The Smooth and the Grainy

Essay · physics · September 2026

Two theories account for everything physics has ever measured, and each has passed every test set for it. One says the world is a smooth, curved geometry that moves under its own rules; the other says it is grainy, probabilistic and built from amplitudes that add. Where both apply at once they contradict each other, and a century of work on the single theory that must lie underneath has produced clues, candidates and no verdict. This essay sets out what each rulebook says, where exactly they fail to fit, what the leading attempts to join them have bought and cost, and the one experiment that might, within a generation, say whether gravity is quantum at all.

Reading time ≈ 33 min Einstein 1915 → Hawking 1974 → a table-top test A standalone essay

The situation

Physics has two rulebooks and no referee. The first, general relativity, was finished by Einstein in November 1915 and says that gravity is not a force but the shape of space and time, which matter bends and along which matter falls. The second, quantum mechanics, was assembled between 1925 and 1927 by Heisenberg, Schrödinger, Born, Dirac and others, and says that the world at small scales is described not by positions and velocities but by amplitudes, which add like waves and give probabilities when squared. Both have been tested to a precision no other scientific theory approaches. Both are, by their own internal logic, incomplete. And they are incompatible: not in the mild sense that they use different words, but in the strong sense that when you try to write down a single set of rules that contains both, the rules give infinite answers, or no answer, or an answer that depends on how you asked.

This has been known since the 1930s, and it is worth being clear about why it does not matter for almost everything. Every experiment ever done falls under one rulebook or the other, never both. The scale at which both would be needed at once is fixed by the three constants that each theory carries: Newton’s G, Planck’s ℏ and the speed of light c. Combine them and you get a length, a time, a mass and an energy, the Planck units, and they are the only quantities you can make from those three constants alone. The Planck length is 1.6 × 10⁻³⁵ metres, twenty orders of magnitude below the size of a proton. The Planck energy is 1.2 × 10¹⁹ GeV, fifteen orders above what the Large Hadron Collider reaches. Nothing we can build gets near either. Figure 1 shows why the world looks the way it does: every object we know sits far from the corner where the two rulebooks would have to agree.

Figure 1. Mass against size, a hundred decades each way. The teal line is the Compton wavelength, ℏ/mc: an object confined to a region smaller than this cannot be treated as a single particle, so below the line the second rulebook is unavoidable. The magenta line is the Schwarzschild radius, 2Gm/c²: an object compressed inside it is a black hole, so below that line the first rulebook is. The lines cross at the Planck mass, 2.2 × 10⁻⁸ kg, and the Planck length, 1.6 × 10⁻³⁵ m. Everything we know lies far from the crossing, most of it in the empty wedge between the lines where neither theory is strained.

So the problem is a corner problem. But the corner is where the interesting things are. It is the first 10⁻⁴³ seconds after the big bang, the point at the centre of every black hole, and, less obviously, the fate of a black hole that has been radiating for long enough to shrink to nothing. General relativity predicts the first two and says that at both its own equations stop meaning anything. Quantum mechanics predicts the third and, applied there, appears to break its own most basic rule. So the two theories are not only incompatible with each other; each one, followed to its edge, points at the other and says: you must finish this.

The first rulebook

Gravity is not a force

Einstein said the idea came to him in 1907, sitting in the patent office in Bern: a person falling freely does not feel their own weight.[1] That sounds like a remark about sensation, but it is a remark about physics. Everything in a falling lift falls together, at the same rate, whatever it is made of, so an experiment done inside the lift cannot tell whether the lift is falling in a gravitational field or floating in empty space. Gravity, unlike every other force, can be switched off by choosing the right observer. A force that can be switched off by a change of viewpoint is not a force. It is a property of the viewpoint, which is to say of the geometry.

It took Einstein eight years to turn that into equations, because the geometry needed was Riemann’s geometry of curved spaces, which physicists did not know, and because the equations had to be found rather than derived. What he wrote down in November 1915 has a compact form that John Wheeler later put into a sentence: matter tells spacetime how to curve, and spacetime tells matter how to move.[2]

G_μν = (8πG / c⁴) T_μν(1)

The left side is curvature, a statement about the shape of spacetime at a point. The right side is the density of matter and energy at that point, and the constant between them, Newton’s G divided by the fourth power of the speed of light, is so small that it takes a planet to bend space by a measurable amount. The Earth curves spacetime enough to make a clock at sea level lose about a microsecond a fortnight relative to one in orbit, which is why the clocks in GPS satellites are built to run slow by exactly that much before launch.[3]

The tests are the strongest in science. The theory accounted, without adjustment, for the 43 arcseconds per century by which Mercury’s orbit drifts beyond what Newton allowed, a discrepancy known since 1859. It predicted the bending of starlight by the Sun that Eddington’s expedition measured during the eclipse of May 1919, which made Einstein famous.[4] It predicted that two neutron stars orbiting each other would lose energy to gravitational waves and spiral inward, and the binary pulsar found by Hulse and Taylor in 1974 has been doing so at the predicted rate, to a fifth of a per cent, for fifty years.[5] On 14 September 2015 the two LIGO detectors recorded the waves themselves, from two black holes of about thirty solar masses each that had merged 1.3 billion years earlier, converting three solar masses of matter into ripples in the geometry in a fraction of a second; the waveform matched the one computed from equation (1) in every detail.[6] In 2019 the Event Horizon Telescope published a picture of the shadow of the black hole at the centre of the galaxy M87, and in 2022 of the one at the centre of our own, and the shadows were the size the theory said.[7]

Three features of this rulebook matter for what follows. It is smooth: spacetime is a continuum, and there is no smallest distance. It is deterministic: given the geometry and the matter now, the equations fix them forever. And it is background-free: there is no stage on which events happen, because the stage is one of the actors. That last feature is the deepest and the one that causes the most trouble later.

