The Paradoxes Dissolve
Ten quantum mysteries that aren't mysterious anymore
This is a bonus ninth piece in “Eight Easy Pieces: The Information Lattice.” The previous eight articles built the framework and tested it against experiment. This article does something different: it takes the quantum phenomena that physicists call “paradoxical,” “mysterious,” or “deeply counterintuitive” — and shows that on the information lattice, most of them are obvious.
A Note on Mystery
Quantum mechanics has been the most successful physical theory for a century. It has never made a wrong prediction. And yet even its creators found it baffling.
Niels Bohr said, “Anyone who is not shocked by quantum mechanics has not understood it.” Richard Feynman said, “Nobody understands quantum mechanics.” These are not idle quips — they reflect a genuine and ongoing confusion about what quantum mechanics means, even among people who use it every day to extraordinary precision.
The confusion is not about the mathematics. The equations are clear. The confusion is about the picture — what is physically happening when we say a particle is “in a superposition,” or when two entangled particles seem to communicate faster than light, or when a wave function “collapses.”
The standard response from the physics community is: don’t ask. “Shut up and calculate,” as the physicist David Mermin paraphrased the Copenhagen attitude. The mathematics works. The predictions are correct. Asking what is “really happening” is considered, by many physicists, to be a philosophical question rather than a physical one.
The information lattice offers a different response. Because the framework provides a specific, concrete, geometric substrate — qubits on octahedral faces, connected by bridges, evolving under a walk operator — the “what is really happening” question has a specific answer for each of the famous quantum paradoxes.
Not all of these answers are proven. Some are structural arguments rather than rigorous derivations. But each one replaces vague philosophical hand-waving with a mechanical picture that a reader can visualise and, in principle, simulate.
1. Entanglement: Patterns That Remember
The mystery as usually stated: Two particles interact and then fly apart to opposite ends of the universe. Measure one and you instantly know the state of the other, no matter how far away it is. Not at the speed of light - instantly! Einstein called this “spooky action at a distance” and considered it evidence that quantum mechanics was incomplete.
The standard explanation: The two particles share a joint wave function that cannot be separated into independent parts. Measuring one particle “collapses” the joint wave function, determining the other’s state. The explanation is mathematically precise but physically opaque — what does it mean for a wave function to be “joint” and why does measuring one part affect the other?
The lattice picture: Two octahedral voids interact at a bridge. The CNOT gate operates on both voids’ qubits simultaneously. Because the gate is a quantum operation — it acts on each component of a superposition independently and sums the results — it creates correlations between the two voids’ qubit states that cannot be factored apart.
The crucial point: nothing travels between the voids after they separate. The correlation was established at the bridge, during the interaction. It is a pattern — a mathematical relationship between the qubit amplitudes on the two voids — that was created locally and then carried along as each void propagates independently through the lattice.
Think of it this way. Two people meet at a party and agree on a secret code: “if I wear a red shirt tomorrow, you wear blue, and vice versa.” They then fly to opposite sides of the world. The next day, you see one wearing red and instantly know the other is wearing blue. No signal was sent. No “spooky action” occurred. The correlation was established during the meeting and carried as a pattern in each person’s memory.
Quantum entanglement is exactly this — except that the “code” isn’t a conscious agreement but a structural constraint imposed by the CNOT gate on the qubit amplitudes. The qubits don’t “know” they’re correlated. The correlation is a mathematical property of the joint state that was created at the bridge and persists because the walk operator is unitary (it preserves all correlations that exist).
No mystery. No faster-than-light communication. No action at a distance. Just patterns that remember.
2. The Wave Function: Amplitude on a Lattice
The mystery as usually stated: What IS the wave function? Is it a real physical thing (like a field pervading space) or just a mathematical tool for calculating probabilities? Physicists have argued about this since 1926 and still disagree.
The standard explanation: The wave function ψ(x,t) is a complex-valued function that assigns an amplitude to each point in space. Its squared modulus |ψ|² gives the probability of finding the particle at position x. Beyond this, the interpretation is “a matter of taste.”
