Observer Created Violation of Bell's Inequalities

3 Pages·0.08 MB·

by  Helmut Dersch

Observer Created Violation of Bell’s Inequalities
∗
Helmut Dersch
University of Applied Sciences Furtwangen
D-78054 Villingen-Schwenningen
Germany
(Dated: January 6, 2003)
LocalsystemsmayappeartoviolateBell’sinequalitiesiftheyareobservedthroughsuitablefilters.
Thenonlocalityleadingtoviolationisoutsidethesystemandcomprisestheobservercomparingthe
outcomes of the typical two wing Bell experiment. An example based on a well known gedanken
experimentbyMerminispresented,andimplicationsfortheinterpretationofBelltestsarediscussed.
PACSnumbers: 03.65.Ta,03.65.Ud
3
0 I. INTRODUCTION II. A LOCAL SYSTEM PERCEIVED TO BE
0 NONLOCAL
2

n ViolationsofBell’sinequalities[1]inquantummechan- The following example demonstrates this point. It
a ics are closely related to the measurement problem[2]
is closely modeled after a gedanken experiment de-
J
arising from the need to somehow fix results of exper-
vised by Mermin[4] to explain Bell’s inequalities to non-
5 iments. This is problematic if the system is in a super-
specialists. Mermins model catches the essence of the

