Quantum Einstein

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Einstein on the Completeness of Quantum Theory

John D. NortonDepartment of History and Philosophy of Science

University of Pittsburgh

l Einstein's Principal Objection to Quantum Theory

l Goes Does Not Play Dice

l Einstein's Positive Program

l Entanglement

l The EPR Argument

l Separability, Locality and Reality

l Later Formulations

l The Einstein Bohr Debate

l Einstein Loses: The Bell Inequalities

l Einstein in Retrospect

l What you should know

For related material, see my"Little boxes: A simple implementation of the Greenberger, Horne, and Zeilinger result forspatial degrees of freedom,"American Journal of Physics, 79(2)(2011), pp. 182-188.

The Einstein of this chapter is a little removed from the Einstein ofpopular imagination. That Einstein is the f irst of the modernphysicists of the 20th century. He is the the genius of 1905 who

established the reality of atoms, laid out special relativity and E=mc2,and made the audacious proposal of the light quantum. This sameEinstein went on to conceive a theory of gravity unlike anything seenbefore and to reawaken the science of cosmology.

In his later years, a different Einstein emerged. The mainstream ofphysics followed the course of the quantum theory of the mid 1920's.Einstein recognized that this new quantum theory enjoyed remarkableempirical successes, so that it clearly had something very right.However he did not believe that future fundamental physics should be tobuild upon it. Rather he thought the way ahead was to develop thegeometrical approach of general relativity into an all encompassing"unified field theory" within which the results of the new quantum theorywould be derived. While he had contributed to its development, Einstein

became the most prominent criticof the new quantum theory.

Einstein's Principal Objection to Quantum

Theory

That Einstein was uncomfortable with quantum theory attracted muchattention and there have been many accounts of his reservations, sometrying to locate their deeper sources. However these different accountsmay vary, there is no doubt of Einstein's principal objection. He believed

that the quantum wave function of some system, the -function, wasnot a complete descriptionof the system. Rather, it provided somesort of statistical summary of the properties of many like systems. (Theterm "-function" is just an old fashioned term for the quantum wave. is the Greek letter"psi.")

HPS 0410 Einstein for Everyone

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An example--NOT Einstein's--will make this a little clearer. Consider theair in the room. As far as ordinary measurements are concerned, the air

forms a continuous fluid. When sound propagates in air, waves ofcompression and rarefaction move through the air. We can arrive at apowerful theory of air and sound solely using the representation of air asa continuous fluid that harbors pressure waves.

We now know that this theory is incomplete. Air is made up of verymany, very tiny molecules. The familiar pressure waves that we use to

represent sound waves really represent the average positionsof themolecules that comprise the air. If we could zoom in on just a small partof the sound wave, we would see something like this (where the figure

is exaggerating the granularity of air):

The perfectly regular, nicely rounded pressure waves can be so uniform

only because they smooth away all the bumps of the individualatoms. They do however provide a serviceable theory of air and soundwaves for many many practical purposes. But they are ultimately anincomplete picture of any particular sound wave. Many differentdistributions of molecules can be smoothed to give the same wave. Soif we are given one wave, we cannot know which particular distribution ofair molecules lies behind it. It could be one of very many.

or or or ...

Eventually the differences between them will matter. In this example, if

we use only the pressure wave picture, it will never be possible to traceout the trajectory of a single molecule, even though the completemechanical description of the system assigns a definite trajectory toeach of the very many molecules.



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Einstein's attitudeto the quantum wave was analogous. The -functionis not a complete description of any particular system. It is a descriptionof the average of many similar systems. For many purposes, this willsuffice, but ultimately it will fail. He wrote:

Goes Does Not Play Dice

If the quantum wave is not a complete description of the physicalsystem, then Einstein has a ready explanation of the probabilitiesthat have now entered into physics in quantum measurementprocesses: they are merely expressions of our ignorance. If an atomhas a probability of one half of radioactive decay over an hour, then allthat really means is that its wave function describes an ensemble ofmany different atomic systems, half of which decay in an hour. Whetherone particular atom in the ensemble will decay in one hour is definitelydeterminable. However we will not be able to discern it if all we know isthe quantum wave associated with it. Whether it decays or not dependsupon properties of that system that have been smoothed away by thequantum wave and thus are unknown to us. It is our ignorance of thesesmoothed away properties that makes a probabilistic assertion the bestwe can do.

Albert

Einstein,

"RemarksConcerning

the Essays

Brought

Together in

this Co-

operative

Volume," (1949)

in, P. A.

Schilpp, ed.,

Albert

Einstein-

Philosopher

Scientist. 2nd

ed. New York:

Tudor

Publishing,1951, pp. 671-72.

"Within the framework of statistical quantum theory thereis no such thing as a complete description of the individualsystem. More cautiously it might be put as follows: Theattempt to conceive the quantum-theoretical description

as the complete description of the individual systemsleads to unnatural theoretical interpretations, whichbecome immediately unnecessary if one accepts theinterpretation that the description refers to ensembles ofsystems and not to individual systems...