The lattice picture: The wave function is not mysterious. It is the amplitude distribution across the void lattice. Each void has a complex number associated with each of the 48 valid codewords. The probability of finding a specific particle at a specific void is the squared modulus of the corresponding amplitude. That is Born’s rule, and on the lattice, it is not a postulate — it is a mathematical consequence of the walk operator being unitary (norm-preserving).
The wave function is as physical as the lattice itself. It is the pattern of amplitudes sitting on the voids. When we say “the electron is here,” we mean “the amplitude for the electron codeword is concentrated at this void.” When we say “the electron is delocalised,” we mean “the amplitude is spread across many voids.” There is no mystery about what the wave function is — it is a list of numbers, one per void per codeword, evolving according to a specific rule (the walk operator).
The Pusey-Barrett-Rudolph (PBR) theorem of 2012 proved, under mild assumptions, that the wave function must be “ontic” — a real, objective feature of the physical system, not merely a description of our ignorance. The lattice satisfies this naturally: the qubit amplitudes on the octahedral faces ARE the physical state. There is no deeper layer to be ignorant about.
3. Wave Function Collapse: Information Dilution
The mystery as usually stated: When you measure a quantum system, the wave function “collapses” — it jumps instantaneously from a spread-out superposition to a single definite state. This is bizarre: it is the only non-unitary, non-deterministic process in all of quantum mechanics. What triggers it? When does it happen? Does consciousness play a role?
The standard explanation: The Copenhagen interpretation says collapse happens when a “measurement” occurs but refuses to define what counts as a measurement. The Many-Worlds interpretation says collapse never happens — all outcomes occur in parallel branches. The decoherence programme says the environment effectively destroys interference, making the system look collapsed without any actual discontinuity.
The lattice picture: Collapse is information dilution, and it happens at a specific speed through a specific mechanism.
When a superposed void interacts with a measuring device (which is itself a vast collection of voids), the CNOT gate at each bridge entangles the measured void with the detector voids, one by one. After N voids have been entangled, the interference between the two branches of the superposition is suppressed by a factor of (3/16)^N — because the fraction of the joint Hilbert space that satisfies all code constraints simultaneously shrinks exponentially.
After just 40 voids are entangled, the suppression factor is 10⁻²⁹. After a few thousand (a tiny fraction of a macroscopic detector), the interference is suppressed beyond any conceivable measurement. The superposition hasn’t been destroyed — it has been diluted across so many qubits that reconstructing it would require coherently reversing every CNOT operation in the measurement chain. This is thermodynamically impossible for any macroscopic system.
Consciousness plays no role whatsoever. “Collapse” is the walk operator propagating entanglement outward from the measurement site at the Lieb-Robinson velocity v = √(2/3). It is physical, mechanical, and occurs whether or not anyone is watching. It has a specific speed (limited by the bridge propagation rate), a specific spatial structure (a forward light cone from the measurement site), and a specific suppression rate (determined by the code’s valid-subspace fraction).
The one thing the lattice does NOT explain is why you get one specific outcome rather than both. The walk operator is deterministic; the branching is deterministic; but which branch you experience is genuinely random. This is the irreducible core of quantum randomness, and the lattice framework — like every other interpretation — leaves it as a fundamental feature of nature rather than a derivable consequence.
4. Spooky Action at a Distance: Nothing Travels
The mystery as usually stated: When you measure one member of an entangled pair, the other instantly “knows” the result, regardless of distance. This seems to require faster-than-light communication, violating relativity.
The lattice picture: This was already covered in the entanglement section, but it is worth stating the resolution explicitly and simply.
Nothing travels. No signal is sent. No information is transmitted.
The correlations between two entangled voids were created locally, at the bridge where they interacted. After separation, each void carries its half of the correlated pattern. Measuring one void reveals what the pattern says about the other — just as opening one of two sealed envelopes reveals the content of the other. The envelopes don’t communicate. The information was inside them all along.