The rulebook also carries its own confession. In 1965 Roger Penrose proved that once matter has collapsed past a certain point, the equations force the formation of a singularity: a place where curvature becomes infinite, and the geometry, and therefore the theory, ceases to exist.[8] Every black hole contains one. Run the expansion of the universe backwards and there is one at the start. Penrose got the Nobel prize for that theorem in 2020, and what he had proved was that general relativity predicts, from its own equations, the circumstances of its own breakdown. A theory that does that is telling you it is an approximation to something else.

The second rulebook

Amplitudes that add

The second rulebook was not the work of one person and did not come from one idea. It came from a decade of failure to explain the light that atoms emit, and it was finished in a rush between Heisenberg’s paper of 1925 and Dirac’s of 1928.[9] Its content can be put in three sentences. The state of a system is not a list of where things are and how fast they move, but a list of amplitudes, complex numbers, one for each way the system could be. To find how the state changes, you add the amplitudes for every route from the start to the finish, and routes can cancel each other. To find what you will see, you square the amplitude, and that is a probability, and it is the only thing the theory will tell you.

iℏ ∂ψ/∂t = Hψ(2)

Schrödinger’s equation, (2), is the rule for how amplitudes change in time. Two things about it are worth noticing now. The time in it is the ordinary time of Newton, a parameter that ticks the same everywhere and is not itself part of the system. And the equation is linear: if two states are each allowed, then any sum of them is allowed too, which is what superposition means, and which is the source of everything strange about the theory, from interference to entanglement to the cat.[10]

The precision here is if anything greater than for gravity. The theory’s extension to fields, quantum electrodynamics, predicts the strength of the electron’s magnetism, a number close to 2 called the g-factor. The measured value, from a single electron held in a trap at Harvard for months, is 2.002 319 304 360 71 with an uncertainty in the last two digits, and the theoretical value, from summing amplitudes for some twelve thousand ways the electron can interact with its own field, agrees to about a part in a trillion.[11] The same machinery, applied to the three non-gravitational forces, is the Standard Model, which has predicted every particle found at an accelerator since 1970, the last being the Higgs boson in 2012, and has been contradicted by none.

The three features to hold against the first rulebook are the mirror images of its three. This rulebook is grainy: energy comes in quanta, angular momentum in units of ℏ, and the very act of looking closely at a small region costs energy. It is probabilistic: the rules fix the amplitudes exactly and the outcomes only statistically, and no one has found a way to remove the second part without breaking the first. And it is background-dependent: every version of it, up to and including the Standard Model, is a theory of things happening on a fixed stage of space and time that the theory does not describe and cannot alter.

Its confession is quieter than Penrose’s theorem but as real. The theory has two rules for how a state changes: equation (2), which is smooth, deterministic and reversible, and the rule for what happens when a measurement is made, which is sudden, random and irreversible. It does not say what a measurement is or when the second rule applies. A century of argument has produced several ways of living with that and no agreement, and the one thing most physicists would accept is that a theory containing two contradictory rules for the same process is not the final form of anything.[12]

The seam

Four places where the rulebooks contradict each other

It is tempting to say the problem is that gravity is weak and quantum effects are small, so their overlap is out of reach and the incompatibility is a technicality. It is not a technicality. There are at least four distinct places where putting the two rulebooks together yields nonsense, and they are of different kinds.

The first is the stage. Quantum theory needs a background: a fixed spacetime on which to define the amplitudes, and above all a time in which to evolve them. General relativity says there is no such thing; the geometry is dynamical, and time is one of the things that gets bent. The most direct attempt to write a quantum equation for the geometry itself, the Wheeler–DeWitt equation of 1967, has no time variable in it at all: the state of the universe, in that formulation, does not evolve, and where the ticking of clocks comes from is a problem that has a name, the problem of time, and no agreed solution.[13]

The second is arithmetic. In a quantum field theory, the strength of a force is a dimensionless number, and the theory is usable when that number is small enough that adding up amplitudes route by route converges. For electromagnetism the number is about 1/137 and changes slowly with energy; for the strong force it is about 1/10 at the energies of a collider. Gravity’s coupling has a dimension, because G is not a pure number, and the dimensionless version is the energy of the process squared over the Planck energy squared. Figure 2 plots it. At the energy of a proton’s mass it is 6 × 10⁻³⁹, which is why gravity is negligible in every particle experiment; at the Planck energy it is 1, and beyond that the sum over routes not only fails to converge but requires an infinite number of new, unmeasurable constants to make sense at all. The technical name is non-renormalisability. It was proved at one loop for gravity with matter by ’t Hooft and Veltman in 1974 and at two loops for pure gravity by Goroff and Sagnotti in 1986, and it means that the method which gives the electron’s g-factor to twelve digits gives, for gravity, nothing at all.[14]

