raj bhakta polymathic thesis

8/9/2019 Raj Bhakta Polymathic Thesis

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THE QUANTUMAVE-’S

THE NATURE OF SPACE IN THE

QUANTUM WAVE-FUNCTION

[Document sut!t"eA Po"#m$t%!c T%es!s !n Philosophy

Physic

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Quantum Wave-Function Realism

Introduction

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What is the Wave-Function?

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60B '!mens!ons T%!s !s t%e 2o!nt $t /%!c% t%e 2%!"oso2%!c$" 2(o"ems

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(e"$t!!t# %$s%$e o5e(e' to ou( 2$($'!4m o1 t%e s2$t!$" 2(o2e(t!es o1 ou(

/o("'3 %o/ c$n /e (econc!"e t%e 1$ct t%$t t%e /$e-1unct!on eo"es !n $

s2$ce t%$t !s 2(o2o(t!on$" to t%e tot$" nume( o1 2$(t!c"es !n t%e Un!e(se

un!e(se /%en ou( 2(e!ous 2%#s!cs t%eo(!es su44est t%$t /e "!e !n $ 66-

'D!mens!on$" /o("'? T%!s !s t%e c(u, o1 t%e !ssue $t %$n' $n' t%!s !ssue %$s

t$*en $(!ous '!mens!ons 1o(ms3 $s seen !tse"1 t%(ou4% t%e /o(*s o1 see($"

o1 2P%!"oso2%e(s o1 P2%#s!cs

Ho/ee(3 t%e 'e$te %$s not #et een sett"e' ec$use t%e(e $(e $

m#(!$' o1 !ssues $t 2"$# 4!en t%e e(# 1un'$ment$" $n' 1oun'$t!on$" !ssue

o1 t%e /$e-1unct!on9s s2$t!$" n$tu(e Peo2"e suc% $s A"e(t 2os!ts t%$t ou(

/o("' t%(ee6 '!mens!on$"6-'!mens!on$" s2$ce !s illusory " ec$use t%e

m$t%em$t!cs %!4%"# su44ests /e "!e !n t%!s 6N 6N-con84u($t!on s2$ce3

/%e(e$s 2eo2"e "!*e Monton su44ests /e c$n (econc!"e 6N 6N-con84u($t!on

s2$ce # e,2"o!t!n4 un!.ue m$t%em$t!c$" 2(o2e(t!es $n' s%$2!n4 t%e

onto"o4# to 8t ou( !e/ o1 6D 6-'!mens!on$" s2$ce Ho/ee(3 t%e(e $(e !ssues

'!<cu"t!es /!t% ot% o1 t%ese !e/s3 $s I /!"" coe( !n t%!s 2$2e('!scuss

e"o/ One t%!n4 !s 1o( ce(t$!n3 t%e /$e-1unct!on !s $t t%e %e$(t o1 .u$ntum

mec%$n!cs $n' $''(ess!n4 !ts st$tus /!"" 4!e us $ ette( 2!ctu(e3 o1 not on"#

L



o1 !ts n$tu(e3 ut $"so o1 .u$ntum mec%$n!cs $s /e""

What is Wave-Function Ontology?

Onto"o4# 'e$"s /!t% t%e 2%!"oso2%!c$" stu'# o1 (e$"!t# $n' e,!stence

:Ho1/ee(> In t%!s 2$2e(3 /%en t%e te(m ontological’ !s use' /%$t !s me$nt

!s s!m2"# t%$t$s !t conce(ns t%e n$tu(e $n'o( e,!stence o1 :t%e /$e

1unct!ons2$cet%e to2!c o1 '!scuss!on>’ T%e /$e-1unct!on (e2(esents t%e

st$te o1 $ 2%#s!c$" o)ect $s somet%!n4 "!*e $ com2"e, 8e"' eo"!n4 t%(ou4%

$ %!4%-'!mens!on$" m$t%em$t!c$" s2$ce ot%e(/!se *no/n $s 6N-

con84u($t!on6N-con84u($t!on s2$ce :A"e(t J6> T%!s !s one o1 t%e cent($"

$s2ects $t !ssue /%en /e $ttem2t to '!sce(n t%e /$e-1unct!on’s onto"o4!c$"

