The Early History of Quantum Entanglement, 1905-1935tam.ung.si/2007/slides/20070828_Howard.pdf ·...

“Early History of Quantum Entanglement,” TAM 2007, August 28, 2007

The Early History of QuantumEntanglement, 1905-1935

Don HowardDepartment of Philosophy andProgram in History and Philosophy of ScienceUniversity of Notre Dame

TAM 2007August 28, 2007

Einstein and Bohr ca. 1927


Entanglement is everywheretoday.


Schrödinger introduces the term, “entanglement,”and the quantum interaction formalism:

Erwin Schrödinger. “Die gegenwärtige Situation in derQuantenmechanik.” Die Naturwissenschaften 23(1935), 807-812, 823-828, 844-849.

Erwin Schrödinger. “Discussion of Probability RelationsBetween Separated Systems.” Proceedings of theCambridge Philosophical Society 31 (1935), 555-662.

Erwin Schrödinger. “Probability Relations BetweenSeparated Systems.” Proceedings of the CambridgePhilosophical Society 32 (1936), 446-452.


Erwin Schrödinger. “Die gegenwärtige Situation in der Quantenmechanik.” Die Naturwissen-schaften 23 (1935), 807-812, 823-828, 844-849.

If two separated bodies, about which, individually, we have maximal knowledge, come into asituation in which they influence one another and then again separate themselves, then thereregularly arises that which I just called entanglement [Verschränkung] of our knowledge of the twobodies. Athe outset, the joint catalogue of expectations consists of a logical sum of the individualcatalogues; during the process the joint catalogue develops necessarily according to the known law[linear Schrödinger evolution] . . . . Our knowledge remains maximal, but at the end, if the bodieshave again separated themselves, that knowledge does not again decompose into a logical sum ofknowledge of the individual bodies.


Einstein and Entanglement, 1905-1927

Einstein ca. 1905 Einstein in the 1920s


Albert Einstein. “Über einen die Erzeugung und Verwandlung des Lichtes betreffendenheuristischen Gesichtspunkt.” Annalen der Physik 17 (1905), 132-148.

Monochromatic radiation of low density (within the domain of validity of Wien's radiationformula) behaves from a thermodynamic point of view as if it consisted of mutually independentenergy quanta of the magnitude Rßí /N.

If we have two systems S1 and S2 that do not interact with each other, we can put

S1 = ö1(W1),S2 = ö2(W2).

If these two systems are viewed as a single system of entropy S and probability W, we have

S = S1 + S2 = ö(W)

and

W = W1 A W2.

The last relation tells us that the states of the two systems are mutually independent events.


Einstein to H. A. Lorentz, 23 May 1909 (EA 16-419).

I must have expressed myself unclearly in regard to the light quanta. That is to say, I am not atall of the opinion that one should think of light as being composed of mutually independent quantalocalized in relatively small spaces. This would be the most convenient explanation of the Wien endof the radiation formula. But already the division of a light ray at the surface of refractive mediaabsolutely prohibits this view. A light ray divides, but a light quantum indeed cannot divide withoutchange of frequency.

As I already said, in my opinion one should not think about constructing light out of discrete,mutually independent points. I imagine the situation somewhat as follows: . . . I conceive of the lightquantum as a point that is surrounded by a greatly extended vector field, that somehow diminisheswith distance. Whether or not when several light quanta are present with mutually overlapping fieldsone must imagine a simple superposition of the vector fields, that I cannot say. In any case, for thedetermination of events, one must have equations of motion for the singular points in addition to thedifferential equations for the vector field.


Mieczys³aw Wolfke. “Antwort auf die Bemerkung Herrn Krutkows zu meiner Note: ‘WelcheStrahlungsformel folgt aus den Annahme der Lichtatome?’” Physikalische Zeitschrift 15(1914), 463-464.

In fact the Einsteinian light quanta behave like the individual, mutually independent molecules of agas . . . . However, the spatial independence of the Einsteinian light quanta comes out even moreclearly from Einstein’s argument itself. From the Wien radiation formula Einstein calculates theprobability W that all n light quanta of the same frequency enclosed in a volume v0 find themselves atan arbitrary moment of time in the subvolume v of the volume v0. The expression for this probabilityreads:

W = (v/v0)n.

