Schrodinger's Cat

How Fat is Schrödinger’s Cat?

There is more than one absurdity hidden behind the gauzy clouds of quantum physics.  No matter how hard the Ecclesiastes of the quantum canon have tried to hide them, the absurdities always tended to shine through.  Niels Bohr, the high priest of the quantum, established the dogma in the raiment of the Copenhagen interpretation that became a windmill tilted at by the Don Quixote’s of physics.  Surprisingly, two of the first to tilt at Copenhagen were also two of the founders of the field: Einstein and Schrödinger. Schrödinger created an absurdity—his “Cat”—that he thought would slay Bohr’s windmill, only to see it embraced by the enemy in its tiniest form, and then to grow ever larger until today some of the cat’s descendants are so fat they can be seen with the naked eye.

Einstein’s Spooky Action and Schrödinger’s Cat

Albert Einstein and Erwin Schrödinger were founders of quantum physics.  Einstein, on his part, blew past Planck by embracing quanta in the form of the quantum of light—the photon.  Schrödinger, just as important, found the wave equation that governed the behavior of quantum particles.  These two physicists believed that quantum dynamics should be just as deterministic as classical dynamics, and they pushed hard against Max Born and Niels Bohr and Werner Heisenberg who embraced the fundamental uncertainties of quantum measurement.

In the view of Einstein and Schrödinger, beginning in 1925, quantum mechanics had slowly veered off the tracks, and by 1935 they felt it had coagulated into a form that was both unrecognizable and unpalatable. 

Einstein took the first pass, tilting at the nonlocal character of quantum physics that allowed a measurement at one location to determine the measurement at a distant location, no matter how far apart the two locations were.  This is the famous “EPR Paradox”, named after the three authors of the paper published in the Physical Review in 1935 by Einstein, Podolsky and Rosen.  Einstein called it “Spooky action at a distance.” 

After reading the EPR paper, Schrödinger sent a congratulatory note to Einstein, applauding him on his clever thought experiment that showed one of the absurdities of quantum physics.  This note launched an intense correspondence between the two physicists, as each complained to the other about the overbearing Copenhagen interpretation and about the indifference of a ballooning number of physicists who were happy to adopt Bohr’s attitudes without worrying about the underlying philosophical contradictions.

1927 Solvay Congress with Einstein, Compton and Schrödinger.
Fig. 1 Schrödinger (top) and Einstein (bottom) at the 1927 Solvay Congress.

Inspired by his correspondence with Einstein, Schrödinger launched his own attack on Copenhagen.  Where Einstein attacked the nonlocality of quantum phenomena, Schrödinger attacked the scale of quantum phenomena.

Schrödinger’s Cat

In late 1935, Schrödinger published a series of papers discussing the current situation in quantum mechanics [1].  Schrödinger had remained a realist.  Although Born had established almost ten years before that the quantum wavefunction was not related to the physically real electron density, Schrödinger continued to ascribe to it a level of physical reality.  To reduce the Copenhagen interpretation to absurdity, he took Bohr’s measurement argument to extremes.

Schrödinger proposed placing a cat in a sealed box with a radioactive substance known to have a half-life of an hour.  If the particle decays, a Geiger counter in the box releases a hammer that smashes a vial of poison, killing the cat.  At the end of an hour, the chance the cat is alive or dead is 50/50.  In the Copenhagen interpretation, because all elements in the box consist of quantum mechanical wavefunctions, and no overt measurement is made, the cat must be in a quantum superposition of both alive and dead states.  Now if an observer opens the box to look inside, the wavefunction of the cat collapses into one state or the other.  To Schrödinger, such a state of affairs was absurd, clearly illustrating the limitations of the Copenhagen interpretation that required wavefunction superpositions to remain unmolested if no overt measurement takes place.

Schrödinger's Cat introduced in Naturwissenschaften 1935
Fig. 2 Schrödinger’s introduction of his cat in the Nov. 29 issue of Naturwissenschaften of 1935 in the article “The Current Situation of Quantum Mechanics”.