st$tus T%!s ($!ses t%e .uest!on %o/ c$n /e t%!n* o1 $ .u$ntum s#stem $s

eme''e' !n t%(ee6 '!mens!on$"6-'!mens!on$" met(!c s2$ce !1 t%e /$# t%$t

!t !s est (e2(esente' /!t%!n ou( 2%#s!c$" t%eo(# $22e$"s to $ muc% %!4%e(

'!mens!on$"3 $n' non-met(!c con84u($t!on s2$ce? T%!s .uest!on 1o(ces us to

mo(e c$(e1u""# e,$m!ne ou( un'e(st$n'!n4 t%e n$tu(e o1 not on"# t%e /$e-

1unct!on’s s2$ce3 ut$n' $"so o1 ou( $c*4(oun' o( 2(esu22ose' met(!c

s2$ce As !t /!"" e '!scusse'3 tT%e(e $(e t/o m$!n $22(o$c%es to t%!s T%e

8(st !e/ !s %e"' # D( A"e(t3 /%o conten's t%$t s!nce t%e /$e-1unct!on

eo"es t%(ou4% t%e %!4%e(-'!mens!on$" s2$ce o1 6N-con84u($t!on6N-

con84u($t!on s2$ce3 ou( 2%#s!c$" s2$ce !s $ctu$""# $ sus2$ce o1 t%e 6N-

K



con84u($t!on6N-con84u($t!on s2$ce :A"e(t JJ> T%e secon' !e/ !s %e"' #

Monton3 /%o conten's t%$t t%e 6N-con84u($t!on6N-con84u($t!on s2$ce !s

)ust $ m$t%em$t!c$" (e2(esent$t!on t%$t 'esc(!es t%e /$e-1unct!on $n' !s

not to e t$*en !n $ "!te($" sense to %$e $n# 2%#s!c$" !m2"!c$t!on on t%e

n$tu(e o1 ou( 2%#s!c$" s2$ce T%ese $(e t/o com2et!n4 onto"o4!es t%$t /!"" e

t%o(ou4%"# '!scusse' !n t%!s 2$2e(

In "!4%t o1 '!scuss!n4 t%!s 'e$te $n' un'e(st$n'!n4 t%e n$tu(e o1

/$e-1unct!on onto"o4# /!t% (es2ect to t%e !m2"!c$t!ons on t%e n$tu(e o1

s2$ce3 !n o('e( to 1un'$ment$""# un'e(st$n' t%e '!st!nct!ons et/een t%ese

com2et!n4 onto"o4!es3 one %$s to un'e(st$n' t%e t#2es o1 s2$ces !no"e'

$n' t%e!( (es2ect!e 2(o2e(t!es T%e(e $(e t/o '!st!nct s2$ces t%$t $(e

'!scusse' !n t%ese onto"o4!es $n' t%e# $(e st$te s2$ces $n' met(!c s2$ces

7ot% o1 t%ese s2$ces $(e m$t%em$t!c$" !n n$tu(e $n' $(e use' to (e2(esent

ou( 2%#s!c$" s2$ce !n t%e /o("' $(oun' us T%e n$tu(e o1 t%ese t/o '!st!nct

s2$ces /!"" e '!scusse' 1u(t%e( on

A"" !n $""3 /$e-1unct!on onto"o4!es $(e me$nt to %e"2 us to un'e(st$n'

t%e n$tu(e o1 t%e /$e-1unct!on In t%e 2%!"oso2%# o1 2%#s!cs3 !t !s e(# e$s#

to con1use t%e m$t%em$t!c$" n$tu(e st(uctu(e $n' n$tu(e o1 t%e 2%#s!c$"

t%eo(!es $sto %$!n4 $ one-to-one (e"$t!ons%!2 /!t% t%e 2%#s!c$" /o("' Fo(

e,$m2"e3 !t !s e$s# to con1use t%e %!4%e( '!mens!on$" n$tu(e o1 $

m$t%em$t!c$" s2$ces to e "!*ene' to t%e n$tu(e o1/!t% ou( 2%#s!c$" s2$ces

T%us3 !t !s 2$($mount to 1o( un'e(st$n'!n4 t%e $(!ous onto"o4!es o1 t%e

0



/$e-1unct!on /!t% (es2ectto '!st!n4u!s% '!5e(ent to t%e 1un'$ment$" not!ons

o1 s2$ce $n' !n 2$(t!cu"$( to note t%e '!st!nct!ons et/een m$t%em$t!c$"

s2$ce $n' 2%#s!c$" s2$ce $s /e"" $s t%e '!st!nct!on et/een m$t%em$t!c$"

o)ects $n' 2%#s!c$" o)ects T%!s e"us!e '!st!nct!on3 $s Resn!* conc"u'es !n

%!s /o(*3 !s $tt(!ute' to t%e "on4st$n'!n4 2(o"em o1 com2et!n4 onto"o4!es

1o( $(!ous t%eo(!es !n 2%#s!cs :Resn!* 6BK>

What is 3N-Confguration3N-confguration !ace?

As %$s een s%o/n !n t%e 2(e!ous sect!on3 t%e eo"ut!on o1 t%e /$e-

1unct!on occu(s !n $ m$t%em$t!c$" s2$ce c$""e' 6N-Con84u($t!on6N-

con84u($t!on s2$ce /%e(e N !s t%e nume( o1 2$(t!c"es !n t%e 4!en s#stem

:A"e(t J6> T%!s 2$(t!cu"$( con84u($t!on s2$ce !s t%e m$t%em$t!c$" s2$ce !n

/%!c% $"" t%e 2oss!"e st$tes o1 $ .u$ntum s#stem e,!st :A"e(t J6> $n' /!""