This probability may be interpreted as the product of the individual probabilities v/v0 that anindividual one of the light quanta under consideration lies in the subvolume v at an arbitrary momentof time. From the fact that the total probability W is expressed as the product of the individualprobabilities v/v0, one recognizes that it is a matter of individual mutually independent events. Thuswe see that, according to Einstein’s view, the fact that a light quantum lies in a specific subvolume isindependent of the position of the other light quanta .


Paul Ehrenfest and Heike Kamerlingh Onnes. “Simplified Deduction of the Formula from theTheory of Combinations which Planck Uses as the Basis of His Radiation-Theory.”Amsterdam Academy of Sciences. Proceedings . 17 (1914), 870-873. Appendix: “The Contrastbetween Planck’s Hypothesis of the Energy-Grades and Einstein’s Hypothesis of Energy-Quanta.”

Planck does not deal with really mutually free quanta g, the resolution of the multiples of g intoseparate elements g, which is essential in his method, and the introduction of these separate elementshave to be taken “cum grano salis”; it is simply a formal device . . . . The real object which iscounted remains the number of all the different distributions of N resonators over the energy-grades0, g, 2g, . . . with a given total energy P. If for instance P = 3, and N = 2, Einstein has to distinguish23 = 8 ways in which the three (similar) light-quanta A, B, C can be distributed over the space-cells1, 2.

A B C

I 1 1 1II 1 1 2III 1 2 1IV 1 2 2V 2 1 1VI 2 1 2VII 2 2 1VIII 2 2 2


Paul Ehrenfest and Heike Kamerlingh Onnes. “Simplified Deduction of the Formula from theTheory of Combinations which Planck Uses as the Basis of His Radiation-Theory.”Amsterdam Academy of Sciences. Proceedings . 17 (1914), 870-873. Appendix: “The Contrastbetween Planck’s Hypothesis of the Energy-Grades and Einstein’s Hypothesis of Energy-Quanta.” [Continued]

Planck on the other hand must count the three cases II, III, and V as a single one, for all threeexpress that resonator R1 is at the grade 2g, R2 at g; similarly he has to reckon the cases IV, VI andVII as one; R1 has here g and R2 2g. Adding the two remaining cases I (R1 contains 3g, R2 0g) and II(R1 has 0g, R2 3g) one actually obtains

different distributions of the resonators R1, R2 over the energy-grades.We may summarize the above as follows: Einstein’s hypothesis leads necessarily to formula ( ÷) for

the entropy and thus necessarily to Wien’s radiation formula, not Planck’s. Planck’s formal device(distribution of P energy-elements g over N resonators) cannot be interpreted in the sense ofEinstein’s light-quanta.


Albert Einstein. Äther und Relativitätstheorie. Rede gehalten am 5. Mai 1920 and der Reichs-Universität zu Leiden. Berlin: Julius Springer, 1920.

The special theory of relativity does not compel us to deny the aether. We may assume theexistence of an ether; only we must give up ascribing a definite state of motion to it, i.e., we must byabstraction take from it the last mechanical characteristic which Lorentz had still left it. . . .

Think of waves on the surface of water. Here we can describe two entirely different things. Eitherwe may follow how the undulatory surface forming the boundary between water and air alters in thecourse of time; or else–with the help of small floats, for instance–we can follow how the position ofthe individual particles of water alters in the course of time. If the existence of such floats fortracking the motion of the particles of a fluid were a fundamental impossibility in physics–if, in fact,nothing else whatever were discernible than the shape of the space occupied by the water as it variesin time, we should have no ground for the assumption that water consists of movable particles. Butall the same we could characterize it as a medium.

We have something like this in the electromagnetic field. For we may picture the field to ourselvesas consisting of lines of force. If we wish to interpret these lines of force to ourselves as somethingmaterial in the ordinary sense, we are tempted to interpret the dynamic processes as motions of theselines of force, such that each individual line of force is tracked through the course of time. It is wellknown, however, that this way of regarding the electromagnetic field leads to contradictions.

