Bose, Schrödinger, and the Determinism Debate

 

Copyright: Sanjay Basu

Gained knowledge, lost faith: S. N. Bose, Schrödinger, and the 1944 determinism debate

In October 2026, a physics historian in Geneva, Flavio Del Santo, published three handwritten pages that had sat in the Schrödinger Archive in Vienna for more than 80 years. The title on the first page was "Collapse of Determinism." Most of the coverage ran it as a lost manuscript with a twist. Schrödinger, the man usually filed next to Einstein, had built a hidden-variable model. That is the kind of thing a determinist builds.

The twist that caught me sits a few paragraphs further into Del Santo's paper. He names the two talks that restarted the determinism debate in the 1940s. One was E. T. Whittaker's Guthrie Lecture in London in May 1943. The other was Satyendra Nath Bose's presidential address to the Indian Science Congress in Delhi on 3 January 1944. A report on Bose's address ran in Nature in July 1944 under the same title Schrödinger later used. Del Santo calls that report "the real trigger." Schrödinger's three pages were his unpublished answer to the argument that followed.

So the chain runs Delhi, then London, then Vienna. An address given in India set off the debate that Schrödinger's lost manuscript was written to settle. One caution before going on. Schrödinger's model rebuts Whittaker's specific photon argument, not Bose's. Bose lit the fire. Whittaker is the one Schrödinger aimed at.

I should say why this is personal. I grew up in Calcutta, and the name Bose in my family was spoken the way families speak of a distant branch of the tree. A relation by marriage, a few steps removed, never a photograph on the wall, always a sentence from an elder at the dinner table. Nobody in my house claimed him. But when I was at South Point and first met the words Bose-Einstein statistics in a textbook, that sentence came back, and the physics felt a little less like it belonged to other people. That is the whole connection. It is faint. It is enough to make me read him more carefully than I otherwise would, and to notice when the rest of the world reads past him.

One line is not enough

The popular picture puts everyone on a single line. Einstein at one end, saying God does not play dice. Bohr, Heisenberg and Born at the other. Schrödinger a little to the right of Einstein, holding the cat.

The dice line is real. Einstein wrote it to Born on 4 December 1926: "I am at all events convinced that He does not play dice." But the line misleads, and Pauli said so. On 31 March 1954 he wrote to Born that "Einstein's point of departure is 'realistic' rather than 'deterministic'," and that Einstein "does not consider the concept of 'determinism' to be as fundamental as it is frequently held to be." Two years earlier Einstein had called Bohm's deterministic reconstruction of quantum mechanics "too cheap." He wanted a world that was there whether or not anyone looked. Determinism was a preference, not a creed.

Schrödinger is misfiled too. Del Santo and Nicolas Gisin have argued, in a 2026 note in Nature Reviews Physics, that he embraced indeterminism from his earliest years, following his Vienna mentor Franz Exner, and held that physics was statistical at the bottom before quantum theory arrived.

So the piece needs two axes, not one.

Axis A asks whether individual events are fixed by laws plus initial conditions. Determinist or indeterminist.

Axis B asks whether physics describes a reality that is there without an observer, or only the outcomes of measurements. Realist or instrumentalist.

Draw the second axis and Einstein and Bohr stop being opposites on everything. They become opposites on one thing. And a space opens where Bose, who never signed up to either camp, can be placed with some care. I will draw the map after walking through what he actually said, because the placement is earned by the record and not the other way round.

The faith, and the first cracks

Bose described the old faith better than most people who held it. In 1944 he put it in one sentence: "If the mass, position, and velocity of all the particles were known at any instant, these equations would theoretically enable the physicist to predict the position and motion of every particle at any other subsequent moment." That is Laplace, stated plainly for a Delhi audience.

Statistical mechanics did not break the faith. Boltzmann's probability was a measure of ignorance. You could not track 10^23 molecules, so you averaged. The laws underneath stayed exact. Whittaker and Bose both used the word crypto-deterministic for this. Chance on the surface, clockwork below.

Two things cracked it before quantum mechanics proper. One was Vienna. Exner taught that "Nature's laws are of thoroughly statistical character," and the young Schrödinger carried that to Zurich in 1922. The other was Einstein. In 1916 and 1917 he introduced transition probabilities, the A and B coefficients, and chance walked into the atom through the front door. Bose remembered this. In his 1955 obituary of Einstein, he credited "his famous conception of transitional probabilities, which hold the field even now." The man who would not let God play dice had handed physics the dice.

1924: the first quarrel about chance

On 4 June 1924 a 30-year-old reader in physics at Dacca University wrote to Einstein. "Respected Sir, I have ventured to send you the accompanying article," the letter began. The article derived Planck's law by counting light quanta in a new way. Einstein translated it himself, sent it to Zeitschrift für Physik, and on 2 July sent a postcard calling it "a beautiful step forward." That is the part everyone knows. The counting implied a statistical dependence between quanta that nobody had suspected, and it carries both men's names.

