The Einstein, Podolsky, and Rosen Paradox in Atomic, Nuclear, and Particle Physics

256 Pages·1999·6.14 MB·English

by  Alexander Afriat

The Einstein, Podolsky,
and Rosen Paradox
in Atomic, Nuclear, and
Particle Physics
The Einstein, Podolsky,
and Rosen Paradox
in Atomic, Nuclear, and
Particle Physics
Alexander Afrial
London SchoolofEconomics
London,England
and
Franco Selleri
UniversityofBari
Bari, Italy
Springer Science+Business Media, LLC
Library of Congress Cataloging-In-PublicatIon Data
Afriat. Alexander.
The Einstein. Podolsky. and Rosen paradox in atomic. nuclear.
and particle physics I Alexander Afriat and Franco Selleri.
p. em.
Includes bibliographical references and index.
1. Einstein-Podolosky-Rosen experiment. 2. Nuclear physics.
1. Sellart, Franco. II. Title.
OC174.12.A38 1998
530.12--dc21 98-43177
CIP
ISBN978-1-4899-0256-6 ISBN978-1-4899-0254-2(eBook)
DOI 10.1007/978-1-4899-0254-2
© SpringerScience+BusinessMediaNewYork1999
OriginallypublishedbyPlenumPress,NewYorkin1999.
Softcoverreprintofthehardcover Istedition1999
http://www.plenum.com
Allrights reserved
10987654321
Nopart ofthis book maybereproduced, stored inaretrieval system, ortransmitted in
anyform orby anymeans, electronic,mechanical. photocopying,microfilming,
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Preface
"Paradox" conjures up arrows and tortoises. But it has a speculative,gedanken
ring: no one would dream of really conjuring up Achilles to confirm that he
catches the tortoise. The paradox ofEinstein, Podolsky,and Rosen, however,is
capable of empirical test. Attempted experimental resolutions have involved
photons, but these are not detected often enough to settle the matter.Kaons are
easier to detect and will soon be used to discriminate between quantum
mechanics and local realism.
Theexistenceofanobjectivephysicalreality,whichhaddisappearedbehind
the impressive formalism of quantum mechanics, was originally intended to be
the central issue of the paradox; locality, like the mathematics used, was just
assumed tohold. Quantum mechanics, with itsincompatiblemeasurements, was
born rather by chance in an atmosphere ofgreat positivistic zeal, in which only
the obviously measurable had scientific respectability. Speculation about occult
"unobservable" quantities was viewed as vacuous metaphysics, which should
surely form no part ofa mature scientific attitude. Soon the "unmeasurable, "
once only disreputable, vanishedaltogether.One hadfirstbeen told not toworry
about it; then, as dogma got more carefully defined, one was assured that the
unobserved wasjust not there. This made it easier not to think about it and to
avoid hazardous metaphysical temptation.
If a theory indicates, in such a climate, that two quantities cannot be
measured at the same time, a first, moderate reaction, is exclusive interest in
one ortheother.Onlyone canbe "implemented" atatime, sowhyworry about
bothtogether?The next step,onceonehasgot usedtothefirst, istoclearup the
ontological background by doing away with the complementary quantity alto
gether.It iswrong to saythatithad apreciserealitybeforemeasurement,forthe
situation before measurement was unmeasured.What littlethere isofrealityhas
to be invoked by measurement, and complementary realities cannot be invoked
together.
Common sense suggested that measurement revealed the value of one
quantity in an imperfectly described reality while it disturbed others; according
v
vi PREFACE
todogma, ontheotherhand,measurement implemented oneaspectofanebulous
but completely described reality to the detriment of complementary features.
With a single particle the matter could not be decided, so another particle was
introduced. The reality criterion of Einstein, Podolsky, and Rosen allowed
elements ofreality corresponding to incompatible descriptions to be assigned
to an object through potential measurements on another.