Generalizing we must say this: There may be supposed to be extended physical objects to whichthe idea of motion cannot be applied. They may not be thought of as consisting of particles that allowthemselves to be individually tracked through time. In Minkowski’s idiom this is expressed asfollows: Not every extended structure in the four-dimensional world can be regarded as composed ofworld-threads. The special theory of relativity forbids us to assume the ether to consist of particlesthat can be tracked through time, but the hypothesis of the ether in itself is not in conflict with thespecial theory of relativity. Only we must be on our guard against ascribing a state of motion to theether.


The theory of genidentity has received quite a blowfrom the criticism of the concept of substance, which wasbrought about by a reconsideration of the ether theory.Accordingly it is no longer necessary to consider theworld-lines of a material field as striated in a definite direction; the choice of the grain includes a certainamount of arbitrariness. If the state of a field is graph-cally represented in the customary fashion, as in Fig. 46, then the vertical lines as well as the dotted slanted linesmay be considered as world-lines of the individual“field particles.” Particle A1 may thus be considered asgenidentical with A2, A3 . . . as well as with B2, C3, D4 . . . . Nature does not supply a unique rule in this case. Einstein saw in this fact the collapse of the old concept of substance.1

This means only (and that is how it is formulated byEinstein) that there are material fields in which thisarbitrariness exists. Einstein thus wishes to characterize the metrical field that propagatesgravitational forces. On the other hand, there are also material fields in which there is a naturalstriation; an example is atomic matter, the world-line bundles of which can by no means beconsidered as arbitrary in the sense of Fig. 46.___________________________________

1 A. Einstein, Äther und Relativitätstheorie , Springer 1920.

Reichenbach. Philosophie der Raum-Zeit-Lehre . Berlin and Leipzig: Walter de Gruyter, 1928.


Albert Einstein. “Quantentheorie des einatomigen idealen Gases. Zweite Abhandlung.”Preussische Akademie der Wissenschaften. Physikalisch-mathematische Klasse.Sitzungsberichte (1925), 3-14.

Bose’s theory of radiation and my analogous theory of ideal gases have been reproved by Mr.Ehrenfest and other colleagues because in these theories the quanta or molecules are not treated asstructures statistically independent of one another, without this circumstance being especiallypointed out in our papers. This is entirely correct. If one treats the quanta as being statisticallyindependent of one another in their localization, then one obtains the Wien radiation law; if onetreats the gas molecules analogously, then one obtains the classical equation of state for ideal gases,even if one otherwise proceeds exactly as Bose and I have.

. . .

It is easy to see that, according to this way of calculating [Bose-Einstein statistics], the distribution ofmolecules among the cells is not treated as a statistically independent one. This is connected with thefact that the cases that are here called “complexions” would not be regarded as cases of equalprobability according to the hypothesis of the independent distribution of the individual moleculesamong the cells. Assigning different probability to these “complexions” would not then give theentropy correctly in the case of an actual statistical independence of the molecules. Thus, the formula[for the entropy] indirectly expresses a certain hypothesis about a mutual influence of themolecules–for the time being of a quite mysterious kind–which determines precisely the equalstatistical probability of the cases here defined as “complexions.”


Einstein to Erwin Schrödinger, 28 February 1925 (EA 22-002).

In the Bose statistics employed by me, the quanta or molecules are not treated as being independentof one another. . . . A complexion is characterized through giving the number of molecules that arepresent in each individual cell. The number of the complexions so defined should determine theentropy. According to this procedure, the molecules do not appear as being localized independentlyof one another, but rather they have a preference to sit together with another molecule in the samecell. One can easily picture this in the case of small numbers. [In particular] 2 quanta, 2 cells:

Bose-statistics independent molecules

1st cell 2nd cell 1st cell 2nd cell

1st case !! – 1st case I II –

2nd case I II2nd case ! !

3rd case II I

3rd case – !! 4th case – I II

According to Bose the molecules stack together relatively more often than according to thehypothesis of the statistical independence of the molecules.


Erwin Schrödinger. “Zur Einsteinschen Gastheorie.” Physikalische Zeitschrift 27 (1926), 95-101.

In the new gas theory recently developed by A. Einstein, this surely counts, in general, as theessential point, namely, that an entirely new kind of statistics, the so-called Bose statistics, are to beapplied to the movements of gas molecules. One’s natural instinct rightly resists viewing this newstatistics as something primary, incapable of further explanation. On the contrary, there seems to bedisguised within it the assumption of a certain dependence of the gas molecules upon one another, oran interaction between them, which nevertheless in this form can only be analyzed with difficulty.