The second paper is the one that matters here. Ten days after the first, on 14 or 15 June, Bose sent a second paper, "Thermal Equilibrium in the Radiation Field in the Presence of Matter." He said he had "arrived at a different law for the probability of elementary processes, which seems to have simplicity in its favour." In it, emission and absorption were two faces of one probabilistic process, and that process depended on the field. Bose did away with Einstein's separate spontaneous emission, the part that happens with no field present.

Einstein published it and attached a note of dissent. "Your principle is not compatible with the following two conditions: (1) The absorption coefficient is independent of the radiation density. (2) The behavior of a resonator in a radiation field should follow from the statistical laws as a limiting case."

Bose did not back down. From Paris on 27 January 1925 he wrote to "Dear Master" that "the additional hypothesis of a spontaneous change, independent of the state of the field, seems to me not necessary." He had tried, he said, "to look at the radiation field from a 'new' standpoint," separating "the propagation of the Quantum of energy from the propagation of the electromagnetic influence." He promised a third paper. It was never published. No copy has turned up in the Einstein Archives.

Partha Ghose, who knew Bose, reads the exchange this way. Bose's hypothesis involved "intrinsically probabilistic interactions," and Einstein's resistance to fundamental randomness made it hard for him to accept. There is an anecdote that fits. Bose thought the width of spectral lines came from the atom's surroundings. Einstein answered that a single excited hydrogen atom alone in an empty universe would still emit. Bose called the reply "sharp and cryptic."

I want to be careful. Bose never wrote a sentence in 1924 saying he was an indeterminist. What the record shows is a 30-year-old comfortable with elementary laws that were probabilistic all the way down, writing to a 45-year-old who was not. Read as interpretation, Ghose's and mine, that is the earliest marker of where Bose stood. On this one question he was a step ahead of his master, and I think he knew it.

Berlin followed. Bose met Einstein there in November 1925 and found him excited by the new quantum mechanics but "very much troubled by the unreasonableness of it all." He heard Born lecture on matrix mechanics in Göttingen in 1926. Einstein set him problems on light-quantum statistics inside the new formalism, and Bose seems to have got nowhere with them. There is also the story Ghose tells about the factor of 2 in the first paper. Bose had explained it by giving the photon a spin. Einstein struck the explanation out. "The old man crossed it out!" Bose said later. He was right and the old man was wrong, and it does not seem to have bothered him much.

1931: two cities, one crisis

Bose wrote in Bengali as well as in physics. In August and September 1931 he published an essay in the Calcutta magazine Parichay called "Vijnaner Sankat," The Crisis of Science. Arnab Rai Choudhuri translated it for Resonance in December 2005.

Three lines from it. "None of the laws of physics are now regarded as sacrosanct." "This is an age of critical self-questioning in physics." Physical laws may not have "the same definiteness as the axioms of geometry." He also asks, and does not answer, whether a theory might rest on quantities nobody has measured. That is a hidden-variable question, posed in Bengali, four years before Grete Hermann and 21 years before Bohm.

On 16 June of the same year Schrödinger lectured in Berlin on "Indeterminism in Physics." "Absolute determinism," he said, "was, in a manner, the fundamental dogma of practical physics." Two men, Calcutta and Berlin, neither aware of the other, both naming 1931 as the year the dogma gave way.

Delhi, 3 January 1944

The address is called "The Classical Determinism and the Quantum Theory." Bose gave it as president of the 31st Indian Science Congress in Delhi on 3 January 1944. It was printed that year as a supplement to Current Science, volume 13, and reprinted in Everyman's Science in 2007. The 2007 reprint's footnote says 30th session and gives different dates. The Bose Archive and the 1944 Proceedings both say 31st session, 3 January. I follow them.

He opens with modesty about speaking outside his own line of work and a promise to dwell on "doubts and criticisms." Then he builds the classical ideal. Continuity, a description in space and time, and "universal laws independent of observers which inexorably determine the course of future events."

Relativity, he says, did not break this. "In spite of its apparently revolutionary character, the theory of relativity upheld the ideal of causality and determinism." He notes Einstein's continuing search for a unified field theory, a search Bose himself would join a decade later.

Then the break. "Facts have been discovered which demonstrate the breakdown of the fundamental equations which justified our belief in determinism." He walks through Planck, Einstein, Bohr, his own statistics, Heisenberg, Schrödinger and Dirac. Schrödinger's waves get a paragraph of their own. They looked at first like a road back to causality, but "later developments" left them as mathematical constructs to be read statistically.

