Reply to the Comment by A. J. Leggett and Anupam Garg

August2010
EPL,91(2010)40002
www.epljournal.org
doi:10.1209/0295-5075/91/40002
Reply
ReplytotheCommentbyA.J.LeggettandAnupamGarg
K.Hess 1(a) ,K.Michielsen 2(b) andH.DeRaedt 3(c)
1 BeckmanInstitute,DepartmentofElectricalandComputerEngineeringandDepartmentofPhysics,
UniversityofIllinois-Urbana,IL61801,USA
2 InstituteforAdvancedSimulation,JülichSupercomputingCentre,ResearchCentreJülichD-52425Jülich,
Germany,EU
3 DepartmentofAppliedPhysics,ZernikeInstituteforAdvancedMaterials,UniversityofGroningen
Nijenborgh4,NL-9747AGGroningen,TheNetherlands,EU
received15May2010;acceptedinfinalform5August2010
publishedonline3September2010
PACS 03.65.Ud–Entanglementandquantumnonlocality(e.g.EPRparadox,Bell’sinequalities,
GHZstates,etc.)
PACS 03.65.Ta–Foundationsofquantummechanics;measurementtheory
PACS 03.65.-w–Quantummechanics
Copyright c○EPLA,2010
IntheirComment[1]onourletter[2],LeggettandGarg
claimthattheyhaveintroducedintheiroriginalpaper
(LG1) a dependence on measurement times. They also
claimthateqs.(HMDR1)and(LG2a)canthereforenot
belinkedinsuchawaythattheargumentsof[2]can
betranscribed.However,(LG1)distinguishesonlythree
timedifferences,andallexperimentalresultscorrespondingtothesametimedifferencesareidenticallylabeledand
thereforetreatedasmathematicallyidentical.WethereforecannotagreewiththeargumentationofLeggettand
Garg:exceptforachangeofnomenclature,eqs.(HMDR1)
and(LG2a)arethesame.Amoreextensivediscussionof
thispointcanbefoundinref.[3].
AccordingtoBoole[4],itislogicallyandmathematicallyimpossibletoviolatetheinequality
|F 12 ±F 13 |1±F 23 , (1)
where F ij = ∑ M
α=1 A i,αA j,α /M, 1i

Reply
However,thereexistsnoreason,logicalorphysical,that
statementSalwaysneedstobesatisfied.Srepresentsan
assumptionandrestrictsthediscussiontosituationsin
whichtheactualactofmeasurementcannotaffectthe
outcome.Inouropinion,assumptionS mayindeedbe
applied to the elements of reality emanating from the
sourceandoftendenotedbyλ,butitisagiantleapto
applyStothebinarydatathatarefoundbyinvolvement
of sophisticated measurement equipment and that may
thereforebesignificantlyinfluencedbythatequipment.
Forexample,thatequipmentmaycontainsomeformof
“clock”thatimpressesthemeasurementtimet m onthe
outcomes of the measurements so that we are justified
tointroduceatimelabelandthendealwithfunctions
A i,α,tm ,asiscustomaryforstochasticprocesses[5].
The example with doctors and patients presented in
ourletter 1 ,basedonevery-dayexperienceandrequiring
knowledgeofelementaryarithmeticonly,ismacro-realistic
inthecommonsenseofthewordbutnotifmacro-realistic
isusedinthenarrowsenseofthestatementSbecauseof
thelocalinfluencesonthedata.Theexampleshowsthat
aviolationofaBooleinequalitycanbeaccomplishedby
droppingBoole’sconditionofaone-to-onecorrespondence
of data and experiments. Other explicit examples pertaining
to EPR experiments are given in ref. [3]. A
rigoroustreatmentoftheproblemwithintheframeworkof
Kolmogorov’sprobabilitytheorycanbefoundinref.[6].
Notethatourproperlyprepared“physicalensemble”of
doctorsandpatientsisdefinitelyrealizable,whichproves
thatthestatementSofLeggettandGargdoesnotalways
needtobesatisfied,eveninthemacroscopicrealm.
REFERENCES
[1] LeggettA.J.andGargAnupam,EPL,91(2010)40001
(thisissue).
[2] Hess K., Michielsen K.andDe Raedt H.,EPL,87
(2009)60007.
[3] De Raedt H., Hess K. and Michielsen K., to be
publishedinJ.Comput.Theor.Nanosci.;http://arxiv.
org/abs/0901.2546.
[4] BooleG.,Philos.Trans.R.Soc.London,152(1862)225.
[5] WilliamsD.,WeighingtheOdds(CambridgeUniversity
Press,Cambridge)2001.
[6] KhrennikovA.Yu.,InterpretationsofProbability(VSP
InternationalSciencePublishers,Utrecht)1999.
1 Theword“each”inthesecondlineofpage5shouldbereadas,
“eachdoctor”.
40002-p2