The Jar of Nothing That Contains Everything
Why empty space isn't empty — and why physics has no idea what's in it
This is Part 1 of “Eight easy-pieces: The Information Lattice,” an 8-part series exploring whether the universe might be built from error-correcting codes rather than continuous fields.
Take a glass jar. Pump out every molecule of air. Shield it from all light, all radiation, all heat. Cool it to absolute zero — the coldest anything can possibly be.
Common sense says you now have a jar of nothing. A perfect void. The purest emptiness achievable in nature.
Physics says you’re wrong. The jar is full.
The Vacuum Is Not Empty
The word “vacuum” comes from the Latin vacuus — empty. But the quantum vacuum, as physicists understand it, is anything but. It is a seething, restless, energetic medium, and we have measured its effects directly in the laboratory.
This isn’t speculation. It isn’t theoretical hand-waving. Here are four experiments — all performed, all replicated, all beyond dispute — that prove empty space is doing something.
1. The Casimir Effect: Empty Space Pushes
In 1948, the Dutch physicist Hendrik Casimir made an extraordinary prediction. Take two perfectly flat metal plates. Place them in a vacuum, a few millionths of a metre apart. According to classical physics, nothing should happen. There’s nothing between them.
Casimir predicted they would be pushed together by the vacuum itself.
In 1997, Steve Lamoreaux measured it. The plates move. Empty space exerts a measurable, physical force.
The standard explanation: the vacuum is filled with electromagnetic fluctuations at all possible wavelengths. Between the plates, only wavelengths that fit the gap can exist — like standing waves on a guitar string. Outside the plates, all wavelengths are present. The imbalance creates a pressure difference. The plates are pushed together by the excess of vacuum energy on the outside.
The force is tiny — roughly equivalent to the weight of a single red blood cell spread over a square centimetre. But it is real, repeatable, and precisely matches the theoretical prediction.
2. The Lamb Shift: Empty Space Jostles Atoms
According to the Dirac equation — one of the foundational equations of quantum mechanics — two specific energy levels in the hydrogen atom (called 2S₁/₂ and 2P₁/₂) should have exactly the same energy. If the vacuum were truly empty, an electron in either state would behave identically.
In 1947, Willis Lamb measured these energy levels using microwave spectroscopy. They weren’t equal. There was a tiny but definite split — about one part in a million.
The electron is being jostled by the vacuum. The electromagnetic fluctuations of “empty” space buffet the electron as it orbits the proton, and because the two orbital states bring the electron to slightly different distances from the nucleus, the jostling affects them differently. Lamb won the Nobel Prize for this measurement.
3. The Anomalous Magnetic Moment: Empty Space Alters Magnets
An electron is a tiny magnet. The Dirac equation predicts exactly how strong this magnet should be — a quantity called g, which should equal precisely 2.
It doesn’t. The measured value is 2.00231930436256, known to twelve significant figures. It is the most precisely measured number in all of experimental science.
That extra 0.00231930436256 comes entirely from the vacuum. As the electron exists in “empty” space, it interacts with the vacuum’s electromagnetic fluctuations, which slightly alter its magnetic properties. When physicists calculate this interaction — accounting for the vacuum’s contribution — the theoretical prediction matches the measurement to better than one part in a trillion.
If the vacuum were truly empty, the calculation would be catastrophically wrong.
4. Spontaneous Emission: Empty Space Makes Atoms Glow
Excite an atom — give an electron enough energy to jump to a higher orbit. In a truly empty vacuum, there would be no reason for it to come back down. Nothing is pushing it. Nothing is pulling it. It should stay excited forever.
It doesn’t. It drops back down and emits a photon. Every neon sign, every LED, every laser depends on this. Atoms in excited states spontaneously emit light, even in a perfect vacuum.
The vacuum is nudging the electron. The electromagnetic fluctuations of empty space gently push the excited atom, triggering it to release its energy as light. No active vacuum, no neon signs, no lasers, no stars.
What’s Actually in There?
So the vacuum is full of something. But what?
The standard answer from quantum field theory goes like this. The universe is permeated by invisible quantum fields — one for each type of particle. There is an electron field, a photon field, a quark field, and so on. A “particle” is simply a localised ripple in the relevant field.
The vacuum is the state where all these fields are at their lowest possible energy — the “ground state.” There are no ripples, which means no detectable particles. But the Heisenberg uncertainty principle forbids the fields from having exactly zero energy. They must always jitter, at least a little. These jitters are called quantum fluctuations, and they produce all four of the effects described above.
So far, so good. The theory works. The predictions match. But there is a catastrophic problem hiding in the mathematics.
The Worst Prediction in the History of Science
If the vacuum contains fluctuations at every possible frequency, you can calculate the total energy of all those fluctuations by adding them up. Each frequency contributes a tiny “zero-point energy” of ½ℏf, where f is the frequency and ℏ is Planck’s constant.
The problem: there is no upper limit on frequency. The sum diverges to infinity.
Obviously, the vacuum does not contain infinite energy. Physicists “fix” this by imposing an artificial cutoff — they tell the mathematics to stop counting at some very high frequency, typically the Planck scale (about 10⁴³ Hz, the frequency at which quantum gravity effects are expected to dominate).
