Two kinds of twin. Lab 1 is what accelerator physicists mean by a digital twin: a model of a specific machine whose physics is settled, used to tune the real thing. Labs 2–4 are the twin that fits your three questions: a quantum-circuit simulator, which is exactly how researchers prototype quantum computers, teleportation protocols, and the information physics of time loops before (or instead of) touching hardware.
Lab 5 draws the geometry behind the questions: 4D shapes, the block universe, black-hole and wormhole surfaces, and the light cones that tip over into time loops. Lab 6 goes underneath: string theory’s hidden dimensions, light bending and gravitational waves, a tesseract unfolding, black holes evaporating, and crystals in time, each labelled measured, theory, or speculation.
Lab 7 zooms out to the whole universe: the dark matter that keeps galaxies spinning, the dark energy speeding up the expansion, the COBE chart of the Big Bang’s afterglow, and what a Dyson sphere would look like from outside.
Lab 8 charts the numbers: time dilation and GPS, black-hole lifetimes, the scale of the universe, the Kardashev scale, quantum error correction, teleportation over fibre and the wormhole budget. Lab 3 also asks what it would take to teleport matter.
Every lab states a hypothesis, the fastest test, and what would refute it. Log runs to the notebook at the bottom and copy them out as JSON.
Accelerator twin: FODO lattice
A beamline is a chain of focusing (QF) and defocusing (QD) quadrupole magnets separated by drifts. The twin propagates the beam envelope through the lattice with transfer matrices. Real twins (SLAC LCLS, Fermilab Twinac, STFC CLARA) do the same with thousands of elements, fed by the live magnet settings.
Lattice settings
Thin-lens model. Stability of a FODO cell needs |Tr M| < 2, which for thin lenses means f > L/2. Beam size σ = √(ε·β).
Readouts
Top: beam size along the ring (one cell = QF, drift, QD, drift). Bottom: one-cell trace vs focal length; inside the band the beam stays bounded cell after cell. A real twin adds the parts this one lacks: live settings read from the control system, diagnostics compared against the prediction, and a model that is re-fit when they disagree.
Experiments
| Hypothesis | Fastest test | Refuted if |
|---|---|---|
| A thin-lens FODO cell is stable iff f > L/2. | Sweep f on the bottom chart with L fixed. | Tr M stays inside ±2 for some f < L/2, or leaves the band for f > L/2. |
| Beam size scales as √ε, not ε. | Set ε = 5 then 20; size at QF should grow ×2. | Size grows ×4 or does not change. |
| Near the stability edge (f → L/2) the beam gets large even while stable. | Slide f down toward 2.1 with L = 4. | β max does not rise as the edge is approached. |
Qubit lab: state-vector simulator
A classical computer can hold the full quantum state of a few qubits (2ⁿ complex amplitudes) and apply gates exactly. This is the standard research twin for quantum computing: write a circuit, run it ideal, then add noise and measure how far the result drifts. Up to 8 qubits here; Qiskit Aer and Cirq do the same thing at 30+.
Circuit
Gates: H X Y Z S SDG T TDG · RX RY RZ q angle (angles accept pi, e.g. RY 0 pi/3) · CX c t · CZ a b · SWAP a b · M [qubits]. Bitstrings read q0 q1 q2… left to right.
Readouts
Experiments
| Hypothesis | Fastest test | Refuted if |
|---|---|---|
| Interference is physical, not statistical: H·Z·H sends |0⟩ to |1⟩ every time. | Preset “Interference”, noise 0. | Any count of “0”. |
| Fidelity decays roughly as (1−p)^gates under per-gate depolarizing noise. | GHZ preset at p = 0.02 and 0.05; compare fidelity to (1−p)^3. | Fidelity is flat or non-monotone in p. |
| Syndrome bits locate a single flip without measuring the data qubits. | Bit-flip code at p = 0.05; the syndrome histogram should be mostly 00 with 10 / 01 / 11 minorities. | Syndromes are uniform, or 00 is not the mode. |
| One Grover iteration on 2 qubits finds the target with certainty. | Grover preset, noise 0. | Any outcome other than 11. |
Teleportation lab: Bennett protocol with a noisy channel
Quantum teleportation moves a qubit’s state, not matter: Alice and Bob share an entangled pair, Alice measures her qubit together with the message qubit and sends Bob two classical bits, Bob applies a correction. The lab runs the full three-qubit circuit shot by shot, with depolarizing noise on Bob’s half of the pair, and compares Bob’s output to the message.
