16 micrograms: the heaviest Schrödinger's cat yet is a sliver of sapphire

Part IA cat made of sound

Chapter 1Sixteen micrograms

On 20 April 2023 a team at ETH Zurich (Marius Bild, Matteo Fadel, Yiwen Chu and colleagues) reported in Science that they had put a vibration of a sapphire crystal into a Schrödinger cat state.¹ The vibration is sound: a standing wave near 6 GHz, trapped in a sliver of crystal about as wide as a hair. For about ten microseconds it rang two opposite ways at once. The paper's title calls the system "a 16-microgram mechanical oscillator". More precisely, the vibration has an effective mass of sixteen micrograms (16.2 µg), and about 10¹⁷ atoms take part in it, in the authors' estimate.

Three more numbers set the scene. The two states the crystal held at once differed by 2.1 × 10⁻¹⁸ m, about one eight-hundredth of a proton's diameter (this page's arithmetic, with the CODATA 2022 proton radius).² The quantum fingerprint of the superposition lasted about 10 µs. And 16.2 µg is 0.74 of the Planck mass, the unit of mass built from ħ, c and G (this page's arithmetic). As of 24 October 2026 we found no heavier cat state of motion reported anywhere.

The page follows three twists. First, "sixteen micrograms" is a choice of ruler: the same state can honestly be given a different mass, and only one combination of mass and distance is fixed (Chapter 5). Second, the distance, not the mass, is the hard part, and the reason is the same combination (Chapters 6 to 8). Third, Roger Penrose proposed that gravity itself ends superpositions, and his proposal counts that combination too; for this cat his clock reads millions of years (Chapter 10). The two frontiers, quantum objects getting heavier and sources of gravity getting lighter, meet near the Planck mass (Chapter 12).

Chapter 2A quite ridiculous case

In late 1935 Erwin Schrödinger published a long essay in three parts, "Die gegenwärtige Situation in der Quantenmechanik" ("The present situation in quantum mechanics").³ In its fifth section he introduced a cat. In John Trimmer's 1980 translation the passage opens: "One can even set up quite ridiculous cases."⁴ A cat is shut in a steel chamber with a Geiger counter and a tiny bit of radioactive substance, so little that in the course of an hour perhaps one atom decays, and with equal probability perhaps none. A decay sets off a hammer that shatters a flask of hydrocyanic acid. After an hour, the wavefunction of the whole system would contain the living and the dead cat "mixed or smeared out in equal parts".

Schrödinger meant this as an absurdity. His point was that an indefiniteness that seems harmless while it is confined to an atom can be passed, by an ordinary chain of cause and effect, to something as large as a cat, where it plainly makes no sense. He was not claiming that cats are in superpositions; he was saying that the theory's description could not simply be read as a picture of reality.

A superposition is not "secretly one or the other, we just don't know which". It is a state that contains both possibilities together with a definite relation between them, a phase, and that relation has consequences: it makes the two possibilities interfere, like two overlapping sets of waves. Interference is what tells a superposition apart from a mere coin toss, which is why every superposition experiment on this page is an interference experiment of one kind or another.

Two landmark laboratory "cats" came in 1996. At NIST, Christopher Monroe, David Wineland and colleagues put a single trapped atom into a superposition of two separated positions.⁵ In Paris, Serge Haroche's group made a superposition of two phases of a weak microwave field in a cavity and watched it progressively lose its quantum character as it leaked information to its surroundings.⁶ Since then, "cat state" has become a working term: a superposition of two states that are clearly distinguishable. For a vibrating object, the natural choice is a superposition of two coherent states:

|cat⟩ ∝ |α⟩ ± |−α⟩|α⟩ is a coherent state: the quantum version of a definite oscillation with complex amplitude α, blurred only by the zero-point motion that even the ground state has. |α|² is its mean number of quanta. |−α⟩ is the same oscillation in the opposite phase. The + sign gives an "even" cat, the − sign an "odd" one.

The ETH cat is exactly this: one vibration of the crystal, in two opposite phases at once. "Clearly distinguishable" has a precise meaning here. The two oscillations must differ by more than their own quantum blur, so that a single measurement could, in principle, tell them apart.¹

Chapter 3A portrait of two states at once

To see a cat state you need a map with two directions: where the vibrating thing is (position, horizontally) and how fast it is moving (momentum, vertically). Physicists call it phase space. Nº 2 pictured a state as a single dot in an imaginary map with one axis per quantity. For a classical oscillator the dot circles the origin once per vibration. In quantum mechanics the uncertainty principle forbids a dot: the calmest possible state, the ground state, is a round smudge as wide as the zero-point motion (squeezing can narrow it one way only by widening it the other), and a cat is two smudges with stripes between them.

The map is the Wigner function W, introduced by Eugene Wigner in 1932.⁷ It behaves almost like a probability distribution over phase space: adding it up along the momentum direction gives the probability of each position, and adding it up along the position direction gives the probability of each momentum. A coherent state is a single round hill. A cat state of the kind ETH made has the form

W(β) = [e^{−2|β−α|²} + e^{−2|β+α|²} ± 2e^−2|β|²cos(4α Im β)] / [π(1 ± e^−2α²)]For real α. β is a point of phase space: Re β measures position and Im β momentum, in the oscillator's natural units; the ground state is a round hill of height 2/π. Bild et al. 2023, supplement, eq. S33, at the moment the cat is made.

The first two terms are two hills, at +α and −α: the two oscillations. The third term is the interference between them, a set of stripes across the middle of the map. Its cosine swings below zero. A probability can never be negative, so no mixture of ordinary oscillations, no classical uncertainty about which way the crystal is ringing, can produce those negative stripes. They are the fingerprint of a genuine superposition, and the quantity ETH measured.^1,8 The stripes have a period of π/(2α) along the momentum direction, so bigger cats have finer stripes.

Figure 1 draws this map for the ETH cat. Grow the cat from nothing to α = 3, switch between the even and odd cat, then press Play: the cat loses energy at the crystal's measured rate. Before you do, guess which fades first, the hills or the stripes.

Figure 1🗺️ Try it

A portrait of two states at once

Grow the cat, then let it fade

How big is the cat?

α, the size of each of the two vibrations; the mean number of phonons is about α².

Time after it was made

Which fades first?

Average phononsQuanta of sound, on average

Stripes left

Deepest dip below zero

Split, in the real crystal

Stripes left, e^{−2α²(1−η²)} Energy left, η²

The Wigner function of an ideal cat state |α⟩ ± |−α⟩ of one vibration mode, losing energy at the measured rate T₁ = 84 µs (Bild et al. 2023): W(β) = [e^{−2|β−ηα|²} + e^{−2|β+ηα|²} ± 2e^−2|β|²e^{−2α²(1−η²)}cos(4ηα Im β)] / [π(1 ± e^−2α²)], η = e^−t/2T₁ (their supplement, eq. S33), normalised so the ground state peaks at 2/π. Horizontal: position (Re β); vertical: momentum (Im β), on equal scales. Brass is positive, violet negative; the strip is the slice along the dashed line. The interference term fades 2α² times faster than the energy; under pure energy loss any negativity is gone once half the energy has leaked out (t = T₁ ln 2 ≈ 58 µs). The split converts α into the crystal's displacement with the paper's rms definition, 2√(2(1 + 2α²)) x_zpf, x_zpf = 2.95 × 10⁻¹⁹ m for the 16.2 µg effective mass at 5.96 GHz (this page's arithmetic). The real states had 66% fidelity to an ideal cat and extra dephasing, so their negativity faded in about 10 µs, a little faster than this ideal model (whose negative volume falls to 1/e in about 14 µs at α = 1.61).A map of the crystal's vibration: left to right is how far the atoms have swung, up and down is how fast they move. Two hills mean two opposite vibrations at once. The violet stripes between them dip below zero, and only a true "both at once" can do that; the strip beside the map is a slice through the middle. Make the cat bigger and watch the stripes get finer; then press play and see how much faster the stripes fade than the hills.