With contiguous objects, the implementation of an aspect of one might
cause the implementation ofa corresponding aspect ofthe other. According to
quantum mechanics, however,elements ofreality and incompatible descriptions
can be attributed by ameasurement made atanydistance. At first,thepossibility
of action at a distance was hardly even considered or was dismissed as
necromancy: "That would be magic," as Schrodinger said. This magic was,
however,soon enthusiastically embraced bymany,who welcomed itas anexotic
influence that entangled the constituents of a world whose workings would
otherwise have been too straightforward. Ofcourse Einstein not only believed
that the world really existed, but did not accept such nonlocality:
Ifoneaskswhat,irrespectiveofquantummechanics,ischaracteristicoftheworldof
ideasofphysics,oneisfirstofallstruckbythefollowing:theconceptsofphysicsrelate
toarealexternalworld,thatis,ideasareestablishedrelatingtothingssuchasbodies,
fields, etc., which claim a "real existence» that is independentof the perceiving
subject....Itisafurthercharacteristicofthesephysicalobjectsthattheyarethought
ofasarrangedinaspacetimecontinuum.Anessentialaspectofthisarrangementof
thingsinphysicsisthattheymayclaim,atacertaintime,toanexistenceindependent
ofoneanother,providedtheseobjects'aresituatedindifferentpartsofspace'.Unless
onemakesthiskindofassumptionabouttheindependenceoftheexistenceofobjects
whicharefarapartfromoneanotherinspace...physicalthinkinginthefamiliarsense
wouldbeimpossible....Thefollowingideacharacterisestherelativeindependenceof
objectsfarapartinspace(AandB):externalinfluenceonAhasnodirectinfluenceon
B; this is known as the 'principle of contiguity'.... If this axiom were to be
abolished...thepostulationoflawswhichcanbecheckedempiricallyintheaccepted
sense,wouldbecomeimpossible,'!'
If the various parts of the world influenced each other instantaneously, no
regularities could be observed, no laws established.
The existenceofanobjectiverealityisbecoming moreandmoredifficultto
contest. The very practice ofphysics, chemistry,biochemistry,neurophysiology,
etc., strongly supportstherealityofobjects, foritisnowunderstood howsignals
that give rise to perceptions are emitted, how they are propagated, and, at least
partially, how neurophysiological processes transform the signals into percep
tions. The realist postulate so understood is hardly arbitrary because the active
relation between the subject and the worldinwhich he operates establishes, ina
sense, the existence ofan objective reality aposteriori. Realism was character
ized by de la Peiiaand Cetto(2) as follows:
PREFACE vii
Realism is a philosophical term to which there correspond many nonequivalent
notions....In its broad ontological meaning, (objective) realism postulates that
independently ofour theories and prior to them, there is an objective reality; in
otherwords,itpositstheexistenceofanindependentrealitywhichprecedesanyeffort
todiscloseit.Thetaskofscientificendeavourisjusttodisclosethenatureofthisreality
andthelawsofbehaviourofitsthings.Ontheepistemologicalplane,realismopposes
subjectivism;however,thereisarichvarietyofepistemologic versionsofrealism.
Bell derived his celebrated inequality, however, from realism and locality,
andshowedthat itisgrossly violated byquantum mechanics. So itis impossible
to accept realism, locality, and quantum mechanics. The fact that experiments
performed to decide the matter have not refuted a genuine (that is, weak) Bell
inequality iswellknowntotheexperts, butthereisawidespread beliefthatthisis
only due to the nonideality of the measuring devices (in particular the low
efficiencyofavailablephoton counters). Itisalsobelievedthatthisdifficultywill
eventually be overcome'<"
IalwaysemphasizethattheAspectexperimentistoofarfromtheidealinmanyways
counterefficiencyisonlyoneofthem.AndIalwaysemphasizethatthereisthereforea
big extrapolation from practical present-day experiments to the conclusion that
nonlocalityholds. Imyselfchoose tomaketheextrapolation,forthepurpose atleast
ofdirectingmyownfutureresearches.Ifotherpeoplechoosedifferently,Iwishthem
everysuccess andIwillwatchfortheirresults....