ot%e(/!se%ence1o(/$(' e *no/n'es!4n$te' $s .u$ntum con84u($t!on

s2$ce to '!st!n4u!s% !t 1(om c"$ss!c$" 6N-con84u($t!on6N-con84u($t!on s2$ce

E$c% 2o!nt !n t%!s .u$ntum con84u($t!on s2$ce %$s $n $m2"!tu'e $n' 2%$se

:A"e(t J6> T%us3 ou( un!e(se /ou"' %$e $ con84u($t!on s2$ce /!t% $n

e,t(eme"# "$(4e nume( o1 '!mens!ons T%!s con84u($t!on s2$ce !s $t t%e

%e$(t o1 t%e 'e$te $out t%e /$e-1unct!on $n' t%e n$tu(e o1 s2$ce $s $

(esu"t o1 !t Ho/ee(3 t%e 6N-con84u($t!on6N-con84u($t!on s2$ce !sn’t $



met(!c s2$ce "!*e Euc"!'e$n s2$ce !s3 ($t%e( !t !s $ H!"e(t ecto( s2$ce :c!te>

Fu(t%e(mo(e3 /%$t !s un!.ue $out t%e t%e con84u($t!on s2$ce !s t%$t !t !s not

$ met(!c s2$ce "!*e !n t%e c"$ss!c$" mec%$n!c$" con84u($t!on s2$ceM!n*o/s*!

s2$ce o( Ne/ton!$n 6D6-'!mens!on$" s2$ce :c!te> Fo( e,$m2"e3 !n c"$ss!c$"

mec%$n!cs t%e con84u($t!on $c*4(oun' s2$ce !s $ s!n4"e met(!c s2$ce o1

t%e 2oss!"e 2os!t!ons o1 $ s#stem o1 2$(t!c"es T%e(e !s $ 2(o2e(t# o1

“distance” t%$t c$n e c$"cu"$te' 1(om t%e con84u($t!on$22"!e' /!t%!n t%!s

s2$ce $n' t%us !t !s t%!s '!st!nct!on t%$t '($/s t%e "!ne et/een c"$ss!c$"

con84u($t!on2%#s!c$" met(!c s2$ce $n' .u$ntum con84u($t!on s2$ce In t%e

.u$ntum :$s /e"" $s c"$ss!c$"> con84u($t!on s2$ce3 t%e(e !s no 2(o2e(t# o1

“distanceIdistanceG@---e$c% 2$(t!c"e %$s $n $m2"!tu'e $n' 2%$se $ssoc!$te'

/!t% !t t%$t !s (e2(esente' # com2"e, nume(s In c"$ss!c$"

con84u($t!on2%#s!c$" met(!c s2$ce3 e$c% 2o!nt !s (e2(esente' # t%(ee6t%(ee

o( 1ou( (e$" nume(s T%!s !s $not%e( '!st!nct!on In .u$ntum con84u($t!on

s2$ce3 t%e $m2"!tu'e $n' 2%$se t%$tt (e2(esents e$c% 2o!nt $(e com2"e,

nume(s /%!c% $(e out2utte' $s (e$" nume(s /%en $n ose($t!on o( $

m$t%em$t!c$" o2e($to( !s o2e($te' on t%e 4!en con84u($t!on s2$ce In ot%e(

/o('s3 !n t%e .u$ntum con84u($t!on s2$ce3 t%e(e !s no not!on o1 $ 2%#s!c$"

'!st$nce et/een 2o!nts t%$t c$n e me$su(e' !n t%e 2%#s!c$" /o("' 'ue to

t%e un!.ue m$t%em$t!c$" n$tu(e o1 t%e .u$ntum con84u($t!on s2$ce T%ese

un!.ue 2(o2e(t!es o1 .u$ntum con84u($t!on s2$ce %$e some un!.ue

!m2"!c$t!ons 1o( t%e /$e-1unct!on T%ese !m2"!c$t!ons /!"" e '!scusse'



t%e s$me so(t o1 "o4!c In c"$ss!c$" con84u($t!on s2$ce3 t%e s$me !'e$ !s

$22"!e' to con'ense t%e 2%#s!c$" 2(o2e(t!es o1 2$(t!c"es3 n$me"# t%e!(

2os!t!on $n' e"oc!t!es to $ ecto( !n t%e con84u($t!on s2$ce3 $n' t%us c$n

(e2(esent t%e ent!(e st$te o1 t%e s#stem !n t%e s$me /$# t%$t .u$ntum

con84u($t!on s2$ce !s e,2(esse' Ho/ee(3 t%e(e !s $ *e# onto"o4!c$"