Assuming the success of ef forts to accomplish acomplete physical description, the statistical quantumtheory would, within the framework of future physics, takean approximately analogous position to the statisticalmechanics within the framework of classical mechanics. Iam rather firmly convinced that the development oftheoretical physics will be of this type; but the path will belengthy and difficult.

"



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The alternative to this view of incompleteness was to accept that thequantum wave is a complete description of the system. Then theprobabilities of different measurement outcomes reflect an ineliminableunderdetermination in the world. Figuratively speaking, the decision asto which outcome is realized lies outside the physical system. Thephysics tells us that any of several outcomes is possible. Einsteinreferred to this situation in his oft repeated quip that he could not

believe that God plays dice. The remark seems to have been madefrequently, but mostly in conversation. Here is how he put it, when it waswritten:

Einstein's Positive Program

A note of caution is needed. The analogy to pressure waves in air is myanalogy. It suggests that Einstein somehow imagined a real, point-likeparticle hiding behind the quantum wave, a picture not so removed fromthe Bohm hidden variable theory. Perhaps Einstein did entertain apicture like this in his earlier speculations. However what is quitedistinctive about his mature statements of the incompleteness ofquantum theory is that they are extremely cautious in describing the

reality that may be hidden the statistical wave. Einstein remains asuncommittedon the question as he can possibly be.

We do know, however, where Einstein hoped to find the theory that

would ultimately complete and even replace quantum theory. After hecompleted his general theory of relativity in the 1910s, Einsteinembarked on the program of extending it to cover electromagnetism.The general theory of relativity had shown that gravity could beincorporated into the geometry of spacetime if we allowed for a curvedgeometry. The hope was that further generalizations of the geometry ofspacetime would allow a geometrical treatment of electricity and

magnetism. This was his famed goal of a "unified field theory." In theprocess, Einstein hoped, a fuller account of quantum processes mightemerge.

Einstein pursued this project for decades, up to his death. However, the

final results were inconclusive. As he dug himself deeper into theseinvestigations, the mainstream of physics turned in otherdirections.While Einstein was struggling to understand how to unify two forces,gravity and electromagnetism, physics had discovered two more

To Max Born, December 4, 1926. In Born,

Born Einstein Letters, 91.

"Quantum mechanics is very worthy of regard. But an inner voice tells me thatthis not yet the right track. The theory yields much, but it hardly brings uscloser to the Old One's secrets. I, in any case, am convinced that Hedoes

not play dice.

"

To Cornelius Lanczos, March 21, 1942,Einstein Archive, 15-294.

Both quoted from Alice Calaprice, ed., The

Expanded Quotable Einstein. Princeton

University Press, 2000. p.245, p. 251.

"It is hard to sneak a look at God's cards. But that he would choose to playdice with the world...is something I cannot believe for a single moment.

"



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fundamental forces, the weak and strong nuclear forces. And whileEinstein focussed on the geometrical approach that proved so fruitful inthe 1910s, quantum physicists were dealing with a new theory in whichthe idea of an observer independent reality was becoming elusive.

Entanglement

Einstein was relentlessly consistent in his principal complaintconcerning quantum theory: it could not be a complete theory. And hewas correspondingly single-minded in the principal argument he used in

his efforts to establish this incompleteness. The argument dependedessentially on a highly non-classical element of quantum theory thatSchroedinger in the 1930s called "entanglement." (He called it"Verschrnkung", in the same paper in which he presented his catparadox.)

When two statesbecome entangled, a complete account of theproperties of one of the systems is not possible i f it does not includethe other system; and this will be true no matter how far apart the two

systems may be spatially.

Entanglement can be illustrated if we consider the property of position

in space of a quantum particle. If there is just one particle, we havealready seen how the position property is discerned. The particle will ingeneral be represented by a wave spread in space. We measure theposition of the particle and this triggers a collapse to just one point inspace.

In this simplest case, the particle wave is spread over a small interval ofspace. Slightly more complicated situations are possible. The particlemay be spread into discontinuous regions of space. For example, the

wave may have two lobesand we might measure just whether theparticle is in the left or right lobe. The measurement operation has the

effect of collapsing the wave to one of its two lobes with a probabilitydetermined by the magnitude of the two lobes. (In the figure, the twolobes are of equal magnitude, so collapse to each is equally probable.)

How do we get two lobes like this? It is the situation that would arise ifwe confined the particle to a box that had two disconnectedchambers. The particle wave is non-vanishing only inside the twochambers but is zero everywhere else. We do not pe rform ameasurement that discerns the exact position of the particle. Rather, we



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merely measure whether the particle is in the left or right chamber. Themeasurement will collapse the wave to one or other of its two lobes.