1 positionofstateseachofwhichcorrespondstodistinctive effect and is briefly repeated below:
outcomes. Only one of the states survives, and it is not
v A source throws two particles in opposite directions
clear when and how this is decided. While neither the
0 (left and right wings of the setup). The particles are
1 time nor the mechanism of this reduction or collapse is capturedandanalyzedinindependent measuringinstru-
0 relevant for most practical purposes, it is of crucial im-
ments consistingofanindicator lampwhichcanflashei-
1 portanceforinterpretingBelltests. Someinterpretations
ther red(R) or green(G) [13] and a three position switch
0 of quantum mechanics place this event late in the mea-
(1-2-3). Switch positions are arbitrarily selected and the
3
surementchain,e.g. intheconsciousnessoftheobserver,
0 outcome(RorG)isrecorded. Thestatisticsissuchthat
or they omit the collapse alltogether.
/ identicalswitchsettingsalwaysleadtocoincidentcolours
h
of the corresponding indicator lamps, while overall the
p This paper is motivated by a recent seriesof contribu-
outcome is random, i.e. R and G appear with equal
- tions by Mermin[3] who argues in this direction
t probability. Such a system can be realized with quan-
n
tummechanicaltwoparticlesystemsinthesingletstate:
a
u The three position switch selects angles for polarisation
q Ifweleaveconsciousbeingsoutofthepicture detections (0◦-120◦-240◦ for spin 1/2, or 0◦-60◦-120◦ for
: and insist that physics is only about correla- photons). The red light left indicates detection parallel
v
i tion, then there is no measurement problem and the green light detection perpendicular (antiparallel
X inquantummechanics. Thisisnottosaythat for spin 1/2) to the selected polarisation angle. This as-
r there is no problem. But it is not a problem signement is reversed on the right side. The statistical
a
for the science of quantum mechanics. It is featuresofthisexperimentviolatesomeversionsofBell’s
an everyday question of life: the puzzle of inequalitiesandcannotberealizedusinganyconceivable
conscious awareness. local mechanism.
The variant I am going to discuss assigns particular
instructionsetstoeachoftheparticleswhichareemitted
This notion can be extended to the interpretation of from the source. The instruction set assigns colors to be
flashedbythemeasurementdevice(RorG)toeachofthe
Bell tests: If violations of the famous inequalities are at-
possible settings of the switch (1-2-3). This instruction
tributedtotheobserverthenthereisnoneedfornonlocal
set reads
interpretations of quantum mechanics or of nature inde-
pendent of any applicable theory. It should then be pos- Position 1: R
sible to create violations of Bell-type inequalities also in
classical systems by modelling a suitable observer. This Position 2: G
is the purpose of the present paper which deals with ob-
Position 3: (R+G)
servers who perceive nonlocality in purely local systems.
The last entry (R+G) means that the lamp flickers both
red and green. Flicker seams to invalidate this as a vari-
antofMerminsexperiment. However,wespecify apecu-
∗Electronicaddress: [email protected] liar observer, who is not able to resolve this flicker. He
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perceives random flicker as just one colour, R or G. We with the locality assumption: Rule (c) above states that
furtherspecifyhisperceptionofflicker(case3)asfollows: the perceived outcome of one wing depends on the out-
come of the other. The point is that this influence does
(a) If the observer watches just one wing, he perceives notoccurinthesystemorduringmeasurementbutislo-
flicker as R in half of all cases, and G in the other cated in the observer. Any test of Bell’s inequality (suc-
half. cessful or unsuccessful) has to adopt a connection of the
supposedly independent two wings of the setup, namely
(b) If the observer watches left and right wing simul-
at the moment of recognizing the correlation of the re-
taneously, and the lamps in both wings flicker, he
sults. This unavoidable connection suffices to establish
perceives the same colours for both wings (i.e. ei-
the correlation.
ther RR or GG).
Obviously,thismodelreferstodescriptionsofquantum
(c) If the observer watches left and right wing simulta- mechanics with superpositions of macroscopic states. It
neously, and only one lamp flickers while the other istheconsciousobserverwhocorrelatestojustoneofthe
flashes one single color, then he will get biased in contributing states in the fashion that[3]
hisperceptionofflicker. Flickerwillnowappearto
even though I know that photomultiplier #1
bemoreliketheoppositeofthesinglecolor,specif-
fired, this correlation between me and the
ically the same color will only be observed in 3/8
photomultipliers is associated with merely
of all cases. Example: The combination R on the
one component of a superposition of states
left wing and (R+G) in the right wing is perceived
of the me-photomultipliers system. There is
asRRin3/8andRGin5/8ofallcases. Note that
anothercomponentinwhichIknowthatpho-
this bias does not change the statistics on either
tomultiplier #2 fired.
wing, i.e. it averagesto zero.
ByobservingentangledparticlesinthetwowingBellex-
Randompermutationsoftheinstructiontablearegen-
periment correlation is established by the consciousness
erated by the source, but the two particles emitted at
which couples to the appropriate states of the combined
each instant carry the same set. For this particular ob-
me-left-wing-right-wing system.
servertheexperimentappearsasarealization[14]ofMer-
mins thought experiment. It creates the same statistical
features as the quantum mechanical versions:
III. ADDING WAVEFUNCTION COLLAPSE
• The same switch setting always results in coinci-
dences.
Themodelisabletovisualizeotherpossibleinterpreta-
• Coincidences between left and right occur in 50% tionsofquantummechanics. Anobjectivecollapseofthe
of all cases. wavefunctionindependentoftheobservercorrespondsto
