Quantum physics indicates there is more than matter

A revolution born out of a crisis

At the end of the nineteenth century, classical physics — that of Newton, Maxwell and Boltzmann — seems complete. In 1900, Lord Kelvin declares that only « two little clouds » remain to be dispelled from the sky of physics^[10]. Yet those two clouds contained the storm of an entire revolution.

The first cloud — black-body radiation — led Max Planck to postulate, on 14 December 1900, before the Berlin Physical Society, that energy is exchanged only in discrete packets, quanta, proportional to the frequency of the radiation: E = h ν^[11]. Planck, who describes himself as a « classical physicist » in spite of himself, immediately understands that his discovery is « an act of despair » that shatters the foundations of all previous physics.

Five years later, Albert Einstein extends Planck's idea to light itself: light is made of photons, particles of energy E = h ν. It is this work (the photoelectric effect, 1905) — and not relativity — that will earn Einstein the 1921 Nobel Prize^[12].

Between 1913 and 1925, Bohr and Sommerfeld formulated a first "semi-classical" model of the atom. But in 1925-1927, under the impetus of Heisenberg (matrix mechanics), Schrödinger (wave mechanics) and Born (probabilistic interpretation), an entirely new physics took shape. At the 1927 Solvay Conference (Solvay Council V, 24-29 October, Brussels), Bohr and Einstein clashed over its meaning: Bohr defended the Copenhagen interpretation, Einstein refused indeterminism — « God does not play dice » (a phrase addressed to Born as early as 1926)^[13]. The debate remained philosophical: no experiment could settle the two positions before Bell's theorem (1964) and Aspect's measurements (1982).

The word "quantum": nature proceeds by jumps

The term quantum comes from the Latin quantum (how much?) and refers to the discrete packets that physical quantities take on at the atomic scale: energy, angular momentum, spin, charge. As Yves Dupont explains:

« It is as if the speed of your car could only take discrete values — 20 km/h, 30 km/h, 40 km/h — and no other values. They are said to be quantised. » — Yves Dupont, L'Empreinte de Dieu dans le monde quantique^[14]

This fundamental discontinuity breaks with all classical physics, which assumed continuous quantities. It also implies that the atom itself is not a « miniature solar system » with electrons on planetary orbits, but a structure of discrete energy levels in which electrons jump by leaps — the famous « quantum jumps »^[15].

The architects of the revolution

The construction of quantum mechanics between 1900 and 1930 is the most densely packed intellectual adventure in the history of science. Half a dozen physicists, almost all Nobel laureates, are its architects:

• Max Planck (1858-1947), Nobel Prize 1918 — the quanta (1900)
• Albert Einstein (1879-1955), Nobel Prize 1921 — the photon (1905)
• Niels Bohr (1885-1962), Nobel Prize 1922 — the quantum atomic model (1913) and the Copenhagen interpretation (1927)
• Louis de Broglie (1892-1987), Nobel Prize 1929 — wave-particle duality (1924)
• Werner Heisenberg (1901-1976), Nobel Prize 1932 — matrix mechanics (1925) and the uncertainty principle (1927)
• Erwin Schrödinger (1887-1961), Nobel Prize 1933 — the wave equation (1926)
• Paul Dirac (1902-1984), Nobel Prize 1933 — the relativistic equation of the electron (1928), prediction of antimatter
• Wolfgang Pauli (1900-1958), Nobel Prize 1945 — the exclusion principle (1925), the neutrino
• Max Born (1882-1970), Nobel Prize 1954 — the probabilistic interpretation of the wave function

Quantum physics has produced a constellation of unprecedented concepts that profoundly transform our intuition of reality. Four of them are decisive for understanding why local realism — particles possessing properties of their own, independent of any measurement — no longer holds.

Wave-particle duality

The initial idea — raised by Louis de Broglie in his doctoral thesis defended in November 1924 — is that every particle is associated with a wave. The proposal is so bold that the examining panel, bewildered, hesitates to approve the thesis. Paul Langevin forwards the text to Einstein, who replies with a famous letter: “this young Frenchman has lifted a corner of the great veil”^[16]. The thesis is accepted. Four years later, in 1927, the experiments of Davisson-Germer (Bell Labs) and G.P. Thomson (Aberdeen) experimentally confirm that electrons diffract like waves^[17]. A Nobel Prize follows in 1929 for de Broglie.

De Broglie's wave is not, however, a mechanical wave propagating through water or air. It is a mathematical wave that unfolds in an abstract space of complex numbers — the wave function, denoted Ψ (psi). As Dupont explains:

“When there is one particle, the wave propagates in three-dimensional space. But when there are a large number of particles, they propagate — there is only one wave function — in a far vaster abstract space called configuration space.” — Yves Dupont, L'Empreinte de Dieu dans le monde quantique^[18]

For a single particle, the wave function Ψ lives in a 3-dimensional space; for two particles, in a 6-dimensional space; for N particles, in a 3N-dimensional space. This configuration space is not ordinary physical space — it is a purely mathematical object, and yet it is what contains all the physical information of the system.

The superposition of states

The second concept is that of superposition. According to the Schrödinger equations, as long as a particle is not measured, its state is a linear combination of all possible states. The famous Schrödinger's cat (paradox formulated in 1935) illustrates the situation: shut in a box with a random radioactive device, the cat is mathematically described as “dead + alive” as long as the box is not opened^[19].

The simplest concrete example is that of the half-silvered mirror. When a particle (a photon) is sent toward a partially transparent mirror, it has a 50% chance of being reflected, a 50% chance of being transmitted. As long as it is not detected, it is in both states simultaneously — not like an object that would hesitate, but like a single wave passing through both paths. Only at measurement does this superposition “collapse” onto one of the two possibilities, according to what is called the reduction of the wave packet.

Irreducible randomness

The third concept is the most metaphysical: quantum physics introduces genuine randomness, distinct from classical randomness. When you toss a coin, you speak of “chance”, but this is mere ignorance: if you knew all the initial conditions (force of the throw, rotation, air currents), you could predict the outcome with certainty. That kind of randomness is reducible.

Quantum randomness is radically different. When a photon is sent toward a half-silvered mirror, no physical cause can predict whether the photon will go straight or be reflected. Since all particles are strictly identical, nothing in the particle determines its behaviour. As Nicolas Gisin writes:

According to Nicolas Gisin, this randomness is absolute and without physical cause: faced with a series of 0s and 1s from a quantum measurement, predicting the next bit is impossible in principle, and not out of ignorance (thesis here paraphrased from the work)^[20].

This randomness is so pure that the Geneva-based company ID Quantique sells worldwide small boxes (the Quantis) that generate true random numbers, used by national lotteries, banks, and gaming and cryptography operators — precisely because no computer algorithm can reach this purity^[21].

Quantum entanglement

The fourth concept — perhaps the most astonishing — is that of entanglement. If two particles are prepared at the same point and then sent in opposite directions, some of their properties become correlated in a way that defies space-time. Whether the first particle is measured in Geneva, or even on Sirius 8.6 light-years away, the second one “freezes” instantaneously into the correlated state — as if there were between them a communication at infinite speed.