The stripes go first, and fast. While the hills have barely drifted towards the centre, the interference term is gone. In the model, the stripes fade 2α² times faster than the energy leaks away: about five times faster for the biggest ETH cat, and the bigger the cat, the bigger the factor. Chapter 7 explains why. Two other things are worth noticing. At α = 0 the even cat is just the ground state, one hill; the odd cat is a single phonon, a ring whose centre dips below zero, so even one quantum of sound is a state no classical vibration can imitate. And the real states were not ideal: their fidelity to an ideal cat was 66%, with extra loss of phase, so their negativity faded a little faster than in this model.¹

Chapter 4A cat made of sound

The device is a sandwich of two sapphire chips. One carries a thin disc of aluminium nitride, a piezoelectric material that turns an oscillating electric field into a mechanical strain and back. It is flip-chip bonded face to face over a second chip that carries a superconducting transmon qubit.^1,9 The qubit's microwave field squeezes the disc, the disc launches sound into the sapphire, and the sound bounces between the chip's two faces as standing waves, a ladder of overtones about 12 MHz apart. The qubit is tuned into resonance with one of them, near 6 GHz.

That one mode is a standing wave about 500 half-wavelengths long across the 435 µm thickness of the chip, and confined sideways to a Gaussian beam with a waist of 27 µm. It fills a sliver about 54 µm wide, roughly the width of a hair, with a volume of about 0.001 mm³ (this page's arithmetic for the width and volume). One quantum of sound in it, one phonon, carries hf ≈ 25 µeV, about 0.29 K in temperature units (this page's arithmetic). The experiment runs at a small fraction of that, far colder than the 2.7 K of deep space, so the mode starts in its quantum ground state.

The recipe has three steps.¹ First, a microwave pulse displaces the mode into a coherent state with α = 1.75. Second, the qubit is put into a superposition of its two states. Third, qubit and sound are left to exchange energy resonantly. Because the exchange runs at a different rate for each phonon number, the qubit's oscillation washes out after about 0.9 µs and comes back at about 6.7 µs. In between, at about 2.9 µs, the qubit almost disentangles from the sound and leaves the mode in a superposition of two coherent states turning in opposite directions. That is the cat.

Reading it out uses the same qubit. In this device the qubit's frequency depends on the number of phonons, so a short sequence of qubit pulses can ask a single question: is the number of phonons even or odd?¹⁰ The average answer, after the state has been shifted by a chosen amount in phase space, gives the Wigner function at one point. Repeated thousands of times over a grid of shifts, it rebuilds the whole portrait, negative stripes included. The team made cats of three sizes, which the paper labels D = 1.09, 1.43 and 1.61, where D² is the mean number of phonons: 2.6 for the largest. The measured states matched the state expected from the protocol with 76% fidelity, and an ideal two-component cat with 66%.¹

The platform has a short lineage. In 2010 a team at the University of California, Santa Barbara, with Andrew Cleland and John Martinis as senior authors, put a human-made mechanical resonator into its quantum ground state and controlled it one phonon at a time.¹¹ In 2017 Chu and colleagues coupled a qubit to bulk sound in a crystal, the design ETH uses.⁹ The parity readout followed in 2022,¹⁰ and in 2024 the same ETH group turned a crystal vibration into a qubit of its own.¹² The deeper ancestry is the superconducting circuit itself. The 2025 Nobel Prize in Physics went to John Clarke, Michel Devoret and Martinis for experiments in 1984 and 1985 showing that an electrical circuit built from superconductors, far larger than any atom, could tunnel through a barrier and absorb energy only in discrete amounts, as a single quantum object would.¹³ The ETH cat is made and read with a descendant of that circuit.

Chapter 5Which sixteen micrograms?

What, exactly, has a mass of sixteen micrograms? Not the chip, which is far heavier. Not a piece of crystal moving as one body either. In a standing wave, neighbouring half-wavelength slabs of crystal move in opposite directions; the amplitude is largest on the axis of the beam and falls off sideways like a Gaussian; and the centre of mass of the crystal hardly moves at all. Every atom in the sliver moves a different amount.

To compare such a mode with the textbook picture of a mass on a spring, you have to choose a reference displacement x_eff, then define the effective mass M_eff so that the energy comes out right:

E = ½ M_eff ω² x_eff² ⇒ M_eff x_eff² = 2E/ω²The energy E and the angular frequency ω are fixed by the physics. How the product is split between a mass and a displacement is a convention.

The paper's supplement gives two choices.¹ Take x_eff as the root-mean-square displacement of the atoms in the mode and the effective mass is 16.2 µg; the two states of the largest cat then differ by 2.1 × 10⁻¹⁸ m. Take x_eff as the maximum displacement, on the beam axis, and the effective mass is 1.0 µg, with the two states 8.4 × 10⁻¹⁸ m apart. The naive mass of the mode's cylinder, density × πw₀² × length, is 4.0 µg, in between. Both definitions are honest; the analysis of the same platform by Schrinski and colleagues used the 1.0 µg one.¹⁴ What they agree on is the product: 16.2 µg × (2.1 × 10⁻¹⁸ m)² = 1.0 µg × (8.4 × 10⁻¹⁸ m)² = 7.1 × 10⁻⁴⁴ kg m² (this page's arithmetic).

Figure 2 draws a few of the sliver's half-waves frozen at full swing, every dot (a parcel of atoms) drawn twice, once for each branch of the cat. Pick a ruler, or drag the handle along the line, and watch the mass and the split trade places.

Figure 2⚖️ Try it

Which sixteen micrograms?

Pick a ruler

Effective mass

Split between the two statesDistance between the two states

As a slice of a proton

Mass × split²Mass × distance²

A standing longitudinal wave in the sapphire, u ∝ cos(mπz/L) e^{−r²/w₀²}, with waist w₀ = 27 µm through the L = 435 µm chip (Bild et al. 2023, supplement). Only a few of the roughly 500 half-wavelengths are drawn; each dot stands for a parcel of atoms and is drawn in both branches of the cat; the displacement is exaggerated about ten billion times relative to the drawing's scale along the beam, and the beam is drawn far narrower than it is. Because the mode is not a centre-of-mass motion, its mass is defined only together with a reference amplitude through ½M_effω²x_eff² = E: the rms displacement gives 16.2 µg and a split of 2.1 × 10⁻¹⁸ m, the maximum displacement 1.0 µg and 8.4 × 10⁻¹⁸ m. The chart interpolates between them on logarithmic axes; M_effd² = 7.1 × 10⁻⁴⁴ kg m² either way (this page's arithmetic). The paper estimates that a half-wavelength slab, about 30 ng, approximates a centre-of-mass mode; it gives no split for it. Proton fractions use the CODATA 2022 radius, 0.84075 fm.The sliver of crystal, ringing two opposite ways at once: every dot (a little bunch of atoms) is drawn twice, once for each way. Most of it moves a little and the middle moves most, so its "weight" depends on where you hold the ruler. Pick a way of counting, or drag the dot along the line: the mass and the distance trade places, but mass × distance² never changes.

The "weight" changes sixteen-fold, the split four-fold, and mass × split² not at all. That is more than a curiosity. Anything that depends on the energy of the motion, or on the mass-weighted squared displacement of the atoms, gives the same answer on either ruler: decoherence by most mechanisms (Chapter 7) and Penrose's gravitational collapse for smooth matter (Chapter 10). The physics of this page does not depend on the definition, even though its headline does.

The paper also offers a third, more physical unit. A single half-wavelength slab, the authors write, "approximates a center-of-mass mode", and they estimate its mass at about 30 ng; they call it "by far the most massive object that has been placed into a cat state". That is the authors' claim, and a reasonable one, but it uses a different object from the 16.2 µg of the title. And none of it was seen. The chip is visible to the eye; the mode is a 0.001 mm³ sliver inside it, and the superposition was inferred from thousands of qubit measurements. Headlines that called the cat visible to the naked eye were describing the chip. ETH's own press release compared the 16 micrograms to a fine grain of sand: a comparison of masses, not a picture of what moved.