Even with this cutoff, the calculated vacuum energy density is approximately
10¹²¹ times larger than the observed value.
That is not a typo. The theoretical prediction exceeds the measurement by a factor of a 1 followed by 121 zeros. It is sometimes called the cosmological constant problem, and it is arguably the worst quantitative prediction in the history of science.
To put the scale of the mismatch in perspective: if you predicted the distance from London to New York and were off by a factor of 10¹²¹, your answer would overshoot the observable universe by more than a googol — ten thousand trillion trillion trillion trillion trillion trillion trillion trillion times.
Something is profoundly, catastrophically wrong with our understanding of empty space.
Do All Frequencies Actually Exist?
Here is a question that rarely gets asked in popular accounts of physics, but which a thoughtful reader might wonder about: is there actually any evidence that the vacuum fluctuates at all frequencies?
The answer is no.
Every experiment that confirms the vacuum’s activity — the Casimir effect, the Lamb shift, g−2, spontaneous emission — measures the vacuum’s effects within a specific, finite range of frequencies. The Casimir plates only respond to wavelengths that are comparable to the gap between them. The Lamb shift only samples the frequencies relevant to the hydrogen atom’s orbital structure. The g−2 measurement integrates over a specific set of virtual loops.
Nobody has ever measured a vacuum fluctuation at 10⁴³ Hz. Nobody has ever confirmed that the spectrum is continuous rather than discrete. Nobody has confirmed that every conceivable frequency is present.
The assumption that all frequencies exist in the vacuum comes from a theoretical requirement: Lorentz invariance. Einstein’s special relativity demands that the vacuum look the same to all observers regardless of their speed. The only spectrum that is invariant under Lorentz boosts (which shift frequencies via the Doppler effect) is a continuous spectrum extending to infinity. A discrete spectrum — one with specific, identifiable frequencies — would look different to observers moving at different speeds, violating the principle of relativity.
So the infinite spectrum is not measured. It is assumed, in order to preserve a symmetry.
And that assumed infinity is what produces the 10¹²¹ catastrophe.
The Vacuum Is Tearing the Universe Apart
The 10¹²¹ mismatch is not merely an academic embarrassment. The vacuum energy — whatever its true value — has a directly observable, cosmological consequence. It is accelerating the expansion of the universe.
In 1998, two teams of astronomers (led by Saul Perlmutter, Brian Schmidt, and Adam Riess, who shared the 2011 Nobel Prize) were measuring the distances and recession velocities of distant supernovae. They expected to find that the expansion of the universe was slowing down — decelerating under the mutual gravitational attraction of all the matter in it.
Instead, they found the opposite. The expansion is speeding up. Something is pushing the universe apart, and it’s winning against gravity.
That something is the vacuum energy — a tiny but non-zero energy density permeating all of space. Einstein called it the cosmological constant, Λ, and it enters his field equations as a property of empty space itself. Its measured value is astonishingly small: roughly 10⁻²⁹ grams per cubic centimetre, equivalent to about 6 × 10⁻¹⁰ joules per cubic metre. To put that in perspective, a single grain of sand contains more energy than the vacuum energy in a volume of space the size of the Earth.
And yet this whisper of energy, summed over the immensity of intergalactic space, is enough to overpower the gravitational pull of every galaxy, every star, every atom in the observable universe. It is tearing the cosmos apart.
This is the cosmological constant problem in its full horror. Quantum field theory predicts the vacuum energy should be 10¹²¹ times larger than observed. If the prediction were even roughly correct, the universe would have blown itself apart in the first fraction of a second after the Big Bang — or collapsed into a singularity, depending on the sign. The fact that we exist at all means the vacuum energy is fantastically, absurdly, almost impossibly small compared to the theoretical expectation.
Why? Nobody knows.
Physicists have named this mysterious energy “dark energy,” and it accounts for approximately 68% of the total energy content of the universe. We can measure its effects with extraordinary precision. We can describe it mathematically. We cannot explain it.
The Missing 95%
Dark energy is not the only invisible occupant of the vacuum. There is another: dark matter.
In the 1970s, astronomer Vera Rubin measured the rotation speeds of galaxies. She expected stars at the outer edges of a galaxy to orbit more slowly than those near the centre — just as Neptune orbits the Sun more slowly than Mercury, because the gravitational pull weakens with distance.
Instead, she found that stars at the edges orbit just as fast as those near the centre. The galaxies are spinning so fast that they should fly apart. Something invisible is holding them together — something with mass, exerting gravitational pull, but emitting no light, absorbing no light, and interacting with nothing except through gravity.
We call it dark matter, and it accounts for approximately 27% of the universe’s total energy content. We can map its distribution through gravitational lensing (the bending of light from distant galaxies). We can measure its influence on the cosmic microwave background. We can simulate galaxy formation with and without it, and the simulations only match observations when dark matter is included.
But we have no idea what it is.
The Standard Model of particle physics — our best theory of fundamental particles and forces — describes ordinary matter: protons, neutrons, electrons, neutrinos, quarks, gluons, photons, and the Higgs boson. This ordinary matter accounts for just 5% of the universe.
