Making gravity

What the game asks for

The field in game.js, measured in the 0.65× Hollow: the ground is 97.5 m from the centre.

• It points at the nearest ground, on all three shapes: the sphere, the Lens and Rama.
• It is 22 m/s² everywhere on the ground, 2.2 times Earth's, with no stronger or weaker latitudes.
• It fades with height. It is about a third at 29 m and 2% by 60 m, and nothing at the middle. A faint slope of 2% remains so nobody hovers in the middle for ever. Climbing all the way to the middle costs 575 J per kilogram, as much as climbing 59 m on Earth.
• It is still. Nothing turns, so there is no Coriolis push and no weightless pole.
• The floating rocks have wells of their own, and the ground's pull fades inside them.
• It can change. The world can morph into other shapes mid-match, and field events move bands of push through it at 24 m/s.

Four ways to make the pull

The field has to come from somewhere. Here are four candidates, measured against that list.

The Loom isn't a fifth source. It's the machine in the hull that makes and holds the fourth.

What the field is made of

Einstein's version of Gauss's law counts energy plus three times the pressure, called the active mass (Ehlers and colleagues, 2005). Run it on our field and the air must carry −3.1×10¹⁵ kg of active mass. It is densest 15–20 m up, with 83% of it in the lowest 30 m. Negative active mass pushes things away from the middle, toward the ground.

The ground carries +3.1×10¹⁵ kg of active mass, so that below it the two cancel. That's why the hull is weightless and the droids hold on to rails.

Is it possible?

Negative active mass can come two ways: negative energy, or positive energy under enough tension. The research sweep says known physics rules out the first at this size, and allows the second at an enormous cost.

Route 1: negative energy, ruled out at this size

• What it needs: −1.2×10⁹ kg/m³ at the peak, through a layer 20 m thick, held for ever.
• Quantum physics caps negative energy. The deeper a dip below zero, the shorter it can last. Averaged over a time t, the energy density can't go below −3ħ/(32π²c³t⁴) (Ford and Roman). Over one second the floor is about 4×10⁻⁷⁹ kg/m³. Our density would be allowed for 10⁻²² s.
• The only lasting negative energy we know is the Casimir effect, between metal plates: about −5×10⁻²¹ kg/m³ with the plates 1 µm apart. Only its force has ever been measured. To match us, the plates would have to be 45 fm apart, the size of an atomic nucleus.
• By our estimate it also breaks the averaged null energy condition along lines through the middle. That condition is proven for quantum fields in flat space (2016–17).

That puts it with the Alcubierre warp drive: Einstein's equations allow it, and quantum fields rule it out. No proof covers every field in curved space, so "ruled out" means by everything we know.

Route 2: tension, allowed but enormous

• Pressure gravitates. In Einstein's theory, tension counts against energy three times over. A medium whose tension equals its energy, like the vacuum energy of a cosmological constant, has negative active mass while its energy stays positive. Dark energy does this to the whole universe, which is why its expansion speeds up (Riess and colleagues, 1998; Perlmutter and colleagues, 1999). Domain walls repel for the same reason (Ipser and Sikivie, 1984).
• So the Loom holds a layer of false vacuum against the ground. At the peak that is 6×10⁸ kg/m³ of vacuum energy under equal tension. That is 10³⁵ times the universe's dark energy, but about 10⁸ times less than the difference between the vacuum inside a proton and outside it (in the bag model). Its energy is positive, so the quantum cap above doesn't apply.
• It has to be held. A false vacuum decays (Coleman, 1977), and no static lump of a field holds itself together (Derrick, 1964). So the Loom holds the layer the way a trap holds an atom, keeping the barrier up and the layer in shape, and the Keeper rewrites any patch that slips. Catching decays as they happen wouldn't work: once a decay bubble starts, it grows at nearly the speed of light.
• Tension needs a frame. In anything that stands still, tension must be matched by compression (von Laue's theorem), so the ground and the outer skin carry it in about equal halves. The frame's mass is the layer's energy divided by how stiff the frame is, so it has to be the stiffest matter possible, with sound moving at nearly the speed of light (Zel'dovich, 1962). Even neutron-star cores fall short (Bedaque and Steiner, 2015). At that limit the frame is about 1.6×10¹⁵ kg, a membrane tens of nanometres thick under the soil. Like the vacuum, it is the story's material.
• It costs a share of a star. The layer and its frame hold at least 2.8×10³² J, the world's own E = mc². The black skin's 41 MW would need 2×10¹⁷ years, so the world was charged by builders who could harvest a good share of a star's light. The next section has the bill.
• From outside, it has weight. The world's total energy shows up as mass: with the spare ground for morphs, about 4.7×10¹⁵ kg, as much as an asteroid 15 km across. Standing on the outer skin you'd feel about 32 m/s², more than on the meadow.