The reason this feels “spooky” in standard quantum mechanics is that the correlations are stronger than any classical mechanism can produce (this is Bell’s theorem, discussed below). But on the lattice, the mechanism IS quantum — the CNOT gate creates genuinely quantum correlations (not classical ones), and the qubits carry superpositions (not definite values). The correlations are stronger than classical because the substrate is quantum. No spookiness required.
5. The Double Slit: Amplitude Through Two Paths
The mystery as usually stated: Fire electrons one at a time at a barrier with two slits. Each electron arrives at the detector as a single dot (particle-like). But over many electrons, the dots form an interference pattern (wave-like). Somehow, each individual electron “goes through both slits at once.” Block one slit and the interference pattern vanishes — the electron “knows” the other slit is closed. This seems to require the electron to be in two places at the same time.
The standard explanation: The electron’s wave function passes through both slits, and the two portions interfere at the detector. When you block one slit, there’s only one path, and no interference occurs. But don’t ask what the electron “really” does between the source and the detector — that question is considered meaningless in Copenhagen quantum mechanics.
The lattice picture: The electron is a pattern of qubit amplitudes propagating through the void lattice under the walk operator. The walk operator is linear — it sends amplitude along every available path simultaneously. When the amplitude reaches the barrier, it splits: some goes through the left slit (a chain of voids leading left) and some through the right slit (a chain leading right). The two streams recombine at the detector.
At each detector void, the total amplitude is the sum of the amplitudes arriving from the two paths. Because these are complex numbers with phases, they can add constructively (bright fringe) or destructively (dark fringe), depending on the path-length difference. This is the interference pattern.
When a single electron is detected, the measurement collapses the spread-out amplitude onto a single void (as described in section 3). The detection point appears random, but the probability of detection at each void is |amplitude|², which follows the interference pattern. Over many electrons, the dots accumulate into fringes.
Block one slit and there’s only one path contributing to the amplitude at each detector void. No second path means no phase difference means no interference. The pattern becomes a single smooth blob.
The electron doesn’t “go through both slits.” The amplitude goes through both paths — because the walk operator sends amplitude along every available bridge. The electron is found at one void when measured — because measurement collapses the amplitude to one location. Between source and detector, there is no electron — there is only a pattern of amplitudes spreading across voids. Asking “which slit did the electron go through?” is like asking “which pipe did the water pressure go through?” — pressure goes through all pipes simultaneously. The water comes out of one tap.
The delayed-choice mystery: In Wheeler’s delayed-choice experiment, the decision to observe which slit the electron went through is made after the electron has already passed the slits. The electron appears to retroactively change its behaviour — going through one slit if observed, both if not.
On the lattice, there is no mystery. The amplitude always goes through both paths. The “observation” at the slits is just an additional CNOT interaction that entangles the electron’s amplitude with a detector void at one slit. This entanglement destroys the phase coherence between the two paths (because the detector void’s state is now correlated with which path the electron took). The interference pattern vanishes not because the electron “changed its mind” but because the phase information was diluted into the detector void. Whether you place the detector before or after the slits doesn’t matter — the entanglement is what kills the interference, and entanglement is a local operation at the bridge where the detector sits.
6. Bell’s Inequality: Qubits, Not Hidden Variables
The mystery as usually stated: Bell’s theorem (1964) proves that no “local hidden variable” theory can reproduce the predictions of quantum mechanics. If particles carried pre-determined values (hidden variables) that were set during their interaction and revealed during measurement, the correlations between measurements on entangled pairs would satisfy a mathematical inequality. Quantum mechanics predicts, and experiments confirm, that this inequality is violated. This seems to rule out any mechanistic, deterministic explanation of entanglement.
The standard worry: If particles don’t carry hidden variables, what determines the measurement outcomes? The standard answer — “nothing determines them until measurement” — is unsatisfying to anyone who wants a physical picture.
The lattice picture: The information lattice is NOT a hidden variable theory, because the bits on the octahedral faces are NOT definite values between measurements. They are qubits — quantum superpositions.
A hidden variable theory says: “each face secretly has a definite value (0 or 1), and measurement just reveals it.” Bell proved this cannot reproduce quantum correlations.