Figure 2. The dimensionless strength of three forces against the energy of the process, from the electron’s mass to beyond the Planck energy. Electromagnetism (teal) and the strong force (black) are nearly flat, near 1/100 and 1/10; one-loop running is shown. Gravity (magenta) is (E/E_P)²: 10⁻³⁰ at the LHC’s collision energy and 1 at the Planck energy, where the method that gives the electron’s g-factor to twelve digits gives nothing.

This needs one qualification, because it is often overstated. Below the Planck energy, the sum does converge if you treat gravity as an effective theory and ignore what happens above the cut-off, and John Donoghue showed in 1994 that you can compute the quantum correction to Newton’s law this way: the potential between two masses acquires a term of order the Planck length squared over the distance squared, which at a millimetre is a correction in the sixtieth decimal place.[15] So there is a working quantum theory of gravity at low energies, and it agrees with everything. What there is not is a theory at the corner, which is exactly where the questions live.

The third is superposition. A mass can be in two places at once; the Standard Model does it with electrons routinely, and matter-wave experiments have done it with molecules of two thousand atoms.[16] What is the gravitational field of a mass in two places? If the field is classical, as in the first rulebook, it must have one shape, and the natural guess is the average, a field sourced by half the mass in each place. Page and Geilker tested that guess in 1981 with a Cavendish balance and a lead mass whose position was decided by a quantum measurement, and the field followed the mass, not the average.[17] The experiment is not decisive, because the measurement had already happened, but it points at the structural problem: if spacetime is classical it cannot be in superposition, and if matter is quantum then whatever it sources must be too, and there is no consistent way to couple a superposed source to an unsuperposed field.

The fourth is the one that turned the subject from a technicality into a paradox. In 1974 Stephen Hawking applied quantum field theory to the region just outside a black hole’s horizon and found that the hole radiates, with a temperature that goes inversely as its mass.[18]

T = ℏc³ / (8πGMk_B)     S = k_B c³ A / (4Gℏ)(3)

For a black hole of the Sun’s mass the temperature is sixty billionths of a kelvin, far colder than the microwave background, so it absorbs more than it emits and grows. But a hole loses mass as it radiates, and a lighter hole is hotter, so any hole left alone in an empty universe eventually shrinks faster and faster and disappears in a flash. Figure 3 gives the numbers. A solar-mass hole would take 10⁶⁷ years. A hole of about 10¹¹ kilograms, if any had been made in the early universe, would be finishing now.

Figure 3. Hawking temperature against black-hole mass, which is a straight line on these axes because T goes as 1/M. The teal line is the cosmic microwave background at 2.7 K. A hole heavier than about 4.5 × 10²² kg, six tenths of the Moon’s mass, is colder than its surroundings and grows; a lighter one shrinks. A hole of 1.7 × 10¹¹ kg evaporates in the present age of the universe; a solar-mass hole, at 6 × 10⁻⁸ K, would take 2 × 10⁶⁷ years. The line ends at the Planck mass, where the calculation stops meaning anything.

The paradox is this. Hawking’s radiation is thermal, which means it carries no information about what fell in. If a hole made from an encyclopaedia and a hole made from an equal mass of sand radiate identically and then vanish, the information distinguishing them has left the universe. Quantum mechanics forbids that: equation (2) is reversible, and a reversible rule cannot turn two different states into one. So either Hawking’s calculation, which uses both rulebooks in the only region where they can both be trusted, is wrong in some way nobody has found; or the second rulebook is wrong about reversibility, which Hawking argued for a decade and later conceded against; or the information comes out in the radiation after all, encoded in correlations that a thermal spectrum does not show, which would mean the space around a black hole is stranger than the first rulebook says.[19] Every attempt at quantum gravity since has had to say which of these it believes.

A last point about scale, because it is usually stated backwards. The Planck length is tiny. The Planck mass is not: it is 22 micrograms, the mass of a grain of pollen or a flea’s egg. What makes the corner unreachable is not that the mass is small but that you would need to put it inside its own Planck length, and the reason that is impossible was seen by Matvei Bronstein in Leningrad in 1936, two years before he was shot: to measure a gravitational field in a region that small you need a probe of such energy that it makes a black hole of the region and hides the measurement.[20] The corner is not merely hard to reach. Both rulebooks agree that it is fenced.