Message and channel
q0 message · q1 Alice’s half · q2 Bob’s half. The X and Z on q2 are applied only when the classical bits say so.
Readouts
Theory for depolarizing noise with probability p on Bob’s half: F = 1 − 2p/3 with the correction, F = 1/2 without it (Bob holds a random Pauli twist of ψ until the bits arrive, so no signal travels faster than the classical channel).
What would it take to teleport matter?
Readouts
- Teleportation moves a state, not stuff. The destination must already hold the raw material, the same atoms in the same amounts, waiting to take on the state.
- The original is wiped. Quantum states cannot be copied (the no-cloning theorem), and the measurement that sends the state scrambles the original. You get a move, never a copy.
- It cannot beat light. Each qubit costs one entangled pair, shared in advance, plus two ordinary bits. Both travel no faster than light, and the receiver’s half is noise until the bits arrive.
- One qubit per atom is far too generous. An atom’s position, motion and inner state need many qubits each, so the real numbers are much larger. The classical-scan tile is an assumption: each atom’s position to 0.1 nm plus its element, about 100 bits per atom for a person, ignoring motion and chemistry.
- Records so far are single photons (Innsbruck 1997; 44 km of fibre 2020; 1,200 km to the Micius satellite 2017), trapped ions (2004), single atoms 21 m apart (2013) and an error-corrected logical qubit (Quantinuum). See
docs/research.md.
Experiments
| Hypothesis | Fastest test | Refuted if |
|---|---|---|
| Bob’s qubit carries no information until the two classical bits arrive. | Uncheck the correction; expect F ≈ 0.50 and mean Bloch length ≈ 0. | F stays above 0.5 by more than ~3 standard errors, or the mean vector points along ψ. |
| F = 1 − 2p/3 for a depolarizing channel. | p = 0.30, 4096 shots: expect 0.80 ± 0.01. | Measured F is more than ~3σ from 0.80. |
| Alice’s outcomes are uniform whatever ψ is. | Set θ = 0 (message |0⟩) and θ = 180; bits stay ≈ 25% each. | One outcome dominates beyond sampling noise. |
| Even the most generous lower bound (one qubit per atom) makes teleporting a person a geological project: about 7×10²⁷ entangled pairs and billions of years of sending at 100 Gbit/s. | Teleport-matter panel: object “a person”, bandwidth 100 Gbit/s; then raise the bandwidth tenfold. | The atom count is outside 10²⁷–10²⁸, or the sending time does not fall exactly tenfold. |
Time loops: closed timelike curves on a qubit
Nobody can build a closed timelike curve, so physicists simulate what one would do to information. Two models disagree. Deutsch (1991): the qubit inside the loop must come out in the same state it went in, ρ = Tr[U(ρ_in ⊗ ρ)U†], which can be solved and is nonlinear. Post-selected CTCs (Lloyd et al. 2011): the loop is a teleportation that only counts when it is self-consistent, so paradoxical histories get probability zero. Both were run on photons (Ringbauer et al. 2014; Arvidsson-Shukur et al. 2023).
Loop interaction
Readouts
Sweep: the traveler state is swept from |0⟩ (θ = 0) to |1⟩ (θ = 180°) at the chosen φ. Dashed: how distinguishable the input is from |0⟩ (trace distance). Solid: how distinguishable the Deutsch outputs are. Any linear quantum process keeps the solid line at or below the dashed one; where it rises above, the loop is doing something no ordinary channel can. Green: P-CTC success probability.