It is this property that Einstein, Podolsky and Rosen described in 1935 as “spooky action at a distance” (spukhafte Fernwirkung) while trying to refute it^[22]. Experiment has confirmed it. Dupont sums it up:

“And if an observer looks at the state, he can only find 'plus' or 'minus'. He will find 'plus' on the left. Instantaneously, the particle on the other side will freeze into the 'minus' state, as if there were a communication at infinite speed — which is impossible given the laws of relativity in space-time.” — Yves Dupont^[23]

The experiments we will detail further on (Aspect 1982, Delft 2015, Nobel Prize 2022) have proved that this correlation is not an illusion and cannot be explained by “hidden variables” pre-existing in the particles. This is the death blow dealt to local materialism.

No experiment illustrates the quantum mystery better than the double slit. Conceived by Thomas Young in 1801 to demonstrate the wave nature of light, it was redeployed in the 20th century for electrons, atoms, molecules, and even large organic molecules (C60 fullerenes in 1999^[24], up to molecules of more than 25,000 atomic mass units — about 2,000 atoms — in 2019^[25]).

"If you want to choose one experiment that contains all the mystery of quantum mechanics — and there is no other — choose the double-slit experiment." — Richard P. Feynman, Nobel Prize 1965^[26]

The Classical Setup

A source emits particles toward a screen pierced with two parallel slits. Behind it, a detector records where the particles land. If the source sends bullets (the classical interpretation), the detector shows two bands corresponding to the two slits. If it sends waves (water waves, sound), the detector shows an interference pattern: alternating bright and dark bands, where crests reinforce or cancel each other out.

The Scandal: A Single Particle Produces Interference

The quantum miracle: if the particles are sent one by one, spaced far enough apart that they cannot interact with each other, the interference pattern still appears in the long run! As if each particle, individually, "went through both slits at the same time", and its wave interfered with itself^[27].

A landmark experiment is that of Akira Tonomura at the Hitachi laboratory in 1989: sending electrons one by one through a Möllenstedt biprism, he filmed the interference pattern building up point by point like an invisible puzzle in the long run — direct demonstration that interference is carried by the isolated particle, not by a crowd of particles.

Observation Destroys the Interference

So let us try to find out which slit the electron passes through: let us add a detector near one of the two slits. Immediately, the interference pattern disappears and the two classical bands reappear. This is what is called the effect of measurement: observing the system forces the particle to "decide" on bullet-like or wave-like behaviour. The wave "collapses" onto one of the two paths.

This dependence of the result on observation is neither an artefact nor a mechanical disturbance caused by measurement. It is intrinsic: the mere fact that a piece of information — "which slit?" — can exist destroys the interference pattern, even when that information is, for technical reasons, immediately erased and never read by anyone (quantum eraser experiments by Yoon-Ho Kim and Marlan Scully — 1999 preprint, article published in Physical Review Letters in January 2000)^[28].

Wheeler and the Delayed Choice

More astonishing still: in 1978, John Archibald Wheeler proposed a "delayed-choice" experiment: deciding after the particle has passed through the slits whether to observe its path or its interference. Nature "goes back in time" and conforms to this late choice^[29]. Carried out experimentally by Vincent Jacques et al. in Orsay in 2007, the experiment confirms Wheeler's prediction exactly^[30].

Wheeler draws a dizzying conclusion from all this:

"It is wrong to think that the past already exists in all its details. The 'past' is theory. It has no existence except insofar as it is recorded in the present." — John A. Wheeler, "The "Past" and the "Delayed-Choice" Double-Slit Experiment" (1978)^[31]

The double-slit experiment, by itself, is enough to shake local realism. As Feynman writes: "No deeper mystery has ever been conceived."^[32]

The most fascinating story of the 20th century is the one leading from Einstein's objection in 1935 to Alain Aspect's 2022 Nobel Prize. It constitutes the crucial experiment which, over 80 years, forced the definitive abandonment of local realism (of local hidden-variable theories).

The Einstein–Bohr debate and the EPR argument (1935)

Einstein does not accept quantum indeterminism. In 1935, he publishes with Boris Podolsky and Nathan Rosen a famous paper, known by the initials EPR, which proposes a thought experiment: take two entangled particles, separate them in space, measure the first one. If measuring the first instantaneously determines the state of the second, then — EPR argues — either that state was predetermined by "elements of reality" (hidden variables unseen), or one must admit an influence faster than light, which relativity forbids. Einstein's conclusion: quantum mechanics is incomplete, and hidden variables necessarily exist^[33].

Bohr replies the same year in the same journal: no, quantum mechanics is complete, but it forces us to give up the very idea that the properties of an object exist independently of measurement^[34]. The debate remains philosophical: for thirty years, no experiment can settle the question.

John Bell and his inequality (1964)

Everything changes in 1964 when an Irish physicist at CERN, John Stewart Bell (1928-1990), publishes the founding paper "On the Einstein-Podolsky-Rosen Paradox" (Physics 1, p. 195-200, November 1964)^[35]. Bell mathematically demonstrates that there is a testable numerical difference between the predictions of quantum mechanics and those of any local hidden-variable theory.

Concretely, Bell constructs a statistical expression S concerning correlations between measurements of entangled particles:

• If the particles carry hidden variables (Einstein), then S ≤ 2 — this is Bell's inequality.
• If quantum mechanics is correct, then S can reach 2√2 ≈ 2.83 — the Tsirelson bound.

The trick is diabolical: for the first time, a philosophical difference (local realism vs quantum non-realism) becomes a measurable number. As the physicist Henry Stapp would later say:

"Bell's theorem is the most profound discovery of science." — Henry P. Stapp, Lawrence Berkeley Laboratory^[36]

Alain Aspect and the first experimental confirmation (1982)

It is in the basement of the Institut d'Optique d'Orsay that the decisive measurement is made. The young Alain Aspect, then a teaching assistant at the École Polytechnique, builds between 1979 and 1982 a series of three increasingly refined experiments^[37]. The first (single-channel polarizers, 1981) already violates the generalized Bell inequality by more than 13 standard deviations, and its authors conclude: "Our results, in excellent agreement with quantum predictions, violate strongly the generalized Bell inequalities and exclude the whole class of local realistic theories" (author's translation from the English original)^[38].

The second, with two-channel polarizers, yields the most spectacular result: S = 2.697 ± 0.015, well above the Bell limit (S ≤ 2) — that is, a violation by more than 40 standard deviations, the largest ever reported at that date^[39].

The third and most famous, published in Physical Review Letters on 20 December 1982, closes the "free-choice loophole" by rotating the polarizers while the photons were in flight, that is, too late for any subluminal communication between them to be possible^[40].

Bell's inequality is violated. Einstein was wrong, Bohr was right.

Aspect himself, still a student when he began, would later recount:

"Before my astonished eyes, I saw the detectors yield Bell's quantity. And I saw that in roughly all cases, we were above the Bell threshold. So we were in the purely quantum case." — Alain Aspect, reported testimony^[41]

The loophole-free Delft experiments (2015)

Technical objections nonetheless remain — the "loopholes" — which sceptics invoke for 30 years. On 29 October 2015, the team of Ronald Hanson at the Delft University of Technology (Netherlands) publishes in Nature the first experiment that closes all loopholes simultaneously: the locality loophole (1.3 km distance, thus too great for subluminal communication), the detection loophole (near 100% efficiency thanks to NV centres in diamond), and the free-choice loophole (separate random generators)^[42].

The result is unequivocal: S = 2.42 ± 0.20 over 245 trials, that is, a p = 0.039 value against any local realistic model — a confidence level of about 96%^[43]. Two other teams independently confirm within weeks: Marissa Giustina in Vienna and Lynden Shalm and his team at NIST (Boulder)^[44].