The lattice says: “each face is in a state α|0⟩ + β|1⟩, and measurement forces a probabilistic choice.” The “choice” is not predetermined. The amplitudes determine the probabilities, but the specific outcome is genuinely random. This is standard quantum mechanics — and it satisfies Bell’s theorem because the correlations arise from quantum superposition, not from pre-existing classical values.
The key distinction: hidden variables are classical bits pretending to be quantum. The lattice faces are genuine qubits — they exist in superposition between measurements, and the superposition is the physical reality (as the PBR theorem requires). Bell’s inequality is violated because the substrate is quantum, not because anything travels faster than light.
7. The Speed of Light, Relativity, and Gravity
The mystery as usually stated: Why is there a universal speed limit? Why can’t anything travel faster than light? And why do gravitational waves travel at exactly the same speed as light, even though gravity and electromagnetism are completely different forces described by different mathematics?
The lattice picture: The speed of light is the bridge propagation speed — the maximum rate at which the walk operator can move amplitude from one void to the next. It is the Lieb-Robinson velocity of the lattice, v = √(2/3) in lattice units. Nothing can travel faster because there is nothing faster — the bridges are the only communication channels, and the walk operator advances at one bridge per tick.
Gravitational waves travel at the same speed as light because both use the same bridges. The photon (T₁u branch) and the graviton candidate (E_g branch) are different excitation patterns on the same lattice infrastructure. They share the same maximum propagation speed because they share the same edges. You would need to break the lattice to make them travel at different speeds.
This is arguably the simplest explanation ever offered for why c_gravity = c_light. In general relativity, the equality is a consequence of the equivalence principle and the structure of Einstein’s field equations. On the lattice, it is a consequence of the fact that there is only one kind of bridge.
8. Quantum Tunnelling: Amplitude Leaks Through Barriers
The mystery as usually stated: A particle can pass through a barrier that it classically shouldn’t have enough energy to cross. An electron can appear on the other side of a wall. This is the basis of tunnel diodes, scanning tunnelling microscopes, and radioactive decay. How does the particle get through?
The lattice picture: It doesn’t “get through.” Its amplitude leaks through.
The walk operator sends amplitude along every available bridge at every tick. When a propagating pattern reaches a region of high spectral energy (a “barrier” — a region where the void configurations are unfavourable), the amplitude doesn’t stop. It continues to propagate, but with exponentially decreasing magnitude, because the high-energy region suppresses the amplitude at each bridge crossing.
If the barrier is thin (only a few voids wide), a small but non-zero amplitude reaches the other side. The squared modulus of this leaked amplitude is the tunnelling probability.
There is no paradox. The particle doesn’t somehow teleport through the barrier. Its amplitude — which is a real, physical quantity on the lattice — simply has a non-zero tail that extends through the barrier region. When a measurement is made on the far side, there is a small but non-zero probability of finding the particle there. This probability decreases exponentially with barrier thickness, exactly as observed.
The walk operator treats the barrier as a region of high energy cost but not infinite energy cost. Amplitude leaks through at a rate determined by the ratio of the barrier height to the particle’s energy — the same exponential dependence found in standard quantum mechanics, derived here from the spectral structure of the lattice rather than from the Schrödinger equation.
9. Feynman Diagrams: Allowed Bit-Pattern Transitions
The mystery as usually stated: Feynman diagrams are the standard tool for calculating particle interactions. Lines represent particles, vertices represent interactions, and the rules for which vertices are allowed seem to come from the symmetry structure of the gauge group. But what IS a vertex, physically? What happens at the point where an electron emits a photon?
The lattice picture: A Feynman vertex is a CNOT gate firing at a bridge.
The incoming lines are codewords — specific 8-bit patterns propagating along the lattice. The vertex is the bridge where two voids interact. The outgoing lines are the codewords that result from the gate operation.
An “allowed vertex” is one where the incoming and outgoing bit patterns satisfy the XOR zero-sum rule — the total pattern is conserved across the interaction. A “forbidden vertex” is one where the XOR doesn’t balance, meaning the code constraints would be violated.
