Reply to the Comment by A. J. Leggett and Anupam Garg
Reply to the Comment by A. J. Leggett and Anupam Garg
Reply to the Comment by A. J. Leggett and Anupam Garg
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<strong>Reply</strong><br />
However,<strong>the</strong>reexistsnoreason,logicalorphysical,that<br />
statementSalwaysneeds<strong>to</strong>besatisfied.Srepresentsan<br />
assumption<strong>and</strong>restricts<strong>the</strong>discussion<strong>to</strong>situationsin<br />
which<strong>the</strong>actualac<strong>to</strong>fmeasurementcannotaffect<strong>the</strong><br />
outcome.Inouropinion,assumptionS mayindeedbe<br />
applied <strong>to</strong> <strong>the</strong> elements of reality emanating from <strong>the</strong><br />
source<strong>and</strong>oftendenoted<strong>by</strong>λ,butitisagiantleap<strong>to</strong><br />
applyS<strong>to</strong><strong>the</strong>binarydatathatarefound<strong>by</strong>involvement<br />
of sophisticated measurement equipment <strong>and</strong> that may<br />
<strong>the</strong>reforebesignificantlyinfluenced<strong>by</strong>thatequipment.<br />
Forexample,thatequipmentmaycontainsomeformof<br />
“clock”thatimpresses<strong>the</strong>measurementtimet m on<strong>the</strong><br />
outcomes of <strong>the</strong> measurements so that we are justified<br />
<strong>to</strong>introduceatimelabel<strong>and</strong><strong>the</strong>ndealwithfunctions<br />
A i,α,tm ,asiscus<strong>to</strong>maryfors<strong>to</strong>chasticprocesses[5].<br />
The example with doc<strong>to</strong>rs <strong>and</strong> patients presented in<br />
ourletter 1 ,basedonevery-dayexperience<strong>and</strong>requiring<br />
knowledgeofelementaryarithmeticonly,ismacro-realistic<br />
in<strong>the</strong>commonsenseof<strong>the</strong>wordbutnotifmacro-realistic<br />
isusedin<strong>the</strong>narrowsenseof<strong>the</strong>statementSbecauseof<br />
<strong>the</strong>localinfluenceson<strong>the</strong>data.Theexampleshowsthat<br />
aviolationofaBooleinequalitycanbeaccomplished<strong>by</strong><br />
droppingBoole’sconditionofaone-<strong>to</strong>-onecorrespondence<br />
of data <strong>and</strong> experiments. O<strong>the</strong>r explicit examples pertaining<br />
<strong>to</strong> EPR experiments are given in ref. [3]. A<br />
rigoroustreatmen<strong>to</strong>f<strong>the</strong>problemwithin<strong>the</strong>frameworkof<br />
Kolmogorov’sprobability<strong>the</strong>orycanbefoundinref.[6].<br />
Notetha<strong>to</strong>urproperlyprepared“physicalensemble”of<br />
doc<strong>to</strong>rs<strong>and</strong>patientsisdefinitelyrealizable,whichproves<br />
that<strong>the</strong>statementSof<strong>Leggett</strong><strong>and</strong><strong>Garg</strong>doesnotalways<br />
need<strong>to</strong>besatisfied,evenin<strong>the</strong>macroscopicrealm.<br />
REFERENCES<br />
[1] <strong>Leggett</strong>A.J.<strong>and</strong><strong>Garg</strong><strong>Anupam</strong>,EPL,91(2010)40001<br />
(thisissue).<br />
[2] Hess K., Michielsen K.<strong>and</strong>De Raedt H.,EPL,87<br />
(2009)60007.<br />
[3] De Raedt H., Hess K. <strong>and</strong> Michielsen K., <strong>to</strong> be<br />
publishedinJ.Comput.Theor.Nanosci.;http://arxiv.<br />
org/abs/0901.2546.<br />
[4] BooleG.,Philos.Trans.R.Soc.London,152(1862)225.<br />
[5] WilliamsD.,Weighing<strong>the</strong>Odds(CambridgeUniversity<br />
Press,Cambridge)2001.<br />
[6] KhrennikovA.Yu.,InterpretationsofProbability(VSP<br />
InternationalSciencePublishers,Utrecht)1999.<br />
1 Theword“each”in<strong>the</strong>secondlineofpage5shouldbereadas,<br />
“eachdoc<strong>to</strong>r”.<br />
40002-p2
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