The Schrödinger cat paradox became sensationally famous in ways that Schrödinger himself had not intended.  He had fashioned the example to combat what he saw was an unrealistic acceptance of the Copenhagen interpretation of quantum mechanics. While succeeding in showing that quantum mechanics was bizarre, he had hoped to show that it was wrong, or at least missing something.  To his chagrin, there was general acceptance of the dead-and-alive superposition, at least in principle.  Schrödinger had called the mutual influence of quantum states upon each other as entanglement, and the word stuck.  The discussions elicited by the cat paradox side-stepped the philosophical problems of quantum mechanics and focused instead on the physical differences between microscopic states, where quantum superposition held sway, versus macroscopic states, where classical physics emerges.

Today, the quantum/classical border is understood to be governed by decoherence. When a quantum system (with its well-defined superpositions) interacts with its environment, the internal quantum states become entangled with the environmental states, and the internal states lose their originally clean relationships, becoming fuzzy—less both “dead and alive” to become more “dead or alive”. By the simple combinatorics of large numbers, the bigger a quantum state is, the more avenues there are to interact with its environment, and the faster the effects of decoherence kick in. The question then shifts from whether a quantum cat can exist, to how large the quantum cat can become before decoherence gets too fast to capture the superposition.

Schrödinger’s Cat Grows Up

For the first several decades of its life, the size of Schrödinger’s cat was restricted to the quantum physics of fundamental particles, like electrons, or to electronic superpositions within atoms or molecules. These superpositions were not “spatial”—the two entities of the superposition were not occupying different parts of space. The electronic states of atoms could be in different orbitals that have different spatial distributions, but it is all one object.

This changed in 1974 when Italian physicists Pier Giorgio Merli, Gian Franco Missiroli, and Giulio Pozzi at the University of Bologna used the electron source of an electron microscope to send single electrons, one at a time, through a biprism acting as a double slit (like Young’s double slit experiment with light). This was the first time that the electron double-slit experiment was performed one electron at a time, and despite the fact that there was no “other” electron to interfer with, the experiment produced interference fringes. Each electron was in a superposition, taking both one path and the other, separated spatially by the two halves of the biprism. This was the first demonstration of Schrödinger’s cat as a spatial superposition.

This experiment was followed 15 years later by researchers at Hitachi in Japan who, in 1989, used a scintillator screen to watch the single electrons arrive one at a time, slowly building up the interference fringes first seen by the Italians.

Fig. 3 Promotional video by Hitachi showing the accumulating electrons, forming interference fringes.

Electrons interfering with themselves, by taking different spatial paths, still represents a tiny cat. Of the stable fundamental particles, electrons are the lightest (or the “smallest”). A more impressive cat might be constructed of an atom that is heavier and “larger” than an electron.

In 1996, Chris Monroe and David Wineland at JILA created a Schrödinger Cat superposition using a trapped Beryllium ion [2]. They coupled the internal electronic states to external motional states that allowed the ion to be prepared in a superposition of spatially separated states.

Fig. 4 The Monroe and Wineland experiment. Published May 24, 1996 issue of Science.

An even larger cat was demonstrated in 1999 by Anton Zeilinger‘s group in Vienna by creating a spatial quantum superposition using “Buckyballs” [3] that are C60 molecules. They used a thermal molecular beam at low flux levels that ensured that the average number of molecules transiting the experimental apparatus at a given time was less than one. One member of the group, Markus Arndt, has been “scaling up” the size of his cats into the range of thousands of atoms.

Fig. 5 The Carbon-60 paper from Zeilinger’s group in Nature, Oct 14, 1999

Schrödinger’s Cat Today

In the last 10 years, Schrödinger’s cat has grown to immense size. In 2023 a group at ETH in Zurick, Switzerland, put a “Fat Cat” 16-microgram mass [4] into a spatial superposition of two states of mechanical vibration. The mass contained approximately 1017 atoms (C60 has 60 atoms), which clearly brought quantum mechanics to the edge of the macroscopic world. It was shaped as a disc with a diameter of about 1 millimeter and a thickness of of 100 microns, large enough to be seen with the naked eye (before it is loaded into the ultra-low-temperature cryostat where it is hidden from probing eyes). The states experienced decoherence after about 40 microseconds, but this is a sufficiently long time for experimental probes to test its properties.