For example, beta decay (a down quark becoming an up quark by emitting a W boson) is allowed because the CNOT gate flips I₃ (converting d to u) and the emitted W boson carries exactly the bit-pattern difference. Proton decay (a quark becoming a lepton) is forbidden because it would require flipping the LQ bit, which the gate cannot reach.
The Feynman rules — which vertices are allowed, which are forbidden, what conservation laws apply — are not imposed from outside. They are the wiring diagram of the CNOT gate. The gate can reach certain bits and not others. The bits it can reach determine the allowed transitions. The bits it can’t reach determine the conservation laws.
This makes Feynman diagrams not just a calculational tool but a literal map of what the lattice hardware can and cannot do. Every allowed diagram is a computation the lattice can perform. Every forbidden diagram is a computation the lattice’s wiring prevents.
10. Born’s Rule: A Theorem, Not a Postulate
The mystery as usually stated: Why is the probability of a measurement outcome equal to the squared modulus of the wave function amplitude? Why |ψ|² and not |ψ| or |ψ|³ or something else? In standard quantum mechanics, Born’s rule is a postulate — an axiom added to the theory because it works, with no deeper justification.
The lattice picture: Born’s rule is a mathematical consequence of unitarity.
The walk operator W is unitary: W†W = I. This means it preserves the inner product of any two state vectors. In particular, it preserves the total norm: Σ|c_i|² = 1, where the sum runs over all voids and all codewords.
Because the walk operator preserves Σ|c_i|², this quantity is automatically a probability distribution — it is non-negative and sums to 1. No other power of the amplitudes has this property under unitary evolution. |c_i|³ would not be preserved. |c_i| would not be preserved. Only |c_i|² is invariant under unitary transformation.
Born’s rule is therefore not a mysterious additional postulate. It is the unique probability measure that is consistent with unitary time evolution. On the lattice, asking “why |ψ|²?” is like asking “why does the area of a circle involve π?” — the answer is: because that’s what the geometry implies.
The Pattern
Look at what has happened across these ten examples. In each case, the standard account presents a phenomenon as deeply mysterious — requiring either philosophical hand-waving (“shut up and calculate”), exotic interpretations (Many Worlds, consciousness-induced collapse), or acceptance of permanent puzzlement (“nobody understands quantum mechanics”).
The lattice account replaces mystery with mechanism:
Entanglement is patterns that persist. The wave function is amplitudes on voids. Collapse is information dilution at a specific speed. Spooky action is not action at all. The double slit is amplitude splitting along paths. Bell violations come from qubits, not hidden variables. The speed of light is the bridge rate. Tunnelling is amplitude leaking through barriers. Feynman vertices are gate operations. Born’s rule is a theorem of unitarity.
None of these explanations require new physics. None require exotic interpretations. None require giving up on understanding. They require only the framework developed in Articles 4 and 5 — qubits on octahedral faces, connected by bridges, evolving under a unitary walk operator with a CNOT gate at each bridge.
The explanatory power is not a coincidence. It is a consequence of the framework being specific. When you have a concrete substrate (the lattice), a concrete state space (the 48-dimensional codeword space), and a concrete dynamics (the walk operator), the “mysteries” of quantum mechanics become questions with answers. The mysteries existed because the standard formalism deliberately avoids specifying a substrate. The information lattice provides one.
Whether it is the right substrate is, as always, for experiment to decide. But the clarity it brings to quantum foundations is, we believe, valuable regardless — not because it proves the lattice is correct, but because it demonstrates that quantum mechanics can be understood mechanically, if you’re willing to take the substrate seriously.
Dave Elliman is the founder of Neuro-Symbolic Ltd and was a Professor of Computer Science at the University of Nottingham, he has since had a successful research career in industry. His research spans information theory, neuro-symbolic AI, and quantum information.
The title of this series nods to Richard Feynman’s “Six Easy Pieces” (1995). Feynman needed six. The octahedron needed eight. The paradoxes needed one more.