The 2022 Nobel Prize: official consecration

The Royal Swedish Academy of Sciences puts an end to 40 years of hesitation. On 4 October 2022, the Nobel Prize in Physics is awarded "for experiments with entangled photons, establishing the violation of Bell inequalities, and pioneering quantum information science" to three physicists:

• Alain Aspect (Institut d'Optique, Université Paris-Saclay)
• John F. Clauser (J. F. Clauser & Associates, California)
• Anton Zeilinger (University of Vienna)^[45]

It is the official recognition that experiments on quantum entanglement are not a curiosity but indeed a decisive step: the official citation cites experiments with entangled photons, establishing the violation of Bell inequalities, opening the way to a new science of quantum information^[46].

The verdict: no local hidden variables

The conclusion of 60 years of work is unambiguous: local hidden variables are impossible. This means two things:

1. Particles have no properties of their own before measurement. The "more or less" state of a spin does not exist before it is measured — it is created by the measurement itself.
2. The world is not locally separable. Two particles from a single source remain correlated beyond any distance, instantaneously, independently of space-time.

This is what Bernard d'Espagnat summarizes in À la recherche du réel (1979): one can no longer hold that there would exist an independent reality — in the strong sense of the term — that would be compatible with quantum mechanics and the facts established by experiment (thesis here paraphrased from the work)^[47].

Once the hidden variables hypothesis has been set aside, one must take seriously the absolute character of quantum randomness. This point has philosophical consequences that few authors have fully embraced.

Classical randomness versus quantum randomness

Let us return to the distinction. Classical randomness (rolling dice, heads or tails) is epistemic: there is no objective randomness, only ignorance of the initial conditions. In classical physics, Laplace wrote in 1814: "An intellect which knew all the forces with which nature is animated [...] would embrace in the same formula the movements of the largest bodies of the universe and those of the lightest atom; nothing would be uncertain to it."^[48]

Quantum randomness, on the other hand, is ontological: there is no hidden information to be discovered. Nature has no answer to the question "where will the particle go?" before the measurement. This is not a human limitation; it is an intrinsic feature of reality.

Nicolas Gisin and the Quantis generators

The Swiss physicist Nicolas Gisin, professor at the University of Geneva and founder in 2001 of the company ID Quantique, has drawn the technological consequences of this pure randomness. The Quantis boxes he produces use the random splitting of a photon at a semi-reflective plate to generate genuinely unpredictable 0/1 bits^[49].

These generators are today used by national lotteries — the Swiss Loterie Romande has chosen the Quantis generator for its draws —, by banks and by gaming and cryptography operators; the Quantis generator is moreover certified, notably by the Swiss federal institute of metrology METAS^[50].

Gisin specifies that this absence of a physical cause does not mean an absence of cause altogether (nuance here paraphrased from the work)^[51].

This last nuance — "no physical cause" but "perhaps a cause beyond the physical" — is philosophically decisive. It opens the door to the idea that the cause of the result of each quantum measurement could be non-physical, that is, spiritual. This is precisely the thesis of Antoine Suarez, to which we shall return.

The Kochen-Specker theorem: quantum contextuality

Another way of proving the absence of properties in themselves is the Kochen-Specker theorem, demonstrated in 1967 by Simon Kochen (Princeton) and Ernst Specker (ETH Zurich)^[52]. The theorem is more mathematical than Bell's: it proves that as soon as one has at least three independent measurement directions (this is the meaning of "dimension ≥ 3": the equivalent of a volume, as opposed to a mere line), one cannot simultaneously assign predetermined values to all the measurable quantities compatible with quantum mechanics. To go further: physicists call this calculation framework a Hilbert space, and this dependence on the choice of measurements contextuality.

In other words, the result of a quantum measurement depends on the context of the measurement — on the set of other observables that one has chosen to measure at the same time. The quantum world is "contextual." Yves Dupont illustrates this with a metaphor:

« If the states are predetermined, the particle has to carry in its suitcases the answers to all possible contexts. And the set of configurations is so vast that the suitcase is too small. This is physically impossible. » — Yves Dupont^[53]

Remarkably, Ernst Specker was explicitly interested in the question of divine omniscience: as early as 1960, seven years before his famous theorem, he published a paper (Die Logik nicht gleichzeitig entscheidbarer Aussagen, Dialectica 14, pp. 239-246) in which he relates his logic to "scholastic speculations about the infuturabilia" — the question of whether God's omniscience extends to events that would have happened if something that did not happen had happened (comparison here paraphrased from the paper)^[54].

Level of this chapter. A few technical terms appear here (3N-dimensional space, PBR theorem, contextuality): each is explained in one line, and the essential point comes down to a single sentence — what is most real is not the tiny particle of matter, but the equation that describes it. Mathematical details are flagged as "going further".

If matter has no properties of its own, what is real? The answer of contemporary quantum physics, more radical than anything the founders had dared to imagine, is a paradox: it is the wave function — a mathematical entity — that is real, more so than the particles themselves.

The PBR theorem (2012): the quantum state is ontic

In May 2012, three young physicists — Matthew Pusey (Imperial College London), Jonathan Barrett (Royal Holloway) and Terry Rudolph (Imperial) — publish in Nature Physics a theorem that settles a debate going back to Einstein: under its assumptions, the wave function cannot be reduced to a mere epistemic description of our ignorance^[55].

The PBR theorem (an acronym of the three names) proves, under minimal and natural assumptions, that two distinct quantum states cannot correspond to the same underlying physical reality. In other words, the wave function Ψ characterises a real state — it is not merely a calculational tool.

"Any model in which a quantum state represents mere information about some underlying physical state of the system must make predictions that contradict those of quantum theory." — M. F. Pusey, J. Barrett, T. Rudolph, Nature Physics 8, 475 (2012)^[56]

This result is philosophically decisive. Before PBR, one could defend the idea that the wave function was a convenient fiction, a calculational tool, as Einstein had maintained. After PBR, this position becomes untenable under the theorem's assumptions: the wave function cannot be reduced to a mere calculational tool.

But what is a wave function? A mathematical structure in an abstract space (what physicists call a Hilbert space: a mere calculational framework, not a physical place), living in the 3N-dimensional configuration space (for N particles) — in other words: to describe N particles, the equation needs 3 numbers per particle, or 3N numbers in all — and taking so-called complex values (a complex number is two ordinary numbers combined, one of them multiplied by i, where i² = −1; see §9). Conclusion: what is most fundamentally real is not matter, but a mathematical entity. Pythagorean metaphysics — "all is number" — resurfaces, but this time by virtue of a theorem published in Nature Physics.

Non-separability: the whole precedes the parts

Another fundamental result: for a system of two entangled particles, the wave function of the whole is not the product of the wave functions of the parts. Mathematically:

Ψ(A, B) ≠ Ψ(A) × Ψ(B)

This is non-separability. It implies that the global system possesses properties that neither A alone, nor B alone, nor their juxtaposition possesses. The whole is ontologically "more" than the sum of the parts.

This idea overturns materialist atomism, which assumed that understanding the parts is enough to understand the whole. According to d'Espagnat, quantum non-separability implies that the atomist conception — any complex object wholly reducible to its constituents — no longer holds: the world is not made up of independent material individuals (passage here paraphrased from the work)^[57].