Fig. 6 The “Fat Cat” of the April 21 issue of Science from 2023.

The 16-microgram mass experiment was macroscopic but still comprised a single object in two spatial modes. Therefore, by building on the C60 experiment of Markus Arndt, in early 2026 a matter wave interferometer measured the interference of large metal clusters of sodium [5] containing approximately 7000 atoms passing through a region of space that was macroscopically large relative to the size of the metal clusters. By some measure of “macroscopicity” this is the largest Quantum Cat to date.

Largest Schrödinger's Cat
Fig. 7 The “Fatest Cat” of Jan. 21 issue of Nature (2026)

A simplified schematic of the Pedalino experiment is shown in Fig. 8. A nanoclusters with about 7000 sodium atoms comes from a source and moves towards a standing-wave laser beam. If the cluster moves into an antinode, then it is ionized and removed, but if it enters a node region, it remains neutral and passes through. This creates a spatial superposition of “locations” of the nanoparticle. This superposition creates quantum interference fringes on the far side of the diffraction grating.

Metal nanoparticle interferometer
Fig. 8. Simplified view of the Pedalino experiment. A sodium nanocluster with about 7000 sodium atoms is sent through a standing-wave optical field that acts as a diffraction grating. The nanoparticle passes through any of the anti-nodes of the standing wave in a spatial superposition that causes interference fringes on the far side. At one instance of time, the nanoparticle is both here and there, “dead” and “alive”.

The nanoparticle is about 10 nm in size, which is comparable to some biological macromolecules as well as viruses, raising the possibility that quantum cats may be constructed in the near future of biological matter. It may even become possible to produce quantum cats from living bacteria. Experimental groups continue to push the bounds of large quantum systems. This is of more than “academic” interest, because larger quantum superpositions with longer decoherence times can be enlisted as elements of quantum information systems such as quantum computers and quantum communication systems.

References

[1] Schrodinger, E. (1935). “The current situation in quantum mechanics.” Naturwissenschaften 23: 807-812.

[2] P.G. Merli, G.F. Missiroli, and G. Pozzi, “Electron interferometry with the Elmiskop 101 electron microscope,” Journal of Physics E: Scientific Instruments 7 (1974), 729–732

[3] C. Monroe et al. , A “Schrödinger Cat” Superposition State of an Atom. Science272,1131-1136(1996). DOI:10.1126/science.272.5265.1131

[4] Arndt, M., Nairz, O., Vos-Andreae, J. et al. Wave–particle duality of C60 molecules. Nature 401, 680–682 (1999). https://doi.org/10.1038/44348

[5] Marius Bild et al., Schrödinger cat states of a 16-microgram mechanical oscillator. Science380, 274-278(2023). DOI:10.1126/science.adf7553

[5] Pedalino, S., Ramírez-Galindo, B.E., Ferstl, R. et al. Probing quantum mechanics with nanoparticle matter-wave interferometry. Nature 649, 866–870 (2026). https://doi.org/10.1038/s41586-025-09917-9

The Rise of Wave Mechanics by Erwin Schrödinger

100 Years of Quantum Physics: Schrödinger’s Wave Mechanics (1926)

By the middle of 1925, a middle-aged Erwin Schrödinger was casting about, bogged down in mid career, looking for something significant to say about the rapidly accelerating field of quantum theory.  He was known for his breadth of knowledge, and for his belief in his own creative genius [1], but a grand synthesis had so far eluded him. 

Einsteinian Gas Theory

In the middle of the year, Schrödinger was deep analyzing two papers recently published by Einstein (Sept. 1924 and Feb. 1925) on the quantum properties of ideal gases where Einstein applied the new statistical theory of Bose to the counting of states in a volume of the gas [2].  One of the intriguing discoveries made by Einstein in those papers was a close analogy between the fluctuation of gas numbers and the interference of waves.  He stated:

‘I believe that this is more than a mere analogy; de Broglie has shown in a very important work how a (scalar) wave field can be coordinated with a material particle or a system of material particles’

referring to de Broglie’s thesis work of 1924 that associated a wave-like property to mass.  Einstein had been the first to attribute a wave-particle duality to the quantum phenomenon of black-body radiation, giving a lecture in Salzburg, Austria, in 1909 showing relationships between the particle-like and the wave-like properties of the radiation, and he found similar behavior in the properties of monatomic ideal gases, though his derivations were purely statistical.