Your hypothesis, mapped to the physics
Forward-only without a closed loop; a loop is confined to a zone; it forks spacetime; the energy is planetary to cosmic.
| Claim | Status | Fastest test | Refuted if |
|---|---|---|---|
| You can only go forward in time unless there is a closed timelike curve. | established Time dilation (speed, gravity) moves you forward at different rates; measured with GPS, muons, flown clocks. Going back needs a CTC in the geometry (Gödel, Tipler, Morris–Thorne wormholes). | None needed; textbook relativity. | — |
| A CTC makes a loop inside a zone, not a free trip to the past. | matches GR CTCs live in a chronology-violating region bounded by a Cauchy (chronology) horizon. A wormhole time machine cannot reach any time before it was built. | Swap preset: the traveler emerges as itself; the loop closes on itself and nothing escapes it. | A model where the traveler’s output is unconstrained by the loop. |
| It forks spacetime from the rest. | model-dependent Forking is Deutsch’s picture (consistent with branching / many-worlds). The rival is Novikov self-consistency, modelled by P-CTCs: one history, paradoxes get probability zero. | Grandfather preset: Deutsch gives a 50/50 mixture; P-CTC gives probability 0. | A real CTC experiment that shows forbidden histories (never-seen outcomes) rather than mixed outputs would favour a single self-consistent timeline over forking. |
| Energy on the scale of planets or universes. | right order A metre-scale wormhole throat needs roughly a Jupiter’s worth of mass-energy, and it has to be negative (exotic matter). A Tipler cylinder needs infinite length; Gödel’s solution needs the whole universe to rotate. Refinement: the blocker is the sign and quantum back-reaction near the chronology horizon (Hawking’s chronology-protection conjecture; Ford–Roman limits on negative energy), not just the amount. | Exotic-matter slider below. | A classical-matter CTC solution with ordinary positive energy, which no known solution provides. |
Exotic-matter budget (order of magnitude)
Thin-shell estimate |M| ~ c²·r₀/G of negative mass-energy to hold the throat open (Morris–Thorne 1988; Visser).
Readouts
For scale: a 1 m throat ≈ 0.7 Jupiter masses; a 1 km throat ≈ 0.7 solar masses. Humanity’s annual energy use is ~6×10²⁰ J.
Experiments
| Hypothesis | Fastest test | Refuted if |
|---|---|---|
| Deutsch and P-CTC disagree on the grandfather loop. | Grandfather preset. | Both give the same output state and the same success probability. |
| A Deutsch loop can tell two overlapping states apart with certainty, which no linear channel can. | Tuned π-rotation preset at θ = 45°, φ = 0: Deutsch output fidelity vs input ≈ 0.15 (ψ is sent to |1⟩) while |0⟩ is sent to |0⟩; the solid sweep line reaches 1 at 45°. | The solid line stays at or below the dashed line at the chosen θ. |
| CNOT-then-SWAP squares the input’s z component: output = (0, 0, cos²θ). | CNOT-then-SWAP preset at θ = 60°: output z reads 0.25. | Output z ≠ cos²θ, or the output keeps a phase (x or y ≠ 0). |
| P-CTC “effective time travel” via a swap succeeds one time in four. | Swap preset; success probability reads 0.25 for every input. | The probability depends on the input or is not 0.25. |
| With no interaction the loop is harmless. | “No interaction” preset. | Output differs from input, or P-CTC success is below 1. |
Dimensions: spacetime surfaces and 4D shapes, drawn in 3D
The other labs compute; this one draws the geometry they assume. Every scene squeezes one extra axis into a 3D view you can orbit: a fourth spatial direction w shown as a projection or a moving slice, time shown as height, or curvature shown as an embedding surface. Drag the view to orbit it.