The free will theorem (Conway–Kochen, 2006)

In 2006, John H. Conway (Princeton) — the inventor of the famous "Game of Life" — and Simon Kochen publish the "Free Will Theorem" in Foundations of Physics^[58]. Under three well-established physical axioms (SPIN, TWIN, MIN), they demonstrate a striking equivalence:

"If experimenters have a certain free will — in the sense that their choices of measurement are not a function of their past — then the particles have a free will too: their response cannot be a function of their past either." — J. H. Conway & S. Kochen, Foundations of Physics 36 (2006)^[59]

In other words: if man is free, so is the electron. It is one of the most surprising theorems in contemporary physics. And Antoine Suarez has generalised the result (General Free Will Theorem, arXiv, 12 June 2010): if experimenters have a measure of free will, then non-local correlations require free beings outside space-time (thesis here paraphrased)^[60]. We shall return to this.

The results accumulated over the past 50 years converge on a precise conclusion: local materialism is refuted — particles do not possess locally determined properties independent of measurement. This is not an apologetic slogan; it is the verdict of the Bell and Kochen-Specker theorems and of the experiments from Aspect to Delft, explicitly drawn by physicists of every persuasion, including Bernard d'Espagnat (Templeton Prize 2009)^[61][62].

Veiled reality according to Bernard d'Espagnat

Bernard d'Espagnat (1921-2015), École Polytechnique graduate, professor at Université Paris-Sud, winner of the 2009 Templeton Prize “for his explorations of the philosophical implications of quantum physics, which have opened new perspectives on the definition of reality”^[63], devoted his life to interpreting quantum mechanics without complacency or naïveté. His central conclusion comes down to two words: veiled reality.

Beneath the veil of phenomena, he writes in substance, there exists a reality independent of us, but part of it remains forever inaccessible to us: we perceive only what our physical concepts allow us to grasp — and quantum mechanics forbids us from obtaining a complete description of it, that is, an objective one in the strong sense (passage here paraphrased from the book)^[64].

This veiled reality — d'Espagnat sometimes calls it “Being” or “the Independent” — is neither material nor mental in the ordinary sense. It is the beyond of the phenomenal world. The philosopher insists: denying its existence (strict positivism) is as naïve as claiming to know it in detail (classical realism).

Weak objectivity: there are no longer any properties in themselves

D'Espagnat puts forward a decisive distinction:

• Strong objectivity: a property is objective in the sense that it belongs to the object, independently of any observation. This was the ideal of classical physics. Quantum mechanics forbids it.
• Weak objectivity: a property is objective in the sense that all observers obtain the same statistical results. This is the objectivity that quantum theory allows^[65].

In other words: there is no longer any reality-in-itself of elementary objects. There are only common rules that impose themselves on observers. This distinction is subtle but radical. It means that the classical form of materialism — atoms existing in themselves with determined properties, from Democritus to his modern heirs — rests on a presupposition that these results refute within their own proper domain: that of the local properties of microscopic systems.

Neo-materialism and its dead end

Some contemporary philosophers, aware of the difficulty, attempt a “neo-materialism” that broadens the definition of matter to include quantum fields, the quantum vacuum, and information itself. But this strategy fails.

Indeed, quantum fields are abstract mathematical structures. The quantum vacuum is not absolute nothingness but a potential for creation governed by equations. Information, in quantum theory, is encoded in wave functions. If all of this is called “matter”, the word loses its original meaning: it now designates mathematical abstractions, which is precisely what classical materialists sought to deny. As Pharabod-Ortoli note:

“These pieces of matter have turned out to be in reality nothing but non-local mathematical abstractions — that is, capable of extending across all of space — and moreover not obeying determinism. This deals a fatal blow to classical materialism.” — Sven Ortoli & Jean-Paul Pharabod, Le Cantique des Quantiques, La Découverte 1984^[66]

The philosopher Michel Bitbol (CNRS, ENS) likewise stresses that quantum mechanics cannot be interpreted “materialistically” without conceptual torture; rather, it invites a structural realism, or even a metaphysics of information as the primordial level of reality^[67].

The wave function and quantum fields

At the deepest level of the quantum formalism lies quantum field theory (QFT) — the most advanced form of fundamental physics, at the basis of the Standard Model of particles. In this theory, every particle (electron, photon, quark, etc.) is not a primary object but the localized excitation of a field that fills all of space-time. Particles are the “vibrations” of fields; the fields are mathematical structures defined over space-time.

The vacuum itself is full: it is the minimum-energy state of the fields, but it spontaneously fluctuates into virtual particle-antiparticle pairs, indirectly observable through the Casimir effect (1948, measured in 1997) or through the anomalous magnetic moments of leptons (precision to 12 decimal places). This “full vacuum” is neither nothing nor ordinary matter — it is a mathematical potentiality from which empirical entities can emerge.

As Dupont summarizes:

“You cannot put into matter things that are ultimately entities that emerge from our thought. Quantum fields are mathematical objects. The quantum vacuum is a double potential — a potential for the creation of particles, which are themselves potentials of empirical reality.” — Yves Dupont, L'Empreinte de Dieu^[68]

To describe what he was observing, Werner Heisenberg — one of the three or four deepest minds of the twentieth century — explicitly reached back to an Aristotelian category forgotten since the seventeenth century: the potentia, being in potency.

Being in potency and being in act

For Aristotle (Metaphysics, books IX and XII), reality comprises two modes of being:

• Being in act (energeia / entelekheia): what is fully realised, present, measurable.
• Being in potency (dynamis / potentia): what is capable of being or becoming, without yet being actualised.

Saint Thomas will take up this distinction and place it at the heart of his metaphysics: God alone is pure act (actus purus); every creature is composed of act and potency. Modernity — Descartes, Newton, the philosophers of the Enlightenment — abandoned this ontology in favour of a physics of actual extensions alone. Materialist mechanism assumes that there are only fully real things; nothing is "in potency".

Heisenberg's Aristotelian return

Now Heisenberg, in his seminal book Physik und Philosophie (1958), states with clarity:

« The wave function does not itself represent an event, but a tendency to the event. It contains statements about possibilities, or better: about 'potentialities' ('potentia' in Aristotelian philosophy), and these statements are entirely objective: they depend on no observer. » — Werner Heisenberg, Physics and Philosophy, 1958 (author's translation from the English original)^[69]

And further on:

« Aristotle's matter, which is merely 'potentia', is similar to our concept of energy. This potentia enters into 'actuality' through the form, which creates the elementary particle. » — W. Heisenberg, Physics and Philosophy (author's translation from the English original)^[70]

This rediscovery of Aristotle by the creator of matrix mechanics is philosophically immense. It means that:

1. The physical world has two levels of being: potentiality (wave function, pre-measurement state) and actuality (observable measurement result).
2. Reality is not exclusively "what currently is". There is also "what can be".
3. Greek metaphysics, despised by the moderns, is closer to the truth than the materialist metaphysics that replaced it.

Philosophers such as R. E. Kastner, Stuart Kauffman, and Henry Stapp have recently launched a programme called "Taking Heisenberg's potentia seriously" (2017) which systematises this ontology^[71].