Erwin Schrödinger photo
Fig. 1 Erwin Schrödinger (Source)

Schrödinger was suspicious of the “unnatural” way of counting states used by Einstein and Bose for the gas, and he sought a more “natural” way of explaining how the elements of phase space were filled.  It struck him that, just as Planck’s black-body radiation spectrum could be derived by assuming discrete standing-wave modes for the electromagnetic radiation, then perhaps the behavior of ideal gases could be obtained using a similar approach.  He and Einstein exchanged several letters about this idea as Schrödinger dug deeper into de Broglie’s theory.

The Zurich Seminar

At that time, Schrödinger was in the Chair of Theoretical Physics at the University of Zurich, holding the same chair that Einstein had held 15 years earlier.  Following Einstein, the chair had been occupied by Max von Laue and then by Peter Debye who moved to the ETH in Zurich.  Debye organized a joint seminar between the University and ETH that was a hot social gathering of physicists and physical chemists, discussing the latest developments in atomic and quantum science. 

In November of 2025, Debye, who probably knew about the Einstein-Schrödinger discussion on de Broglie, asked Schrödinger to give a seminar on de Broglie’s theory to the group.  A young Felix Bloch, who was a graduate student at that time, recalled hearing Debye say something like

“Schrödinger, you are not working right now on very important problems anyway. Why don’t you tell us sometime about that thesis of de Broglie, which seems to have attracted some attention?”[3]

Schrödinger gave the overview seminar in early December, showing how the Bohr-Sommerfeld quantization conditions could be explained as standing waves using de Broglie’s theory, but Bloch recalled Debye was unimpressed, saying that de Broglie’s way of talking was “childish” and that what was needed for a proper physics theory was a wave equation.

This exchange between Schrödinger and Debye was recalled only in later years, and there is debate about what exactly was said and what effect it had on Schrödinger.  From Schrödinger’s letters to friends, it is clear that he was already well into his investigations of wavelike properties of matter when Debye asked him to give the seminar.  Furthermore, he had already tried to construct wave packets using superpositions of phase waves propagating along Bohr-Sommerfeld elliptical orbits but had been led to ugly caustics when he tried to apply the packets to the hydrogen atom [4].  Therefore, although Debye was probably not the source of Schrödinger’s interest in de Broglie, it is possible that Debye’s quip about “childishness” may have spurred Schrödinger to find a wave equation subject to boundary conditions rather than working with packets following ray paths.

The Christmas Breakthrough

By this time, Christmas was approaching and Schrödinger arranged to take a vacation away from his family to the Swiss Alpine village of Arosa, and given his unconventional belief in the link between personal pleasure and genius, he did not go alone.  There is no record of what transpired, and no record of which mistress was with him on this particular trip, nor how she spent her time while he worked on his theory, but two days after Christmas he wrote a letter to the physicist Willy Wien saying

“At the moment I am struggling with a new atomic theory. If only I knew more mathematics! I am very optimistic about this thing, and expect that, if only I can . . . solve it, it will be very beautiful.. . . I hope that I can soon report in a little more detailed and understandable way about the matter. At present I must learn a little mathematics in order to completely solve the vibration problem …”[5]

He had uncovered his first wave equation.  When he returned to Zurich, he enlisted the help of his friend, the mathematician Hermann Weyl at the University in Zurich, and Schrödinger had his first eigenfrequencies for hydrogen.  But they were wrong!

Fig. 2 Schrödinger’s first wave equation was relativistic.

The theory of de Broglie was fundamentally a relativistic theory, motivated by mapping the behavior of matter onto the behavior of light.  Therefore, Schrödinger’s first attempt was also relativistic, equivalent to the Klein-Gordon equation.  But there was no clear understanding of electron spin at that time, even though it had been established as a fundamental property of the electron.  It was only several years later when Dirac correctly accounted for electron spin in a relativistic wave equation

Dirac relativistic quantum wave equation
Fig. 3 The full relativistic Dirac equation.