The remaining 95% — dark energy (68%) and dark matter (27%) — is completely outside the Standard Model’s reach. Our most precisely tested theory of nature literally describes only one-twentieth of what exists.
The vacuum, it seems, is not just full. It is full of things we cannot see, cannot touch, and cannot explain.
Three Mysteries in One Jar
So our jar of “nothing” contains at least three profound mysteries:
The fluctuations are real but their total energy is wrong by 10¹²¹. The quantum vacuum jitters, pushes plates together, jostles atoms, and alters magnets. But when we try to calculate the total energy of all those jitters, we get a number so catastrophically large that the universe shouldn’t exist.
The vacuum energy is tearing the universe apart. The tiny, residual energy of empty space — whatever is left after the 10¹²¹ cancellation — is accelerating the expansion of the cosmos. We call it dark energy and it constitutes 68% of the universe. We cannot explain its value.
Something invisible with mass fills the vacuum. Dark matter makes up 27% of the universe, holds galaxies together, and has never been directly detected. It interacts with nothing except gravity. The Standard Model has no candidate for what it is.
These three mysteries share a common root: we do not understand what empty space is made of. The Standard Model treats the vacuum as a structureless, continuous background — an infinite sea of fluctuating fields. But that treatment produces infinite energies, fails to predict the cosmological constant, and has no room for dark matter.
What if the vacuum isn’t structureless at all?
What If Space Is Not Continuous?
What if the vacuum isn’t a continuous field fluctuating at all frequencies, but a discrete structure — like a crystal — with a finite number of specific modes?
This is not a fringe idea. It is the working hypothesis of several major research programmes in theoretical physics:
Loop quantum gravity proposes that space itself is made of discrete units — tiny loops of gravitational field forming a “spin foam” at the Planck scale. In this picture, there is a minimum length and a minimum time step, and the vacuum has a finite number of modes.
Lattice quantum field theory — the most precise method for computing hadron masses from first principles — discretises space onto a grid and performs calculations on that grid. The lattice is usually treated as a computational convenience, but some physicists have argued it may reflect physical reality.
The holographic principle, arising from black hole thermodynamics, suggests that the information content of a region of space is finite and proportional to its surface area, not its volume — implying a fundamental discreteness.
If space is discrete, the 10¹²¹ problem dissolves. A discrete vacuum has a finite number of modes — not an infinite integral but a finite sum. The total vacuum energy is a specific, computable number, not an infinity that must be swept under the rug.
But discretising space creates its own problem: it breaks Lorentz invariance. A lattice has preferred directions. A crystal has axes. Special relativity demands perfect isotropy. How do you have a discrete vacuum that looks continuous from every angle?
The Crystal That Looks Like a Fluid
There is a precedent for this in everyday physics. A polycrystalline metal — steel, aluminium, copper — is made of tiny crystalline grains, each with its own lattice structure and its own preferred axes. Each grain is anisotropic at the atomic scale: the speed of sound, the electrical conductivity, and the elastic modulus all depend on direction within a single grain.
But a bulk sample containing billions of randomly oriented grains is perfectly isotropic. Sound travels at the same speed in every direction. Electricity flows equally in all directions. The microscopic anisotropy averages out at macroscopic scales.
What if the vacuum works the same way? What if “empty space” is a crystal — a specific, discrete, structured lattice — at the Planck scale, but the random orientation of its microscopic domains makes it look perfectly smooth and isotropic at the scales we can measure?
The vacuum fluctuations we detect (Casimir, Lamb, g−2) would not be jitters of continuous fields. They would be the vibrations of a crystal — specific modes at specific frequencies, determined by the lattice geometry. The 10¹²¹ catastrophe would disappear because the crystal has a finite number of modes, and the continuous-spectrum infinity was never real.
The Question
This raises a very specific, very concrete question:
What crystal?
If the vacuum is a lattice, what lattice? How many “atoms” (or qubits, or bits of information) are in each unit cell? What symmetry group does it have? What are its normal modes? What is its spectral energy?
These are not philosophical questions. They are the kind of questions that crystallographers answer about table salt and diamond. They have specific mathematical answers.
In the articles that follow, we will propose one such answer. We will describe a specific three-dimensional lattice — built from regular octahedra, tiled in a unique honeycomb pattern, hosting an 8-qubit error-correcting code on each octahedral face — that reproduces the complete spectrum of known fundamental particles, derives several fundamental constants from pure geometry, and predicts the vacuum energy from first principles without the 10¹²¹ catastrophe.
We do not claim it is the correct lattice. We claim it is the simplest lattice that works — and that it makes specific, falsifiable predictions that no other framework currently provides.
But before we get to the lattice, we need to understand what it’s replacing. In the next article, we survey the Standard Model of particle physics: the most successful and most frustrating theory in science.
Coming Next
Article 2: “The Most Successful Failed Theory in Science” — What the Standard Model gets right (everything we can measure), what it can’t explain (everything we want to understand), and why fifty years of attempted fixes have produced zero new predictions.
The full mathematical details and supporting research papers are available at neusym.ai/research.
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 needs eight.