Yves Dupont's ontological chain

Yves Dupont proposes a four-level ontological structure:

Dupont comments:

« We have the chain: mathematical wave function closer to reality; it is mathematical because it is the fruit of ideas that are Platonic, outside the world as it were; and these ideas, someone thinks them — the omniscient Mind. » — Yves Dupont^[72]

Each level actualises the preceding one — exactly as in the Catholic metaphysics of continuous creation: God thinks the mathematical essences, these essences structure the field of potentialities, and the potentialities are actualised in empirical experience. This is the metaphysical chain of creation.

Level of this chapter. Names from mathematics appear here (SO(3)/SU(2) and SU(3) groups, spinor, complex numbers): each is explained in one line, and the essential point comes down to a single sentence — mathematics invented for the sheer pleasure of the mind describe nature exactly, as if nature obeyed a thought.

One of the most powerful arguments in quantum apologetics rests on an observation that philosophers have not got over since Pythagoras: pure mathematics describes the real world perfectly — and even better than it ought to.

Wigner's "unreasonable effectiveness"

In 1960, Eugene Wigner (1902-1995), Nobel Prize in Physics 1963, published in Communications on Pure and Applied Mathematics an article that became famous: "The Unreasonable Effectiveness of Mathematics in the Natural Sciences"^[73].

« The enormous effectiveness of mathematics in the natural sciences is something bordering on the mysterious, and there is no rational explanation for it. [...] The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. » — Eugene Wigner, The Unreasonable Effectiveness of Mathematics in the Natural Sciences (1960); author's translation from the English original^[74]

Wigner identifies two levels of miracle:

1. Mathematical concepts are almost always adequate to physical phenomena, even though they were developed for purely abstract reasons.
2. The precision with which mathematics describes nature exceeds all reasonable expectation — for example, the anomalous magnetic moment of the electron is predicted by quantum electrodynamics to 12 decimal places, and experimentally confirmed to that precision.

How is this possible? Wigner speaks of a "wonderful gift which we neither understand nor deserve". But the theistic explanation is immediate: if the universe is designed by a Mind whose thoughts are mathematical, then mathematics describes the universe because it expresses the thought-structure from which it springs.

Gödel and the non-provable infinite

In 1931, the Austrian logician Kurt Gödel (1906-1978) proved two incompleteness theorems that revolutionised the philosophy of mathematics^[75]. The first: in any consistent formal system capable of arithmetic, there exist true propositions that cannot be proved from the axioms. The second: such a system cannot prove its own consistency.

Gregory Chaitin (IBM) extended these results in algorithmic information theory: in any given formal system, only a finite number of bits of the real number Omega (Ω) can be established — a perfectly well-defined real number whose digits are random in the mathematical sense — even though each of these bits is a settled truth (presentation paraphrased here from the book)^[76]. In other words, what is provable in any given system remains bounded, in the face of a mathematical truth that exceeds it.

This raises a vertiginous question: how can the human mind know that such truths exist, if it cannot prove them? The classical answer of mathematical Platonism is that mathematics pre-exists all human construction — it forms a "realm of ideas" (in Plato's sense) that the mathematician discovers rather than creates.

The mathematician Alain Connes (Fields Medal 1982) likewise defends an avowed mathematical realism: mathematics is discovered more than it is constructed (thesis paraphrased here)^[77].

For the mathematician Roger Penrose, Nobel Prize winner 2020, "there is a Platonic mathematical world independent of both the physical world and the mental world"^[78]. For theists, this world consists of the eternal thoughts of God — "in mente Dei" in the Augustinian formula^[79].

Spin: predicted by mathematics, found in nature

The most striking example of pure mathematical prediction is that of spin. In the 1920s, the mathematical study of rotations of space — the rotation group SO(3), that is, the set of all possible rotations, and its mathematical twin SU(2) — had led to the abstract discovery of spinors: computational objects which, when rotated by 360°, end up upside down (like a twisted ribbon), and which must be rotated by 720° to return to their original state. These objects had no apparent physical meaning. Going further: mathematicians and physicists speak of spinorial representations (sign change under rotation by 2π, return to self under rotation by 4π).

Yet Pauli (1925), and then Dirac (1928) showed that the electron itself is described by such a spinor: it has "half-integer spin", meaning it must be rotated by 720° (not 360°) to return to its initial state^[80]. This property, mathematically predicted before being measured, is what makes possible:

• The Pauli exclusion principle (1925), which forbids two electrons from occupying the same quantum state.
• The shell structure of atoms — and thus the periodic table, chemistry, and ultimately life.
• The fermionic nature of ordinary matter (as opposed to bosons such as photons).

Without half-integer spin, all the electrons in atoms would pile up at the lowest energy level — there would be neither chemistry nor biology. The diversity of matter rests on an abstract mathematical structure discovered by group theorists.

Quarks: Gell-Mann's eightfold way

More astonishing still is the episode of the quarks.

In 1961, Murray Gell-Mann (Caltech, Nobel Prize 1969) and independently Yuval Ne'eman (Tel Aviv) classified the hadrons known at the time according to the symmetries of an abstract mathematical structure, the group SU(3) (a group is simply a catalogue of symmetries: the set of transformations that leave an object unchanged) — the "eightfold way", so named in reference to Buddhism^[81].

The classification has a hole: the 10-slot representation contains 9 known particles, but none with the properties of the tenth slot. Gell-Mann predicts in 1962 that a missing particle exists: he names it Ω⁻ (omega minus), predicts its mass (~1680 MeV/c²), its charge (−1), its strangeness (−3), and its spin (3/2)^[82].

In 1964, Nicholas Samios and his team find it at Brookhaven in a bubble chamber — measured mass 1672 MeV, exactly in line with the prediction^[83]. More deeply, Gell-Mann (1964) and Zweig (1964) postulate that all hadrons are composed of three unprecedented elementary particles, the quarks, with fractional charges ±1/3 and ±2/3 — totally unexpected in all prior physics. Once again, pure mathematical prediction, followed by experimental confirmation.

As Dupont emphasizes:

« Tiens, il y a un trou dans la représentation mathématique. Donc il doit bien y avoir trois particules de base quelque part. Et bien, ce sont les quarks. On les a trouvés. C'est sorti d'une idée totalement abstraite. » — Yves Dupont^[84]

Complex numbers: abstract invention, physical reality

Complex numbers (i² = −1) were invented in the 16th century by Cardano and Bombelli as a computational trick to solve cubic equations. For 300 years, they were called "imaginary numbers", regarded as useful fictions. Descartes himself scorned "these roots that are called imaginary, which are nothing but chimeras"^[85].

Yet quantum mechanics, from 1925 onward, showed that the wave function must naturally take complex values. The Schrödinger equation explicitly contains the factor iħ — and a paper by Marc-Olivier Renou, Nicolas Gisin, Antonio Acín et al., published in Nature in 2021, argued experimentally that complex numbers are not a mere notational convenience in the standard quantum formalism^[86]. A preprint not peer-reviewed by Timothée Hoffreumon and Mischa P. Woods (arXiv, 19 March 2026 — state of the debate as of 26 September 2026) has, however, challenged the experimental reach of that conclusion, distinguishing operational independence from product independence^[87]. The technical debate therefore remains open, and no definitive philosophical conclusion can be drawn from this preprint — neither for nor against the necessity of complex numbers. What remains established, however, and is enough for the central philosophical point: observable matter depends on a mathematical formalism far deeper than ordinary materialist intuition.

A Renaissance mathematical fiction proved three centuries later to be indispensable to the description of reality. How to explain this? The theist position: complex numbers exist in themselves, in the divine "realm of ideas", and mathematicians discovered them before physicists had need of them.