The clue

Entropy that goes with area

Hawking’s result came with a second formula, the right-hand half of (3), and it is the one thing in the subject that almost everyone agrees is a real clue. A black hole has an entropy, and the entropy is proportional not to its volume but to the area of its horizon: one unit for every four Planck areas. Jacob Bekenstein had guessed this in 1972 on thermodynamic grounds; Hawking’s temperature fixed the constant.[21]

Why this is strange takes a sentence. In every other system physics knows, the amount of information a region can hold grows with its volume, because you can fill the volume with more stuff. But information has to be carried by something with energy, and gravity caps the energy a region can hold: pack in more than a certain amount and the region collapses into a black hole of its own size. Now suppose some arrangement of matter in a region held more entropy than that black hole. Add a little more matter, it collapses, and what remains is a black hole whose entropy is, by assumption, lower than what you started with. Entropy would have fallen, which the second law forbids. So nothing in a region can hold more information than the black hole that just fills it, and the black hole’s information goes with its surface. A room can hold no more information than could be written on its walls at one bit per four Planck areas. Gerard ’t Hooft in 1993 and Leonard Susskind in 1995 took the point literally and called it the holographic principle: a theory of gravity in some region is somehow equivalent to a theory without gravity on that region’s boundary, in one fewer dimension.[22]

That was a slogan until 1997, when Juan Maldacena found a case where it was an equation. For a particular spacetime, anti-de Sitter space, which curves the opposite way to ours and has a boundary at infinity, the full quantum theory of gravity inside is exactly equivalent to a well-understood quantum field theory on the boundary with no gravity in it.[23] The correspondence has been checked in thousands of calculations and never found wrong. In that world the black-hole paradox is settled by construction, because the boundary theory is reversible and so, whatever happens inside, the information must come out. The year before, Strominger and Vafa had counted the states of a particular black hole in string theory one by one and got Hawking’s area formula, the first time the entropy had been derived from anything rather than inferred.[24]

The clue has since sharpened into something close to a claim about what space is. In 2006 Ryu and Takayanagi found that the entanglement between two halves of the boundary theory equals the area of the surface in the interior that separates them, which is Hawking’s formula again but now for entanglement rather than black holes.[25] Mark Van Raamsdonk showed in 2010 that if you reduce the entanglement between the halves, the interior space between them stretches and then tears: less entanglement, less space.[26] And in 2019 two groups computed the entropy of Hawking radiation in a controlled model and found it rises and then falls, as it must if information is conserved, with the turnover produced by a term, an “island”, that the first rulebook’s geometry did not suggest and that emerged only from taking the quantum rulebook seriously in a curved space.[27] That is the nearest thing the field has to a consensus result: in the cases that can be computed, information comes out, and the geometry near a black hole is doing something no one had drawn.

In every other system physics knows, the information a region can hold grows with its volume. A black hole says the true limit is set by the walls.the one clue everyone accepts

The honest qualification is that anti-de Sitter space is not our universe. Ours has a positive cosmological constant and expands; theirs has a negative one and would collapse. Whether the correspondence, and the results derived in it, carry over is not known, and the leading attempts to say what holography means in an expanding universe are a decade old and unfinished. The clue is real. Where it points is not yet a place.

The attempts

Five roads and what each costs

What follows is a scorecard, not a history, and it is deliberately unsentimental. Each programme has a founding idea, a period in which it seemed to be winning, and a bill that has not been paid. None has made a prediction that has been tested at the corner, because nothing has been tested at the corner. The measure of them, for now, is internal: what do they explain that was unexplained, and what do they ask you to believe.

String theory · the largest programme, and the one with a working example

Began as a theory of the strong force in 1968, failed at that, and was found in 1974 to contain, unbidden, a massless particle with exactly the properties of the graviton: replace point particles with vibrating strings and gravity is not added but forced.[28] The amplitudes are finite where gravity’s diverge, because the string’s length smears the corner. It counted black-hole entropy; it produced Maldacena’s correspondence, which is the only complete quantum theory of gravity anyone possesses, in the wrong universe. The bill: the theory is consistent only in ten dimensions, so six must be curled up too small to see; it needs supersymmetry, a partner particle for every known one, and the LHC has found none up to energies where the simplest versions expected them; and the number of ways to curl up the extra dimensions is estimated at 10⁵⁰⁰, each a different universe with different constants, so that the theory as it stands predicts almost nothing about ours and some of its founders now argue that the constants are an accident of which vacuum we live in.[29]

Loop quantum gravity · take the first rulebook seriously

Started from Abhay Ashtekar’s 1986 rewriting of Einstein’s equations in variables that look like those of the other forces, and from the decision, opposite to string theory’s, to keep background independence at all costs.[30] The result, developed by Rovelli, Smolin and others in the 1990s, is a theory in which space itself is quantised: area and volume come in discrete units of order the Planck scale, and the geometry is a network of loops with nothing between them. It has no extra dimensions and no new particles. In cosmology it replaces the big bang singularity with a bounce. The bill: no one has shown that its grainy geometry becomes Einstein’s smooth one at large scales, which is the minimum a theory of gravity must do; it reproduces black-hole entropy only after tuning a free constant to make it so; and it has almost nothing to say about matter, so it is at best half a theory.