No known law forbids this. What's missing is a way to make and hold a false vacuum and its frame, and a good share of a star's light. That's the claim the story makes.

Building a world

The bill is the world's own mass-energy, so no efficiency can shrink it. A sphere's charge, the layer and its frame, is 2.8×10³² J. With the spare ground for morphs (next section) a world holds 4.2×10³² J, about 13 days of the Sun's entire output, caught by collectors all the way round it.

Heat is the real limit. Whatever isn't stored perfectly becomes heat, and it has to leave a 100 m object before the object melts. So worlds are built in a yard, with radiators about 100 km across glowing at 2,000 K and shedding about 2×10¹⁶ W. The build time depends on how little the Loom loses:

We take five centuries per world. The best transformers today lose about one part in a few hundred, so that Loom is the story's.

• Not a Kardashev Type II civilisation. A yard draws about 2.7×10²² W while charging, 1/14,000 of the Sun, so a partial swarm of collectors is enough. On Sagan's sliding version of the scale that is about 1.6.
• Fleets are built in parallel. With the whole Sun, about 14,000 yards run at once and finish about 29 worlds a year. One world costs about 3.5% of a year of the Sun's output.
• Weight comes on slowly. Tension and compression must rise together, so the pull inside grows from nothing to 22 m/s² over the centuries of charging.
• Failure is a flash. A world that lets go releases its 4.2×10³² J as about a million Suns for a second. At Earth's distance that is 1.5×10⁹ J/m², and Earth's facing side would take about half the energy of the dinosaur-killing impact. So fleets orbit far from inhabited planets. That the energy comes out as light is a story choice.

Any shape

The ground carries compression, which pulls like positive mass. The air above it carries tension, which pushes like negative mass. Together they make a gravitational double layer, like a capacitor: the pull exists between the layers and nowhere off them. For a closed layer of even strength that holds whatever the shape (the solid-angle theorem of potential theory). It is exact only for a thin layer, and ours is 60 m thick, so the Loom corrects the rest. That is why the pull follows the nearest ground on a lens, a tube or a waisted world, and why the hull and the middle stay quiet. Spin could never give a non-round world even weight.

The pull has a budget. By Gauss's law, pull × ground area is fixed by the charge, so pull can be moved but not made mid-match: a heavy patch means a light patch somewhere else, and adding charge takes centuries.

Morphs

Morphs can be drastic, so every world keeps spare ground: half a sphere's worth of panels folded against the outer skin, each with its own layer and frame, fully charged. Folded, they make a closed shell outside the meadow and pull nothing inside it. A morph unfolds or folds panels. Each panel brings its own charge, so the pull stays at 22 m/s² on any shape up to 1.5 times the sphere's ground area. Nothing is converted, only moved, so a morph makes no heat and is as fast as the panels can move.

The Loom can also pour charge from panel to panel, so a shape can be made heavier or lighter on purpose. Across the ground, pull = 22 m/s² × charge in use ÷ ground area, with both counted in spheres and at most 1.5 spheres of charge. The sphere itself could run at up to 33 m/s².

Keeping the volume means the air isn't squeezed. Every shape here needs less than 1.5 spheres of ground, so all of them can hold 22 m/s²; the game's current Lens and Rama need 1.06 and 0.95.

• Where layers meet, their pulls add. In a narrow waist, opposite grounds pull against each other and make a weightless bridge. At a lens's rim, things collect along the crease. In a lens thinner than 120 m, the two layers overlap across the whole middle.
• Everything in one place falls the same way. A gravity gun can't single out a target: it moves everyone and everything in its area, rounds included. Holograms are the one exception the story allows.

The world in layers

Rocks, gates, events

Once the Loom holds the field, the rest of the game's physics follows from the same idea.