One may expect that a deeper insight into the real essence of the theory would be obtained if wewere able to leave as it was the old statistical method, which has been tested in experience and islogically well founded, and were to undertake a change in the foundations in a place where it ispossible without a sacrificium intellectus.

Thus one must simply fashion our model of the gas after the same model of cavity radiation thatcorresponds to what is still not the extreme light quantum idea; then the natural statistics–basicallythe convenient Planck method for summing states–will lead to the Einstein gas theory. That meansnothing else than taking seriously the de Broglie-Einstein undulation theory of moving corpuscles,according to which the latter are nothing more than a kind of “foamy crest” on wave radiation thatconstitutes the underlying basis of everything.


Albert Einstein. “Bestimmt Schrödinger’s Wellenmechanik die Bewegung eines Systemsvollständig oder nur im Sinne der Statistik?” Prussian Academy of Sciences, 5 May 1927. “Nachtrag zur Korrektur.”

I have found that the schema does not satisfy a general requirement that must be imposed on ageneral law of motion for systems.

Consider, in particular, a system Ó that consists of two energetically independent subsystems, Ó1

and Ó2; this means that the potential energy as well as the kinetic energy is additively composed oftwo parts, the first of which contains quantities referring only to Ó1, the second quantities referringonly to Ó2. It is then well known that

Ø = Ø1 @ Ø2 ,

where Ø1 depends only on the coordinates of Ó1, Ø2 only on the coordinates of Ó2. In this case wemust demand that the motions of the composite system be combinations of possible motions of thesubsystems.

The indicated scheme [Einstein’s own hidden variables model] does not satisfy this requirement. In particular, let ì be an index belonging to a coordinate of Ó1, í an index belonging to a coordinateof Ó2. Then Øìí does not vanish.


Bohr and Entanglement, 1924-1927


Bohr to Hans Geiger, 21 April 1925:

I was quite prepared to learn that our proposed point of view aboutthe independence of the quantum processes in separated atoms wouldturn out to be wrong. . . . Not only were Einstein’s objections verydisquieting; but recently I have also felt that an explanation ofcollision phenomena, especially Ramsauer’s results on the penetrationof slow electrons through atoms, presents difficulties to our ordinaryspace-time description of nature similar in kind to the those presentedby the simultaneous understanding of interference phenomena and acoupling of changes of state of separated atoms by radiation. Ingeneral, I believe that these difficulties exclude the retention of theordinary space-time description of phenomena to such an extent that,in spite of the existence of coupling, conclusions about a possiblecorpuscular nature of radiation lack a sufficient basis.

Bohr to James Franck, 21 April 1925

It is, in particular, the results of Ramsauer concerning the penetrationof slow electrons through atoms that apparently do not fit in with theassumed viewpoint. In fact, these results may pose difficulties for ourcustomary spatio-temporal description of nature that are similar inkind to a coupling of changes of state in separated atoms throughradiation. But then there is no more reason to doubt such a couplingand the conservation laws generally.


Walther Bothe. “Über die Kopplung zwischen elementaren Strahlungsvorgängen.” Zeitschriftfür Physik 37 (1926), 547.


Niels Bohr. “The Quantum Postulate and the Recent Development of Atomic Theory.” Nature(Suppl.) 121 (1928).

Now, the quantum postulate implies that any observation of atomic phenomena will involve aninteraction with the agency of observation not to be neglected. Accordingly, an independent reality inthe ordinary physical sense can neither be ascribed to the phenomena nor to the agencies ofobservation. . . .

This situation has far-reaching consequences. On one hand, the definition of the state of a physicalsystem, as ordinarily understood, claims the elimination of all external disturbances. But in that case,according to the quantum postulate, any observation will be impossible, and, above all, the conceptsof space and time lose their immediate sense. On the other hand, if in order to make observationpossible we permit certain interactions with suitable agencies of measurement, not belonging to thesystem, an unambiguous definition of the state of the system is naturally no longer possible, andthere can be no question of causality in the ordinary sense of the word. The very nature of thequantum theory thus forces us to regard the space-time co-ordination and the claim of causality, theunion of which characterizes the classical theories, as complementary but exclusive features of thedescription, symbolizing the idealization of observation and definition respectively.