Part IIHeavy, but barely apart

Chapter 6One eight-hundredth of a proton

How far is 2.1 × 10⁻¹⁸ m? The proton's root-mean-square charge radius is 0.84075 fm (CODATA 2022),² so its diameter is about 1.68 × 10⁻¹⁵ m. The split is about 1/800 of that, and one fifty-millionth of a hydrogen atom (this page's arithmetic). On the 1.0 µg ruler it is 1/200 of a proton. Either way it is far smaller than a proton.

Small is not the same as meaningless. The relevant yardstick is the crystal's own quantum blur, its zero-point motion:

x_zpf = √(ħ / 2M_effω) ≈ 2.95 × 10⁻¹⁹ m
split = 2√(2(1 + 2D²)) x_zpf ≈ 7.0 x_zpf ≈ 2.1 × 10⁻¹⁸ mFor 16.2 µg at 5.96 GHz (the mode frequency stated for this geometry by Schrinski et al. 2023) and D = 1.61; the second line is the paper's measure of the split (supplement, eq. S29). This page's arithmetic.

The two branches are about seven times their own blur apart, so they are distinct in the sense that matters: a measurement of the displacement could, in principle, tell them apart. "Macroscopically distinct" in this field means distinct relative to quantum noise, not visible to the eye.

It also means the crystal never went anywhere. Freeze the motion at full swing and the atoms in the mode sit, in rms terms, about 2 × 10⁻¹⁸ m further "forward" in one branch than in the other; the crystal's centre of mass sits still. What is split is the collective coordinate of the mode, not any single atom: each atom's own zero-point jiggle, from all the crystal's other vibrations, is millions of times larger than the split. "A 16-microgram object in two places at once" is the wrong picture. "A 16-microgram vibration ringing two opposite ways at once" is the right one.

For scale, consider a far heavier object whose motion has been brought near its quantum ground state. In 2021 the LIGO collaboration cooled the differential motion of the four 40 kg mirrors of a gravitational-wave detector, a mode with an effective mass of 10 kg, to an average of 10.8 quanta, at a temperature of 77 nK.¹⁵ The zero-point motion of that mode is about 7.5 × 10⁻²⁰ m, one twenty-two-thousandth of a proton (this page's arithmetic). LIGO's mode was near its ground state, never in a superposition, and it is not a cat. Quiet is achievable for heavy things. Two-at-once is much harder.

Chapter 7Why big cats die young

Why is the split so tiny? Because the world keeps asking which branch the crystal is in. Stray phonons, defects in the crystal, the qubit itself and any radiation that reaches the chip all interact with the vibration. Each interaction that could tell the two branches apart carries away a record of which one, even a record nobody reads, and each record weakens the interference. This is decoherence, an idea of Dieter Zeh's from 1970, developed by Wojciech Zurek in the early 1980s and worked out for scattering by Erich Joos and Zeh in 1985.^8,16,17 For splits small compared with the wavelength of whatever is doing the probing, the rate grows with the split squared: twice the distance, four times faster.

For the crystal, the main culprit is the sound leaking away, with an energy lifetime T₁ ≈ 84 µs. Each phonon that escapes is a small record of which way the crystal was ringing, and the paper's analysis gives

τ_cat ≈ T₁ / (2α²)For large cats (Bild et al. 2023, supplement G). Because the split grows in proportion to α, this is the "split squared" law in another form.

The measured negativity of the D = 1.43 cat faded in about 10 µs; the paper's simulations give 24.7, 12.3 and 10.5 µs for the three sizes, and the bigger cats faded faster, as predicted.¹ The 84 µs is how long the sound lasts, not how long the cat lasts. In Figure 1, press Play and watch it happen: the stripes vanish while the hills, which carry the energy, have hardly moved.

Now try to make the same crystal into a bigger cat. With the same T₁ and the same law, a split of one proton diameter, 1.7 × 10⁻¹⁵ m, needs α ≈ 1,400, and the stripes would last about 2 × 10⁻¹¹ s. A split of one atom's width, 10⁻¹⁰ m, would leave them about 6 × 10⁻²¹ s, from phonon loss alone (this page's arithmetic; illustrative). That is why every superposition record is a trade: an enormous mass at an absurdly small distance, as in the crystal, or a tiny mass far apart for a long time, as in the matter-wave experiments of the next chapter.

Decoherence explains why interference disappears, and why what is left behaves like a classical either-or. It does not say which of the two outcomes you will find, or why you find one at all. That is the measurement problem, and it is open: collapse models (Chapter 9) answer it one way, many-worlds and other interpretations another. One argument about whether empty space can fluctuate into anything at all (Nº 3) turns on the same idea: in the many-worlds picture its authors use, without something that records the difference, a quantum possibility never becomes an event.

Chapter 8Biggest by which ruler?

Is the heaviest cat also the biggest superposition? The main rival is matter-wave interferometry, which sends a beam of molecules or clusters through a series of gratings.¹⁸ An interference pattern appears downstream only if each particle passed through several slits at once, that is, if it was spread out over at least the grating period. The records are dated, and they move:

1999, Vienna: football-shaped C₆₀ molecules, 60 carbon atoms each, through a grating with a 100 nm period.¹⁹
2015, Stanford: rubidium atoms whose wave packets were separated by 54 cm.²⁰ Whether the interference proves a superposition of the two distant packets was disputed in a published comment, and the authors replied that it does.²¹
2019, Vienna: molecules heavier than 25 kDa, with up to about 2,000 atoms, in a 2-metre interferometer with gratings of 266 nm period.²²
21 January 2026, Vienna: sodium clusters of more than 7,000 atoms on average (mean mass 172 kDa, about 8 nm across), flying at about 160 m/s through three gratings of ultraviolet light with a 133 nm period, spaced 0.983 m apart.²³ The authors show that each cluster was delocalised over more than ten times its own diameter. The 133 nm is the grating period, not a measured distance between paths. The clusters spent about 12 ms in the interferometer (this page's arithmetic, 2 × 0.983 m ÷ 160 m/s). The journal title differs from the preprint's, which spoke of "nanoparticle Schrödinger cats".

Set the crystal beside the clusters. Its effective mass is 5.7 × 10¹³ clusters (this page's arithmetic). But the clusters' delocalisation, on the scale of the grating period, is about 6 × 10¹⁰ times larger than the crystal's split, and they kept it about a thousand times longer: 12 ms against 10 µs. Figure 3 places every superposition on one map, mass to the right and split upwards. Tap a point for its story, switch the crystal between its two rulers, turn on the band where Penrose's gravity would act within a second (Chapter 10), then switch to the second view, a single score explained below.

Figure 3🏆 Try it

Biggest by which ruler?

Switch the ruler

Selected

Mass

Split

Score μScore

Superpositions by mass and by the distance between their two branches, logarithmic axes, records as of 24 October 2026. The electron (single electrons building up an interference pattern, Tonomura et al. 1989) has no plotted split and sits on the strip at the bottom. For matter-wave interferometers the split is taken as the grating period (the scale over which each particle was delocalised; for the 2026 clusters the bar runs from ten times their 8 nm diameter to the 133 nm period); far-field set-ups spread further downstream. The crystal cat is drawn with either effective-mass definition (Figure 2). LIGO's 10 kg mode was cooled near its ground state, never put in a superposition; its marker sits at twice its zero-point motion. Hollow rings are not superpositions made in a laboratory: LIGO's cooled mode, proposals and a thought experiment. Shaded band: where a smooth uniform sphere of 3,000 kg/m³ would collapse within one second under the Diósi–Penrose model, between normalisations that differ by 8π (this page's estimate; a crystal mode's integral differs by a factor 3, invisible at this scale). Second view: macroscopicity μ (Nimmrichter and Hornberger 2013; Schrinski et al. 2023 for the crystal mode, a single-phonon state; Fein et al. 2019; Pedalino et al. 2026; the proposals from Nimmrichter and Hornberger 2013).Every solid dot is a real "both at once" experiment: farther right is heavier, higher means the two states were farther apart. Tap a dot for its story. The crystal is by far the heaviest, but its two states barely differ. Switch to the score to see which experiment tests quantum physics hardest: a different winner. Hollow rings are LIGO's quiet mirrors, proposals and Schrödinger's own cat, none of them a superposition made in a lab.