He gives the determinist his best move. "A follower of determinism will interpret such statements as betraying imperfect knowledge, either of the attendant circumstances or of the elementary laws." He illustrates it with a die. You say one in six because you do not know the throw well enough. Then he closes that door with von Neumann and Bohr. No causal completion is possible "without an essential modification or sacrifice of some parts of the existing theory." "We are thus doomed to have only statistical laws for these elementary particles."

The sentence that carries the address is this one. "Fifty years ago the belief in causality and determination was absolute. Today physicists have gained knowledge but lost their faith."

And this one, which tells you what the loss felt like to him: "It is the assertion of the impossibility of even conceiving such elementary determining laws for the atomic system that is disconcerting to the classical physicist."

He sets out the two camps fairly. One side holds causality as "an indispensable postulate." The other looks "upon old determinism as an inhuman conception... which regards humanity as inanimate automata in the hands of an iron law of causation." He does not join either. Del Santo reads his words as clearly betraying sympathy for the second camp. So do I.

But he will not stop there. "The quantum theory is frankly utilitarian in its outlook; but is the ideal of a universal theory completely overthrown?" His answer: "More than ever now, Physics does need such a generalization."

That is the Bose of 1944 in one line. An indeterminist about elementary laws, and not a positivist about physics. He had accepted chance 20 years earlier. He would not accept that physics was only a book of recipes. On the two-axis map that puts him nearer to Schrödinger than to either Bohr or Einstein, which is not where anyone would have guessed.

One irony should be named. Like Whittaker, Bose leaned on von Neumann's 1932 proof that hidden variables were impossible. The proof was too narrow, as Hermann had argued in 1935 and as Bell showed in 1966. Bose's address helped spread a conclusion resting on a theorem that did not prove it.

The argument in Nature, and the twelfth letter

H. T. H. Piaggio, a mathematician at Nottingham, read Bose's address and wrote it up for Nature in July 1944 under the title "Collapse of Determinism." That report, not the address itself, is what reached Europe. From there the sequence, as Del Santo reconstructs it, runs like this.

Eleven letters made it into print. The twelfth sat in Vienna for 80 years.

What do Schrödinger's three pages say? Whittaker had argued that a photon meeting a polarizer could not carry a hidden instruction, because a two-valued instruction cannot reproduce the cosine-squared law. Schrödinger answers that the "absurdity is visibly produced by the simplifying assumption of two discrete parameter values only." Then he builds the counterexample. Give the photon a hidden number x spread evenly between 0 and 1. Let it pass when x is at least the sine squared of the angle. Malus' law, cosine squared of the angle, falls out. He adds a deterministic rule for how x updates after each outcome, so the model survives repeated measurement.

Then the philosophy, which is the part worth keeping. "Experimental evidence + logical deduction can never prove that either the deterministic or the indeterministic view is impossible." And: "The strongest plea in favor of indeterminism is older than quantum mechanics."

Why he never sent it is unknown. Del Santo suggests he may have seen Pelzer's similar models and felt the point had been made.

Here is the center of the piece, and it is subtle. Bose and Whittaker said quantum mechanics plus von Neumann meant determinism was finished. Schrödinger, an indeterminist for 20 years, refused to say determinism was impossible, and built a working deterministic model to prove the refusal. He was defending the possibility of a view he did not hold. Both men leaned toward indeterminism. They differed on whether an impossibility proof can settle a question like this. Bose thought it could. Schrödinger thought no proof ever would. Bell's work two decades later says Schrödinger had the better of it.

Where each man stood 

The horizontal axis is the one everybody draws. The vertical one is the one that separates Einstein from Bohr and puts Bose in Schrödinger's corner.

Einstein. Realist first. Determinism preferred, negotiable. He thought quantum mechanics incomplete, and Bose's 1955 obituary records that he never accepted "the positivistic attitude of the new theory" and saw it as "at best a temporary phase." He introduced transition probabilities in 1917 and objected to Bose's purer probabilistic law in 1924. The dice line is true and beside the point.

Schrödinger. Indeterminist since his Zurich inaugural lecture of 1922, following Exner. Realist, and Einstein's ally on incompleteness. The letters between them in the summer of 1935 produced the cat, and Einstein's keg of gunpowder on 8 August. Einstein wrote to him in 1950: "You are the only contemporary physicist, besides Laue, who sees that one cannot get around the assumption of reality." The 1944 model was a proof of principle, not a confession.

Bohr, Heisenberg, Born. Indeterminists who set reality aside. Bose's own 1944 summary of Bohr: no future theory would restore causality; complementarity; uncertainty. Born's statistical interpretation of 1926 is the cleanest statement of the position.