Now take the case of two boxes, A and B,each with its own particle.As before the particles are spread over the two chambers. Drawing theirwave functions is a little more complicated and this complication will beorigin of entanglement. A picture of the A particle wave in its A spaceand a picture of the B particle wave in its B space by themselves omitsessential information about how the two particles are correlated.



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In fullest quantum account, we do not have two waves, one for eachparticle. There is only one wave corresponding to the two particles andthat one wave resides not in ordinary three dimensional space, but in

the six dimensional configuration spaceof the two particles. Thissix dimensional space has three axes for the possible positions of the Aparticle; and another three axes for the possible spatial positions of theB particle. Picking one point in the space specifies a position for boththe A and the B particle.

The resulting six dimensional space is impossible to draw easily.

However we get the essential idea if we idealize each particle as living ina one dimensional space: a one dimensional A space and a one

dimensional B space. The corresponding configuration space is a twodimensionalspace. One of its dimensions is A space; and the other isB space. Each point in this two dimensional space gives us one spatialcoordinate for the A particle and one spatial coordinate for the Bparticle. The wave that represents both particles is a wave in the twodimensional configuration space.

Here is one waythat the two particle system wave can be distributed inthis AB space:

The wave is zero everywhere except for two lobes. There is a lobe inthe region that corresponds to the left chamber "L" of box A and the leftchapter "L" of box B; and there is a second lobe in the region of the theright chamber "R" of box A and the right chamber "R" of box B. If we

measure the positionof the A particle, the wave will collapse to oneor other lobe. For concreteness, let us say it is the first lobe; the Aparticle will now definitely be in the left chamber. That same collapse willautomatically induce collapse of the B particle to i ts left lobe andthereby confer on the B particle the property of definitely being in theleft chamber.



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That is the remarkable outcome. As a result of a measurement on the Aparticle, the B particle has acquired a more definite position, even

though the two particles may be widely separated in space.



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The A particle may be in a box on my table. The B particle may be in abox on a space station on Mars. This is entanglement. The properties ofthe B particle are simply not separate from those of the A particle nomatter how far apart they may be in space. We measured the A particlethat resides on earth; and the B particle on Mars was affected. If you are

learning of entanglement for the first time and you are not amazedbythis result, you should go back and re-read the last few paragraphs.

The case just analyzed is the case of the left-right positions of the two

particles perfectly correlated: that is, a "left" for the A particle alwaysgoes with a "left" for the B particle; and a "right" for the A particle alwaysgoes with a "right" for the B particles.

Other cases are possible. Here is t he wave for the case of two

perfectly anti-correlatedparticles. You should reflect on the figureuntil you are convinced that on measurement a "left" on particle Aalways goes with a "right" on particle B; and conversely.

The EPR Argument

T h e differencebetween correlated and anti-correlated particles cannot be represented in the Aor B spaces of the two particles individually. Theycan only be represented in their joint configurationspaces. That is why the use of configuration spaceis so essential. It lets us represent otherwise elusivephysical properties.

Those of you who have seen entanglement discussed elsewhere will probably

have seen it expressed differently, as an impossibility of factoringthecommon wave function into the product of a separate A and a separate B wave.

This is the same idea as expressed here in the figures. If we just take one lobe

of the common wave function--the left lobe, say, it can be formed by multiplying

together the left lobes of the individual wave functions. Undoing the

multiplication is just factoring the one lobe into the two separate waves.

When we have the fully entangled state with both left and right lobes present,

we can no longer represent the combined wave as a simple product of two

waves, one from each of the A and B spaces.



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The argument of the paper depends essentially on exploit ing

entanglement. If one has two entangled systems, one can performmeasurements on one of the systems and thereby learn the propertiesof the other. We have seen how this would work in my example aboveof a particle distributed over two chambers. The key idea is that the

measurement we perform on the firstsystem will not disturb thesecond, so that whatever property we learn of the second system mustbe one it possessed prior to our making the measurement.

This is why entanglement is such a powerful idea. We can allow that ameasurement on the first particle will disturb the first particle. However

EPR insist that a measurement on the first particle will not disturbthesecond particle, which could be removed many light years from the first

in space.

The argument is then completed by noting that we could havemeasuredmany different properties of the first system and, as a result,discovered many properties of the second--many more than anassumption of completeness would allow.

This can be seen in the illustration EPR giveof their generalargument. We imagine two particles that are entangled in such a waythat their momenta and position coordinates are equal but opposite insign. The simplest way to create such an entangled pair is through an

atomic event that ejects two particles of the same type in oppositedirections.

The earliest fully developed and published versionof Einstein'sargument against the completeness of quantum mechanics appeared ina 1935 article co-authored with Boris Podolsky and Nathan Rosen anduniversally known by the initials of its authors, "EPR."