Among real superpositions, the crystal sits alone at the bottom right: by far the heaviest, by far the smallest split; only LIGO's hollow ring, a cooled mode that was never split, lies beyond it. The matter waves sit far up and to the left. Nothing real comes near the corner where Schrödinger's cat would be. Which point is "biggest" depends on how you weigh mass against distance and time.

Stefan Nimmrichter and Klaus Hornberger proposed one way to weigh them in 2013: macroscopicity, μ.²⁴ Imagine the gentlest possible modification of quantum mechanics that would make large objects behave classically, characterised by how long it would let a single electron stay coherent, τ_e. Each experiment that sees interference rules out every modification strong enough to have spoiled it, and μ is the base-10 logarithm of the longest τ_e ruled out, in seconds. For an object smaller than the path separation, it takes a simple form:

μ ≈ log₁₀[ (1/|ln f|) (M/m_e)² (t / 1 s) ]Nimmrichter and Hornberger 2013, eq. 8. M is the mass, t the coherence time, f the fraction of the expected interference visibility that was observed. Valid only when the separation exceeds the model's critical length, tens of nanometres to a micrometre. It reproduces 14.1 for the 2019 molecules and 15.2–15.7 for the 2026 clusters (this page's arithmetic; the published value is 15.5).

So μ rewards mass squared times time, but only when the separation is large enough to count in full. On this ruler the order changes.^{24,25,14,22,23} Two interfering sodium Bose–Einstein condensates (MIT, 1997) score 8.4. Fullerene molecules in 1999 scored 10.6. A bulk-acoustic crystal mode at ETH, the same kind of device but in a single-phonon state with a 1.0 µg effective mass, scores 11.3, "on par with state-of-the-art atom interferometers" in its authors' words. That is not the cat: we found no published μ for the cat state itself. The 2019 molecules score 14.1 and the 2026 clusters 15.5, the record. The crystal's atoms move far less than the critical length, so its mass is not squared in full. Proposals reach 19 to 23. Schrödinger's cat, as Nimmrichter and Hornberger idealise it (4 kg kept coherent across 10 cm for a second), would score about 57: some 41 orders of magnitude beyond the record.

A third family uses electrical circuits rather than moving matter. In 2000, groups at Stony Brook and Delft put superconducting loops into superpositions of currents circulating clockwise and anticlockwise at once,²⁶ and cat states of microwave fields are now engineering components: in 2025 a logical memory was built from five "cat qubits".²⁷ Heaviest, farthest and most macroscopic are three different titles, and as of 24 October 2026 they belong to three different experiments.

Part IIIDoes gravity kill cats?

Chapter 9A size limit for quantum mechanics?

Perhaps large things cannot stay in superpositions at all. Collapse models add a small random, nonlinear term to the Schrödinger equation: negligible for one particle, amplified for many, so that superpositions of large objects end by themselves. In the model proposed by Giancarlo Ghirardi, Alberto Rimini and Tullio Weber in 1986 (GRW), every nucleon is spontaneously localised to about 100 nm at random moments, at a rate λ ≈ 10⁻¹⁶ s⁻¹.²⁸ One nucleon would be hit about once every 300 million years; a body of 10²³ nucleons about every 10⁻⁷ s (this page's arithmetic). A hit settles the outcome only if the branches are farther apart than that 100 nm; for smaller splits its effect shrinks with the split squared, which is why a split like the crystal's barely registers. Philip Pearle, and then Ghirardi, Pearle and Rimini, turned this into a continuous process, continuous spontaneous localisation (CSL), in 1989 and 1990.^29,30,31

Collapse models are testable, and not only with cats. The random localisations jiggle every charged particle, and jiggling charges radiate. A collapse model therefore predicts a faint, steady glow of X-rays from ordinary matter. A detector built to be as quiet as possible, deep underground, can look for that glow without making any superposition at all.

The strongest such test so far came from a dark-matter detector. On 23 March 2026 the XENON collaboration published an analysis of low-energy events (1–140 keV) from the first science run of XENONnT, a liquid-xenon detector in the Gran Sasso underground laboratory in Italy, recorded between July and November 2021.³² For the Markovian (white-noise) version of CSL it set λ/r_C² < 3.0 × 10⁻³ s⁻¹ m⁻² at 90% confidence, about two orders of magnitude beyond the previous best, from the Majorana Demonstrator in 2022.³³ The values Ghirardi, Rimini and Weber originally proposed (λ = 10⁻¹⁶ s⁻¹, r_C = 10⁻⁷ m) are excluded at 9.1σ, which the authors describe as a first. Variants with coloured noise or dissipation are less constrained, and more XENONnT data are in hand.

So the strongest limits on collapse come from a detector looking for dark matter, not from cats. XENONnT's limit is the strongest for correlation lengths up to about 10 µm; at longer ones, quiet masses compete, among them the free-falling test masses of the LISA Pathfinder spacecraft, which a collapse model's random kicks would have made jitter.³⁴ Cat experiments test the same models more directly, by keeping something coherent whatever it radiates, but the crystal's split is far too small to compete. The models that care most about cats are the ones that tie collapse to gravity.

Chapter 10Penrose's clock

Lajos Diósi in 1987 and 1989, and Roger Penrose, who first floated the idea in 1986 and made it precise in 1996, proposed that gravity sets the rate of collapse.^35,36,37 Penrose's argument goes like this. Two branches of a superposition with different mass distributions come with two different curvatures of spacetime, and quantum mechanics has no clear way to superpose two spacetimes. He suggested that nature tolerates the mismatch only for a limited time, inversely proportional to the gravitational self-energy E_G of the difference between the two mass distributions:

τ ≈ ħ / E_G, E_G = (G/2) ∬ Δρ(x) Δρ(y) / |x − y| d³x d³yΔρ is the difference of the two branches' mass densities. Normalisations differ: Diósi's convention, which XENONnT uses and which reproduces the numbers of Donadi et al. 2021, gives an E_G 8π times larger than Penrose's (as the XENONnT 2026 supplement notes). This page brackets every collapse time between τ and τ/8π, a factor of about 25, and calls the result an estimate.

For point-like nuclei E_G would be infinite, so each nucleus has to be smeared over some size R₀. Penrose's natural choice was the spread of each nucleus's own position in the crystal, about 0.05 Å in cold germanium: the "parameter-free" version. In a paper published in September 2020, Sandro Donadi and colleagues searched data from a germanium detector in the Gran Sasso laboratory for the radiation this version predicts and found none, setting R₀ > 0.54 Å and excluding it.³⁸ Germanium data from the Majorana Demonstrator raised the bound to 2.5 Å (95% C.L.; published in 2022, corrected in 2023), and in March 2026 XENONnT pushed it to R₀ > 4.9 Å (90% C.L.; 4.5 Å at 95%), eight to nine times Donadi's value.^32,33 From the other side, if R₀ were too large the model would fail to collapse everyday objects; Figurato and colleagues placed that limit near 10⁻⁴ m on an admittedly rough criterion.³⁹

The fair summary is this: the simplest, parameter-free version of Penrose's idea is ruled out; versions with a free size survive, squeezed between underground detectors and the requirement that cats do collapse. Donadi and colleagues said as much themselves, and whether the excluded version is the one Penrose and Stuart Hameroff use in Orch OR, their speculative theory of consciousness, has been disputed in a preprint.⁴⁰ "Penrose is ruled out" overstates the case.

