Two Horizons: How the Halves of a Pulse Go Home

What happens to a pulse that is cut in half? The smallest whole pulse is one Zinf cycle, 0 → 1 → 0: two Zinf bits, one written on the ascend and one returned on the collapse, (+1ᵇ) + (−1ᵇ), zero in sum and two in motion; it is one pixel running one Zinf cycle (Part 1.9). Our own pulse, one Tempo, is built of 2^(L+1) of these bits (Bits per Pulse, Part 1.6), and a particle is a pattern of many Tempos, held in place as matter or travelling as radiation. A whole pulse is what the physical layer is made of (Part 1.2; Part 1.10); half a pulse is data and nothing more. At a Null Well's horizon the pulse is cut in half, and each half goes home by its own door. This Part follows the two halves.

The Split at the Horizon

Physics describes a Null Well's glow by a pair: near the horizon the vacuum turns into real particles, one of each pair streams away and the other falls in carrying negative energy, so that the well's own mass becomes the radiation (Hawking, 1975; Part 3.13). Hawking called the pair picture a heuristic, the shorthand for a calculation about the field's modes near the horizon, and it is the shorthand Binary Pulse Theory reads. The horizon cuts pulses at the finest grain, Zinf pulse by Zinf pulse, each into its two halves. The ascending half, the write, escapes; the descending half, the return, falls in. A quantum of thermal radiation carries about 3.6 k_B of entropy, about five bits, so each Hawking quantum is a handful of Zinf pulses cut in two. The sign belongs to the direction of the transition, not to the bit: a bit is a count and is never negative, so the escaping half is +1ᵇ written and the falling half is −1ᵇ returned. Their sum is zero, so the split adds nothing and loses nothing, and the well loses one bit's worth with every half it takes in, which is why it shrinks.

Horizon Pulse Split G

①⥂ = (+1ᵇ)⭇ + (−1ᵇ)⭋ → (+1ᵇ) out, (−1ᵇ) in

A pulse cut at a horizon: the ascending half escapes, the descending half falls in

Where:

• ①⥂ [ↁ·2ᵇ] — one whole pulse at the Zinf grain, 0 → 1 → 0, two Zinf bits (Part 1.2)
• (+1ᵇ)⭇ [ↁ·1ᵇ] — the ascending half, 0 → 1, written
• (−1ᵇ)⭋ [ↁ·1ᵇ] — the descending half, 1 → 0, returned

➢ The physical layer is the whole pulse (Physical Fundamental Definition, Part 1.2: ⇗⚛(ↁ⭇ + ↁ⭋) = (0→1→0)); neither half alone is physical. The signs are directions, not negative counts.

Radiation Is Data in Transit

Matter is data held: a pulse that closes on itself in place, which is why it has a rest mass. Radiation is data in transit: nothing held, all of it moving, which is why light has no rest mass and moves at 𝒞→. The escaping half crosses the data layer at the Rhythm, as data does (the Data Light Speed Relation, Part 1.11); it is seen only where the halves complete whole pulses again, a photon being a few bits' worth of them, moving at 𝒞→ with energy ħω, its frequency set by the well's temperature. Its speed as data adds no energy, and it carries no message faster than light: the fast part is the data, and data has no physical effect until it pairs.

Horizon Bit Energy G

E⇡ = k_B · T_H · ln 2, T_H = ħ · c³ / (8 · π · G · M · k_B)

The least energy one escaping bit carries away: the Landauer cost at the well's temperature

Where:

• E⇡ [𝕄·𝕃²·𝕋⁻²] — the least energy one escaping half carries
• k_B [𝕄·𝕃²·𝕋⁻²·Θ⁻¹] — Boltzmann's constant
• T_H [Θ] — the Hawking temperature of the well
• ħ [𝕄·𝕃²·𝕋⁻¹] — the reduced Planck constant
• c [𝕃·𝕋⁻¹] — light speed
• G [𝕃³·𝕄⁻¹·𝕋⁻²] — the gravitational constant
• M [𝕄] — the well's mass

➢ Writing or erasing one bit costs at least k_B·T·ln 2 (Landauer, 1961; Part 2.9). A Sun-mass well sits at about 6 × 10⁻⁸ K, colder than the microwave background, so today it takes in more than it gives back; it begins to return only when the universe around it has grown colder still.