The philosophical synthesis of Yves Dupont, in the line of Antoine Suarez, Bernard d'Espagnat, and the founders themselves, can be formulated as follows: the results of quantum mechanics (Bell, PBR) make local materialism untenable and open up a philosophical inference — that of a cause beyond the physical world, which the Catholic tradition identifies as God. This is a debated hypothesis, supported by converging lines of evidence, not a dogma measured in the laboratory.

Mathematics thought by a Mind

First link: mathematics exists independently of the human mind (mathematical Platonism). It structures the physical reality in its entirety (unreasonable effectiveness). It surpasses what any given formal system can prove (Gödel-Chaitin). Conclusion: it must be thought by an infinite Mind, prior to and greater than all human thought.

This is the argument of the Logos, taken up from Plato to Christianity, and formalized by Saint Augustine (De ideis, around 388): the eternal ideas pre-exist in the mind of God, and it is through them that God creates and sustains the world^[88].

Berkeley rediscovered: esse est percipi

In the eighteenth century, the Irish bishop George Berkeley (1685–1753) had proposed a thesis then considered extravagant: « To be is to be perceived » (esse est percipi). According to Berkeley, material objects have no existence independent of perception. But then, who perceives them when no one is there to see them? God. It is His permanent perception that maintains the universe in existence^[89].

This philosophy, mocked for two centuries, finds a strange new relevance with quantum mechanics. If observation is necessary for a particle to pass from potentiality to actuality, and if the whole universe precedes the appearance of human observers, then there must be a primordial Observer who guarantees the coherence of the physical world before and beyond human observation. Antoine Suarez speaks of a « transcendent observer »^[90].

Saint Augustine's continuous creation

This is exactly the Catholic doctrine of continuous creation, formulated by Saint Augustine in De Genesi ad litteram (412–415): God, after having "rested" on the seventh day, does not cease on that account to govern the creatures He has set in place — the sabbatical rest is not a withdrawal of His power (doctrine paraphrased here)^[91].

Saint Thomas takes up this doctrine in the Summa Theologica under the name of conservation of the world (conservatio mundi):

« The conservation of things by God is not accomplished by a new action, but by the continuation of the action by which God gives them being: this action is without motion and without time. » — Saint Thomas Aquinas, Summa Theologica, Iª, q. 104, a. 1, ad 4^[92]

Creation is not a past event followed by the autonomy of nature. It is a continuous act by which God maintains the world in being at every instant. Quantum mechanics, by showing that each particle is « re-actualized » at each measurement by a process with no identifiable physical cause, offers this doctrine an unexpected philosophical illustration — received by faith, not measured by physics: the scientific level (the observed result) and the metaphysical level (its interpretation) remain distinct, and this is in no way a scientific proof of continuous creation.

The Johannine Logos and the transfer of information

For Yves Dupont, what happens at each quantum actualization is a transfer of information: the inaccessible ontological state communicates to the observable empirical state the « answer » to the experimental question posed. This is exactly the logic of the creative Word in Genesis — « God said, and it was so » — and of the Johannine Logos:

« In the beginning was the Word, and the Word was with God, and the Word was God. [...] All things were made through him, and without him nothing was made. » — Gospel according to Saint John 1, 1-3^[93]

Saint John chose the Greek word Logos — which means at once word, reason, mathematical structure, information — to designate that through which God creates. Twenty centuries later, quantum physics rediscovers that matter is, at its most fundamental level, mathematical information transmitted from a non-physical source. The convergence is no incidental coincidence; it is metaphysically profound.

« There is a trace of God in the quantum world. The metaphysical chain runs from the ontological state — linked to the omniscient Mind — to the wave function as potentiality, then to the empirical state. And each of these levels is a transfer of information from the previous one, like the creative Word of Genesis. » — Yves Dupont, L'Empreinte de Dieu dans le monde quantique^[94]

Antoine Suarez's analysis: a mind outside space-time

Antoine Suarez, doctor of physics from ETH Zürich and founder of the Center for Quantum Philosophy in Geneva, pushed the analysis so far as to propose a scientifically testable formulation of the theist thesis. With Valerio Scarani, he proposed as early as 1997 the « before-before » experiment: to use reference frames in relative motion in order to verify whether the non-local correlations really come from « before » the measurement in all reference frames, or only in some. The tests, carried out in Geneva by Gisin's group — first in a relativistic configuration (Zbinden et al., 2001), then with moving beam-splitters (Stefanov et al., 2002) — show that the correlations cannot be explained within space-time: they come from « outside »^[95].

Suarez draws from this that there exists a free cause, outside space-time, at the origin of the non-local correlations — what tradition names God (thesis here paraphrased after Suarez)^[96].

With Alfred Driessen (TU Eindhoven), Suarez edited in 1997 with Kluwer a collective volume entitled Mathematical Undecidability, Quantum Nonlocality and the Question of the Existence of God, which brings together contributions from physicists and theologians on this theme — an academic collective work explicitly formulating the link between quantum non-locality and the question of God^[97]. His General Free Will theorem (2010) extends that of Conway-Kochen in the same direction (see §6)^[98].

An argument often invoked in favour of a theistic reading of quantum physics is that several of its founders themselves — those who devised its equations and understood its paradoxes better than anyone — reached conclusions of an explicitly spiritual or theistic scope. This convergence is partial: other founders — Einstein, Bohr, Born, or the young Dirac — kept their distance, as their positions recalled in this article show. It is no less remarkable for that.

Max Planck — a conscious and intelligent mind (attributed quotation)

Max Planck (1858-1947), founding father of quantum mechanics, Nobel Prize 1918, professor at the University of Berlin, came from a deeply Protestant family (his grandfather and great-grandfather were theologians in Göttingen). In a text attributed to him, presented as a lecture given in Florence in 1944 and entitled Das Wesen der Materie (The Nature of Matter), one reads:

"As a man who has devoted his whole life to the most rational of sciences — the study of matter — I can tell you this as the outcome of my research into atoms: there is no such thing as matter in itself. All matter originates and exists only by virtue of a force which sets the atomic particles in vibration and holds together this most minute solar system of the atom. We must assume the existence of a conscious and intelligent mind behind this force. This mind is the matrix of all matter." — Statement attributed to Max Planck, Das Wesen der Materie (alleged lecture, Florence, 1944)^[99]

Degree of certainty: the alleged archival reference (Archiv zur Geschichte der Max-Planck-Gesellschaft, Abt. Va, Rep. 11 Planck, Nr. 1797) could not be verified by facsimile, and a lecture in Florence in 1944 remains historically doubtful. This quotation therefore stands as secondary testimony — not as an established primary source — and cannot by itself bear the weight of a proof.

Werner Heisenberg — the first sip and the bottom of the glass

Werner Heisenberg (1901-1976), inventor of the uncertainty principle, Nobel Prize 1932, raised in Bavarian Lutheranism, often reflected on the relationship between science and faith. The phrase most often put in his mouth — reported remarks, not found in his published writings — is lent to him by his student and collaborator Hans-Peter Dürr:

"The first gulp from the glass of the natural sciences turns you into an atheist — but at the bottom of the glass, God is waiting." — Remarks attributed to Werner Heisenberg, reported by Hans-Peter Dürr^[100]

Heisenberg set down his reflections on the relations between science, philosophy and faith in his essays and memoirs, notably Der Teil und das Ganze (1969)^[101] — but the phrase about Catholic doctrine sometimes put in his mouth is not to be found there, its exact German wording and page having been impossible to establish.