Asymptotic safety · perhaps the arithmetic can be rescued

Weinberg suggested in 1979 that gravity’s coupling might stop growing at high energy and settle at a fixed value, so that the infinite list of constants collapses to a finite one and the ordinary quantum field theory of the metric is complete after all.[31] Martin Reuter found evidence for such a fixed point in 1998 and the computations have grown steadily. Its one striking success: in 2010 Shaposhnikov and Wetterich used the idea to predict the mass of the Higgs boson at about 126 GeV, two years before it was found at 125.[32] The bill: every calculation truncates an infinite set of terms and the answer depends on where you cut, so the fixed point could be an artefact; and whether the resulting theory respects the probability rules of the second rulebook is unresolved.

Discrete spacetimes · sum over shapes

Two programmes assume space is made of pieces and ask what emerges. Causal dynamical triangulations, from Ambjørn, Jurkiewicz and Loll, builds spacetime from four-dimensional simplices glued together in every way consistent with cause preceding effect, and in 2004 found that a large, smooth, four-dimensional universe emerges from the sum, which earlier attempts without the causal rule had failed to do.[33] Causal sets, from Rafael Sorkin and colleagues, keep only the order of events and drop the geometry entirely. That programme made the one genuine prediction in this list: in the early 1990s, from the fluctuations in the number of elements, Sorkin predicted a cosmological constant of about the size that was measured in 1998, when most physicists expected zero.[34] The bill for both: neither has yet produced particles, forces or dynamics beyond the geometry itself.

Emergent gravity · perhaps there is nothing to quantise

Ted Jacobson showed in 1995 that Einstein’s equation (1) follows from the first law of thermodynamics applied to the horizons seen by accelerating observers, together with Bekenstein’s area entropy: if entropy goes with area, spacetime must curve as Einstein said.[35] The moral drawn is that the equation is a relation among averages, like the gas laws, and that quantising it directly is as misguided as quantising the pressure of a gas: the microscopic theory is something else, and space and gravity are what it looks like from far away. The entanglement results in anti-de Sitter space are this idea with a worked example. The bill: nobody knows what the microscopic something is, and a claim that gravity is emergent is a promissory note until someone says emergent from what.

Two newer lines deserve a paragraph each, because they come at the problem sideways. The first is the discovery, from about 2008, that the amplitudes for gravitons can be obtained by squaring the amplitudes for gluons, the carriers of the strong force: term by term, gravity is the strong force multiplied by itself.[36] Nobody knows why, and the relation has no explanation in Einstein’s geometry, which is one of the reasons the people who found it suspect that the geometry is not the fundamental description. A reader of the earlier essay on this blog about Feynman’s diagrams will recognise the pattern: a calculational shortcut that turns out to be simpler than the theory it was a shortcut for, and which the theory itself cannot account for.

The second is the contrarian possibility that gravity is not quantum at all. Penrose has argued since the 1990s that the second rulebook’s measurement problem and the first rulebook’s resistance to quantisation are the same problem, and that gravity is what collapses superpositions: a mass in two places bends spacetime in two ways, the two geometries cannot be held in superposition beyond a certain mismatch, and one wins.[37] In 2023 Jonathan Oppenheim published a consistent framework in which spacetime stays classical while matter stays quantum, at the cost of an irreducible randomness in the geometry itself.[38] Both are minority views. Both make predictions that experiments now being built can reach, which is more than can be said for the five above.

The test

A table-top experiment

For most of the century the assumption was that only a collider the size of the galaxy could test any of this. In 2017 two groups, one led by Sougato Bose in London and one by Chiara Marletto and Vlatko Vedral in Oxford, pointed out a way around the corner.[39] You do not need to reach the Planck scale to ask whether gravity is quantum. You need only ask whether gravity can do a thing that no classical field can do, which is to entangle two objects.

The argument is one paragraph long. Take two small masses, put each into a superposition of two positions, and let them sit near each other for a while. Each mass feels the other’s gravity, and the strength depends on which of the four combinations of positions they are in, so each combination acquires a slightly different phase. When the superpositions are recombined, those phase differences show up as correlations between the two masses that can be measured. A theorem from quantum information says that no classical intermediary can create entanglement between two systems: if the two masses end up entangled and the only thing that passed between them was gravity, then gravity has a quantum character. It does not say what the theory of quantum gravity is. It says the first rulebook, taken as fundamental, is false.

The numbers are the reason this is a plan rather than a wish. The phase each pair of branches acquires is Newton’s constant times the mass squared times the time, divided by Planck’s constant times the separation. Figure 4 plots it against mass for the geometry Bose’s group proposed: two diamonds of 10⁻¹⁴ kilograms, each in a superposition of positions a fraction of a millimetre apart, held for two and a half seconds. The phase comes out at about 0.8 radians, which is measurable. The heaviest objects ever put into superposition, molecules of 25 000 daltons in Markus Arndt’s Vienna laboratory in 2019, would give a phase eighteen orders of magnitude too small.[16] The gap is nine orders in mass, from 4 × 10⁻²³ to 10⁻¹⁴ kilograms.

Figure 4. The phase two masses in superposition acquire through each other’s gravity, G m² t / ℏ d, against mass, for a separation of 200 µm held for 2.5 s (solid) and 1 µm (dashed). The heaviest objects put into superposition so far, the 25 000-dalton molecules of 2019, give 10⁻¹⁷ radians; the proposed 10⁻¹⁴ kg diamonds give 0.8. The gap is nine orders of magnitude in mass and eighteen in phase.