For an object of uniform density the integral can be done in closed form:

E_G = (Gm²/R)(2δ² − 3δ³/2 + δ⁵/5) for δ = d/2R ≤ 1
E_G = (Gm²/R)(6/5 − 1/(2δ)) for δ ≥ 1
crystal mode, smooth density: E_G ≈ 2πGρM_effd²A sphere of mass m and radius R displaced by d, in the normalisation above. For small d, E_G ≈ (2π/3)Gρmd²: like decoherence, it grows with the split squared. The crystal line (this page's derivation) holds for an R₀ above the 4.9 Å bound and well below about 0.3 µm, the 1.7 µm acoustic wavelength divided by 2π (wider smearing averages away the wave's density ripple); it depends only on M_effd², so on neither choice of ruler. Here d is the 1.9 × 10⁻¹⁸ m between the two branches' centres at full swing (the paper's 2.1 × 10⁻¹⁸ m also counts the zero-point motion both branches share), and because that difference swings with the sound, E_G averaged over a vibration is half of 2πGρM_effd².

Figure 4 sets Penrose's clock against how long each superposition actually lasted. Pick an object and slide its split; the brass band is the collapse time, the violet flag the measured lifetime.

Figure 4🕰️ Try it

Penrose's clock

Pick an object, split it further

How far apart are the two states?

Penrose's clock (this page's estimate)

It actually lasted

Verdict

Diósi–Penrose collapse times τ = ħ/E_G (this page's estimate). Uniform spheres use Penrose's formula for the self-energy of the difference of the two mass distributions; the crystal mode uses the smooth-density result E_G = 2πGρM_effd², which depends only on M_effd² (Chapter 5), halved because the split swings with the sound and taken with d = 1.9 × 10⁻¹⁸ m, the distance between the two branches' centres (the slider shows the paper's measure, which also counts zero-point motion). The brass band spans published normalisations that differ by up to 8π ≈ 25; the violet flag marks how long the superposition lasted (dashed: planned). Valid for a smearing length R₀ above the 4.9 Å bound of XENONnT (2026) and below the object's size (for the crystal mode, well below about 0.3 µm, its acoustic wavelength divided by 2π); Penrose's parameter-free choice (R₀ ≈ 0.05 Å, the zero-point spread of the nuclei in germanium) is excluded (Donadi et al. 2021) and would give the crystal 470–12,000 years, still far too slow. Lifetimes: crystal negativity about 10 µs (Bild et al. 2023); clusters about 12 ms in the interferometer (this page's arithmetic from the 0.983 m grating spacing and 160 m/s, Pedalino et al. 2026); the diamond test's planned 2.5 s (Bose et al. 2017). Schrödinger's cat has no flag: its hour is a story, not a measurement. Densities assumed: dust speck 2,000 kg/m³, diamond 3,500 kg/m³, sodium cluster and cat about 1,000 kg/m³, sapphire 3,980 kg/m³. The cluster's split uses the 133 nm grating period as its scale; once a split exceeds an object's diameter (8 nm for the clusters), splitting it further gives almost the same time. The R₀ chips (crystal only) smear each nucleus, or at 10⁻¹⁵ m each nucleon, into a uniform sphere of radius R₀; for splits much smaller than R₀ this multiplies E_G by (R*/R₀)³, with R* ≈ 0.9 Å for sapphire's nuclei and 0.32 Å for a nucleon (this page's estimate).Roger Penrose suggests that gravity can't put up with a mass being in two arrangements for long: the heavier it is and the farther apart, the sooner it must pick one. The gold band shows when, for each object (our rough estimate). The violet flag shows how long the real superposition lasted. Slide the split and watch the clock move. Only the proposed diamond test gets there in time. The blur buttons (crystal only) try versions of the idea that are already ruled out: even they leave the clock far too slow at the real split.

The verdicts, all this page's estimate:

The crystal cat: about 3–70 million years, against about 10 µs measured. Penrose's clock is more than a billion billion times too slow to have mattered. Even the excluded parameter-free smearing (R₀ ≈ 0.05 Å, the germanium value) would give 470–12,000 years, and a smearing of about 10⁻¹⁵ m, the size of a nucleon, excluded long ago,^34,41 would still only bring it down to between a second and a minute (at that scale the smeared unit is each nucleon, not each whole nucleus). Matteo Fadel, one of the experiment's authors, has used the cat's measured fading to test the model directly: it requires only R₀ above about 10⁻¹⁷ m, far weaker than the underground bounds.⁶²
The 2026 sodium clusters: 80–2,100 years, against about 12 ms in the interferometer. Any split well beyond their 8 nm diameter gives almost the same time: once the two copies no longer overlap, separating them further barely changes E_G.
A 10 µm dust speck (density 2,000 kg/m³) split by its own diameter: 0.4–10 µs, by coincidence about the time the crystal cat actually survived. Nobody has made such a superposition.
Schrödinger's cat, 4 kg split by 10 cm: 1.2 × 10⁻²⁷ to 3 × 10⁻²⁶ s. That is the model's point: in this picture large superpositions end almost at once.

No superposition made so far comes near Penrose's clock. The heaviest cat is no test of gravitational collapse, because the clock counts mass × split², and the crystal has mass without split. A test needs both. One proposed experiment has them (Chapter 12).

Chapter 11Gravity's quantum ladder

Gravity already acts on quantum waves at the other end of the mass scale. In 1975 Roberto Colella, Albert Overhauser and Samuel Werner tilted a neutron interferometer so that its two paths ran at different heights, and saw Earth's gravity shift the interference.⁴² The two paths of a single neutron felt different gravitational potentials, and the neutron noticed.

A cleaner case is a neutron sitting in gravity. Ultracold neutrons move so slowly, a few metres per second, that a polished glass mirror reflects them. Above a horizontal mirror a neutron is in a simple well: gravity pulls it down, the mirror stops it. Quantum mechanics allows only certain energies:

E_n = a_n m_ngz₀, z₀ = (ħ² / 2m_n²g)^1/3 ≈ 5.87 µma_n = 2.338, 4.088, 5.521, … are the zeros of the Airy function Ai(−x), and the wavefunctions are Airy functions. a_nz₀ is the height a classical neutron of that energy would reach.

On Earth that gives 1.41, 2.46 and 3.32 peV for the first three levels, with classical turning heights of 13.7, 24.0 and 32.4 µm (this page's arithmetic, which reproduces the published values).⁴³ The first rung is lower than even a fine human hair is thick. Its energy, 1.41 peV, corresponds to 16 nK in temperature units, and a classical neutron bouncing that high would leave the mirror at 1.6 cm/s. The rungs are not evenly spaced. Valery Nesvizhevsky and colleagues saw them at the Institut Laue–Langevin in Grenoble in 2002: neutrons passing through a narrow gap between the mirror and an absorber above it got through not smoothly but in steps, as the gap grew.^43,44

Figure 5 draws the six lowest rungs above the mirror and the frequencies that connect them. Pick a rung, then shake the mirror and look for the frequency that lifts neutrons out of the lowest one. Then try the Moon.