Paul Dirac — the "mathematician God" (1963, documented)

Paul Adrien Maurice Dirac (1902-1984), Nobel Prize 1933, predictor of antimatter, regarded as the purest theoretical mind of the twentieth century, was reputedly agnostic in his youth. Yet in his 1963 article on the evolution of the physicist's picture of nature, he writes:

"One could perhaps describe the situation by saying that God is a mathematician of a very high order, and that He used very advanced mathematics in constructing the universe." — Paul A. M. Dirac, Scientific American, May 1963^[102]

Degree of certainty: this is the only theistic phrase of Dirac's documented by a primary source. The phrase "There must therefore be a God", sometimes attributed to a remark at the Trieste symposium in 1971 and relayed by apologetic literature, having been impossible to verify verbatim, is withdrawn here.

Eugene Wigner — the miracle of mathematics

Eugene Paul Wigner (1902-1995), Nobel Prize 1963 "for his contributions to the theory of the atomic nucleus and elementary particles", is the author of the thought experiment known as "Wigner's friend". For him, quantum mechanics necessarily implies a role for consciousness in the measurement process. In his collection Symmetries and Reflections (Indiana University Press, 1967), he writes:

"It has not been possible to formulate the laws of quantum mechanics in a fully consistent way without reference to the consciousness." — Eugene P. Wigner, Remarks on the Mind-Body Question (1961), reprinted in Symmetries and Reflections (1967); translated by the author from the English original^[103]

Wigner explicitly acknowledged that this position was a renewed form of idealism in the sense of Berkeley — consciousness plays a primary role in the constitution of observable reality.

Bernard d'Espagnat — reality is non-physical

Bernard d'Espagnat (1921-2015), graduate of the École Polytechnique, professor at the University of Paris-Sud, former director of the CNRS theoretical physics laboratory in Orsay, winner of the 2009 Templeton Prize *"for his explorations of the philosophical implications of quantum physics, which have opened new perspectives on the definition of reality"^[104], devoted forty years to interpreting quantum mechanics. His mature conclusion:

Reality exists, he concludes, but it is not material: matter is empirical — an appearance imposed on our consciousness by a deeper reality, neither material nor mental in the ordinary sense, which quantum mechanics invites us to glimpse without being able to fully describe it (passage here paraphrased from the book)^[105].

Any serious apologetic argument must honestly address the strongest objections. Here are the six main ones — formulated in their most charitable form — along with the responses that can be raised against them.

Objection 1 — Bohm's Non-Local Hidden Variables

The objection: David Bohm (1917-1992) proposed in 1952 an alternative formulation of quantum mechanics, "Bohmian mechanics" or "pilot wave theory", in which particles do have definite trajectories, but are guided by a "quantum potential" that extends instantaneously across all of space. This theory reproduces all the predictions of ordinary quantum mechanics, including entanglement. If it is true, there is no metaphysical mystery: only a non-local realism.

Response. Bohmian mechanics does not erase the problem; it displaces it. It posits non-local influences — that is, instantaneous and beyond space-time — in order to reproduce entanglement. These influences are not reducible to classical physics: they still presuppose a "something" that is not spatial. Moreover, Bohmian mechanics remains a minority position among physicists (less than 10% support in surveys), precisely because it pays a very high conceptual price without solving the real problem. Finally, the PBR theorem (2012) also applies to Bohmian mechanics: the wave function there is necessarily real, which preserves the mathematical-ontological character of reality.

Objection 2 — Everett's Many-Worlds Interpretation

The objection: Hugh Everett III (1957) proposed that all branches of the wave function actualize in parallel universes. At every quantum measurement, the world splits. There is then no more need for "wave packet collapse", no need for an observer, no need for ontological chance. Everything is deterministic — but on the scale of the multiverse. This interpretation, popular among cosmologists (Sean Carroll, David Deutsch), eliminates the metaphysical problem.

Response. First, this interpretation is unfalsifiable by definition: the other universes are inaccessible. It is therefore more metaphysical than standard quantum mechanics. Second, it multiplies ontology in a dizzying way: every second, 10⁸⁰ new universes are born — the very opposite of Ockham's razor. Third, it does not solve the probability problem: if all outcomes occur, why do we observe precisely this world with its precise statistics? Fourth, it does not remove the need for an underlying mathematical structure — the Logos argument applies to it too: who thinks the equations that describe the multiverse?

Objection 3 — Tegmark's Mathematical Multiverse

The objection: Max Tegmark (Our Mathematical Universe, Knopf, 2014) proposes that every consistent mathematical structure exists physically. The universe is just one structure among an infinity of others. Fine tuning and the effectiveness of mathematics are then automatically explained: we necessarily inhabit a universe mathematically compatible with our existence, among all possible universes.

Response. Tegmark's thesis is philosophically audacious but conceptually fragile. First, it presupposes as solved what it claims to explain: why would mathematical structures exist physically? Tegmark identifies "mathematical existence" and "physical existence", which is precisely the thesis to be demonstrated. Next, it multiplies ontology beyond what is reasonable: an infinity of phantom universes to explain ours. Finally and above all, it does not eliminate the ontological chain: these mathematical structures are thought by something. As Yves Dupont writes:

"I find it hard to understand how an infinitely complex structure could be the origin of the world by itself. In philosophy, one rather holds that being is simple — God is simple, He is not infinitely complex. And abstract objects have no causal power of their own." — Yves Dupont^[106]

Objection 4 — The God of the Gaps

The objection: invoking God to explain what science does not yet understand is a "God of the gaps" — a strategy discredited by the history of science, which has progressively filled all the gaps that theologians once invoked.

Response. The thesis defended here is not a "God of the gaps". On the contrary: it is the analysis of what science has actually proven. Bell's theorem, the Aspect experiment, the PBR theorem, the Kochen-Specker theorem, are not gaps — they are positive results established with unassailable precision. They demonstrate that there are no local hidden variables, that the wave function is ontic, that correlations are non-local. These conclusions are as solid as the conservation of energy.

Inferring from these positive results to a non-physical cause is not filling a gap but reading the ontological consequences of an established physics. This is exactly what is done, for example, in the move from the Big Bang to an "absolute beginning" that requires a cause. Prudence consists only in not confusing laboratory protocol and philosophical inference: apologetics speaks of proofs in the sense of converging and convincing arguments, not in the sense of a direct measurement of God by a scientific instrument^[107]. As John Lennox writes: "When an astronomer concludes that a radio signal is artificial and not natural, one does not speak of a 'gap ETI'. One speaks of a legitimate inference to design."^[108]

Objection 5 — Shut Up and Calculate

The objection — the most common among physicists — is the instrumentalist interpretation: quantum mechanics is a spectacularly effective calculation tool, but one with no ontological meaning. As David Mermin (sometimes attributed to Feynman or Weinberg) allegedly said: "Shut up and calculate" (Tais-toi et calcule !)^[109].

Response. This position is respectable as scientific discipline, but it is incoherent as philosophy. To assert "quantum mechanics is a tool with no ontological content" is already a strong ontological claim, which requires justification. Moreover, it ignores the fact that the physicists who achieved the greatest breakthroughs — Planck, Heisenberg, Dirac, Wigner, d'Espagnat, Bell, Suarez — were on the contrary deeply reflective about the meaning of their science.