. . .

According to the quantum theory a general reciprocal relation exists between the maximum sharp-ness of definition of the space-time and energy-momentum vectors associated with the individuals.This circumstance may be regarded as a simple symbolical expression for the complementary natureof the space-time description and the claims of causality.


The Textbooks, 1927-1935


Hermann Weyl. Gruppentheorie und Quantenmechanik, 2nd. ed. Leipzig: S. Hirzel, 1931.

Ch. II, § 10, “The Problem of Several Bodies. Product Space.”

Conditions that insure a maximum of homogeneity within c [a composite system] need not require amaximum in this respect within the partial system a. Furthermore: if the state of a and the state of bare known, the state of c is in general not uniquely specified, for a positive definite Hermitian form2ai,k, iNkN2 in the product space, which describes a statistical aggregate of states c, is not uniquelydetermined by the Hermitian forms

to which it gives rise in the spaces R, S. In this significant sense quantum theory subscribes to theview that “the whole is greater than the sum of its parts,” which has recently been raised to the statusof a philosophical creed by the Vitalists and the Gestalt Psychologists.


Wolfgang Pauli. “Die allgemeinen Principien der Wellenmechanik.” Handbuch der Physik, 2nded. Hans Geiger and Karl Scheel, eds. Berlin: Julius Springer, 1933.

§5 “Interaction of Several Particles. Operator Calculus.”

An additive decomposition of the Hamiltonian operator in independent summands thus correspondsto a product decomposition of the wave function in independent factors. This corresponds to thecircumstance that, in the case of statistically independent particles, the probability W(q1 . . . qf; t) canbe decomposed as a product.


Einstein contra Bohr, 1927-1955


The Photon-Box Thought Experiment


Paul Ehrenfest to Bohr, July 9, 1931

He [Einstein] said to me that, for a very long time already, he absolutely no longer doubted theuncertainty relations, and that he thus, e.g., had BY NO MEANS invented the “weighable light-flashbox” (let us call it simply L-F-box) “contra uncertainty relation,” but for a totally different purpose.

Compare this to:

Max Jammer. The Philosophy of Quantum Mechanics: The Interpretations of QuantumMechanics in Historical Perspective . New York: John Wiley & Sons, 1974.

Einstein, continued Ehrenfest in his letter to Bohr, no longer intends to use the box experiment as anargument “against the indeterminacy relations” but for a completely different purpose.

The actual German text of Ehrenfest’s letter:

“Er sagte mir, daß er schon sehr lange absolut nicht mehr an die Unsicherheitsrelation zweifelt unddass er also z.B. den ‘wägbaren Lichtblitz-Kasten’ (lass ihn kurz L-W-Kasten heissen) DURCHAUSnicht ‘contra Unsicherheits-Relation’ ausgedacht hat, sondern für einen ganz anderen Zweck.”


The published EPR paper


Einstein to Erwin Schrödinger, 19 June 1935

I was very pleased with your detailed letter, which speaks about the little essay. For reasons oflanguage, this was written by Podolsky after many discussions. But still it has not come out as wellas I really wanted; on the contrary, the main point was, so to speak, buried by the erudition [dieHauptsache ist sozusagen durch Gelehrsamkeit verschüttet].

. . .

My way of thinking is now this: properly considered, one cannot get at the talmudist if one doesnot make use of a supplementary principle: the “separation principle.” That is to say: “the secondbox, along with everything having to do with its contents, is independent of what happens withregard to the first box (separated partial systems).” If one adheres to the separation principle, thenone thereby excludes the second point of view, and only the Born point of view remains, accordingto which the above state description is an incomplete description of reality, or of the real states.

. . .

After the collision, the real state of (AB) consists precisely of the real state A and the real state ofB, which two states have nothing to do with one another. The real state of B thus cannot dependupon the kind of measurement I carry out on A. (“Separation hypothesis” from above.) But then forthe same state of B there are two (in general arbitrarily many) equally justified ØB, which contradictsthe hypothesis of a one-to-one or complete description of the real states.