'!st!nct!on et/een t%e 2u(2ose $n' use o1 con84u($t!on s2$ce !n e$c%

(e4!me In t%e .u$ntum (e4!me3 con84u($t!on s2$ce (e2(esents t%e eo"ut!on

o1 t%e st$te o1 $ .u$ntum s#stem /!t% N 2$(t!c"es ec$use $ /$e-1unct!on !s

2%#s!c$""# !n $ su2e(2os!t!on o1 st$tes T%e su2e(2os!t!onT%e su2e(2os!t!on

o1 st$tes $n' t%e 4!en 2(o$!"!t!es o1 e$c% 2$(t!c"e to t$*e on $ $"ue o1

2os!t!on $n' momentum3 !s one o1 t%e$(e t/o o1 t%e m$!n '!st!nct!ons t%$t

'!5e(ent!$te c"$ss!c$" con84u($t!on s2$ce 1(om !ts .u$ntum counte(2$(t In

t%e c"$ss!c$" con84u($t!on s2$ce3 t%e 2$(t!c"es $(e not !n $ su2e(2os!t!on o1

st$tes@---t%e(e $(e 'e8n!te $"ues t%e# c$n t$*e $se' on t%e!( 'ete(m!n$te

st$tes T%!s !s t%e *e# onto"o4!c$" '!st!nct!on $n' !t /!"" e use1u" !n

un'e(st$n'!n4 t%e $(!ous 2e(s2ect!es o5e(e' !n t%!s 2$2e(

In $''!t!on3 t%e *e# '!5e(ence et/een met(!c $n' con84u($t!on s2$ce

!n t%e .u$ntum $n' c"$ss!c$" (e4!me3 !s t%$t 1un'$ment$""#3 t%e(e !s no

met(!c not!on o1 distance !n t%e con84u($t!on s2$ces T%e not!on o1 '!st$nce

!n $ met(!c s2$ce $22"!es !n $ 2%#s!c$""# (e"e$nt sense3 ut !t 'oes not $22"#

!n $ 2%#s!c$""# (e"e$nt sense 1o( con84u($t!on s2$ces Con84u($t!on s2$ces

=



'o not 'e$" /!t% s2$t!$" coo('!n$te (e2(esent$t!ons !n t%e s$me (es2ect $s

met(!c s2$ces@---t%e# 'e$" /!t% t%e st$tes o1 $ s#stem ($t%e( t%$n t%e

!n'!!'u$" 2%#s!c$" 2o!nts o1 t%e s#stem Mo(e c"e$("# st$te'3 $ met(!c s2$ce

!s $ s2$ce o1 s2$t!$" 2o!nts $n' $ con84u($t!on s2$ce !s $ s2$ce o1 st$tes Fo(

e,$m2"e3 $ con84u($t!on s2$ce /ou"' %$e $"" t%e 2oss!"e e"oc!t# o(

momentum $"ues t%$t cou"' e,!st 1o( e$c% s2$t!$" 2o!nt Us!n4 t%e

con84u($t!on s2$ce coo('!n$tes3 $n' 2e(1o(m!n4 $ m$t%em$t!c$" o2e($t!on

on t%e con84u($t!on s2$ce t%$t c$"cu"$tes '!st$nce !s not 2%#s!c$""#

me$n!n41u" !n t%!s so(t o1 s2$ce Pe(1o(m!n4 suc% $n o2e($t!on on $

con84u($t!on s2$ce !s $*!n to 8n'!n4 t%e '!st$nce et/een t/o st$tes !n t%e

s2$ce o1 st$tes T%!s !sn9t t%e s$me $s 8n'!n4 t%e '!st$nce et/een t/o

2o!nts !n $ 2%#s!c$" s2$ce Fo( e,$m2"e3 !n t%e .u$ntum con84u($t!on s2$ce3

e$c% s2$t!$" 2o!nt !s (e2(esente' # $ 2(o$!"!t# $"ue C$"cu"$t!n4 t%e

'!st$nce et/een t/o 2(o$!"!t!es 'oes not me$n t%e s$me $s c$"cu"$t!n4

t%e '!st$nce et/een t/o 2o!nts !n 2%#s!c$" s2$ce

T%us3 !n $ met(!c s2$ce !t !s 2%#s!c$""# me$n!n41u" to c$"cu"$te t%e

'!st$nce et/een 2o!nts ec$use t%e 2o!nts $(e (e2(esent!n4 $ 2%#s!c$"

s2$ce In $ con84u($t!on s2$ce3 t%e 2o!nts $(e (e2(esent!n4 2oss!"e

e"oc!t!es3 momentum3 o( 2(o$!"!t# $"ues 1o( e$c% s2$t!$" 2o!nt3 t%us

$ttem2t!n4 to c$"cu"$te t%e '!st$nce et/een t/o suc% 2o!nts /!"" not #!e"'

t%e s$me 2%#s!c$" me$n!n4 $s !t 'oes 1o( met(!c s2$ces T%!s !s t%e

1un'$ment$" '!st!nct!on et/een con84u($t!on s2$ces $n' met(!c s2$ces $n'

J



!t /!"" e use' !n t%e 1u(t%e( sect!ons to ette( un'e(st$n' A"e(t $n'

Monton9s !e/s

"athematical O$%ects vs &hysical O$%ects a!!lied to 3N-

Confguration3N-confguration !ace and &hysical !ace

In o('e( to un'e(st$n' t%e onto"o4!c$" st$tus o1 con84u($t!on s2$ce3

'!st!nct!ons et/een m$t%em$t!c$" o)ects $n' 2%#s!c$" o)ects %$e to e

m$'e T%ese '!st!nct!ons /!"" e $22"!e' to 6N 6N-con84u($t!on s2$ce $n'