The very possibility ofapplying the reality criterion ofEinstein et al. and
deducing Bell's inequality represents a kind ofontologicalviolation, not onlyof
complementarity but also ofHeisenberg's uncertainty relations. It is a violation
accepted only by realists, however, because(4):
Theuncertainty principle"protects" quantummechanics.Heisenbergrecognizedthat
if itwerepossibletomeasuremomentum andposition simultaneouslywithagreater
accuracy, quantum mechanics would collapse. So he proposed that it must be
impossible. Then people sat down and tried to figure out ways of doing it, and
nobody could figure out a way to measure the position of anything-a screen, an
electron, a billiard ball, anything-with any greater accuracy.Quantum mechanics
maintainsitsperilousbutstillaccurateexistence.
Asnoted by Croca(5)the situation israpidly changing.The theoretical resolution
limit ofa microscope was established in the late XIXth century by Abbe and
Rayleigh from diffraction theory as halfwavelength (A/2). The basic working of
these microscopes is a fundamental example ofthe validity ofthe Heisenberg
uncertainty relations. In the middle ofthe 80s this picture changed drastically
with thedevelopment ofanewgeneration ofmicroscopes that inpracticeviolate
Abbe's theoretical barrier. The new generation ofmicroscopes is typified by the
scanning tunnelling electronmicroscope, forwhichBinnigandRohrer(6)received
theNobel prize.The scanning tunnelling microscope triggered awholevarietyof
Scanning ProbeMicroscopes (SPM),wheretheword "Probe" canbereplacedby
Force(SFM), Capacitance (SCM) and Ion Conductance (SICM), opening a new
viii PREFACE
era for the study ofthe micro world. Similar achievements were also obtained in
the optical domain. In 1984 Pohl etal.(7) were able to demonstrate the feasibility
of a scanning apertureless optical microscope based on Near-field Optics
(SNOM) with a spatial resolution of A/20. Ten years later it was possible to
attain a resolution ofA/50 or even better.(8) These authors did not consider the
implications of their accomplishments for fundamental physics, but Croca
stressed that theway leading toaviolationofHeisenberg'sinequalitiesacceptable
by all physicists, whether realists or positivists, seems now to be finally open.
The present book does not try to cover all the important issues concerning
the foundations ofquantum theory, but focuses on the Einstein, Podolsky,and
Rosen paradox. Anotherbook providinganadequatebackgroundforanyone with
a graduate-level knowledge of quantum mechanics to follow the exciting new
developments in this area has recently been written by D. Home(9) who has
managed to give a fair and balanced presentation of different viewpoints,
notwithstanding his own preference for the realist approach.
The book is organized as follows. The first chapter is historical and traces
the developmentofthe EPR paradoxfromthe original argumentofEinstein etal.
(1935) to Wigner's probabilistic formulation ofBell's inequality (1970), dealing
with Bohr's reply to Einstein et al. (1935), Schrodinger's (1935) and Furry's
(1935) contributions, Bohm's simplification (1951), and Bell's inequality (1965)
along the way. In the second chapter the principles ofrealism and locality are
looked at, Bell's inequality is deduced from them, and other formulations ofthe
paradox are considered.Otherways ofdiscriminating between local realism and
quantummechanics are examined inthe third chapter, inwhich the distinction is
also made betweenweak inequalities,deducedfrom localrealism alone and never
violated experimentally, and strong inequalities, which are easier to violate
because they depend on further assumptions regarding detection. The more
general probabilistic treatment, which rests on a generalization ofthe determi
nistic reality criterion used by Einstein et al., is also dealt with. In the fourth
chapter inequalities are deduced to distinguish local realism and quantum
mechanics for pairs of neutral kaons. Proposed solutions, including variable
probability ofdetection, are reviewed in the fifth chapter.