Einstein’s Critique of the Quantum Theory

The argument that Einstein intendedto give:

Separability + Locality Y Incompleteness

(No assumption of Heisenberg indeterminacy)

Separability: Independent real states of affairsin spatially (spatio-temporally?) separatedregions.

Locality: No causal influences betweenspacelike separated regions.

From: James T. Cushing. “A Background Essay.” In James T. Cushingand Ernan McMullin, eds. Philosophical Consequences of QuantumTheory: Reflections on Bell’s Theorem. Notre Dame, IN: University ofNotre Dame Press, 1989.


Niels Bohr. “Natural Philosophy and Human Cultures.” Nature 143 (1938).

The elucidation of the paradoxes of atomic physics has disclosed the fact that the unavoidableinteraction between the objects and the measuring instruments sets an absolute limit to the possibilityof speaking of a behavior of atomic objects which is independent of the means of observation.

We are here faced with an epistemological problem quite new in natural philosophy, where alldescription of experience has so far been based on the assumption, already inherent in ordinaryconventions of language, that it is possible to distinguish sharply between the behavior of objects andthe means of observation. This assumption is not only fully justified by all everyday experience buteven constitutes the whole basis of classical physics . . . . As soon as we are dealing, however, withphenomena like individual atomic processes which, due to their very nature, are essentiallydetermined by the interaction between the objects in question and the measuring instrumentsnecessary for the definition of the experimental arrangement, we are, therefore, forced to examinemore closely the question of what kind of knowledge can be obtained concerning the objects. In thisrespect, we must, on the one hand, realize that the aim of every physical experiment—to gainknowledge under reproducible and communicable conditions—leaves us no choice but to useeveryday concepts, perhaps refined by the terminology of classical physics , not only in all accountsof the construction and manipulation of the measuring instruments but also in the description of theactual experimental results. On the other hand, it is equally important to understand that just thiscircumstance implies that no result of an experiment concerning a phenomenon which, in principle,lies outside the range of classical physics can be interpreted as giving information about independentproperties of the objects.


Albert Einstein. “Remarks Concerning the Essays Brought together in this Co-operativeVolume.” In Albert Einstein: Philosopher-Scientist. Paul Arthur Schilpp, ed. The Libraryof Living Philosophers, vol. 7. Evanston, IL: The Library of Living Philosophers, 1949.

Of the “orthodox” quantum theoreticians whose position I know, Niels Bohr’s seems to me to comenearest to doing justice to the problem. Translated into my own way of putting it, he argues asfollows:

If the partial systems A and B form a total system which is described by its Ø-function Ø(AB),there is no reason why any mutually independent existence (state of reality) should be ascribed tothe partial systems A and B viewed separately, not even if the partial systems are spatiallyseparated from each other at the particular time under consideration. The assertion that, in thislatter case, the real situation of B could not be (directly) influenced by any measurement taken on Ais, therefore, within the framework of quantum theory, unfounded and (as the paradox shows)unacceptable.


Einstein to Max Born, 18 March 1948

I just want to explain what I mean when I say that we should try tohold on to physical reality. We are, to be sure, all of us aware of the situation regarding what will turn out to be the basic foundational concepts in physics: the point-mass or the particle is surely not among them; the field, in the Faraday-Maxwell sense, might be, but not with certainty. But that which we conceive as existing(“real”) should somehow be localized in time and space. That is, the real in one part of space, A, should (in theory) somehow “exist” independently of that which is thought of as real in another part of space, B. If a physical system stretches over the parts of space A and B, then what is present in B should somehow have an existence independent of what is present in A. What is actually present in B should thus not depend upon the type of measurement carried out in the part of space, A; it should also be independent of whether or not, after all, a measurement is made in A.

If one adheres to this program, then one can hardly view the quantum-theoretical description as acomplete representation of the physically real. If one attempts, nevertheless, so to view it, then onemust assume that the physically real in B undergoes a sudden change because of a measurement inA. My physical instincts bristle at that suggestion.

However, if one renounces the assumption that what is present in different parts of space has anindependent, real existence, then I do not at all see what physics is supposed to describe. For what isthought to be a “system” is, after all, just conventional, and I do not see how one is supposed todivide up the world objectively so that one can make statements about the parts.

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