Five things “4D” means
| Meaning | The extra axis | Scene here |
|---|---|---|
| A fourth direction of space (Hinton’s tesseract, Abbott’s Flatland) | w, at right angles to x, y and z | 4D shape: projection, and hyperplane slice |
| Spacetime (Minkowski, Einstein) | time t; light cones fix what can reach what | Block universe; Misner and Gödel light cones |
| Curved space (Schwarzschild, Morris–Thorne) | none: the embedding height is a drawing aid, not a direction anyone can travel | Black hole and wormhole surfaces |
| Captured 4D: volumetric video, 4D Gaussian splats, a 3D globe with a replay clock | time attached to a 3D capture | Block universe: scrub “now” like a replay; events fade in and out around it |
| Interactive 4D (Roblox Cube: 3D plus behaviour) | function: parts, rigging, scripts | Not modelled. It is a product term for behaviour, not geometry |
Scene
View
Experiments
| Hypothesis | Fastest test | Refuted if |
|---|---|---|
| A tesseract met by a 3D hyperplane through its middle leaves a cube; tilt the tesseract in x–w and the slice becomes a different polyhedron. | Slice scene, tesseract, all rotations 0, w₀ = 0: 8 vertices, 12 edges. Then x–w = 40°. | The untilted count is not 8 / 12, or the tilted slice still reads 8 / 12 at every w₀. |
| Rotating through w turns the projection inside out: the inner cube and the outer cube trade places at x–w = 180°. | Projection scene, perspective, spin off; slide x–w from 0 to 180°. | The inner and outer cubes keep their colours (w sign) after 180°. |
| The black-hole funnel has the same shape at every mass; only its size in km changes. | Black-hole scene; slide the mass from 1 to 10¹⁰ Suns. | The drawn surface changes shape, or r_s does not scale linearly with mass. |
| A Misner loop is a time machine only above the chronology horizon, never before it. | Misner scene: T = −0.3, 0, 0.3. | The loop reads timelike at T ≤ 0, or spacelike at T > 0. |
| Gödel light cones tip past horizontal at r = ln(1 + √2) ≈ 0.881. | Gödel scene: r = 0.87 then 0.89. | The loop type does not flip between them. |
| Moving observers disagree about “now” but nothing leaves its light cone. | Block scene: β = 0.6, then tick the rest-frame box; the now slice tilts by 0.6, every worldline stays inside the cone. | A worldline is steeper than the cone (speed ≥ c), or the slope differs from β. |
Deep structure: hidden dimensions, bent spacetime, evaporating black holes, crystals in time
Lab 5 draws the shapes; this lab asks what spacetime is made of and how it moves. Nine scenes, from measured facts (light bending, gravitational waves, time crystals) through accepted but unobserved theory (Hawking radiation) to pure speculation (string theory’s extra dimensions, grains of spacetime). Each scene says which it is. Drag the view to orbit it; Spin animates.
What is measured and what is a guess
| Idea | Status | Scene here |
|---|---|---|
| Extra dimensions curled up small (Kaluza 1921, Klein 1926) | Speculative; colliders see no sign of them | Kaluza–Klein circles |
| Six extra dimensions shaped as a Calabi–Yau space; particles as vibrating strings on branes | Speculative; mathematics with no experimental evidence | Calabi–Yau slice; strings and branes |
| Mass bends light; gravitational waves stretch space | Measured (Eddington 1919; LIGO 2015) | Light bending; gravitational wave |
| A fourth direction of space | Geometry; no physical evidence | Tesseract unfolding (rotation and slicing are in Lab 5) |
| Black holes evaporate (Hawking 1974) | Accepted theory, never observed | Hawking evaporation |
| Time crystals: matter that repeats in time | Observed 2017–2021 | Discrete time crystal |
| Spacetime made of discrete grains | Speculative quantum gravity | Causal set |
Scene
View
Experiments
| Hypothesis | Fastest test | Refuted if |
|---|---|---|
| A smaller extra circle hides better: its first particle copy weighs ħc/R, about 197 GeV at R = 10⁻¹⁸ m. | Kaluza–Klein scene: R = 10⁻¹⁸ m, then 10⁻¹⁹ m. | m₁c² is not 197 GeV, or shrinking R tenfold does not make it ten times heavier. |
| Every point of the Calabi–Yau picture lies on z₁⁵ + z₂⁵ = 1. | Calabi–Yau scene: read the residual tile; turn the angle. | The residual exceeds 10⁻⁹ for any angle. |
| Einstein’s weak-field bending 2r_s/b is right far from a black hole and wrong close in; below b = 3√3/2 r_s light is captured. | Light-bending scene: b = 30, then 6, then 2.5. | The gap between the exact ray and 2r_s/b does not shrink as b grows (about 5 % at 30, 26 % at 6), or the ray at b = 2.5 escapes. |
| A gravitational wave stretches one direction while squeezing the other; cross polarization is plus turned by 45°. | Gravitational-wave scene, Spin off: switch plus to cross. | A ring changes area at first order in h, or the two patterns are not 45° apart. |