ACKNOWLEDGMENTS. Wewish to express our gratitude to all those with whom
we so often discussed the EPR paradox, Bell's theorem, and all that. We
especially mention Jose R. Croca, Fasma Diele, Augusto Garuccio, Ramon
Risco Delgado, and Caroline H.Thomson.The generousand friendly hospitality
granted to one ofus(A.A.) by the Istituto perRicerche di Matematica Applicata
ofBari and byitsdirectorRoberto Peluso during tenure ofagrant awarded bythe
Consiglio Nazionale delle Ricerche is gratefully acknowledged.
REFERENCES ix
REFERENCES
I. A.EINSTEIN,TheBorn-EinsteinLetters,Macmillan,London(1971),pp.170-171.
2. L. DELA PENA and A. M. CETTO, TheQuantum Dice. An Introduction to Stochastic Electro
dynamics,Kluwer,Dordrecht(1996),p.7.
3. 1.S.BELL,lettertoE.Santos.See:M.FERREROandE.SANTOS,Found.Phys.27,765-800(1997)
atp.787.
4. R.P.FEYNMAN, R.B.LEIGHTONandM.SANDS,TheFeynman Lectures on Physics, Addison
Wesley,Reading(1965),vol.III,p.1-11.
5. 1.R. CROCA, The limitsof Heisenberg's UncertaintyRelations, in: Causality and Locality in
Modern Physics and Astronomy, pp. 1-19, S. Jefferset al. (eds.), Kluwer AcademicPubl.,
Dordrecht(1997).
6. G.BINNIGandH.ROHRER,Rev.Mod.Phys.59,615-625(1987).
7. D.W. POHL,W. DENKandM.LANZ,Appl.Phys.Lett.44,651--653(1984).
8. H.HEINZELMANNandD.W. POHL,Appl.Phys.A59,89-101 (1994).
9. D.HOME,Conceptual FoundationsofQuantum Physics,PlenumPress,NewYorkandLondon
(1997).
Contents
Chapter 1
Early Formulations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I
1.1. The Original Einstein-Podolsky-Rosen Argument. . . . . . . . . . . . I
1.2. Bohr's Reply: Complementarity . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3. Schr6dinger's Extension ofthe Paradox. . . . . . . . . . . . . . . . . . . 9
1.4. Furry's Hypothesis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.5. Bohm's Simplification ofthe Paradox. . . . . . . . . . . . . . . . . . . . 13
1.6. Bohm-Aharonov and the Experimental Issue. . . . . . . . . . . . . . . 16
1.7. EPR Correlations for PairsofNeutral Kaons . . . . . . . . . . . . . . . 18
1.8. Bell's Inequality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
1.9. Additional Assumption and Strong Inequalities . . . . . . . . . . . . . 23
1.l0. Wigner's ProofofBell's Inequality. . . . . . . . . . . . . . . . . . . . . . 27
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
Chapter 2
Bell's Inequality and Its Elementary Background . . . . . . . . . . . . . . 31
2.1. Local Realism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.1.1. The Reality Postulate . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.1.2. The Locality Postulate . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.1.3. The Postulate ofTime's Arrow. . . . . . . . . . . . . . . . . . . . . 37
2.1.4. Definition ofLocal Realism. . . . . . . . . . . . . . . . . . . . . . . 39
2.2. Elementary ProofofBell's Inequality. . . . . . . . . . . . . . . . . . . . . 40
2.2.1. Preliminaries. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.2.2. Demonstration ofBell's Inequality . . . . . . . . . . . . . . . . . . 43
2.2.3. Incompatibility with Quantum Mechanics . . . . . . . . . . . . . 46
2.2.4. Original Proof of Bell's Inequality ~ . . . . . . . . . 48
2.3. Other Formulations ofthe EPR Paradox. . . . . . . . . . . . . . . . . . . 49
2.3.1. Systems without a State . . . . . . . . . . . . . . . . . . . . . . . . . 49
2.3.2. Determination at a Distance ofthe State . . . . . . . . . . . . . . 51
2.4. Criticism ofthe Copenhagen Approach. . . . . . . . . . . . . . . . . . . . 54
xi