Bose. 1924. A probabilistic elementary law Einstein would not accept. 1931. No laws sacrosanct. 1944. Sympathy for indeterminism, reliance on von Neumann, and a demand for a universal generalization. Then, from 1952 to 1955, about five papers on Einstein's unified field theory, among them "The Affine Connection in Einstein's New Unitary Field Theory" in the Annals of Mathematics in 1954. Einstein replied on 4 October 1952 and sent a long letter on 22 October 1953.

Does the unified field work mean Bose moved toward Einstein's realism late in life? Or was it loyalty and the pleasure of hard mathematics? No letter settles it. The loyalty was real. "As one who owes much to you and your guidance in life," he wrote on 9 December 1945. He kept his disagreements with Einstein largely private, which is one reason the 1924 quarrel is so little known. My own guess is that the mathematics pulled him and the loyalty let him go. On Axis B I leave him open, a little toward the realist side, and I mark it as my judgment rather than his statement.

My summary, as plain as I can make it. Einstein wanted reality and could live without determinism. Schrödinger wanted reality and preferred indeterminism. Copenhagen accepted indeterminism and set reality aside. Bose had accepted chance in elementary processes since 1924, and refused to let physics settle into what he called a "frankly utilitarian" outlook.

How it ended

Von Neumann's proof was questioned by Grete Hermann in 1935, bypassed in practice by Bohm in 1952, and taken apart by Bell in 1966. Bell's 1964 theorem and the experiments that followed ruled out local hidden variables. Not all hidden variables. Schrödinger's 1944 caution stands.

In 1955 Born arrived on his own at the view Schrödinger had held since 1922, that classical physics is itself indeterministic once you take finite precision seriously. The modern form of that argument, in Gisin and Del Santo, is built on information: a real number with infinitely many digits is not a physical quantity. Bose's 1931 suspicion that physical laws may not have the definiteness of geometry sits comfortably next to it.

Einstein died on 18 April 1955. Ghose has said the news shattered Bose and that he tore up a paper he had been writing. I have not been able to verify the second part and give it here as Ghose's recollection, nothing more.

I will add one thing of my own, because the die passage in the 1944 address invites it. Bose lets the determinist say that one in six is a confession of ignorance. He answers with von Neumann. I would answer differently. I hold with QBism, where a probability is not a property of the die or of the atom but a bet the physicist makes, and the Born rule is a rule for making good bets. On that reading, "gained knowledge, lost faith" is not a loss at all. The faith that was lost was the faith that the odds were out there in the world. What remains is the physicist, the die, and the bet. Bose's demand for a universal generalization survives that move intact. It lands on the agent instead of the atom.

If I ever do future research on this, my list

• Did Schrödinger read Bose's address or only Piaggio's report? The Bose Archive records no letter or meeting between the two men. The Schrödinger Archive in Vienna is the place to check.
• Einstein's letter of 22 October 1953 to Bose. The text is not online. Albert Einstein Archives, Jerusalem; a copy is held at the Institute for Advanced Study.
• The lost third paper of 1925. Family papers, and the S. N. Bose National Centre archive.
• Bose's Bengali essays after 1931 on causality or quantum theory, in Jnan o Bijnan and in "Life, Lectures and Addresses."
• Any reaction from Bose to Piaggio's report or to the Nature debate.
• Our own family material: letters, an annotated book, anyone still alive who heard the sentence I heard.
• People to write to: Partha Ghose (Tagore Centre for Natural Sciences and Philosophy, Kolkata), Flavio Del Santo (Geneva), the S. N. Bose National Centre archive.

Sources

Primary

• Bose, "The Classical Determinism and the Quantum Theory" (1944): Everyman's Science reprint; 1944 Proceedings, Internet Archive
• Bose, "The Crisis of Science" (1931), Resonance translation, Dec 2005
• Bose, "Albert Einstein," Science and Culture, May 1955, reprint
• Bose, Collected Scientific Papers (1994), Bose Archive PDF
• Schrödinger, "Indeterminism in Physics" (1931), Information Philosopher
• Schrödinger, "Collapse of Determinism" (c. 1944 to 1945), transcribed in Del Santo, arXiv 2610.20752
• Piaggio, "Causality or Indeterminism?" Nature 155 (1945), Nature

Secondary

1. Del Santo, "Schrödinger's unpublished hidden-variable model" (2026), arXiv 2610.20752
2. Del Santo and Gisin, "Was Schrödinger ever a determinist?" Nature Reviews Physics 8 (2026), arXiv 2608.10160
3. Del Santo, "Striving for Realism, not for Determinism," arXiv 1807.07656
4. Ghose, "Bose's Probabilistic Interactions, Einstein's Objections," arXiv 2509.15686
5. "The man behind Bose statistics," Physics Today
6. Masters, "Satyendra Nath Bose and Bose-Einstein Statistics," Bose Archive
7. Bose Archive biographical résumé
8. Partha Ghose interview, Nature India, 2024
9. ScienceAlert on the lost manuscript