Nine orders of magnitude is a great deal, and the obstacles are the ones that always defeat large superpositions: any gas molecule or photon that scatters off the diamond measures its position and kills the superposition, so the experiment needs a vacuum, a temperature and an isolation from vibration beyond anything yet achieved together. But the approach from both sides is real. In 2021 a group in Vienna measured the gravitational pull between two gold spheres of 90 milligrams, the smallest masses whose gravity has been detected, and the record has been falling since.[40] In 2020 a nanoparticle was cooled to its quantum ground state of motion in an optical trap, which is the starting point for putting a solid object into superposition.[41] Several groups now describe the entanglement test as a fifteen-year project rather than a thought experiment. It would be the first experiment in history to bear on the seam directly.

There are other windows, each narrower. If spacetime is grainy at the Planck scale, light of different energies might travel at very slightly different speeds, and the effect would accumulate over cosmological distances; the Fermi satellite’s observation of a gamma-ray burst in 2009 found the highest-energy photon arriving within a second of the lowest after seven billion years, and ruled out the simplest form of graininess up to beyond the Planck energy itself.[42] If the universe’s first moments were a quantum process, they should have left gravitational waves whose imprint on the microwave background would be the first direct evidence that gravity has quanta; the searches have found nothing yet and have cut the allowed signal by a factor of ten in a decade.[43] And since 2016 Jeff Steinhauer has been making analogue black holes in a cloud of ultracold atoms, in which sound plays the role of light, and observing the analogue of Hawking radiation with the predicted thermal spectrum, which tests the calculation rather than the gravity but is the only place Hawking’s formula has been seen to work.[44]

Coda

What the century taught

A hundred years after the second rulebook was written, the position is this. Both theories are correct in their domains to every decimal place anyone has reached. Neither is complete, and each predicts the circumstance in which the other must take over. Every attempt to write the theory underneath has had to give up something that one of them holds sacred: string theory gives up the four dimensions we live in, loop gravity gives up the smooth continuum, emergent gravity gives up gravity as a fundamental thing, the classical-spacetime proposals give up the universality of the quantum. No one knows which sacrifice is the right one, and it is possible that the right one has not been proposed.

What has changed is the character of the clue. In 1975 the problem looked like a problem about a force: how to quantise gravity as the others had been quantised. The results since, the area law, the holographic correspondence, the equation of entanglement with distance, the islands, all point the same way, and it is not at gravity. They point at spacetime: at the possibility that distance, and duration, and the smooth geometry Einstein found, are not things the fundamental theory contains but things it produces, the way a fluid produces pressure, from the entanglement of something that has no position at all. If that is right, then the two rulebooks were never rivals. One was a description of the stuff and the other a description of the stage, and the stage was made of the stuff all along.

That is a conjecture, and this blog has spent some months on the question of when physicists should trust a conjecture because it is beautiful. The answer arrived at was: when it can be checked. The check here is a pair of diamonds in a vacuum chamber, and the people building it think they are a generation away.

On method and tools

This piece was written collaboratively with Claude Fable 5.1 (Anthropic): human specification, editorial direction and critical review; machine synthesis, drafting, computation and figure generation.

The figures are computed, not traced. The script scripts/two_rulebooks.py evaluates the Compton wavelength and Schwarzschild radius across a hundred decades of mass, the one-loop running of the electromagnetic and strong couplings against the gravitational coupling (E/E_P)², the Hawking temperature and evaporation time as functions of mass, and the gravitationally induced phase G m² t / ℏ d for the Bose et al. geometry, from CODATA 2018 constants; its numerical output is in docs/two-rulebooks-results.json. Historical claims and experimental results are sourced below; the assessment of the research programmes is the author’s reading of the literature to mid 2026 and should be weighed as such.

Authored by: Luis Matos Ferreira — Physicist, Developer, Writer

Related essays on this blog

1. The Happiest Thought — how the first rulebook was made: one person, eight years, an eclipse, and forty years of neglect.
2. An Act of Desperation — how the second rulebook was made: twenty people, twenty-seven years, and an argument that became an experiment.
3. The Interference Machine — what amplitudes that add can do, and how a quantum computer uses them.
4. The Diagram That Did the Sum — Feynman’s diagrams, and the discovery that gravity’s amplitudes are the strong force’s squared.
5. Invented, Then Unavoidable — why physicists trust beauty, and when they should not.