A. Einstein, B. Podolsky, and N. Rosen, "Can

Quantum-Mechanical Description of Physical

Reality Be Considered Complete?" Physical

Review, 47 (1935), pp. 777780.



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Assume the event is such that the total momentum of the pair is zero.Then, if the first particle has momentum +10 units, the other must have

momentum -10 units; and so on for all other possible values. Similarly,the symmetry of the pair assures us that if the first particle has moved toa position +100 units of distance from the creation event, then the othermust be at -100 units of distance; and so on for all other possiblepositions.

It follows that we can discover the properties of the secondparticleat will and without disturbing it, merely by performingmeasurements on the first particle. We could, for example, discern thesecond particle's momentum by measuring the momentum of the firstparticle. Or we could find the position at some moment of the secondparticle by measuring the position of the first.

We do not actually need to performany of the measurements to beassured that the second particle possesses the properties mentioned.The mere possibility of the measurements is enough to assure us thatthe properties are really there. That is, we do not need to know themomentum and position of the second particle to be assured that it hasa definite momentum and position.

We conclude that the second particle must possess both a definiteposition and a definite momentum. The wave representing the secondparticle, however, will in general assign neither definite position nor

definite momentum to it. Therefore, EPR conclude, the quantum wave

is an incomplete description.

Are you sensing something familiarabout the EPR argument but cannot quite place it?What was distinctive about Einstein's early work was his uncanny ability to find ways ofrevealing the hidden, inner structure of matter from its measureable properties. We saw thisin Einstein's work of 1905 in statistical physics. ("Atoms and the Quantum.") There he lookedat the measurable properties of sugar solutions--their viscosity and rates of diffusion--to inferto the size of molecules. The analysis of Brownian motion also led him to an estimate the thesize of molecules. And, most revolutionary, he recognized the signature of atoms in themeasurable thermodynamic properties of heat radiation. That led him to his light quantumhypothesis. In the EPR argument, we see something analogous. Einstein once again wantsto reveal the hidden properties of quantum particles and he finds a way based onmeasurement to get at them. This time the measurements are on remote entangledsystems.

Separability, Locality and Reality

The discussion above summarizes the EPR argument. However it doesnot fully expose the assumptions that it makes. For the argument to

succeed, there are two assumptionsneeded and both have beensubject to quite intense scrutiny in the literature.

The first is separability. EPR tacitly assume that two systems widelyseparated in space have independent existences, so that the state ofone can be specified fully without consideration of the second.

The second assumption is locality. EPR assume that a measurement

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herecannot affect a system there i f here and thereare spacelike

separated, that is, any influence propagating from one place to the othermust proceed faster than light.

Both assumptions are disavowed by standardquantum mechanics.Entangled states violate separability and measurement collapse isinstantaneous. The admissibility and persuasiveness of the EPRargument depend essentially on the extent to which one accepts thesetwo assumptions. One might discard them just because quantumtheory, our most successful theory of matter, does not adhere to them.Or one might adopt them precisely because one senses this is the

beginning of the escape from the deeper woes of the measurementproblem.

The EPR paper did clearly stateone of its premises that is closelyconnected with these last two ideas. It is the "criterion of reality" thattakes a definite stance on a central issue in philosophy: how do weknow what is real and what is not:

Criterion of reality"If, without in any way disturbing a system, we can predict with certainty(i.e. with probability equal to unity) the value of a physical quantity, then

there exists an element of physical reality corresponding to this physicalquantity."

Later Formulations

The EPR paper is the best-known expression of Einstein's argument

against the completeness of quantum theory. The logic of thepaper isa little more tangled than the sketch just given. There is clear evidencethat Einstein felt the tangles unnecessary, attributing them to his co-author. He wrote shortly afterwards to Schroedinger of his concern(June 19, 1935):

"For reasons of language this [paper] was written by Podolsky afterseveral discussions. Still, it did not come out as well as I had originallywanted; rather, the essential thing was, so to speak, smothered by theformalism [Gelehrsamkeit]. (Translation from http://plato.stanford.edu/entries/qt-epr/)

"Einstein's own later statementsof the essential argument were muchbriefer and clearer. Here is version from his article "Physics andReality" (Journal of the Franklin Institute, 221, 1936).

"Consider a mechanical system consisting of two partial systems A andB which interact with each other only during a limited time. Let the function before their interaction be given. Then the Schrdingerequation will furnish the function after the interaction has taken place.Let us now determine the physical state of the partial system A as

completely as possible by measurements. Then quantum mechanicsallows us to determine the function of the partial system B from themeasurements made, and from the function of the total system. Thisdetermination, however, gives a result which depends upon which of thephysical quantities (observables) of A have been measured (for



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instance, coordinates or momenta). Since there can be only onephysical state of B after the interaction which cannot reasonably beconsidered to depend on the particular measurement we perform onthe system A separated from B it may be concluded that the functionis not unambiguously coordinated to the physical state. Thiscoordination of several functions to the same physical state of systemB shows again that the function cannot be interpreted as a (complete)description of a physical state of a single system. Here also thecoordination of the function to an ensemble of systems eliminates

every difficulty.*

[Footnote] *A measurement on A, for example, thus involves a transitionto a narrower ensemble of systems. The latter (hence also its function) depends upon the point of view according to which thisreduction of the ensemble of systems is carried out.