• Rocks. A rock pulls toward itself, so it needs positive active mass. At 0.65× the big rock pulls with 20 m/s² near its surface, which takes about 1.6×10¹³ kg. As rock, that would be denser than a white dwarf. So each rock is a store of energy and stiff matter that the Loom keeps. The Loom also thins the vacuum layer under it, which is why the ground's pull fades inside a rock's well.
• Field events. A band of push in open sky has to carry its own sources: for the starting sweep, about 7.5×10⁸ kg/m³ of active mass, positive ahead and negative behind. The ground alone can't make a push that peaks in mid-air. So a sweep is a flying double layer, a small copy of the wall, that players pass through. The Loom lifts its charge from the nearby ground, so the ground gets lighter first, which warns players. A change can't outrun light, and a sweep at 24 m/s is about twelve million times slower.
• Gates. Wheeler and Misner coined "wormhole" in 1957. Recent theory allows traversable ones, held open by a little quantum negative energy (Gao, Jafferis and Wall, 2017; Maldacena, Milekhin and Popov, 2018). The catch is that going through is never faster than going around. Ours pass that test: light needs 0.65 µs to cross the world, and a gate trip takes a whole frame. They need negative energy in the throat, the thing ruled out above for the field, and the known constructions are microscopic or need a hidden dark sector. So gates sit a rung below the field, and a gate a person can walk through is the story's work.
• Void swim and air dash. Arms push on almost nothing in air, so these are small fields the Loom writes when it reads what you mean to do. It already does that for the skins.
• The Skylance. Its rounds feel the wells three times harder than bodies do. That breaks the equivalence principle, which says everything falls alike and has been tested to one part in 10¹⁵. The fix that fits the story: the rounds are projections, like the guns, so the Loom can bend them on purpose. It's open.

Wheeler

Wheeler named or launched most of this world's vocabulary: the geon, the wormhole, the black hole, and "spacetime tells matter how to move", which is the whole mechanic. Gravitational-wave detection started with Weber on a sabbatical with him, and his student Kip Thorne co-founded LIGO.

He is also the builders' creed. Wheeler drew the universe as a U: it grows observers who look back at its beginning and, he argued, help make that beginning real. His 1989 "it from bit" belongs to the same belief: "every it — every particle, every field of force, even the spacetime continuum itself — derives its function, its meaning, its very existence entirely — even if in some contexts indirectly — from the apparatus-elicited answers to yes or no questions, binary choices, bits." The story keeps it as belief, not as how the field works.

Two bigger roles were tried and dropped. Having the Loom write the vacuum's bits added nothing that the tension doesn't already do. And bits don't set the price. Erasing a bit costs heat (Landauer, 1961), but charging a world takes the vacuum from one known state to another and erases nothing (Bennett, 1982). Even when the Keeper resets a slipped patch, the bit costs about ten million times less than the energy the slip threw away.

Decided and open

• decidedFun first. The physics explains and enables the mechanics; where it runs out, the story fills the gap.
• decidedNo spin. The world is still, and the field comes from the Loom, not from turning or from mass.
• decidedNo mirrors. The black outer skin collects the energy.
• decidedThe field is a held layer of false vacuum under tension, not negative energy.
• decidedGates are wormholes that are never faster than light.
• decidedMorphs may be drastic, and players should feel them.
• new hereThe frame is the stiffest matter possible. The Loom is a trap, and the Keeper repairs what slips.
• new hereFive centuries per world in a radiator yard, about 1/14,000 of the Sun while it charges. The Kardashev Type II line is gone.
• new hereThe double layer: any shape, a fixed pull budget, and charged spare ground for morphs up to 1.5 times the sphere's area.
• new hereField events carry their own sources, and the ground gets lighter first.
• new hereWheeler is lineage and creed, not the mechanism. The Lantern is the skin's sunlight, and the geon is dropped.
• dropped"It from bit" as the mechanism, the negative-temperature screen, and the 490-year charge, which assumed negative energy.
• openWhether some shapes run heavier or lighter on purpose, and whether a failing world's flash is visible.
• openThe names: the Loom, the Keeper, the Skin and the Lantern. Also whether the ground mist should be the visible face of gravity, and the Skylance fix above.