Figure 5🏀 Try it

Gravity's quantum ladder

Shake the mirror

Shake the mirror at

Height of this rung

Energy

Jump from rung 1

Kicked up

Stationary states of an ultracold neutron above a horizontal mirror: V = m_ngz for z > 0, a hard wall at z = 0, ψ_n ∝ Ai(z/z₀ − a_n), z₀ = (ħ²/2m_n²g)^1/3 = 5.87 µm on Earth. Energies 1.407, 2.460, 3.321, 4.083, 4.780, 5.428 peV; dashed lines are the classical turning heights a_nz₀ (13.7 to 53.0 µm) (this page's arithmetic, matching Nesvizhevsky et al. 2002 and qBounce). The brass cloud is where the neutrons are; the violet outline is |ψ_n|² for the chosen rung. The strip shows the share of neutrons left in the lowest state after a drive with Rabi line shapes, a 20 ms interaction and full transfer on resonance (illustrative widths and depths); f_1n = (E_n − E₁)/h = 254.6, 463.0, 647.2, 815.6 and 972.5 Hz at g = 9.80665 m/s². qBounce measured the 1→6 transition at 972.81(12) Hz in 2021 (conference proceedings), implying a g 3.9σ above the local value; less precise repeat runs in 2023 agreed with the local value, and the next transitions up, 1→7 and 2→9 near 1,120 and 1,142 Hz (beyond this strip), first measured in 2024, gave a g about 2σ below it (Lachaume 2026, TU Wien thesis). Moon (1.62 m/s²) and Mars (3.71 m/s²): the same physics with their surface gravity; heights scale as g^−1/3, energies and frequencies as g^2/3. The neutron is a quantum wave in classical Newtonian gravity; this is not quantum gravity.Very slow neutrons bounce above a mirror, but only to certain heights, like the rungs of a ladder. Pick a rung to see how high it reaches. Then shake the mirror: at just the right frequency, neutrons jump up a rung, and the dips in the strip show which notes work. Try the Moon: weaker gravity, taller rungs.

The qBounce collaboration of TU Wien, working at the same reactor, turned this into a measuring tool. Shake the mirror at exactly the frequency of a transition, (E_n − E₁)/h, and neutrons are kicked up a rung; an absorber removes them, and the transmitted beam dips. They call it gravity resonance spectroscopy.⁴⁵ The transitions from the lowest rung lie at 254.6, 463.0, 647.2, 815.6 and 972.5 Hz for standard gravity (this page's arithmetic). The method has set limits on hypothetical short-range forces from some dark-energy and dark-matter models.⁴⁶ In 2021 data, the 1→6 transition came out at 972.81(12) Hz; the value of g it implies is 3.9σ above the locally measured one.⁴⁷ Less precise repeat runs in 2023 agreed with the local value, and in 2024 the team measured the next transitions up, 1→7 and 2→9, near 1,120 and 1,142 Hz, the highest so far, with a g about 2σ below it.⁶³ These results are in conference proceedings and a 2026 doctoral thesis, not yet a journal paper.

What this is not: quantum gravity. The neutron is a quantum wave, but the gravity it sits in is the ordinary Newtonian field of the Earth, an external potential like the field between the plates of a capacitor. Nothing about gravity is quantised by this experiment, and the neutron is not a cat. It is the cleanest place where gravity shapes a quantum wave, at the light end of the scale.

Chapter 12Meeting near the Planck mass

The Planck mass is m_P = √(ħc/G) = 21.76 µg (CODATA 2022).² It is roughly the mass at which an object's quantum length, its Compton wavelength, becomes comparable to its gravitational length, the radius of a black hole of that mass. It is a natural unit, not a known threshold: no established theory says that quantum mechanics changes at the Planck mass.

Still, it is where the two frontiers meet. On the quantum side, the crystal cat is 0.74 Planck masses (0.046 on the 1.0 µg ruler; this page's arithmetic). On the gravity side, the lightest object whose own gravitational pull has been measured, as far as we know as of 24 October 2026, is a 90 mg gold sphere, in a 2021 experiment in Vienna.⁴⁸ That is about 4,100 Planck masses and 5,600 times the cat's effective mass (this page's arithmetic). Gravity has also been measured acting on a levitated magnet of less than half a milligram, but there the source was a set of kilogram masses; the tiny particle was the probe.⁴⁹ The heaviest superposition sits just below the Planck mass; the lightest measured source of gravity sits a few thousand times above it.

The experiment that would join the two was proposed in two companion papers published on 13 December 2017, by Sougato Bose and colleagues and by Chiara Marletto and Vlatko Vedral.^50,51 Two diamonds of 10⁻¹⁴ kg, each carrying a spin, are each put into a superposition of two positions 250 µm apart, and fall side by side for about 2.5 s, interacting only through gravity. If they come out entangled, the argument runs, gravity must be able to carry quantum information, which a classical field cannot do. Seeing that entanglement would be strong evidence that gravity is quantum.

How strong is disputed. In June 2025 David Trillo and Miguel Navascués found that the Diósi–Penrose model, in which gravity stays classical, itself predicts gravitationally induced entanglement at short range, and argued that seeing entanglement would therefore not by itself prove gravity quantum.⁵² In May 2026 Tianfeng Feng, Vedral and Marletto replied that collapse-based models do not violate the entanglement witness, because of their nonlocal features.⁵³ In October 2025 Joseph Aziz and Richard Howl raised a second challenge in Nature: describing the masses with full quantum field theory rather than as simple particles, they found that even classical gravity can entangle them through local processes, though with a different scaling from quantum gravity, so a convincing test must check how the entanglement grows, not only that it appears. Marletto, Vedral and colleagues dispute that conclusion too, as does Lajos Diósi, in preprints.⁶⁰ The argument continues.

There is a further twist. On this page's estimate, Diósi–Penrose collapse would end each diamond's superposition in 0.5–12 ms, some 200 to 5,000 times sooner than the 2.5 s the experiment needs. If Penrose's idea is right in this form, the diamonds' superpositions would end long before the fall does. So the same experiment would test Penrose as well as quantum gravity. In Figure 4, the diamond test is the only object whose brass band lands before its violet flag.

Part IVWhat comes next

Chapter 13Bigger cats

Several routes lead towards bigger cats, and each fights the split-squared law in its own way.

Levitated nanoparticles. A glass nanosphere held by a laser in vacuum has no crystal mount to leak its motion into. In 2020 one was cooled to its motional ground state,⁵⁴ and in 2021 two groups achieved quantum control of such particles, one in cryogenic free space and one at room temperature.^55,56 In August 2025 Massimiliano Rossi and colleagues softened the trap and let a nanosphere's wavefunction spread to more than three times its initial coherence length.⁵⁷ That is still far smaller than the particle itself; the goal is a coherence length comparable to the object's size.

Heavier matter waves. The 2026 paper already shows fringes from clusters of 0.4 to 1 million daltons, but at those masses the set-up cannot yet tell a quantum pattern from a classical shadow; slowing the clusters to about 25 m/s should. The Vienna group names clusters of millions of daltons as its next step, and a vertical interferometer that could gain about a hundred times in both mass and time, which on the μ ruler would be six orders of magnitude.^23,58

Longer-lived crystal cats. Because τ_cat ≈ T₁/2α², every gain in the phonon lifetime buys a bigger or longer-lived cat directly.

New proposals. In July 2026 a theory preprint proposed interference of superconducting microparticles above a picogram, levitated in shaped magnetic traps.⁵⁹ It is a proposal, not an experiment.

Collapse limits. XENONnT has more data than its first science run, so the limits on CSL and on R₀ are expected to tighten.³²

As of 24 October 2026, no experiment has claimed gravitationally induced entanglement, and we found no cat state of motion heavier than ETH's. The heaviest cat ever made was split by an eight-hundredth of a proton, and that was the point. Heavy is easy. Far is hard. Gravity has not yet had its turn.