| A tesseract’s 8 cubes unfold into 3D with no overlaps (Dalí’s net). | Unfolding scene: slide to 1. | The overlap tile is not 0, or fewer than 8 cubes appear. |
| Smaller black holes are hotter and die sooner: T ∝ 1/M, lifetime ∝ M³; a solar-mass hole is colder than the microwave background. | Hawking scene: M₀ = 1 M☉, then 10⁻¹⁸ M☉. | T does not rise a millionfold per factor 10⁶ in mass, or the 1 M☉ hole reads hotter than 2.7 K. |
| Interactions make the period-doubled flipping robust to an imperfect pulse; without them it melts. | Time-crystal scene: ε = 0.1, then 0.3. | At ε = 0.1 the 2T response with interactions is not far above the one without. |
| A random sprinkle of grains “knows” it is 2-dimensional: half its pairs are causally related. | Causal-set scene: ρV = 300, try several seeds. | The dimension estimate strays far from 2 (say outside 1.8–2.2). |
Cosmos: dark matter, dark energy, the Big Bang’s afterglow, Dyson spheres
What the universe is made of, and how we know. Four scenes: why galaxies spin too fast for the matter we can see (dark matter), why the expansion of the universe is speeding up (dark energy), what the famous COBE chart actually shows (the leftover heat of the Big Bang), and what a star wrapped in solar collectors would look like from outside (a Dyson sphere). Every chart is computed live from the formula named in its notes; none is a traced picture.
What we know and what we don’t
| Question | Measured | Still unknown |
|---|---|---|
| Dark matter (about 27 % of everything) | Its gravity: galaxies spin too fast at their edges (Rubin & Ford 1970), clusters bend light more than their visible mass can, and it shapes the ripples in the microwave background. | What it is. No dark-matter particle has been detected. Modified gravity (MOND) fits single galaxies but struggles with clusters and the microwave background. |
| Dark energy (about 68 %) | The expansion has been speeding up for about 6 billion years: distant exploding stars (1998–99, Nobel 2011), confirmed by the microwave background and maps of galaxies. | What it is. The simplest answer is Einstein’s cosmological constant; galaxy surveys (DESI, 2024–25) hint it may be changing, not yet a discovery. Two ways of measuring today’s expansion rate disagree (about 67 vs 73 km/s/Mpc, the “Hubble tension”). |
| Ordinary matter (about 5 %) | Atoms, counted two independent ways: from the microwave background and from the helium and deuterium made in the first minutes. Most of it is thin hot gas between galaxies. | Why there is matter at all, rather than equal amounts of antimatter. |
| A hot, dense beginning | The microwave background is a blackbody at 2.725 K, matching the theory curve to 50 parts per million (COBE/FIRAS); its 1-in-100,000 ripples (COBE/DMR) are the seeds of galaxies. Nobel 2006. | What happened before the hot phase. Inflation is the leading idea, not confirmed. |
| Dyson spheres | Physics allows a swarm of collectors around a star; its waste heat would make the star glow in infrared. | None found. Searches (Project Hephaistos, 2024) list a few infrared candidates; none is confirmed and some look like background galaxies. Speculation. |
Scene
View
Experiments
| Hypothesis | Fastest test | Refuted if |
|---|---|---|
| Visible matter alone cannot explain how fast the outer galaxy spins: its curve falls like a planet’s (1/√r), the measured one does not. | Rotation scene: “Nothing”, then a dark halo; read the 30 kpc tile. | The visible-only curve stays near 220 km/s at 30 kpc, or doubling the radius far out does not cut its speed by about 30 %. |
| Without dark energy the universe would be younger than its oldest stars; with it, 13.8 billion years. | Expansion scene: Planck 2018 values, then Matter only. | The age is not 13.8 Gyr within 1 %, matter-only is not 2/(3H₀) ≈ 9.7 Gyr, or the speed-up does not start near z ≈ 0.6–0.7. |
| The afterglow’s peak moves in step with its temperature: ν_peak = 58.79 GHz per kelvin. | COBE scene: 2.725 K, then 5.45 K. | The peak is not 160.2 GHz, or doubling T does not double it exactly. |
| A Dyson swarm cannot hide its star’s power: everything captured comes back out as infrared heat, near 10 µm for 300 K collectors. | Dyson scene: capture 100 %, collectors at 300 K. | The heat glow does not peak near 9.7 µm, or the total power seen from outside is not the star’s full 3.8 × 10²⁶ W. |
Graphs: the numbers behind the questions
The other labs simulate; this one charts. Each chart takes one question from the rest of the workbench and puts real numbers on it, with landmarks you can recognise: a GPS satellite, the Sun, the LHC, a 44 km fibre link. Pick a chart and move its sliders; the markers, tiles and explanation update. Axes marked “log” step by factors of ten, so a straight line means “multiplies by the same amount at every step”.
