A large part of theoretical physics now works on the assumption that space and time are not the bottom layer of reality. Several serious answers exist for what sits underneath. Almost none of them can currently be told apart by any measurement. This piece maps the candidates, then does the harder thing: it asks what evidence would actually decide between them — and finds that the single experiment everyone was counting on has spent the last eleven months being argued to a standstill in Nature and on the arXiv, by the people who invented it.
The slogan belongs to Nima Arkani-Hamed, and it is more careful than it sounds. Nobody is claiming that space and time are illusions in any everyday sense. The claim is narrower and stranger: that in the equations describing how particles interact, the concepts of locality (things only affect what is next to them) and unitarity (probabilities sum to one) appear to be derived features rather than starting assumptions — and that when you push to the shortest distances, the operational meaning of "position in spacetime" gives out entirely.
Three separate pressures push in the same direction. General relativity and quantum mechanics disagree about what happens at the Planck scale. Black hole thermodynamics says the information content of a region scales with its surface area, not its volume — which is not how a normal three-dimensional thing behaves. And the mathematics of scattering amplitudes turns out to be dramatically simpler when you stop drawing Feynman diagrams in spacetime and start computing volumes of abstract geometric objects instead.
So: several fields arrived at "not fundamental" independently. That convergence is the strongest thing going for the claim. What they have not converged on is what replaces it.
| Programme | What spacetime is made of | Standing |
|---|---|---|
| Holography / quantum information Maldacena, Ryu–Takayanagi, "It from Qubit" |
Entanglement. Geometry is the pattern of quantum correlation in a lower-dimensional system. The entanglement entropy of a region on the boundary equals the area of a minimal surface in the bulk, divided by 4G. | Strongest mathematics. Precise, checked, generative. Works in a universe with the wrong sign of the cosmological constant — i.e. not ours. |
| Positive geometry Arkani-Hamed, Trnka, Benincasa, Postnikov |
Combinatorics. Scattering amplitudes are volumes of polytopes — the amplituhedron, the associahedron, cosmological polytopes — that live in no spacetime at all. Locality and unitarity fall out of the geometry's boundaries. | Spectacular results, mostly in simplified theories. Extension to cosmology (cosmological polytopes, "cosmohedra") is the live frontier. |
| Discrete causal structure Causal sets (Sorkin); loop quantum gravity / spin foams; causal dynamical triangulations |
Order plus number. Sorkin's slogan. A discrete set of events with a partial order of "before and after"; continuous geometry is the coarse-grained approximation. | The only family that makes a genuine, published cosmological prediction (below). Also the family most exposed to observational constraint. |
| Thermodynamic / entropic Jacobson 1995; Verlinde 2011, 2017 |
Statistics. Gravity is not a force but an equation of state — what you get when you write thermodynamics for the horizons an accelerating observer sees. | Jacobson's derivation is a landmark. Verlinde's cosmological extension is genuinely near-term falsifiable, which is rare — and has had mixed results. |
| Spectral / noncommutative Connes, Chamseddine, Mukhanov |
A spectrum. Geometry is recovered not from points but from the eigenvalues of an operator. Impose one commutation relation and volume comes out quantised — spacetime as a very large number of Planck-scale quanta. | Deep mathematics; derives the Standard Model's algebraic structure. Almost invisible in the Anglophone popular account of this question. |
A sixth claimant sits outside physics and is dealt with separately in §6: Donald Hoffman's conscious agents, which asserts that spacetime is an interface projected by a network of conscious subjects.
Since 2017, quantum gravity has had something it had lacked for a century: a tabletop experiment with a plausible chance of deciding something. The idea traces to a question Richard Feynman posed at the 1957 Chapel Hill conference, and was made concrete by two groups working independently — Sougato Bose and colleagues, and Chiara Marletto with Vlatko Vedral.
Put a small mass into a quantum superposition of two locations. Put a second mass nearby, also in superposition. Let them interact only through gravity — screen out everything else. Then check whether the two masses have become entangled.
The logic that made this exciting is a theorem, not an intuition. In quantum information theory, a purely classical channel cannot create entanglement between two systems — it can only transmit classical information. So if gravity is the only thing connecting the two masses, and entanglement appears, then gravity cannot be a classical channel. Gravity would have to be quantum. That result would not by itself tell you which candidate in the table above is right, but it would eliminate an entire class of theories in which gravity stays classical while everything else is quantised — and it would be the first positive experimental result quantum gravity has ever had — as opposed to the null results and upper limits, like the one in §3, that make up the rest of the record.