"

Here's the version given in Einstein'sAutobiographical Notes, writtenover a decade after the EPR paper. It is worth quoting at length since itsurely represents Einstein's most considered view, expressed in theway he thought most fitting.

"There is to be a system that at the time t of our observation consists oftwo component systems S

1and S

2, which at this time are spatially

separated and (in the sense of the classical physics) interact with eachother but slightly. The total system is to be described completely interms of quantum mechanics by a known -function, say 12. All

quantum theoreticians now agree upon the following. I f I make acomplete measurement of S

1, I obtain from the results of the

measurement and from 12an entirely definite -function 2of the

system S2. The character of 2then depends upon what kind of

measurement I perform on S1.

Now it appears to me that one may speak of the real state of the partialsystem S

2. To begin with, before performing the measurement on S

1,

we know even less of this real state than we know of a systemdescribed by the -function. But on one assumption we should, in myopinion, insist without qualification: the real state of the system S2is

independent of any manipulation of the system S1, which is spatially

separated from the former. According to the type of measurement Iperform on S1, I get, however, a very different 2for the second partial

system (2, 21, . . . ). Now, however, the real state of S2must be

independent of what happens to S1. For the same real state of S

2it is

possible therefore to f ind (depending on one's choice of themeasurement performed on S1) different types of -function. (One can

escape from this conclusion only by either assuming that themeasurement of S

1(telepathically) changes the real state of S

2or by

denying altogether that spatially separated entit ies possessindependent real states. Both alternatives appear to me entirelyunacceptable.)

If now the physicists A and B accept this reasoning as valid, then B will

have to give up his position that the -function constitutes a completedescription of a real state. For in this case it would be impossible thattwo different types of -functions could be assigned to the identicalstate of S2.



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The statistical character of the present theory would then follownecessarily from the incompleteness of the description of the systemsin quantum mechanics, and there would no longer exist any ground forthe assumption that a future foundation of physics must be based uponstatistics.

It is my opinion that the contemporary quantum theory represents anoptimal formulation of the relationships, given certain fixed basicconcepts, which by and large have been taken from classicalmechanics. I believe, however, that this theory offers no useful point ofdeparture for future development...

"

One remark is especially noteworthy since it makes clear the

importance of locality and separabilityin Einstein's argument. Hecanvasses two possible escapes from his conclusion of theincompleteness of quantum theory. They are "measurement of S

1

(telepathically) changes the real state of S2"--that corresponds to a

violation of locality. The second is "denying altogether that spatiallyseparated entities possess independent real states"--that is the violationof separability.

In plumbing the depths of Einstein's objections to quantum theory, his

concern to preserve separabilityseems to be the deepest and mostfundamental. Certainly separability is logically prior to locality. Onecannot require systems hereto interact locally with systems there

unless one can already distinguish systems herefrom systems there.

That distinction requires separability.

Here's one of Einstein's remarks on the question from a paper"Quantum Mechanics and Reality," Dialectica, 2 (1948), pp. 320-24:

"Without such an assumption of the mutually independent existence ...of spatially distant things, as assumption which originates in everydaythought, physical thought in the sense familiar to us would not bepossible. Nor does one see how physical laws could be formulated andtested without such a clean separation."Translation from Don Howard, "Einstein on Locality and Separability," in Studies in History andPhilosophy of Science, 16 (1985), pp. 171-201 on .

The Einstein Bohr Debate

In all this, Einstein was defending a minority view in the physicscommunity. The task of responding to Einstein was taken up by NielsBohr. The debate in which they engaged was surely one of the

monumental debatesof the 20th century. Here were two titans ofmodern physics with quite opposed positions, struggling to establishtheir view of the meaning of the quantum.

The great difficulty in following the debate, however, is that its canonical history has



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This led Bohr immediately to what seems to be the central idea:

"This crucial point, which was to become a main theme of thediscussions reported in the following, implies the impossibility of anysharp separation between the behaviour of atomic objects and theinteraction with the measuring instruments which serve to define theconditions under which the phenomena appear. In fact, the individualityof the typical quantum effects finds its proper expression in thecircumstance that any attempt of subdividing the phenomena willdemand a change in the experimental arrangement introducing newpossibilities of interaction between objects and measuring instrumentswhich in principle cannot be controlled. Consequently, evidenceobtained under dif ferent exper imental condit ions cannot becomprehended within a single picture, but must be regarded ascomplementary in the sense that only the totality of the phenomenaexhausts the possible information about the objects.