Sources

1. Einstein, “Über das Relativitätsprinzip und die aus demselben gezogenen Folgerungen”, Jahrbuch der Radioaktivität und Elektronik, 1907; the “happiest thought” recollection is from his 1920 manuscript for Nature, unpublished, Einstein Archives.
2. Einstein, “Die Feldgleichungen der Gravitation”, Sitzungsberichte der Preussischen Akademie der Wissenschaften, 25 November 1915; “Die Grundlage der allgemeinen Relativitätstheorie”, Annalen der Physik 49, 769 (1916). Wheeler’s sentence is in Misner, Thorne & Wheeler, Gravitation, 1973, and in his Geons, Black Holes, and Quantum Foam, 1998.
3. Ashby, “Relativity in the Global Positioning System”, Living Reviews in Relativity 6, 1 (2003): a net 38 microseconds a day, 45 from the gravitational potential and −7 from orbital speed.
4. Le Verrier, Comptes rendus 49, 379 (1859), on the anomalous perihelion advance; Dyson, Eddington & Davidson, “A Determination of the Deflection of Light by the Sun’s Gravitational Field”, Philosophical Transactions A 220, 291 (1920).
5. Hulse & Taylor, Astrophysical Journal 195, L51 (1975); Weisberg & Huang, Astrophysical Journal 829, 55 (2016), ratio of observed to predicted orbital decay 0.9983 ± 0.0016.
6. Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration), “Observation of Gravitational Waves from a Binary Black Hole Merger”, Physical Review Letters 116, 061102 (2016).
7. Event Horizon Telescope Collaboration, Astrophysical Journal Letters 875, L1 (2019), M87*; 930, L12 (2022), Sagittarius A*.
8. Penrose, “Gravitational Collapse and Space-Time Singularities”, Physical Review Letters 14, 57 (1965); Nobel Prize in Physics 2020.
9. Heisenberg, Zeitschrift für Physik 33, 879 (1925); Schrödinger, Annalen der Physik 79, 361 (1926); Born, Zeitschrift für Physik 37, 863 (1926); Dirac, Proceedings of the Royal Society A 117, 610 (1928).
10. Schrödinger, “Die gegenwärtige Situation in der Quantenmechanik”, Naturwissenschaften 23, 807 (1935), the cat.
11. Fan, Myers, Sukumar & Gabrielse, “Measurement of the Electron Magnetic Moment”, Physical Review Letters 130, 071801 (2023), 0.13 parts per trillion; Aoyama, Kinoshita & Nio, Atoms 7, 28 (2019), the tenth-order calculation. The comparison is limited by independent measurements of the fine-structure constant, which disagree with each other at about a part in 10¹⁰.
12. For the state of the argument: Bell, Speakable and Unspeakable in Quantum Mechanics, 1987; Schlosshauer, Kofler & Zeilinger, “A snapshot of foundational attitudes toward quantum mechanics”, Studies in History and Philosophy of Modern Physics 44, 222 (2013).
13. DeWitt, “Quantum Theory of Gravity. I. The Canonical Theory”, Physical Review 160, 1113 (1967); Isham, “Canonical quantum gravity and the problem of time”, 1992, arXiv:gr-qc/9210011.
14. ’t Hooft & Veltman, “One-loop divergencies in the theory of gravitation”, Annales de l’Institut Henri Poincaré A 20, 69 (1974); Goroff & Sagnotti, “The ultraviolet behavior of Einstein gravity”, Nuclear Physics B 266, 709 (1986).
15. Donoghue, “General relativity as an effective field theory: The leading quantum corrections”, Physical Review D 50, 3874 (1994); Bjerrum-Bohr, Donoghue & Holstein, Physical Review D 67, 084033 (2003), for the coefficient 41/10π.
16. Arndt et al., “Wave–particle duality of C₆₀ molecules”, Nature 401, 680 (1999); Fein et al., “Quantum superposition of molecules beyond 25 kDa”, Nature Physics 15, 1242 (2019).
17. Page & Geilker, “Indirect Evidence for Quantum Gravity”, Physical Review Letters 47, 979 (1981).
18. Hawking, “Black hole explosions?”, Nature 248, 30 (1974); “Particle creation by black holes”, Communications in Mathematical Physics 43, 199 (1975).
19. Hawking, “Breakdown of predictability in gravitational collapse”, Physical Review D 14, 2460 (1976); Page, “Information in black hole radiation”, Physical Review Letters 71, 3743 (1993); Hawking’s concession at GR17, Dublin, July 2004, and Physical Review D 72, 084013 (2005).
20. Bronstein, “Quantentheorie schwacher Gravitationsfelder”, Physikalische Zeitschrift der Sowjetunion 9, 140 (1936); Gorelik, “Matvei Bronstein and quantum gravity”, Physics-Uspekhi 48, 1039 (2005).
21. Bekenstein, “Black Holes and Entropy”, Physical Review D 7, 2333 (1973), from his 1972 Princeton thesis.
22. ’t Hooft, “Dimensional Reduction in Quantum Gravity”, 1993, arXiv:gr-qc/9310026; Susskind, “The World as a Hologram”, Journal of Mathematical Physics 36, 6377 (1995).
23. Maldacena, “The Large N Limit of Superconformal Field Theories and Supergravity”, Advances in Theoretical and Mathematical Physics 2, 231 (1998), arXiv November 1997.
24. Strominger & Vafa, “Microscopic Origin of the Bekenstein-Hawking Entropy”, Physics Letters B 379, 99 (1996).