Joseph Aziz and Richard Howl (Royal Holloway, University of London), "Classical theories of gravity produce entanglement," Nature 646, 813–817 (2025).
Their argument: the no-go theorems everyone was relying on describe the matter in the experiment using ordinary quantum mechanics. Redo the calculation with matter described by full quantum field theory — the framework physics actually uses — and, they claim, theories with classical gravity can transmit quantum information and generate entanglement, through local, physical processes.
If that holds, seeing entanglement would not prove gravity is quantum. The experiment would lose its punchline.
What happened next is worth watching closely, because it is a live example of how a field actually adjudicates — fast, in public, and with the original authors' own instruments turned on them.
Even taking the rebuttals at full strength, Aziz and Howl leave behind something useful, and they say so themselves in the abstract: whatever effect classical gravity produces scales differently from the effect quantum gravity predicts. That is a design instruction. It tells experimentalists which parameters and which form of the experiment would produce a result that no classical story can absorb.
This is the pattern to notice. The paper's headline claim may well be wrong. Its structural contribution — forcing the community to state exactly which assumption the interpretation rests on — is the part that will still matter in ten years.
Worth noting: this objection is not new in kind. Charis Anastopoulos and Bei-Lok Hu made a version of it in 2018, arguing that Newtonian gravity-induced entanglement is agnostic about whether gravity's true degrees of freedom are quantum. What is new is that the argument has now been made in the language of quantum field theory, published in Nature, and answered by half a dozen separate groups within six months. Their 2018 preprint was subsequently withdrawn from the arXiv over a copyright issue with material it contained — the argument itself survives in their later published work, and I flag the withdrawal here rather than cite a dead link as though it were live.
Against all that theory, here is a real measurement.
LHAASO Collaboration, Physical Review Letters 133, 071501 (2024); revised February 2026.
On 9 October 2022 the Large High Altitude Air Shower Observatory in Sichuan caught the very early TeV afterglow of GRB 221009A — the brightest gamma-ray burst ever recorded, with the best TeV photon statistics ever obtained from a burst.
Many discrete or "granular" models of spacetime predict that the speed of light in vacuum should depend slightly on photon energy — a violation of Lorentz invariance. Over billions of light years, a vanishingly small effect accumulates into a measurable difference in arrival time between high- and low-energy photons.
LHAASO saw none. The 95% confidence lower limits on the quantum-gravity energy scale: more than 10 times the Planck energy for a linear effect, and 6×10⁻⁸ of the Planck energy for a quadratic one — improving the previous best quadratic bounds by a factor of five to seven.
What this means, precisely. The linear limit is the striking one: the effect is excluded even above the energy scale where quantum gravity is supposed to switch on. The naive picture — that spacetime is a fixed lattice, and light ripples across it like waves on a grid, with the grid spacing showing up as energy-dependent speed — is dead at first order.
What this does not mean. It does not falsify discreteness as such, and it is important not to overstate it. Causal set theory is built precisely so that its discreteness is Lorentz invariant: events are sprinkled randomly rather than laid on a grid, which is the whole point of the construction. Loop quantum gravity has similar reasons to expect no first-order effect. So the constraint bites hardest on the phenomenological models that had been standing in for discreteness in the popular account — and leaves the serious discrete programmes intact.
Causal set theory is the only programme in the table that made a specific, published, cosmological prediction ahead of the data: everpresent Λ. If spacetime is fundamentally discrete, the number of spacetime "atoms" in any volume fluctuates, and that uncertainty propagates into the cosmological constant. Λ should therefore not be constant. It should fluctuate about zero, at all epochs, with amplitude falling as the inverse square root of spacetime volume — which naturally puts it at roughly the critical density, the order of magnitude actually observed.
The prediction was made by Sorkin before the 1998 discovery of accelerated expansion. It has since been confronted with Type Ia supernova and CMB data (Zwane, Afshordi and Sorkin, Classical and Quantum Gravity 35, 194002, 2018; extended by Santanu Das, Arad Nasiri and Yasaman Yazdi in 2023). The honest verdict: the model is stochastic, so it does not predict one universe — it predicts a distribution of them. A minority of random realisations fit the supernova data better than standard ΛCDM. Most do not. That is a weaker result than a clean prediction, but it is still more than any other candidate in the table has offered.