"

been written by Bohrin his contribution to the Schilpp Einstein volume. There onefinds a story of a far-sighted Bohr, who recognizes the profound philosophical re-orientation brought by quantum theory; and a reactionary, recalcitrant Einstein unableto accommodate the novelty. Einstein's view was, we would expect, somewhatdifferent. Unfortunately Einstein gave no extended, published account of hisperspective on the debate. In private correspondence, he was quite disparaging ofBohr, calling him a "talmudic philosopher [who] doesn't give a hoot for 'reality,' whichhe regards as a hobgoblin of the naive..." (Einstein to Schroedinger, June 19, 1935. Translation from DonHoward, "Einstein on Locality and Separability," in Studies in History and Philosophy of Science, 16 (1985), pp. 171-201 on

p. 178.)

Niels Bohr, "Discussions with

Einstein on Epistemological

Problems in Atomic Physics"

in, P. A. Schilpp, ed., Albert

Einstein-Philosopher Scientist.

2nd ed. New York: Tudor

Publishing, 1951.

Available online here.

It is easier to report on Bohr's views than to justify them. So let me attempt just toreport and a few expressions of my own hesitations. The point of view advocated by Bohr

was labeled "complementarity" by Bohr and its starting point was an insistencethat we must describe experiments in classical terms:

"...it is decisive to recognise that, however far the phenomena transcendthe scope of classical physical explanation, the account of all evidence

must be expressed in classical terms. The argument is simply that by the

word "experiment" we refer to a situation where we can tell others what wehave done and what we have learned and that, therefore, the account ofthe experimental arrangement and of the results of the observations mustbe expressed in unambiguous language with suitable application of theterminology of classical physics.

"

The "must be" seems to me excessive and

unwarranted. Somehow, in a way he does not

describe, Bohr is able to preclude the

description of my sensing a flash of light as "I

sensed a photon" where photon is a term

whose meaning is given by quantum theory.

Classical terminology is peculiarily well-

adapted to ordinary sized objects since it

arises in a theory designed to describe them.So it is easy to continue to use classical

terms when we describe quantum experiments

with ordinary sized objects. We should not

confuse that comfort with our having no

alternative.

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Bohr then developed further examples, included the celebrated Einstein"photon in a box" thought experiment.

Overall, on Bohr's account so far, Einstein's approach was decisivelydefeated in the resulting analyses. Needless to say, that did not seem

to be Einstein's view. You can read the detailsof Bohr's discussion inhis textand, for a suggestion on Einstein's side, see Don Howard,"Revisiting the Einstein-Bohr Dialogue."

All this display of realistic measuring devices was a prelude to Bohr'sresponse to the EPRargument. In giving it, he quoted from an earliertext he'd written that captured his central response

"From our point of new we now see that the wording of the above-mentioned criterion of physical reality proposed by Einstein, Podolsky,

and Rosen contains an ambiguity as regards the meaning of theexpression ' without in any way disturbing a system.' Of course there isin a case like that just considered no question of a mechanicaldisturbance of the system under investigation during the last criticalstage of the measuring procedure. But even at this stage there is

The main theme was then illustrated vividly and effectively with aseries of descriptions of the various measurement devices,described in a "semi-serious" realistic style, in order to makeclear that performing one measurement precludes the

performing of another. For example, a position measurementon a propagating particle might employ a slit firmly bolted to thebench through which the particle passes. We then know the exactheight of the particle when it passes through the slit.

A momentum measurement, however, would require a movable slit, whose recoilunder the passage of the particle would let us determine the size of a momentum transferto or from the particle. That essential moveability of the slit precluded the fixed slitarrangement of the position measurement.

The mutual exclusivity of the two arrangements of measurement apparatus is reflected inthe complementarity of the quantities of position and momentum.

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essentially the question of an influence on the very conditions which

define the possible types of predictions regarding the future

behaviour of the system. Since these conditions constitute an inherent

element of the description of any phenomenon to which the term"physical real i ty" can be proper ly at tached, we see that theargumentation of the mentioned authors does not justify their conclusionthat quantum-mechanical description is essentially incomplete. On thecontrary, this description, as appears from the preceding discussion,may be characterised as a rational utilisation of all possibilities ofunambiguous interpretation of measurements, compatible with the finiteand uncontrollable interaction between the objects and the measuring

instruments in the field of quantum theory. In fact, it is only the mutualexclusion of any two experimental procedures, permitting theunambiguous definition of complementary physical quantities, whichprovides room for new physical laws, the coexistence of which might atfirst sight appear irreconcilable with the basic principles of science. It isjust this entirely new situation as regards the description of physicalphenomena that the notion of complementarityaims at characterising.