As the philosopher Michel Bitbol emphasizes:

"The 'Shut up and calculate' position is not a defended philosophical position; it is a refusal of philosophy. Now, to refuse philosophy is to do bad philosophy without knowing it." — Michel Bitbol, Mécanique quantique — Une introduction philosophique, Flammarion, 1996^[110]

Objection 6 — Decoherence Erases Quantum Effects at the Macroscopic Scale

The objection: even if superposition and entanglement exist at the subatomic scale, the phenomenon of decoherence annihilates them as soon as quantum systems interact with their environment. An electron in superposition decoheres within a few femtoseconds upon contact with other particles; a macroscopic object can never exhibit real superposition. Consequently, quantum physics would remain a strictly microscopic phenomenon, with no bearing on cosmology, consciousness, or theology.

Reply. Decoherence is a real and well-understood mechanism, for which the physicist Wojciech Zurek (Los Alamos National Laboratory) provided the most rigorous theory in his work between 1981 and 2003^[111]. It explains why the world appears classical at our scale: entanglement spreads into the macroscopic environment, rendering interference locally undetectable. But it leaves the measurement problem entirely open — why does one definite outcome emerge rather than another? This is precisely the central conclusion of the landmark review by Maximilian Schlosshauer (University of Portland): decoherence solves the preferred basis problem and explains the absence of observable interference, but it “does not solve the measurement problem in the full sense” — that is, it does not tell us which single outcome actually occurs^[112].

More deeply, the arguments supporting a non-materialist reading of quantum physics — the ontological reality of the wave function (PBR theorem, 2012), the non-locality proven by Bell and Aspect, the “unreasonable effectiveness of mathematics” (Wigner) — do not depend at all on the macroscopic survival of quantum effects. They concern the fundamental structure of reality at its most elementary level. Decoherence cannot erase the fact that deep reality is non-local, non-material and mathematical: it merely masks its direct effects at our observable scale.

The Catholic Church holds no dogmatic position on quantum mechanics itself — it is a science, and science falls within the scope of natural reason. But she consistently affirms three principles that illuminate and welcome these discoveries: the natural knowledge of God from creatures, continuous creation, and the dialogue between science and faith as a convergence toward the one truth.

Vatican I: God Knowable by Natural Reason

First, the First Vatican Council (24 April 1870) solemnly defined, in the dogmatic constitution Dei Filius, that God can be known “with certainty by the natural light of human reason, from the things that are made”^[113]. This definition does not confine the natural knowledge of God to a single path: Vatican I makes it possible, and each generation is called to develop it through the science and philosophy of its time. Fine tuning and the quantum results are contemporary illustrations of this: they are not “proofs of God” in the sense of an irrefutable syllogism, but converging indications that natural reason can integrate into an overall metaphysical inquiry.

Saint Paul had written as much from the very beginning:

“For what can be known about God is manifest to them, for God has manifested it to them. Ever since the creation of the world, his invisible attributes — his eternal power and deity — have been clearly perceived through the things that have been made.” — Saint Paul, Letter to the Romans 1:19–20^[114]

Continuous Creation: Creatio Continua in the Catechism

Second, the Magisterium affirms the doctrine of continuous creation. God not only created the universe at an initial instant: he sustains it in being at every moment. The Catechism of the Catholic Church puts it this way:

“Creation has its own goodness and perfection, but it did not spring forth complete from the hands of the Creator. It was created in a state of journeying (in statu viæ) toward an ultimate perfection yet to be attained, to which God has destined it.” — Catechism of the Catholic Church, §302^[115]

“With creation, God does not abandon his creatures to themselves. He not only gives them being and existence, but he sustains them in being at every moment, grants them activity, and brings them to their fulfilment.” — Catechism of the Catholic Church, §301^[116]

This doctrine, already sketched by Saint Augustine (De Genesi ad litteram, IV, 12) and systematised by Saint Thomas (ST, Iª, q. 104), finds an unexpected illumination in quantum mechanics: at each measurement, the wave function reactualises potentiality into actuality, with no locally identifiable physical cause — a striking image of the metaphysical act Augustine attributes to the Creator, as he sustains the world in being “at every moment.” This is an interpretive convergence, not a demonstration: physics describes the result; metaphysics — enlightened by faith — proposes its meaning, in keeping with the distinction recalled above (Vatican I: converging indications, not an irrefutable syllogism).

The Dialogue Between Science and Faith According to John Paul II and Benedict XVI

Finally, John Paul II and Benedict XVI insisted on the dialogue between science and faith as a convergence toward the one truth. In his message to the members of the Pontifical Academy of Sciences gathered in plenary assembly, dated 22 October 1996, John Paul II states:

“For we know that truth cannot contradict truth.” — Saint John Paul II, message to the Pontifical Academy of Sciences, 22 October 1996, §2^[117]

This text is not an address: it is a written message, sent during the Pope's convalescence — he had been operated on for appendicitis on 8 October 1996 — and never delivered before the Academy. It is the lowest level of papal teaching: a message addressed to a scientific academy, not a doctrinal act. And the same text sets out the safeguards that are invariably left uncited alongside the famous sentence: “If the human body takes its origin from pre-existing living matter, the spiritual soul is immediately created by God”; and theories that make the mind emerge from the mere forces of living matter, or that make it a mere epiphenomenon, “are incompatible with the truth of man”^[118].

Earlier, in his letter to the director of the Vatican Observatory, the Pope had framed the issue in striking terms: “Science can purify religion from error and superstition; religion can purify science from idolatry and false absolutes.”^[119] This critical reciprocity is exactly what quantum physics illustrates: it purifies believing thought of any crude representation of matter, and it purifies science of the ideological temptation of materialism.

Benedict XVI, in his address at Regensburg (12 September 2006), recalls that scientific rationality itself presupposes a rationality of the real that it cannot account for by itself:

“The reason of the modern natural sciences, with the Platonic element it contains, bears within itself a question that transcends it and its methodological possibilities. It must simply take as given the rational structure of matter, as well as the correspondence between our mind and the structures that govern nature: its methodological path is founded on this given. But the question ‘why is this so?’ remains.” — Benedict XVI, address at the University of Regensburg, 12 September 2006^[120]

Summary: Quantum Physics at the Service of the Logos

It is in this sense that quantum physics, far from being a challenge to the Catholic faith, spectacularly confirms its metaphysical backdrop: a universe structured mathematically, continuously created by a transcendent Logos, in which matter has being only by participation in a non-material source. The founders — Planck, Heisenberg, Dirac, Wigner, d'Espagnat — needed no catechising to perceive this convergence: it was imposed upon them by their own equations. The believer's task is not to overlay an apologetic onto their results, but to receive those results as a light shed on what Revelation has always said about the world.

• Cosmological fine-tuning — the complementary argument of the 30 finely adjusted physical constants
• The Kalam cosmological argument — the argument from the beginning of the universe
• The argument from contingency — Leibniz and the question of why there is something rather than nothing
• The existence of God — a synthesis of the great rational paths
• Creation — the Catholic doctrine of ex nihilo and continuous creation
• Atheism and zetetics — responses to rationalist objections
• Evolution — Catholic doctrine in the face of evolutionary biology
• Saint Augustine — continuous creation, De Genesi ad litteram
• Saint Thomas Aquinas — the conservatio mundi