Full title: 量子情報が拓く宇宙・時空・物質の新パラダイム — "The Natural Laws of Extreme Universe: A New Paradigm for Spacetime and Matter from Quantum Information." A MEXT-KAKENHI Grant-in-Aid for Transformative Research Areas (A), FY2021–2025, headquartered at the Yukawa Institute for Theoretical Physics, Kyoto University, led by Tadashi Takayanagi — co-author of the Ryu–Takayanagi formula, which is the single most-used equation in the "spacetime from entanglement" programme.
The structure is what makes it unusual: the programme is deliberately split across quantum information, theoretical physics and experimental physics groups, on the premise that the question is not purely a string theory problem. It ran annual international workshops through to Extreme Universe 2025 at YITP in late October 2025.
Its most pointed recent output is Takayanagi's 2025 Physical Review Letters Essay, which does something the Anglophone account rarely does — it names the unfinished parts. Three of them: work out which quantum circuit each holographic spacetime corresponds to; extend holography beyond the anti-de Sitter case to the spacetimes that appear in realistic cosmology; and address how time emerges, for which he proposes pseudo-entropy and timelike entanglement as tools.
That third item deserves emphasis. Almost every popular treatment of this question is about how space emerges from entanglement. Time is the harder half, it is being worked on hardest in Kyoto, and it is largely absent from the English-language story.
Alain Connes' noncommutative geometry replaces the notion of a space made of points with an algebra and an operator; geometry is recovered from the operator's spectrum. In Chamseddine, Connes and Mukhanov, "Quanta of Geometry: Noncommutative Aspects," Physical Review Letters 114, 091302 (2015), imposing a higher-degree Heisenberg-type commutation relation involving the Dirac operator makes the volume come out quantised — the manifold decomposes into a very large number of Planck-scale spheres of two kinds, and those two kinds turn out to correspond to the algebras that generate the Standard Model's gauge structure.
Why it is underseen: it is a French mathematical tradition with a high entry cost, it is not marketed with a slogan, and it produces its most impressive result in the wrong place for popular attention — particle physics rather than cosmology. It nonetheless gives an independent route from "spacetime is not fundamental" to a specific quantum of geometry, and it rarely appears in lists of candidates.
This section is my interpretation of the material above, not a finding reported by any of the researchers cited. Read it as a proposition to argue with.
Set them side by side and something becomes visible that the usual "rival theories of quantum gravity" framing hides. These programmes are not five competing answers to one question. They are answers to four different questions, and each has quietly agreed to pay for its answer in a different currency.
| Programme | Question it is really answering | What it gives up |
|---|---|---|
| Holography | What is geometry made of? | A fixed number of dimensions; the independence of the bulk from the boundary. |
| Positive geometry | What are dynamics made of? | Locality and unitarity as starting assumptions. |
| Causal sets / LQG | What is causal order made of? | The continuum. |
| Entropic gravity | What status does gravity have? | Gravity's standing as a fundamental interaction at all. |
| Spectral geometry | What is a point? | Commutativity — the assumption that the order of two measurements doesn't matter. |
This reframing has a practical consequence. The question "which of these is right?" is malformed, and the reason no experiment discriminates between them is partly that they are not, in the main, mutually exclusive. Holography and positive geometry could both be true. Causal sets and spectral geometry are answering questions that barely touch.
The dividing line that does discriminate is not discrete-versus-continuous. It is the currency column: which classical assumption are you willing to abandon, and by how much? A programme that names its currency and states a magnitude becomes testable. A programme that says only "spacetime is emergent" has said something that cannot be wrong.
Which yields a criterion I will use going forward, and hold myself to:
A candidate replacement for spacetime is empirically live only if it names (a) the classical assumption it violates, and (b) the size of the violation. Direction is not enough. LHAASO could rule out energy-dependent light speed precisely because the models named a scale. Causal sets can be tested against supernovae precisely because everpresent Λ names an amplitude. Everything else in the table is currently unfalsifiable — not because it is unscientific, but because it has not yet been made specific enough to be embarrassed.
