich (2013, "A Universe without expansion") showed that the standard cosmological history can be rewritten exactly, by a change of field variables, as one in which the universe does not expand while the masses of particles and the Planck mass grow together. Because only dimensionless ratios are observable, the redshift, the stretching of supernova light curves, the Tolman dimming and the data read as acceleration come out the same. In Wetterich's model that history is driven by a scalar field; RSI proposes instead that its physical cause is the breathing of the Eternal Consonance's folds. The breathing is primary and matter rides it, since even an atom is mostly medium.

Nothing in this account compresses the medium, and nothing measured locally changes. Folding more tightly changes the shape of the medium's waves, not the volume of any part of the medium, so the medium's flow stays free of compression; its mass-equivalence per length rises measured against free light only because the energy of its waves does. And because every ruler and clock is made of knots that tighten with the fold, every local measurement of the Planck length, the 1.85 × 10⁴³ Hz heartbeat, the 0.73 N tension, the 8.12 × 10⁻¹⁸ kg/m density, the 8.23 × 10²⁸ Pa clamp and the speed of light gives the same value in every era. These are present values, the same everywhere at any one time. Only a comparison with light that has travelled freely since long ago reveals the change, and that comparison is the redshift. Measured against such light, the whole scale of the knots has tightened together; the tension and the medium's density have risen together, each as the square of the rise in mass, since a force is an energy per length and both change; their ratio, and so the speed of light, is unchanged, and the clamp, a force per area, has risen as the fourth power, which is the same statement Wetterich's mathematics makes when the masses of particles and the Planck mass grow together.

Several requirements remain open. RSI must show what makes the medium's folding tighten and slacken over the cycle, how long its rising side lasts, and what happens at the turn. Measured against free light, the knots gain energy as they tighten, as a stretched vortex spins faster, and so does the medium itself, since its tension, inertia and baseline energy density all rise; measured locally nothing changes except that old light reads as weaker. Because every store of energy made of knots, black holes and the Still Core included, scales with the same yardstick, moving energy between them cannot balance the books. RSI proposes instead that the breathing is itself an oscillation of the medium that carries energy of its own, like a pendulum trading motion for height. Counting the energy of the breathing itself, the total is fixed at every moment, as a pendulum's is, and energy is conserved locally at every place and moment. Within a cycle the breathing lends energy and takes it back: measured against free light, the knots and the medium gain as the fold tightens and give it back as it slackens; measured locally, the exchange is with old light, which reads as weaker. Because the breathing returns to the same state each cycle, what it lends over a full cycle it takes back, though light, stars and galaxies made during the cycle need not return to where they began. RSI must still show how much energy the breathing carries, enough to cover the rise in the medium's own baseline energy as well as the knots', and that the exchange balances over the cycle. Gravity must change in step too, so that every measured ratio stays fixed: distant quasars show the fine-structure constant unchanged to a few parts in a million, the natural reactor at Oklo limits change over the last two billion years far more tightly, and lunar laser ranging shows gravity's strength relative to everything else is steady.