"

Einstein's direct responseto Bohr's analysis in the same volumewas terse, even severe:

"...it must seem a mistake to permit theoretical description to bedirectly dependent upon acts of empirical assertions, as it seems to meto be intended [for example] in Bohr's principle of complementarity, thesharp formulation of which, moreover, I have been unable to achievedespite much effort which I have expended on it. From my point of view[such] statements or measurements can occur only as specialinstances, viz., parts, of physical description, to which I cannot ascribe

any exceptional position above the rest"

This explanation of the purported failure of the EPR

argument is not easy to comprehendon a firstreading. One expects it to become clearer on re-reading. My experience is that this does not happenand I have been unable to find a cogent interpretationof the text. Whether we should persevere or notremains an issue that divides the philosophy of

physics community. One part remains convinced thatBohr's insights were profound, but poorly expressed,and we should keep seeking their deeper insights.Another holds that Bohr had vivid thoughts that hebelieved, mistakenly, solved foundational problems;but these thoughts were incoherent and the opacityo f Bohr ' s wr i t ing is s imp ly a resu l t o f tha tincoherence.

I belong to the second group that finds Bohr's

thought opaque. My best efforts find Bohradvocating a kind of ultra-empiricism that entangles

epistemology (how we know things) with ontology

(what things are). The idea is that what something

is, is inseparable from how we actually happened

to find out about it.

The EPR argument requires us to imagine two

different measurements that we might perform on

the first system; and from their possible outcomes

we infer to the properties of the second. EPR

presume that it is possible to know what would happen were two different

measurements performed on the system. Bohr's ultra-empiricism asserts that

the two systems would not be the same system if different measurements

were performed on them. For what the system is, involves essentially which

measurement is performed on it. What EPR think of as one system, explored

by different measurements, is, for Bohr's ultra-empiricism, two differentsystems. It follows that EPR are mistaken in imagining that the two

measurements could be performed on the very same system. The first steps

of the EPR argument are blocked.

While this seems to be Bohr's argument, it is opaque to me why Bohr thought

this ultra-empiricism is compatible with quantum theory. It amounts to a denial

that quantum theory supports what philosophers call "counterfactuals"--

statements of what would have happened were, contrary to actual fact, some

other conditions to be the case. Quantum theory clearly supports

counterfactuals. When we have a spread out quantum wave representing some

particle, standard algorithms in the theory tell us what would happen were we

to perform this measurement, or, instead of it, had we performed that

measurement. Generally the description of what would happen is expressed in

terms of the probabilities of various outcomes. But there is no difficulty in

recovering the result. Thus, there seems no problem as far as quantum theory

is concerned when EPR assert what would happen were this measurement oranother incompatible measurement to be performed.



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Not many scholars have the distinction of being told in print by Einsteinthat he has been unable to discern precisely what they are asserting"despite much effort"!

While the final outcome of the debate remains controversial in thephilosophy of physics literature, I can state my own view. In his debate

with Bohr, Einstein won. Einstein's argument is clear and powerful.Bohr's claims are either obscure or indefensible.

Einstein Loses: The Bell Inequalities

One can win a battle, but lose the war. And that is what happened.Einstein won the debate with Bohr, in my view. In his debate with

quantum theory, Einstein lostand unequivocally so.

The reason for his loss did not emerge during his lifetime. They came in

the decade after his death through the work of John S. Bell. The storyof Bell's work and the flood of work it inspired is too large a topic to treatadequately in this short section. We can see only some preliminary

fragments here.

What Bell noticed was a lacuna in Einstein's argument. Einsteincorrectly notedthat measurements on a system would enable theprediction of outcomes of measurements on another system entangledwith it. By imagining different possible measurements on the firstsystem, one then merely used the computations of the quantum theoryto determine the outcomes of the measurements on the secondsystem.

Bell's arguments cannot be developed here. They go beyond the ideasdeveloped above. But they do so only in the technical details, not inmatters of basic principle. To begin, Bell set his analysis in the context

Einstein presumed that all these possibleoutcomes reflected properties possessed bythe second system. That meant that allpossible measurements would end up

revealing a single set of possessedproperties. What Bell showed was that thislast assumption failed. If one assumed that

the computations of quantum theory correctlypredicted the outcomes of measurement,then there was no consistent set of hiddenpropert ies consistent with al l possiblemeasurements. Or, more precisely, if oneassumed separability and locality, then therewas no such set.

The situation is not so removed from the familiar parable of the blind men and the

elephant, but with an essential twist. In it, several blind men feel different parts of the

elephant, each imagining a very different animal on the basis of the limited portion they

sensed.

We, however, recognize that each part they describe can be fitted together to describe

the one familiar animal.

In the quantum case, however, each of the different measurements yields results that

cannot be fitted together to describe a single independent reality. So it is as if the blind

men report parts that cannot be integrated consistently into one animal.



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of a version of the EPRargument laid out by David Bohm. Thatversion was devoted specifically to the measurement of a quantityknown as "spin." It was used since, in the context of quantummechanics, is it actually one of the simplest magnitudes.