Readers of Investigation №12, published alongside this one, will recognise this. The same structural flaw showed up in consciousness science: an adversarial collaboration in which fifteen authors agreed the direction of their predictions but not the magnitude, and conceded in their own paper that this might prevent the experiment from arbitrating anything. Two fields, no overlap in personnel or method, same failure mode. That is either a coincidence or a fact about how research programmes age, and it is worth watching for a third case before deciding which.
The AdS/CFT correspondence — the mathematical engine behind almost every "spacetime is entanglement" claim — is formulated in anti-de Sitter space, which has a negative cosmological constant. Our universe has a positive one. The de Sitter case is, in the words of the 2026 literature, one of the most vital open frontiers: the dual theories are expected to be non-unitary, and it is unclear how time should emerge from a Euclidean boundary theory at all. A bottom-up tensor-network framework relating boundary data to emergent de Sitter spacetime is still lacking.
This is not a small caveat. The strongest evidence for the strongest candidate comes from a universe that is not ours.
Nick Huggett and Christian Wüthrich, in Out of Nowhere (Oxford University Press, 2025), press a question that will not go away. If the fundamental level contains no spacetime, and only things located in spacetime can be observed, how could such a theory ever have empirical support? Their own answer is spacetime functionalism: what matters is that emergent structures behave functionally as spatiotemporal ones. But the objection has teeth in the specific case where a theory posits a region that is non-spatiotemporal — there, by the theory's own lights, there are no derived spatiotemporal structures, and so nothing observable.
Physicists tend to wave this away. They should not. It is the reason this question is unusually hard to settle empirically, and it is a structural feature of the problem rather than a temporary shortage of funding.
The amplituhedron was constructed for planar maximally supersymmetric Yang–Mills theory — an elegant theory that nobody claims describes our universe. Surfaceology and the curve-integral formalism have since extended the approach to coloured scalars, Yukawa theory and beyond, and the cosmological polytope programme (Arkani-Hamed, Benincasa, Postnikov) is a serious attempt to reach real cosmology via the wavefunction of the universe. But the honest position in 2026 is that this is a rapidly maturing mathematical programme with, as yet, no observational prediction of its own.
Its claim on our attention is different in kind: it is that locality and unitarity emerge from the boundary structure of a polytope. That is a profound structural insight about physics whether or not it ever yields a measurement.
Verlinde's 2016 emergent gravity (SciPost Physics 2, 016, 2017) deserves credit for being checkable. Brouwer and colleagues tested it against weak lensing around 33,613 isolated central galaxies in 2017 and found the zero-free-parameter prediction in good agreement across four stellar mass bins. Against that: attempts to extend entropic corrections to galactic rotation curves run into solar-system and particle-physics constraints; a 2017 JHEP paper is titled, bluntly, "Inconsistencies in Verlinde's emergent gravity"; and there is a standing theoretical objection that gravitational dynamics is reversible and so cannot be driven purely by entropy increase.
A theory that can be tested and returns mixed results is in a healthier epistemic position than one that cannot be tested at all. That is worth saying plainly.
The Wolfram Physics Project proposes that space is a hypergraph updated by simple rewriting rules. The critique is well documented and, as far as I can establish, unanswered: the framework makes no definite new quantitative predictions, and has not reproduced the standard quantitative results of quantum mechanics and general relativity. MIT's Daniel Harlow: the claimed successes are "at best, qualitative." The project's own response — comparing the demand for falsification to asking how one would disprove calculus — concedes the point rather than meeting it.
I include it because it circulates widely in exactly the audience this publication is written for. On the criterion in §5, it names neither a currency nor a magnitude.
An interest to declare first. Donald Hoffman's work is a real influence on my own, and I would not want that hidden behind a critique. His central move — that what we take to be the world may be the format of an interface rather than a report on what is there — is one of the things that pushed me towards a structural rather than a substance account of reality, and his willingness to follow the argument somewhere professionally uncomfortable is a standard worth holding. I am marking down one specific claim precisely because I take the programme seriously. Waving through the weak part of an argument you are indebted to is not loyalty to it.
Donald Hoffman, with Chetan Prakash and Robert Prentner, argues in "Fusions of Consciousness" (Entropy 25(1), 129, 2023) that conscious agents are fundamental, that their dynamics are Markovian, and that spacetime is an interface projected by those dynamics — with scattering processes as "a data structure that codes for interactions of conscious agents."