Chapter 14Glossary and sources

Superposition: A quantum state that contains two or more possibilities together, with a definite phase between them that shows up as interference.
Cat state: A superposition of two clearly distinguishable states; for an oscillator, usually two coherent states in opposite phases, |α⟩ ± |−α⟩.
Coherent state: The quantum version of a definite oscillation, blurred only by zero-point motion. |α|² is its mean number of quanta.
Phonon: One quantum of vibration, of energy hf.
Zero-point motion: The unavoidable quantum blur of an oscillator in its ground state, √(ħ/2Mω).
Wigner function, negativity: A map of a quantum state over position and momentum. Where it dips below zero, no classical mixture can explain the state.
Effective mass: The mass that, with a chosen reference displacement, gives a vibration mode its energy as if it were a mass on a spring. Only mass × displacement² is fixed.
Decoherence: The loss of interference when the environment records which branch a system is in.
T₁: The energy lifetime of a mode or qubit: about 84 µs for the ETH phonon mode.
Transmon qubit: A superconducting circuit with two working energy levels, controlled with microwaves.
HBAR: High-overtone bulk acoustic-wave resonator: a crystal with a thin piezoelectric layer that hosts many standing sound waves.
Macroscopicity μ: The base-10 logarithm of the longest electron coherence time, in seconds, that an experiment rules out for a minimal classicalising modification of quantum mechanics.
Collapse model (GRW, CSL): A modification of quantum mechanics in which superpositions of large objects end spontaneously, with a rate λ and a length r_C.
Diósi–Penrose model, E_G, R₀: Collapse tied to gravity: lifetime ħ/E_G, with E_G the gravitational self-energy of the difference between two branches and R₀ the size over which each nucleus is smeared.
Planck mass: √(ħc/G) = 21.76 µg, a natural unit of mass.
Ultracold neutron: A neutron slow enough, a few metres per second, to be reflected by material surfaces.
peV: Pico-electronvolt, 10⁻¹² eV.
C.L., σ: Confidence level of a limit (90% or 95% on this page); σ counts standard deviations of an exclusion or a discrepancy.