2%#s!c$" s2$ce

Acco('!n4 to C%$("es C%!%$($3 $ 2(om!nent 2%!"oso2%e( $t Un!e(s!t# o1

No(t% C$(o"!n$-C%$2e" H!""3 !n %!s oo* A St(uctu($" Account o1 M$t%em$t!csG3

m$t%em$t!c$" o)ects $(e c$us$""# !ne(t $n' t%e(e1o(e 'o not e,!st !n ou(

2%#s!c$" /o("' :C%!%$($ B> In o('e( to un'e(st$n' t%!s st$tement3 t%e !'e$

o1 $ m$t%em$t!c$" o)ect %$s to e un'e(stoo' C%!%$($ 'e8nes t%e

m$t%em$t!c$" o)ect $s e!n4 $ m$t%em$t!c$" const(uct!on /%!c% o2e($tes

$n' !s 'e8ne' to e,!st !n t%e 2"$ton!c m$t%em$t!c$" un!e(seG :C%!%$($ B>

T%!s mathematical universeG3 so to s2e$*3 !s not c$us$""# connecte' to ou(

2%#s!c$" un!e(se :C%!%$($ B> Ho/ee(3 /W%$t 'oes t%!s %$e to 'o /!t%

ou( 'e$te $out t%e n$tu(e o1 s2$ce 1o( t%e /$e-1unct!on? T%e '!st!nct!on

et/een $ 2%#s!c$" o)ect $n' $ m$t%em$t!c$" o)ect !s "u((e' /%en t$"*!n4

$out t%e /$e-1unct!on ec$use t%e /$e-1unct!on !s m$t%em$t!c$""#

B



const(ucte' $s eo"!n4 t%(ou4% t%e %!4%e( '!mens!on$" s2$ce o1 6N-

con84u($t!on s2$ce3 /%!"e e,!st!n4 !n ou( 2%#s!c$" s2$ce o1 t%(ee6

-'!mens!ons T%!s 2(o2e(t# o1 t%e /$e-1unct!on m$*es !t $ .u$s!-

m$t%em$t!c$" o)ect Resn!* "!*ens m$n# o)ects !n 2%#s!cs to e!n4 .u$s!-

m$t%em$t!c$" ent!t!es o( ent!t!es /!t% 2(o2e(t!es t%$t $(e m$t%em$t!c$" $n'

2%#s!c$" :Resn!* 6> Fo( e,$m2"e3 t%e /$e-1unct!on %$s m$n#

m$t%em$t!c$" 2(o2e(t!es $n' m$n# 2%#s!c$" 2(o2e(t!es In t%e s$me

(es2ectS!m!"$("#3 $ .u$ntum 2$(t!c"e /ou"' $"so e c"$ss!8e' $s $ .u$s!-

m$t%em$t!c$" o)ect3 $cco('!n4 to Resn!*3 s!nce .u$ntum 2$(t!c"es 'o not

%$e 'e8n!te "oc$t!ons !n s2$ce-t!me3 e"oc!t!es3 momentum3 m$sses3 s2!n3

o( ot%e( 2(o2e(t!es (e"$t!n4 to s2$ce-t!me :Resn!* 60> T%us3 t%e m$!n !ssue

$t %$n' !s %o/ t%e /$e-1unct!on %$s 2(o2e(t!es o1 $ 2%#s!c$" $n'

m$t%em$t!c$" o)ect

T%e(e !sc$n e muc% to '!scuss $s to(e4$('!n4 t%e st$tus o1 t%e /$e-

1unct!on’s e,!stence !n t%e mathematical universeG o( !n t%e 2%#s!c$"

un!e(se3 ut t%e *e# !ssue !s !ts onto"o4!c$" st$tus $s !t (e"$tes to 2%#s!c$"

s2$ce esT%ou4%3 !t m$# %$e $ st$tus $s e!n4e $ .u$s!-m$t%em$t!c$"

o)ect3 %o/ee(3 !t !s 1un'$ment$""# $ 2%#s!c$" st$te t%$t c$n e me$su(e'

!n 2%#s!c$" e,2e(!ments !n ou( t%(ee6 '!mens!on$"6-'!mens!on$" s2$ce As

suc%3 !t !s !m2o(t$nt to e,$m!ne t%e e,tent /e s%ou"'to /%!c% to use t%!s

'!st!nct!on et/een m$t%em$t!c$" o)ects $n' 2%#s!c$" o)ects to '!sce(n t%e

onto"o4!c$" st$tus o1 t%e /$e-1unct!on



So 1$(3 t%e(e %$s een muc% '!scuss!on $out t%e $(!ous '!st!nct!ons

$n' 2(o2e(t!es o1 t%e /$e-1unct!on T%ese $(e too"s t%$t /!"" %e"2 !n

un'e(st$n'!n4 t%e /$e-1unct!on !n $ mo(e 2(ec!se m$nne( T%e 2(ece'!n4

'!scuss!ons $(e $u,!"!$(# to t%e '!scuss!ons t%$t A"e(t $n' Monton %$e

2(esente' 1o( t%e n$tu(e o1 s2$ce o1 t%e /$e-1unct!on T%e

$m2"!tutes$m2"!tu'es o1 t%e /$e 1unct!on $(e $*!n to m$t%em$t!c$" o)ects

($t%e( t%$n 'e8n!te 2(o2e(t!es o1 t%e s#stem $s !n t%e c$se o1 c"$ss!c$"

e"ect(!c 8e"'s T%!s !s ce(t$!n"# $ '!st!nct!on t%$t 2!ts .u$ntum /$e-1unct!ons

$4$!nst t%e c"$ss!c$" !e/ o1 ou( 2%#s!c$" /o("' Ho/ee(3 t%!s '!st!nct!on

out"!nes t%e 2otent!$" 1o( t%e .u$ntum /$e-1unct!on to e $ mo(e .u$s!-

m$t%em$t!c$" o)ect t%$n !ts c"$ss!c$" counte(2$(ts T%e not!on o1 t%e /$e-

1unct!on e!n4 $ .u$s!-m$t%em$t!c$" o)ect c$n e $22"!e' !n t%e 'e$te

su((oun'!n4 t%e /$e-1unct!on’s n$tu(e o1 s2$ce

Current vie's o( the 'aveWave-(unctionFunction

T%e 2(e!ous sect!ons %$e $""u'e' to t%e m$t%em$t!c$" $n' 2%#s!c$"