Separating two claims, because they have very different standing. The philosophical claim — that perception presents a species-specific interface rather than an objective world — is a serious position with an argued case behind it, and I have given it a fair hearing before. The physics claim is a different matter. Hoffman's programme frequently invokes the amplituhedron and decorated permutations as vindication. But the relationship runs one way: he cites the physics; the physics does not cite him. I could find no work in the positive-geometry literature that derives anything from conscious agents, and no result in which the conscious-agent formalism reproduces a known scattering amplitude.
On the §5 criterion, it names no currency and no magnitude. As a contribution to the question "what replaces spacetime," I rate its current evidential standing at 1/5. That is a judgement about a physics claim, not about the man or about the interface argument, which stands or falls on separate grounds.
Recursive Field Theory (RFT) is my own structural framework. Its subject is how systems hold together: coherence maintained across difference, with closure treated as a relation between constraint, persistence and threshold rather than as a substance. It is a framework about structure. It is not a theory of fundamental physics, it makes no claim about what replaces spacetime, and I want to be unusually blunt about that here, because this is precisely the territory where structural frameworks get overextended and lose their credibility.
What RFT does have a view on is the shape of the situation, not its content. Every programme in §1 makes the same move: it stops asking what the world is made of and starts asking what relations must hold for the familiar thing to appear. Geometry as a relation between entanglements. Causal order as a relation between events. A point as a relation in an algebra. That is a structural turn, and it happened independently in five places. I find that interesting, and it is part of why I work the way I do.
And now the discipline, which is the same discipline as in the companion piece on consciousness. That convergence is not evidence for RFT. A sufficiently abstract structural claim will converge with almost anything — that is a property of abstraction, not a property of the world. Worse, the §5 criterion I proposed indicts my own framework as squarely as it indicts Hoffman's or Wolfram's: a structural claim that says "coherence determines what a system can hold" without saying how much, measured how, is exactly the kind of claim that cannot be embarrassed by evidence. If I want RFT taken seriously, the obligation is to name a currency and a magnitude — in the domains where it actually applies, which are not these.
I should be clear that this is not a concession offered in the abstract. It is a description of what the theoretical work currently consists of. RFT's closure primitive is already written as a ratio of measurable quantities rather than as a metaphor, which is the first half of the requirement; the second half — stating, in advance, what magnitude the framework predicts in a specific domain, and what observation would count against it — is the live problem I am working on, and the reason the current empirical programme pre-registers its predictions before anything is run. Whether that succeeds is an open question. But the standard set out in §5 is the standard I am building to, not one I have just discovered and conceded.
RFT is my own interpretive framework and original work, offered here as a way of seeing. It is not established physics, it is not a candidate replacement for spacetime, and none of the researchers cited in this piece are aware of it or endorse it.
Format & time. Reflective structured learning · ~30–45 minutes.
Learning outcomes. After completing this unit you will be able to:
Reflection prompts. Write 3–5 lines on each and keep them for your CPD record.
CPD-eligible structured learning. Paid members can download a CPD certificate — see the certificate template. CPD-eligible structured learning; not statutory-regulator endorsement — practitioners self-assess relevance and log accordingly against their own professional body's requirements. Hours shown reflect estimated reflective-learning time; log only genuine time spent. Not medical advice.
Primary sources linked where available. Preprints are labelled as preprints; a withdrawn preprint is labelled as withdrawn and is not used as a live citation. Journal articles behind paywalls are given with DOI and arXiv preprint where one exists. Always consult the originals — this synthesis describes emphasis and findings, not verbatim claims.
How this was made. A structured research pass across theoretical physics, quantum gravity phenomenology, philosophy of physics and non-English research programmes, including the Japanese "Extreme Universe" collaboration and the French spectral-geometry tradition; every citation checked individually against a primary source, then re-checked in a second independent verification pass which caught a misattributed author list and a withdrawn preprint — both corrected before publication rather than quietly dropped; strong evidence separated from contested; the field's own admitted weak points — the de Sitter problem, the empirical incoherence objection, the mixed record of the one falsifiable candidate — stated rather than smoothed over. One claim was marked down after checking whether the citation ran in both directions; it did not. The criterion proposed in §5 is then applied to my own framework, which fails it. A human reviews every word before publication. Reality is the arbiter.
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