being able to fix the perception of the flickering light
Consider the instruction set above and all nine possible without having seen the other. Later comparison of the
switch combinations: resultsconflict(unlessbias(c)isstrongenoughtochange
the memorized impressions).
Switch Result Coincidences
To rescueBell’s inequalities another channelfor appli-
1 1 R R 1
cationofbias(c)hastobeadoptedinthiscase(following
1 2 R G 0
a proposal by Mermin[5], we call this SF-mechanism).
1 3 R (R+G) 3/8
This channel has to transmit the result of the measure-
2 1 G R 0
ment of each wing to the place at where collapse occurs,
2 2 G G 1
and then apply the observation rules. It is not required
2 3 G (R+G) 3/8
totransmittheparticularswitchsettings. Therefore,col-
3 1 (R+G) R 3/8
lapse or reduction of the wave function may take place
3 2 (R+G) G 3/8
any time later than and completely independent on the
3 3 (R+G) (R+G) 1
measurement apparatus.
4.5
Testable consequences of the different interpretations
ariseifitispossibletofixtheresultsateachwingpriorto
Several more Bell type inequalities are violated, e.g con- the transmissionof bias via SF. We do not know exactly
sider the probability for anticoincidences for three cases what happens to the wave function if it independently
of different switch settings (12,23,13) averaged over all collapses in two different locations. It is often implicitly
instructionsets. Theseamountto0.25ineachcase,sum- assumed that correlation will be lost (other more dras-
mingupto0.75. Localtheoriesrequirethissumtobe at tic events are thinkable), which is also the case in the
least 1.0, etc. model considered here. The finding of strong correlation
Of course, this is no refutation of Bell’s conclusions in actual Bell tests therefore can be taken merely as a
since system plus observer as an entity do not comply proof that collapse occurs after SF-synchronization. A
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similar reasoning has been dubbed the “collapse locality and they are not significantly displaced. It is therefor
loophole” by Kent[6]. notstraightforwardto assumecollapsetimes oflessthan
Only by the additional assumption that collapse is in- 10−6s[7], even 3·10−5s[9] may be problematic. While
stantaneous at the moment the photon enters the de- parameters in collapse theories can be adjusted to yield
tector, or by the notion that measurement is completed faster rates, this introduces other measurable effects like
after final registration of the photon [7] do we come to spontaneous temperature rises[8] which have not been
the conclusion of superluminal speeds. This assumption observed. Therefore, even if action-at-a-distance occurs
of fast collapse is not compelling. In the light of objec- during measurement of entangled states, there is little
tive theories for wave function collapse[8] it may even reason to believe in superluminal speeds.
be more problematicthanalternativeinterpretations: In
the typical two-photon-type[7, 9, 10] EPR-Bohm[11, 12]
experiment we are dealing with a photodetector (e.g.
an avalanche diode), electronics for data acquisition and IV. CONCLUSIONS
storage. The result is fixed by writing to a memory de-
vice. This may be a RAM-chip where fixing is accom-
plished by charging a tiny capacitor. If we consider the We have presented a model that accounts for viola-
twopossiblestatesofthis combinedsystemfordetection tion of Bell type inequalities for a classical local system.
ofthe parallelandperpendicular polarisationstate,they The nonlocality leading to the violation is outside the
do not differ appreciably in any positional coordinate of system and comprises the unavoidable connection of the
the apparatus’macroscopicconstituents,atleastnotbe- two wings of the experiment by the observer comparing
yond the 10−5cm given as typical dimension in collapse the two outcomes. The model relates to interpretations
theories. Thedifferenceisduetothestateofchargescon- ofquantummechanicswithoutcollapseofthewavefunc-
tributing to the current pulse which differs as the signal tion, or with observer mediated collapse.
traverses the electronics. CSL[8] theories come up with As a further application, collapse may be introduced
collapse rates of 10−8s for 1013 displaced nucleons, with at various stages. To preserve the statistics, results of
the rate being proportional to the mass of the particles, both systems need to be transmitted to the location of
and the square of their number. The number of parti- the collapse, but not the particular settings of the mea-
cles (i.e. the electrons contributing to the charge men- surementdevices. It is arguedthat the results ofcurrent
tioned above) involved in the case of EPR-experiments EPR experiments does not require this transmission to
is likely to be smaller, they are lighter than nucleons, be fast.
[1] J. S. Bell, Physics 1, 195 (1964). [9] W. Tittel, J. Brendel, B. Gisin, T. Herzog, H. Zbinden,
[2] J. S. Bell, Physics World 3, 33 (1990). and N. Gisin, Phys. Rev. A 57, 3229 (1998),
[3] N. D. Mermin, Am. J. Phys. 66, 753 (1998), quant-ph/9707042.
quant-ph/9801057. [10] A. Aspect, P. Grangier, and G. Roger, Phys. Rev. Lett.
[4] N.D. Mermin, Physics Today 38, 38 (1985). 47, 460 (1981).
[5] N. D. Mermin, Found. Phys. 29, 571 (1999), [11] A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47,
quant-ph/9807055. 777 (1935).
[6] A.Kent,Causal quantum theory and thecollapse locality [12] D.Bohm,QuantumTheory (Prentice-Hall,1951),p.614.
loophole, quant-ph/0204104. [13] The original example uses two separate lights.
[7] G. Weihs, T. Jennewein, C. Simon, H. Weinfurter, and [14] Itreallyisjustanotherthoughtexperiment,butitistriv-
A.Zeilinger, Phys. Rev.Lett. 81, 5039 (1998). ialtoconstructrealisticelectronic,opticalormechanical
[8] P.Pearle,OpenSystemsandMeasurementinRelativistic versions of this setup.
QuantumTheory (SpringerVerlag,1999),chap.Collapse
Models, quant-ph/9901077.