'esc(!2t!on3 t%e 2(o2e(t!es3 t%e '!st!nct!ons3 $n' t%us t%e onto"o4!c$" st$tus

o1 t%e /$e-1unct!on As %$s een !n'!c$te'3 t%e /$e-1unct!on !s $n

!nte(est!n4 o)ect t%$t e,%!!ts 2%#s!c$" $n' m$t%em$t!c$" 2(o2e(t!es t%$t

com!ne to m$*e !ts onto"o4!c$" st$tus $ 'e$t$"e to2!c !n t%e 2%!"oso2%# o1

2%#s!cs 2%#s!cs8e"' Ho/ee(3 t%e(e $(e m$n# com2et!n4 !e/s $s !n'!c$te'

!n t%e $nt%o"o4# to $out t%e /$e-1unct!on3 T%e Met$2%#s!cs on t%e W$e-

L



Funct!on o1 Qu$ntum Mec%$n!csG[:Ne# $n3' A"e(t?&> T%!s $nt%o"o4# %$s

co""ecte' 2e(t!nent $(t!c"es conce(n!n4 t%e n$tu(e o1 s2$ce o1 t%e .u$ntum

/$e-1unct!on!n t%e 2%!"oso2%# T%e cu((ent !e/s o1 t%e /$e-1unct!on’s

onto"o4# 8(st $n' 1o(emost 'e$" /!t% t%e n$tu(e o1 6N 6N-con84u($t!on

s2$ce $s $ 'e8n!n4 1e$tu(e o1 t%e /$e-1unct!on $n' $((!e $t t%e onto"o4!es

$se' on t%e !nte(2(et$t!ons o1 t%e 2(o2e(t!es o1 t%e /$e-1unct!on In t%e

ne,t sect!ons3 I /!"" 2(!m$(!"# e,$m!ne A"e(t $n' Monton’s onto"o4!es T%ese

onto"o4!es $(e o22os!te to e$c% ot%e(3 ut t%e# $(e !nte(est!n4"# $t t%e

!nte(sect!on o1 t%e 'e$te conce(n!n4 t%e n$tu(e o1 6N-con84u($t!on6N-

con84u($t!on s2$ce 1o( t%e /$e-1unct!on

T%ese onto"o4!es $"so nee' to e (e"$te' to t%e sc!ent!8c met%o' T%e

not!on o1 u!"'!n4 $n onto"o4# $se' on t%e e,2e(!ments o1 2%#s!cs !s

somet%!n4 t%$t %$s een e,2"$!ne' # V$"!$ A""o(! t%(ou4% t%e conce2t o1

2(!m!t!e $n' non-2(!m!t!e $(!$"es :A""o(! B=> A""o(! 2os!ts t%$t 2(!m!t!e

$(!$"es $(e t%e $(!$"es t%$t $(e %e"' # mu"t!2"e t%eo(!es to e common3

/%e(e$s t%e non-2(!m!t!e $(!$"es $(e $(!$"es o1 $ t%eo(# t%$t $(e notn’t

.u!te %e"' !n common # com2et!n4 t%eo(!es :A""o(! BJ> W!t% (es2ect to t%e

/$e-1unct!on3 com2et!n4 t%eo(!es %o"' t%e 6N-con84u($t!on6N-con84u($t!on

s2$ce !n common

)l$ert*s Wave-Function Ontology

K



con84u($t!on s2$ce T%e 2(ocess # /%!c% t%e sus2$ces $(e m$22e' $n'

2(o)ecte' onto ou( t%(ee6-'!mens!on$" s2$ce !s $"so not c"e$("#

st$te'!'ent!8e' Ho/ee(3 t%e 1un'$ment$" !ssue !n nee' o1 un'e(st$n'!n4 !s

t%e 1$ct t%$t A"e(t uses t%!s m$t%em$t!c$" st(uctu(e o1 t%e /$e-1unct!on to

c($1t %!s /$e-1unct!on onto"o4# to m!((o( t%e m$t%em$t!cs 8(st $n' 1o(emost

($t%e( t%$n t%e 2%#s!c$" 2%enomen$ He $22e$"s to t%e m$t%em$t!cs to 2os!t

2%#s!c$" c"$!ms I /!"" $(4ue $4$!nst t%!s not!on !n $ se2$($te sect!on $n'