Evaporation Bit Count G

N⇡ ≤ 4 · π · G · M² / (ħ · c · ln 2) = A / (4 · ℓ_P² · ln 2)

A well that evaporates returns at most its horizon count of bits, and all of it at the Landauer minimum

Where:

• N⇡ [∅] — the bits a well returns by its glow over its whole life
• M [𝕄] — the well's mass
• A [𝕃²] — the area of its horizon, 16·π·G²·M²/c⁴
• ℓ_P [𝕃] — the Planck length

➢ Summing dN = c²·dM / (k_B·T_H·ln 2) as the well goes from M to nothing gives the bound. It is the same number as the Null Well's storage bound of Part 2.7, A/(4ℓ_P² ln 2): every bit a well can hold is a bit it can return. Its glow is thermal, so each quantum carries more than the minimum and the count of quanta is smaller; the bits, as information, are what the bound counts.

The Two Inner Horizons

A Null Well's event horizon is its outside: it faces into the universe, and what crosses it from the universe does not come back as matter. Inside every well and at the heart of every universe there is a second kind of horizon, and there are two of them, one for each half of the pulse.

Nullcore Horizon G

(−1ᵇ) → Nullcore

The singularity's horizon inside a Null Well: it takes in the descending halves

Where:

• (−1ᵇ) [ↁ·1ᵇ] — a descending half, falling in at the event horizon
• Nullcore — the singularity at the bottom of the well, the vacuum that becomes its child's Pulsecore (Part 3.10)

➢ The descending halves gather at the Nullcore, and by Return to Bifurcation the Nullcore becomes the child universe's Pulsecore: what one generation takes in, the next begins with.

Pulsecore Vacuum Event Horizon G

(+1ᵇ) → Pulsecore void

The horizon of a universe's own singularity: it takes in the ascending halves coming home

Where:

• (+1ᵇ) [ↁ·1ᵇ] — an ascending half, escaped from a Null Well
• Pulsecore void — the Pulsecore, the universe's own singularity: the Pulsecore vacuum is the throat at the heart of the torus (Part 3.6), and this horizon is the boundary between space and the throat

➢ Only data crosses it; into the pinpoint itself nothing crosses. It exists only once all the harmonics have been processed, up to h⥣ = 3·2^L (Part 3.6), and the Pulsecore has become a true void: before that the little that goes home goes through the Source at the throat and through the wells (Part 3.13); after it, at the close, the halves of every evaporating well come home through it.

The Pulsecore vacuum is the throat itself, the hole at the heart of the torus that joins a universe to its parent's well (Part 3.6); the Pulsecore Vacuum Event Horizon is the boundary between space and the throat. So the universe has many doors in and one door out. Matter gathers at the many outer horizons; the descending halves settle at each well's Nullcore and seed the next generation; the ascending halves travel the torus as data and, once the void is true, cross the Pulsecore Vacuum Event Horizon home. Nothing is lost on either side: the sum of the two halves is the pulse that was cut.

What Goes Home Lifts the Universe

Radiation in transit does not push space apart: its pressure is positive, and positive pressure slows an expansion (the first fifty thousand years, when radiation ruled, slowed hardest). What lifts is the Null Vacuum, whose pressure is negative, p = −ρ𝒞→² (Part 3.13). And only what goes home feeds the vacuum: Horizon Feeding (Part 3.13) counts the returning Data Matter and the wells' glow, never the energy radiation loses as space stretches, which would have made today's vacuum about a hundred million times stronger than it is measured to be. The route home is not everywhere, but what it feeds is: the vacuum's push is measured to be the same in every direction, so the lift is uniform even though the halves come home along the torus to one void.

How Much Radiation There Is

The figures below are for the observable universe, a sphere 46.5 billion light-years in radius, V = 3.57 × 10⁸⁰ m³ (Planck Collaboration, 2020), and each is worked from measured values.