Sources

M. Bild, M. Fadel, Y. Yang et al., "Schrödinger cat states of a 16-microgram mechanical oscillator," Science 380, 274 (2023), doi:10.1126/science.adf7553, arXiv:2211.00449.
NIST, CODATA 2022 recommended values of the fundamental physical constants: proton rms charge radius 0.84075(64) fm; Planck mass 2.176434(24) × 10⁻⁸ kg; neutron mass 1.67492750056(85) × 10⁻²⁷ kg, physics.nist.gov/cuu/Constants.
E. Schrödinger, "Die gegenwärtige Situation in der Quantenmechanik," Naturwissenschaften 23, 807, 823 and 844 (1935), doi:10.1007/BF01491891.
J. D. Trimmer, "The present situation in quantum mechanics: a translation of Schrödinger's 'cat paradox' paper," Proc. Am. Philos. Soc. 124, 323 (1980), JSTOR 986572.
C. Monroe, D. M. Meekhof, B. E. King and D. J. Wineland, "A 'Schrödinger cat' superposition state of an atom," Science 272, 1131 (1996), doi:10.1126/science.272.5265.1131.
M. Brune, E. Hagley, J. Dreyer et al., "Observing the progressive decoherence of the 'meter' in a quantum measurement," Phys. Rev. Lett. 77, 4887 (1996), doi:10.1103/PhysRevLett.77.4887.
E. Wigner, "On the quantum correction for thermodynamic equilibrium," Phys. Rev. 40, 749 (1932), doi:10.1103/PhysRev.40.749.
W. H. Zurek, "Decoherence, einselection, and the quantum origins of the classical," Rev. Mod. Phys. 75, 715 (2003), doi:10.1103/RevModPhys.75.715.
Y. Chu, P. Kharel, W. H. Renninger et al., "Quantum acoustics with superconducting qubits," Science 358, 199 (2017), doi:10.1126/science.aao1511.
U. von Lüpke, Y. Yang, M. Bild et al., "Parity measurement in the strong dispersive regime of circuit quantum acoustodynamics," Nat. Phys. 18, 794 (2022), doi:10.1038/s41567-022-01591-2.
A. D. O'Connell, M. Hofheinz, M. Ansmann et al., "Quantum ground state and single-phonon control of a mechanical resonator," Nature 464, 697 (2010), doi:10.1038/nature08967.
Y. Yang, I. Kladarić, M. Drimmer et al., "A mechanical qubit," Science 386, 783 (2024), doi:10.1126/science.adr2464, arXiv:2406.07360.
The Royal Swedish Academy of Sciences, "The Nobel Prize in Physics 2025" (John Clarke, Michel H. Devoret and John M. Martinis), press release, 7 October 2025, nobelprize.org.
B. Schrinski, Y. Yang, U. von Lüpke et al., "Macroscopic quantum test with bulk acoustic wave resonators," Phys. Rev. Lett. 130, 133604 (2023), doi:10.1103/PhysRevLett.130.133604, arXiv:2209.06635.
C. Whittle, E. D. Hall, S. Dwyer et al., "Approaching the motional ground state of a 10-kg object," Science 372, 1333 (2021), doi:10.1126/science.abh2634, arXiv:2102.12665.
H. D. Zeh, "On the interpretation of measurement in quantum theory," Found. Phys. 1, 69 (1970), doi:10.1007/BF00708656.
E. Joos and H. D. Zeh, "The emergence of classical properties through interaction with the environment," Z. Phys. B 59, 223 (1985), doi:10.1007/BF01725541.
K. Hornberger, S. Gerlich, P. Haslinger et al., "Colloquium: Quantum interference of clusters and molecules," Rev. Mod. Phys. 84, 157 (2012), doi:10.1103/RevModPhys.84.157.
M. Arndt, O. Nairz, J. Vos-Andreae et al., "Wave–particle duality of C₆₀ molecules," Nature 401, 680 (1999), doi:10.1038/44348.
T. Kovachy, P. Asenbaum, C. Overstreet et al., "Quantum superposition at the half-metre scale," Nature 528, 530 (2015), doi:10.1038/nature16155.
D. M. Stamper-Kurn, G. E. Marti and H. Müller, "Verifying quantum superpositions at metre scales," Nature 537, E1 (2016), doi:10.1038/nature19108; reply: T. Kovachy et al., Nature 537, E2 (2016), doi:10.1038/nature19109.
Y. Y. Fein, P. Geyer, P. Zwick et al., "Quantum superposition of molecules beyond 25 kDa," Nat. Phys. 15, 1242 (2019), doi:10.1038/s41567-019-0663-9.
S. Pedalino, B. E. Ramírez-Galindo, R. Ferstl et al., "Probing quantum mechanics with nanoparticle matter-wave interferometry," Nature 649, 866 (2026), doi:10.1038/s41586-025-09917-9; preprint title "Probing quantum mechanics using nanoparticle Schrödinger cats," arXiv:2507.21211.
S. Nimmrichter and K. Hornberger, "Macroscopicity of mechanical quantum superposition states," Phys. Rev. Lett. 110, 160403 (2013), doi:10.1103/PhysRevLett.110.160403, arXiv:1205.3447.
B. Schrinski, S. Nimmrichter, B. A. Stickler and K. Hornberger, "Macroscopicity of quantum mechanical superposition tests via hypothesis falsification," Phys. Rev. A 100, 032111 (2019), doi:10.1103/PhysRevA.100.032111.
J. R. Friedman, V. Patel, W. Chen, S. K. Tolpygo and J. E. Lukens, "Quantum superposition of distinct macroscopic states," Nature 406, 43 (2000), doi:10.1038/35017505; C. H. van der Wal, A. C. J. ter Haar, F. K. Wilhelm et al., "Quantum superposition of macroscopic persistent-current states," Science 290, 773 (2000), doi:10.1126/science.290.5492.773.
H. Putterman, K. Noh, C. T. Hann et al., "Hardware-efficient quantum error correction via concatenated bosonic qubits," Nature 638, 927 (2025), doi:10.1038/s41586-025-08642-7, arXiv:2409.13025.
G. C. Ghirardi, A. Rimini and T. Weber, "Unified dynamics for microscopic and macroscopic systems," Phys. Rev. D 34, 470 (1986), doi:10.1103/PhysRevD.34.470.
P. Pearle, "Combining stochastic dynamical state-vector reduction with spontaneous localization," Phys. Rev. A 39, 2277 (1989), doi:10.1103/PhysRevA.39.2277.
G. C. Ghirardi, P. Pearle and A. Rimini, "Markov processes in Hilbert space and continuous spontaneous localization of systems of identical particles," Phys. Rev. A 42, 78 (1990), doi:10.1103/PhysRevA.42.78.
A. Bassi, K. Lochan, S. Satin et al., "Models of wave-function collapse, underlying theories, and experimental tests," Rev. Mod. Phys. 85, 471 (2013), doi:10.1103/RevModPhys.85.471.
E. Aprile et al. (XENON Collaboration), "Challenging spontaneous quantum collapse with the XENONnT dark matter detector," Phys. Rev. Lett. 136, 120201 (2026), doi:10.1103/2jm3-4976, arXiv:2506.05507.
I. J. Arnquist et al. (Majorana Collaboration), "Search for spontaneous radiation from wave function collapse in the Majorana Demonstrator," Phys. Rev. Lett. 129, 080401 (2022), doi:10.1103/PhysRevLett.129.080401; erratum Phys. Rev. Lett. 130, 239902 (2023), doi:10.1103/PhysRevLett.130.239902.
B. Helou, B. Slagmolen, D. E. McClelland and Y. Chen, "LISA Pathfinder appreciably constrains collapse models," Phys. Rev. D 95, 084054 (2017), doi:10.1103/PhysRevD.95.084054, arXiv:1606.03637.
L. Diósi, "A universal master equation for the gravitational violation of quantum mechanics," Phys. Lett. A 120, 377 (1987), doi:10.1016/0375-9601(87)90681-5.
L. Diósi, "Models for universal reduction of macroscopic quantum fluctuations," Phys. Rev. A 40, 1165 (1989), doi:10.1103/PhysRevA.40.1165.
R. Penrose, "On gravity's role in quantum state reduction," Gen. Relativ. Gravit. 28, 581 (1996), doi:10.1007/BF02105068.
S. Donadi, K. Piscicchia, C. Curceanu et al., "Underground test of gravity-related wave function collapse," Nat. Phys. 17, 74 (2021), doi:10.1038/s41567-020-1008-4, arXiv:2111.13490.
L. Figurato, M. Dirindin, J. L. Gaona-Reyes et al., "On the effectiveness of the collapse in the Diósi–Penrose model," New J. Phys. 26, 113004 (2024), doi:10.1088/1367-2630/ad8c77, arXiv:2406.18494.
K. J. McQueen, "Have underground radiation measurements refuted the Orch OR theory?" arXiv:2301.12306 (2023, preprint).
G. C. Ghirardi, R. Grassi and A. Rimini, "Continuous-spontaneous-reduction model involving gravity," Phys. Rev. A 42, 1057 (1990), doi:10.1103/PhysRevA.42.1057.
R. Colella, A. W. Overhauser and S. A. Werner, "Observation of gravitationally induced quantum interference," Phys. Rev. Lett. 34, 1472 (1975), doi:10.1103/PhysRevLett.34.1472.
V. V. Nesvizhevsky, H. G. Börner, A. K. Petukhov et al., "Quantum states of neutrons in the Earth's gravitational field," Nature 415, 297 (2002), doi:10.1038/415297a.
V. V. Nesvizhevsky, H. G. Börner, A. M. Gagarski et al., "Measurement of quantum states of neutrons in the Earth's gravitational field," Phys. Rev. D 67, 102002 (2003), doi:10.1103/PhysRevD.67.102002.
T. Jenke, P. Geltenbort, H. Lemmel and H. Abele, "Realization of a gravity-resonance-spectroscopy technique," Nat. Phys. 7, 468 (2011), doi:10.1038/nphys1970.
T. Jenke, G. Cronenberg, J. Burgdörfer et al., "Gravity resonance spectroscopy constrains dark energy and dark matter scenarios," Phys. Rev. Lett. 112, 151105 (2014), doi:10.1103/PhysRevLett.112.151105.
J. Micko, J. Bosina, S. S. Cranganore et al., "qBounce: systematic shifts of transition frequencies of gravitational states of ultra-cold neutrons using Ramsey gravity resonance spectroscopy," in Proceedings of the 56th Rencontres de Moriond, Gravitation 2022, p. 143 (2023, conference proceedings), doi:10.58027/1e1n-7973, arXiv:2301.08583.
T. Westphal, H. Hepach, J. Pfaff and M. Aspelmeyer, "Measurement of gravitational coupling between millimetre-sized masses," Nature 591, 225 (2021), doi:10.1038/s41586-021-03250-7, arXiv:2009.09546.
T. M. Fuchs, D. G. Uitenbroek, J. Plugge et al., "Measuring gravity with milligram levitated masses," Sci. Adv. 10, eadk2949 (2024), doi:10.1126/sciadv.adk2949.
S. Bose, A. Mazumdar, G. W. Morley et al., "Spin entanglement witness for quantum gravity," Phys. Rev. Lett. 119, 240401 (2017), doi:10.1103/PhysRevLett.119.240401, arXiv:1707.06050.
C. Marletto and V. Vedral, "Gravitationally induced entanglement between two massive particles is sufficient evidence of quantum effects in gravity," Phys. Rev. Lett. 119, 240402 (2017), doi:10.1103/PhysRevLett.119.240402.
D. Trillo and M. Navascués, "Diósi–Penrose model of classical gravity predicts gravitationally induced entanglement," Phys. Rev. D 111, L121101 (2025), doi:10.1103/PhysRevD.111.L121101, arXiv:2411.02287.
T. Feng, V. Vedral and C. Marletto, "Collapse-based models for gravity do not violate the entanglement-based witness of nonclassicality," Phys. Rev. D 113, 104055 (2026), doi:10.1103/83rl-nygv, arXiv:2503.19774.
U. Delić, M. Reisenbauer, K. Dare et al., "Cooling of a levitated nanoparticle to the motional quantum ground state," Science 367, 892 (2020), doi:10.1126/science.aba3993.
F. Tebbenjohanns, M. L. Mattana, M. Rossi et al., "Quantum control of a nanoparticle optically levitated in cryogenic free space," Nature 595, 378 (2021), doi:10.1038/s41586-021-03617-w.
L. Magrini, P. Rosenzweig, C. Bach et al., "Real-time optimal quantum control of mechanical motion at room temperature," Nature 595, 373 (2021), doi:10.1038/s41586-021-03602-3.
M. Rossi, A. Militaru, N. Carlon Zambon et al., "Quantum delocalization of a levitated nanoparticle," Phys. Rev. Lett. 135, 083601 (2025), doi:10.1103/2yzc-fsm3, arXiv:2408.01264.
F. Kiałka, Y. Y. Fein, S. Pedalino et al., "A roadmap for universal high-mass matter-wave interferometry," AVS Quantum Sci. 4, 020502 (2022), doi:10.1116/5.0080940.
J. Cunill-Subiranas, F. Resare, S. Zhao et al., "Macroscopic quantum interference of the center-of-mass motion of levitated superconducting microparticles enabled by magnetic higher-order traps," arXiv:2607.03622 (2026, preprint).
J. Aziz and R. Howl, "Classical theories of gravity produce entanglement," Nature 646, 813 (2025), doi:10.1038/s41586-025-09595-7; replies: C. Marletto, J. Oppenheim, V. Vedral and E. Wilson, "Classical gravity cannot mediate entanglement," arXiv:2511.07348 (2025, preprint); L. Diósi, "No, classical gravity does not entangle quantized matter fields," arXiv:2511.00852 (2025, preprint).
A. Tonomura, J. Endo, T. Matsuda, T. Kawasaki and H. Ezawa, "Demonstration of single-electron buildup of an interference pattern," Am. J. Phys. 57, 117 (1989), doi:10.1119/1.16104.
M. Fadel, "Probing gravity-related decoherence with a 16 µg Schrödinger cat state," arXiv:2305.04780 (2023, preprint).
F. Lachaume, "Gravitational Ramsey spectroscopy applied to ultra cold neutrons in the qBounce experiment and application of numerical analysis techniques," doctoral thesis, TU Wien (2026), doi:10.34726/hss.2026.125742.

16 micrograms

16 micrograms

A quite ridiculous case

A picture of two states at once

A cat made of sound

Which 16 micrograms?

1/800 of a proton