25. Ryu & Takayanagi, “Holographic Derivation of Entanglement Entropy from AdS/CFT”, Physical Review Letters 96, 181602 (2006).
26. Van Raamsdonk, “Building up spacetime with quantum entanglement”, General Relativity and Gravitation 42, 2323 (2010); Maldacena & Susskind, “Cool horizons for entangled black holes”, Fortschritte der Physik 61, 781 (2013).
27. Penington, “Entanglement wedge reconstruction and the information paradox”, Journal of High Energy Physics 2020, 2; Almheiri, Engelhardt, Marolf & Maxfield, “The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole”, Journal of High Energy Physics 2019, 63; review in Almheiri et al., Reviews of Modern Physics 93, 035002 (2021).
28. Veneziano, Nuovo Cimento A 57, 190 (1968); Scherk & Schwarz, “Dual models for non-hadrons”, Nuclear Physics B 81, 118 (1974); Yoneya, Progress of Theoretical Physics 51, 1907 (1974); Green & Schwarz, Physics Letters B 149, 117 (1984); Witten, “String theory dynamics in various dimensions”, Nuclear Physics B 443, 85 (1995).
29. Bousso & Polchinski, Journal of High Energy Physics 2000, 006; Kachru, Kallosh, Linde & Trivedi, Physical Review D 68, 046005 (2003); Douglas, “The statistics of string/M theory vacua”, Journal of High Energy Physics 2003, 046, the 10⁵⁰⁰ estimate; Susskind, The Cosmic Landscape, 2005. On supersymmetry at the LHC: ATLAS and CMS summary plots, 2024.
30. Ashtekar, “New Variables for Classical and Quantum Gravity”, Physical Review Letters 57, 2244 (1986); Rovelli & Smolin, “Discreteness of area and volume in quantum gravity”, Nuclear Physics B 442, 593 (1995); Ashtekar, Pawlowski & Singh, Physical Review Letters 96, 141301 (2006), the bounce; Rovelli, Quantum Gravity, Cambridge, 2004.
31. Weinberg, “Ultraviolet divergences in quantum theories of gravitation”, in Hawking & Israel (eds), General Relativity: An Einstein Centenary Survey, Cambridge, 1979; Reuter, Physical Review D 57, 971 (1998).
32. Shaposhnikov & Wetterich, “Asymptotic safety of gravity and the Higgs boson mass”, Physics Letters B 683, 196 (2010).
33. Ambjørn, Jurkiewicz & Loll, “Emergence of a 4D World from Causal Quantum Gravity”, Physical Review Letters 93, 131301 (2004); “Spectral dimension of the universe”, Physical Review Letters 95, 171301 (2005).
34. Bombelli, Lee, Meyer & Sorkin, “Space-time as a causal set”, Physical Review Letters 59, 521 (1987); Sorkin, “Forks in the road, on the way to quantum gravity”, International Journal of Theoretical Physics 36, 2759 (1997), recording the prediction made in 1990–91; Riess et al. 1998 and Perlmutter et al. 1999 for the measurement.
35. Jacobson, “Thermodynamics of Spacetime: The Einstein Equation of State”, Physical Review Letters 75, 1260 (1995); Verlinde, “On the origin of gravity and the laws of Newton”, Journal of High Energy Physics 2011, 29.
36. Bern, Carrasco & Johansson, “New relations for gauge-theory amplitudes”, Physical Review D 78, 085011 (2008); “Perturbative Quantum Gravity as a Double Copy of Gauge Theory”, Physical Review Letters 105, 061602 (2010); the earlier tree-level relations are Kawai, Lewellen & Tye, Nuclear Physics B 269, 1 (1986).
37. Diósi, Physical Review A 40, 1165 (1989); Penrose, “On Gravity’s role in Quantum State Reduction”, General Relativity and Gravitation 28, 581 (1996).
38. Oppenheim, “A Postquantum Theory of Classical Gravity?”, Physical Review X 13, 041040 (2023); Oppenheim, Sparaciari, Šoda & Weller-Davies, Nature Communications 14, 7910 (2023).
39. Bose et al., “Spin Entanglement Witness for Quantum Gravity”, Physical Review Letters 119, 240401 (2017); Marletto & Vedral, “Gravitationally Induced Entanglement between Two Massive Particles is Sufficient Evidence of Quantum Effects in Gravity”, Physical Review Letters 119, 240402 (2017).
40. Westphal, Hepach, Pfaff & Aspelmeyer, “Measurement of gravitational coupling between millimetre-sized masses”, Nature 591, 225 (2021).
41. Delić et al., “Cooling of a levitated nanoparticle to the motional quantum ground state”, Science 367, 892 (2020).
42. Abdo et al. (Fermi LAT and GBM Collaborations), “A limit on the variation of the speed of light arising from quantum gravity effects”, Nature 462, 331 (2009), GRB 090510.
43. BICEP/Keck Collaboration, “Improved Constraints on Primordial Gravitational Waves using Planck, WMAP, and BICEP/Keck Observations through the 2018 Observing Season”, Physical Review Letters 127, 151301 (2021), r < 0.036.
44. Steinhauer, “Observation of quantum Hawking radiation and its entanglement in an analogue black hole”, Nature Physics 12, 959 (2016); Muñoz de Nova et al., “Observation of thermal Hawking radiation and its temperature in an analogue black hole”, Nature 569, 688 (2019).