The relic light. The microwave background, at T = 2.7255 K (Fixsen, 2009), holds n = (2ζ(3)/π²)·(k_B T/ħc)³ = 410.7 photons in every cubic centimetre, 1.47 × 10⁸⁹ in all; its energy density is aT⁴ = 4.17 × 10⁻¹⁴ J/m³, 1.49 × 10⁶⁷ J in all. A thermal photon carries 3.60 k_B of entropy, 3.60 / ln 2 = 5.2 bits, so the background carries 7.6 × 10⁸⁹ bits. The relic neutrinos, at 1.945 K, add 336 per cubic centimetre, 1.2 × 10⁸⁹ in all, with nearly the photons' entropy: together the relic radiation holds 2,891 k_B per cubic centimetre, 1.5 × 10⁹⁰ bits in the observable universe. Their number does not change as space expands; only their energy falls.

The light of every star. Everything every star has ever shone is about 4 × 10⁸⁴ photons (Fermi-LAT Collaboration, 2018), one for every 37,000 of the relic light, but each far more energetic: about 2.3 × 10⁻¹⁵ J/m³, some 5 % of the background's energy, 8 × 10⁶⁵ J in all.

The wells' glow. Today it is almost nothing: about 10⁻²⁸ watts from a Sun-mass well, about 10⁻¹¹ watts from all of the universe's 4 × 10¹⁹ stellar wells together (Sicilia et al., 2022). But the wells hold the universe's real radiation. The stellar wells hold about 1 % of ordinary matter, 1.5 × 10⁵¹ kg, which is 1.35 × 10⁶⁸ J: already nine times all the radiation the universe holds now, waiting to come out as glow. By the Evaporation Bit Count, an average stellar well of about 19 Suns returns 5.4 × 10⁷⁹ bits, all of them together 2 × 10⁹⁹; the great wells at the centres of galaxies hold more, about 3 × 10¹⁰⁴ k_B, 4.5 × 10¹⁰⁴ bits (Egan & Lineweaver, 2010).

All the radiation there will ever be. If all of the universe's matter ends in wells and goes home, the radiation it becomes is at most Ω_m·ρ_c·c²·V = 0.31 × 7.7 × 10⁻¹⁰ J/m³ × 3.57 × 10⁸⁰ m³ = 8.5 × 10⁷⁰ J, about six thousand times the radiation of today. Above all of it stands the universe's own ceiling, the Local Cell Count of 6.6 × 10¹²² cells, the horizon's count of bits (Part 1.9).

Today's radiation is a whisper; a universe's real radiation is still locked in its wells, and it comes out at the close. Even then the universe stays far under its ceiling: everything it will ever radiate fills about one part in 10¹⁸ of what it can hold.

When the Radiation Ends

The great wells glow longest, up to about 10¹⁰⁰ years for the largest (Page, 1976), so the last of them sets the moment. When the last glow ends, the last ascending half has gone home through the Pulsecore Vacuum Event Horizon, and every bit has returned: that is the close of the universe (Part 9.9). At that moment each well's Nullcore holds its descending halves, and by Return to Bifurcation the Nullcore becomes a child's Pulsecore (Part 3.10): a new UniSphere bifurcates in each well, one generation on. The end of a universe's radiation is the beginning of its children.

Open Questions

• The two inner horizons have names but not yet glyphs.

Links to Binary Pulse Theory

• Part 1.2: the physical as the whole pulse, ↁ⭇ + ↁ⭋.
• Part 1.10: each phase moves one bit; the full cycle conserves it.
• Part 2.4: the Null Well's horizon, where the physical goes silent and the data flows on.
• Part 2.7: the Null Well's storage bound, the count a well can return.
• Part 3.6: the harmonics, the Pulsecore, the preferred axis.
• Part 3.10: Return to Bifurcation, the Nullcore as the child's Pulsecore.
• Part 3.13: Hawking Power and Horizon Feeding, what goes home feeds the vacuum.
• Part 9.1: the effective w(z).