The Schrödinger Wave Equation

Convinced that he was onto something big, and unwilling to fail, despite his failure to obtain correct values for hydrogen, Schrödinger went back to first principles, to the classical theory of Hamiltonian mechanics, identifying Hamilton’s characteristic function with the phase of an electron wave and deriving a non-relativistic equation using variational principles subject to boundary conditions.  The eigenvalues of this new equation, when applied to hydrogen, matched the Bohr spectrum perfectly!

Fig. 4. Schrödinger’s second wave equation was non-relativistic and correctly matched the Bohr energy levels of hydrogen.

It had been only a few weeks since Schrödinger had given his previous seminar to the Zurich group, but in January he gave his update, probably given with some degree of satisfaction, having Debye in attendance, showing his now-famous wave equation and the agreement with experiment.  Schrödinger wrote up his theory and results and submitted his paper on January 27, 1926, to Annalen der Physik [6].

Hydrogen quantum orbitals
Fig. 5 Hydrogen quantum orbitals (Source)

Schrödinger had been known, but not as a forefront thinker, despite what he believed about himself.  Now he was a forefront thinker, vindicating his beliefs but not always on the right track.  He continued his unconventional lifestyle, marginalizing him socially, and he resisted Max Born’s and Niels Bohr’s probabilistic interpretations of the meaning of his own quantum wavefunction, marginalizing him professionally.  Yet his breakthrough gave him a platform, and his skeptical reactions to his colleague’s successes helped illuminate the nature of the new physics (“Schrödinger’s Cat” [7]) through the decades to follow.


Bibliography

A very large body of historical work exists on the discovery of the Schrödinger equation, partially fueled by the lack of first-person accounts on how he achieved it.  There has been a lot of speculation and a lot of sleuthing to uncover his path of discovery. Several accounts differ mainly in the timing of when he derived his equations, although all agree on the sequence: that the relativistic equation preceded the non-relativistic one. Here is a small sampling of the literature:

• Hanle, P. A. (1977). “The Coming of Age of Erwin Schrödinger: His Quantum Statistics of Ideal Gases.” Archive for History of Exact Sciences, 17(2), 165–192. DOI: 10.1007/BF00328532.

• Hanle, P. A. (1979). “The Schrödinger‐Einstein correspondence and the sources of wave mechanics.” American Journal of Physics, 47(7), 644–648. DOI: 10.1119/1.11587.

• Mehra, Jagdish. “Erwin Schrödinger and the Rise of Wave Mechanics. II. The Creation of Wave Mechanics.” Foundations of Physics, vol. 17, no. 12, 1987, pp. 1141-1188.

• Renn, J. (2013). “Schrödinger and the Genesis of Wave Mechanics.” In W. L. Reiter & J. Yngvason (Eds.), Erwin Schrödinger – 50 Years After (pp. 9–36). Zurich: European Mathematical Society. DOI: 10.4171/121-1/2.

• Wessels, L. (1979). “Schrödinger’s Route to Wave Mechanics.” Studies in History and Philosophy of Science Part A, 10(4), 311–340.


Notes

[1] He led an unconventional lifestyle (some would say emotionally predatory) based on his belief in the personal origins of genius.  Although this behavior presented significant social barriers to his career, he refused to abandon it.

[2] A. Enstein, ‘Quantentheorie des einatomigen idealen Gases’, Preuss. Ak. Wiss. Sitzb. (1924) pp. 261 – 267, and (1925), pp. 3-14.

[3] Quoted in Mehra, pg. 1150

[4] Mehra, pg. 1147

[5] Wessels, pg. 328

[6] Schrödinger, Erwin. “Quantisierung als Eigenwertproblem (Erste Mitteilung).” Annalen Der Physik, vol. 384, no. 4, 1926, pp. 361-376.

[7] Schrödinger, E. (1935). “Die gegenwärtige Situation in der Quantenmechanik.” Naturwissenschaften 23: 807–812, 823–828, 844–849.  Schrödinger, E. (1980). “The Present Situation in Quantum Mechanics: A Translation of Schrödinger’s ‘Cat Paradox’ Paper.” Proceedings of the American Philosophical Society 124 (5): 323–338. (Translated by J. D. Trimmer).



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