2(esent /%# I (e$son t%$t suc% $ cou(se !s m!s4u!'e' I /!"" '!scuss /%# t%!s

cou(se !s m!s4u!'e' !n 4(e$te( 'e2t% e"o/

"onton*s Wave-Function Ontology

7($'"e# Monton !s $not%e( 2%!"oso2%e( /%o o5e(s %!s onto"o4# 1o( t%e

.u$ntum /$e-1unct!on He e4!ns # su22os!n4 t%$t .u$ntum mec%$n!cs !s

1$"se ec$use !t !s !ncom2$t!"e /!t% 4ene($" (e"$t!!t# $n' t%en 2(ocee's to

$s*!n4 st$t!n4 t%e '!mens!on$"!t# o1 2%#s!c$" s2$ce :Monton J=> He $22e$"s

to “commonsense” to su22o(t %!s c"$!m t%$t t%e '!mens!on$"!t# o1 2%#s!c$"

s2$ce !s t%(eet%(ee6 :Monton J=> Monton 2(ocee's /!t% t%ese c"$!ms to

$(4ue $4$!nst A"e(t’s t%es!s t%$t 2%#s!c$" s2$ce !s !n (e$"!t# $ 6N-

'!mens!on$" s2$ce H!s 2(esu22os!t!on !n m$*!n4 t%ese c"$!ms !s t%$t

.u$ntum mec%$n!cs !s 1$"se ec$use !t c$nnot co((ect"# 2(e'!ct t!me '!"$t!on

!n $ st(on4 4($!t$t!on$" 8e"' un'e( t%e 2%#s!cs o1 4ene($" (e"$t!!t# T%en

Monton e4!ns $s*s# $s*!n43 Ho/ 'oes one 'ete(m!ne t%e onto"o4!c$"



content o1 $ t%eo(#?

Monton c"$!ms !1 $ t%eo(# c$n e 2(esu22ose' to e t(ue t%en t%e

u"t!m$te $(!te( o1 t%e onto"o4!c$" content o1 t%e t%eo(# !s (e$"!t# !tse"1

:Monton JJ> He uses t%!s $s %!s ‘epistemic starting point ’ to 2(o!'e $n

$n$"#s!s o1 /%$t c$n e onto"o4!c$""# st$te' $out sc!ent!8c t%eo(!es In

$''!t!on3 %e c"$!ms t%$t $n ent!(e t%eo(# suc% $s .u$ntum mec%$n!cs m$#

not e 1$"se ut !ts $u,!"!$(# %#2ot%es!s m$# e 1$"se T%!s !'e$ touc%es u2on

2(!m!t!e $n' non-2(!m!t!e $(!$"es o1 $ t%eo(# $n' /%$t !t t$*es 1o( $ 4!en

t%eo(# to e $cce2te' T%e 2(o"em /!t% .u$ntum mec%$n!cs3 Monton

2(o1esses3 !s t%$t t%e(e $(e m$n# e(s!ons o1 !t /!t% t%e "!*essuc% $s o1 st(!n4

t%eo(#3 M-t%eo(#3 $n' .u$ntum 4($!t# $"" com2et!n4 to $((!e $t t%e c"osest

com2$t!"e 1o(mu"$t!on (econc!"!n4 .u$ntum mec%$n!cs $n' (e"$t!!t#

7ec$use t%e(e !sn9t $ 2%#s!c$" t%eo(# t%$t 2(o2e("# $''(esses t%e !ssue o1

com2(om!s!n4 .u$ntum mec%$n!cs $n' (e"$t!!t#3 $ 2%#s!cs-$se'-

met$2%#s!cs 1o( .u$ntum mec%$n!cs c$nnot e 2(o2e("# 1o(mu"$te'