Bell then assumed that entangled systems do have properties thatconform with Einstein's expectations of separability and locality; and thatthese hidden properties fix the probabilities of the various outcomesthat arise on measurement. The outcomes are only constrained bythese probabilities, so generally we cannot be sure which ones willappear in any one measurement. However, in many repeated

experiments, definite trends will emerge. They will take the form ofcorrelations between the outcomes returned by measurements on eachof the two entangled particles. What Bell showed is that a characteristicparameter of these correlations will always lie in a small interval of

values. The assertion that they lie in this interval is the Bell inequality.In later treatments, this interval spanned -2 to +2.

The parameter of Bell's inequality can also be determined by assumingthat the measurements conform to the predictions of the quantumtheory. The result of that calculation is that the parameter is greater than2 for the particular case treated. It follows that a theory conforming to

Einstein's expectations cannot yield the samepredictions asquantum theory. Since we have high confidence in quantum theory'spredictions, this was taken as a demonstration of the failure of Einstein'sassumptions.

There was a loophole Was it possibility that the predictions of quantumtheory were incorrect on this parameter? Later experiments, such as

reported byAspectin 1981, affirmed that the quantum predictionswere correct. The loophole was closed.

The final outcome is that the EPR argument for the incompleteness ofquantum theory fails. Whatever reality lies behind quantum processes

does not conform to the presumptions of the EPR argument . Wecannot keep both separability and locality. Something has to begiven up.

F o r m o r e s e e A b n e r S h i m o n y , "Bell's Theorem" , Stanford

Encyclopedia of Philosophy.

An appreciation of Bell's arguments requires requires comfort with thequantity, spin. It is possible, however, to see how the EPR argumentfails using only the simple notions of waves and wave collapse thatwe've developed so far. For such an account see my"Little boxes: A simple implementation of the Greenberger, Horne, and

Zeilinger result for spatial degrees of freedom,"American Journal ofPhysics, 79(2)(2011), pp. 182-188.

Einstein in Retrospect

So what should our verdict be of Einstein's recalcitrance in the face of

the new quantum theory? Here is my view. Einstein was wrong in hissuppositionsof separability and locality in the quantum domain. In his

time, they were entirely reasonable demands and it was very hard to seethen that they would fail. That they do fail is the lesson we have nowlearned.

However, in my view, he was not wrong to resist the foundational

http://www.pitt.edu/~jdnorton/homepage/cv.html#little_boxeshttp://plato.stanford.edu/entries/bell-theorem/


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accounts that surrounded quantum theory in his final decades. He wasquite right to protest that no account of the quantum domain could so

glibly give up the notion of realityas they did. All was not well thenin our accounts of the quantum domain; and all is not well now. Theclearest indication of the trouble is the persistence of the measurementproblem. It shows us that there is something quite unresolved in thefoundations of quantum theory.

In the early years of the theory, as new empirical and theoreticaladvances came in rapid succession, it was easy to overlook these

problems. It is not hard to image the pressures faced by any criticofa new, rising theory. Any new theory has small problems that will beresolved soon enough, we can imagine Einstein hearing from thetheory's proponents. These problem are not usually reasons for graveconcern. Why should one doubt a theory will such a prodigious recordof success? Why hold up real progress with quibbles? Is it notexpedient to suspend criticism?

It took a thinker of strong characterand principle to stand up to thepressures of this expedient view. That thinker was Einstein and he hadlittle company in his hesitations. He wrote to Schroedinger on May 31,1928, at the very start:

"The Heisenberg-Bohr tranquilizing philosophy--or religion?--isdelicately contrived that, for the time being, it provides a gentle pillow forthe true believer from which he cannot very easily be aroused. So lethim lie there."

Quoted from Arthur Fine, The Shaky Game.University of Chicago Press, 1988, p.18.

While we now may not agree with the nature of Einstein's positivecomplaints concerning the newly emerging quantum theory, it is nowabundantly clear that something was not and is not right with the theory.In hindsight that we see that Einstein's resistance was appropriate andshould be celebrated. I can see that clearly now, but I doubt that I would

have had the clarity and character to see it in 1928. I do not have theinsight and principle of Einstein.

What you should know

l What Einstein meant when he asserted the incompleteness of quantumtheory.

l What Einstein intended with his "dice" remark and how it relates to

nineteenth century conceptions of causation.l What quantum entanglement is.l How Einstein used it in his EPR and later arguments aimed at

establishing the incompleteness of quantum theory.l The notions of separability and locality.l How the EPR argument depends upon them.l Some sense of the Einstein-Bohr debate.l That it did not end well for Einstein when Bell's work appeared in the

1960s.l That we should not judge Einstein harshly. HIndsight is 20-20.

opyright John D. Norton. March 27, April 11, April 20, 30, 2010.

Quantum Einstein

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