What each chart is for
| Chart | Question it answers | Status |
|---|---|---|
| Time dilation | How much do speed and height change how fast a clock ticks, and why does GPS have to correct for it? | Measured (GPS, flown atomic clocks, particle lifetimes) |
| Black holes | Which black holes evaporate, which still grow, and how long do they last? | Accepted theory, never observed |
| Scale ladders | Where do atoms, people, galaxies, the LHC and the Planck scale sit on one ruler? | Measured, except the grand-unification and Planck rungs (theory) |
| Kardashev scale | How far is humanity’s power use from a planet-, star- or galaxy-powered civilisation? | A yardstick, not physics |
| Quantum computing | Why do noisy qubits fail on long programs, and why does error correction only help below a threshold? | Measured trend; the formula is a rule of thumb |
| Teleportation over fibre | Why do fibre links stall at around a hundred kilometres, and why did the 1,200 km record use a satellite? | Measured |
| Wormholes | How much negative mass would a wormhole throat of a given size need? | Order-of-magnitude theory; negative mass has never been made in bulk |
Chart
Chart
Experiments
| Hypothesis | Fastest test | Refuted if |
|---|---|---|
| GPS clocks run fast by about 38 µs a day: gravity speeds them up by about 46 µs, their speed slows them by about 7 µs. | Time dilation, altitude 20,200 km. | The net tile is not +38.5 µs within 0.5 µs. (GPS satellites really are tuned slow by 4.465 parts in 10¹⁰ before launch, which is 38.6 µs a day.) |
| Below about 3,190 km (half an Earth radius up) an orbiting clock loses time; above it, it gains. | Time dilation: altitude 408 km (ISS), then 10,000 km. | The ISS net is not negative, or the net line does not cross zero near 3,190 km. |
| A black hole of 4.5×10²² kg (about 60 % of the Moon’s mass) is exactly as warm as the microwave background; lighter ones shrink, heavier ones grow. | Black holes: slide the mass through 4.5×10²² kg. | The temperature at 4.5×10²² kg is not 2.7 K, or the grow/shrink tile does not flip there. |
| Every step up the Kardashev scale is ten billion times more power; humanity sits near 0.73. | Kardashev: 2×10¹³ W, then 2×10²³ W. | K is not 0.73, or the second reading is not exactly 1.73. |
| Error correction only pays below threshold: a bigger code helps at p = 0.1 % and hurts at p = 2 %. | Quantum computing: d = 3 then 9 at each p. | The logical error falls with d above 1 %, or rises with d below it. |
| Fibre loses half its photons every 15 km (0.2 dB/km), so 100 km passes 1 % and 1,200 km passes 10⁻²⁴. | Teleportation over fibre: 100 km, then 1,200 km. | The survival tile is not 1.00 % at 100 km. |
| The negative mass a throat needs grows in proportion to its radius: a 1.48 km throat needs one Sun. | Wormholes: 1 m, then 1 km. | The mass does not rise exactly 1000×, or 1.48 km does not read ≈ 1 Sun. |
Lab notebook
| When | Lab | Parameters | Results |
|---|
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