Ho/ee(3 Monton 'oes not "e$e t%e 'e$te o1 t%e '!mens!on$"!t# o1 s2$ce o1

t%e /$e-1unct!on $t $ st$n'st!"" s!m2"# ec$use %e m$!nt$!ns t%$t .u$ntum

mec%$n!cs !s 1$"se@--- %e o5e(s $ sut"e #et c"$(!1#!n4 $(4ument $4$!nst 6N-

'!mens!on$" s2$ce

Monton e4!ns %!s $(4ument $4$!nst 6N-'!mens!on$" s2$ce # us!n4 $

sem$nt!c !e/ o1 sc!ent!8c t%eo(!es T%!s sem$nt!c !e/ $cco('!n4!e/3

$cco('!n4 to Monton3 (e.u!(es t%$t sc!ent!8c t%eo(!es cons!st o1 t/o 2$(ts $



m$t%em$t!c$" mo'e" $n' $ set o1 t%eo(et!c$" c"$!ms $out %o/ t%e

m$t%em$t!c$" mo'e" (e2(esents (e$"!t# :Monton B0> In o('e( to e"uc!'$te

t%!s sem$nt!c !e/3 Monton connects t%!s /!t% $n$"o4!es o1 t/o

(e2(esent$t!ons o1 .u$ntum mec%$n!cs H!"e(t s2$ces $n' Sc%(o'!n4e(9s

/$e-1unct!on In t%e H!"e(t s2$ce (e2(esent$t!on3 t%e .u$ntum st$te o1 $

s#stem !s (e2(esente' # ecto(s !n H!"e(t s2$ce /%!"e !n t%e Sc%(o'!n4e(

(e2(esent$t!on3 t%e .u$ntum st$te o1 $ s#stem !s (e2(esente' # $ /$e-

1unct!on t%$t eo"es t%(ou4% 6N-con84u($t!on6N-con84u($t!on s2$ce

Monton t$*es t%ese $n$"o4!es 1u(t%e( # st$t!n4

One cou"' 2ut 1o(t% $ t%eo(et!c$" %#2ot%es!s s$#!n4 t%$t H!"e(tH!"e(t

s2$ce !s 2%#s!c$""# (e$"3 $n' t%e(e (e$""# !s $ "!ne o1 $ 2$(t!cu"$( "en4t%

2o!nte' !n $ 2$(t!cu"$( '!(ect!on !n t%$t s2$ce S!m!"$("#3 one cou"' 2ut

1o(t% $ t%eo(et!c$" %#2ot%es!s s$#!n4 t%$t 6N-'!mens!on$" s2$ce !s

2%#s!c$""# (e$"3 $n' t%e(e (e$""# !s $ /$e-1unct!on 1e"' 8e"' eo"!n4 !n

t%$t s2$ce :Monton B>

Monton t%us (!n4s u2 $n e,ce""ent 2o!nt3 o1 4(oun'!n4 t%e 'e$te to !n $

mo(e 2%#s!c$" $22(o$c% to t%e met$2%#s!cs o1 t%e .u$ntum /$e-1unct!on

He !n essenceIn essence3 %e '!st!n4u!s%es t%e ut!"!t# o1 t%e m$t%em$t!c$"

(e2(esent$t!ons o1 $ sc!ent!8c t%eo(# 1(om !ts 2%#s!c$" (e"e$nce :No/3 t%e

met$2%#s!c$" !m2"!c$t!ons o1 t%ese '!st!nct!ons t%emse"es c$n e '!scusse'

1u(t%e( ut t%$t !s not t%e 1ocus o1 t%!s 2$2e(>

H!s conc"us!on $se' on t%ese 2o!nts !s t%$t t%e(e !s $n N-2$(t!c"e

6



s#stem t%$t eo"es !n t%(ee6 '!mens!on$"6-'!mens!on$" s2$ce $n' t%e(e !s $

ce(t$!n 2(o2e(t# o1 t%!s N-2$(t!c"e s#stem t%$t !s (e2(esente' # e!t%e( $ 6N-

'!mens!on$" s2$ce o( $ H!"e(t s2$ce Fun'$ment$""#3 t%!s 2(o2e(t# !s /%$t

c$n e *no/n $out t%e .u$ntum /$e-1unct!on $s !t e,!sts !n t%(ee6-

'!mens!on$" s2$ce In ot%e( /o('s3 $cco('!n4 to Monton /e c$nnot con1use

t%e onto"o4!c$" st$tus o1 t%e m$t%em$t!c$" (e2(esent$t!ons o1 ou( t%eo(!es

/!t% /%$t /e $(e t(#!n4 to (e2(esent 2%#s!c$""# Ho/ee(3 $"t%ou4% Monton

'oes %$e 4oo' 2o!nts3 %!s $ccount o1 .u$ntum mec%$n!cs $s $ 1$"se t%eo(#

o1 t%e /o("' 'ue to !ts !ncom2$t!!"!t# /!t% 4ene($" (e"$t!!t# $n' mo(eoe(

%!s $22e$" to "commonsense" $(e $ !t $"$(m!n4oe(s!m2"!8e' In 2$(t!cu"$(3

%!s (e$son!n4 1o( e"!e!n4 t%$t t%e '!mens!on$"!t# o1 ou( s2$ce !s t%(ee6

$se' on "commonsense" !s $ !t unc"e$( I /!"" '!scuss t%e !ssues /!t%

Monton9s onto"o4# o1 t%e .u$ntum /$e-1unct!on !n $ 1u(t%e( sect!one"o/

Why elevating 3N 3N-Confguration confguration !ace s!ace to a

&hysical !hysical s!ace is misguided

I /!"" no/ 2ose m# $(4uments $4$!nst A"e(t’s !e/s $n' 4o !nto

'et$!" $s to /%# I 'o not t%!n* t%$t %!s 6N-con84u($t!on6N-con84u($t!on

s2$ce onto"o4# !s soun'

T%e !'e$ o1 s2$ce e!n4 6N !s $ m!s4u!'e' !'e$ ec$use t%e /$#

ecto(s $(e $22o!nte' m$t%em$t!c$""# $(e t%(ou4% m$t%em$t!c$" o2e($t!ons

=



$n' $(e !n tu(n $(e use' to (e2(esent 2%#s!c$" 2(o2e(t!es o1 t%e s#stem In

o('e( to m$*e $ sc!ent!8c mo'e" o1 /%$t t%e 2%#s!cs o1 $ 2%enomen$ !s3 one

!m2oses m$t%em$t!c$" mo'e"s onto t%e e,2e(!ment$" s!tu$t!on A 2%#s!c$"

!nte(2(et$t!on !s one t%$t $22e$"s to t%e 2(!m$(# 2(!m!t!e $(!$"es o1 t%e

s#stem :e, 2os!t!on3momentum2os!t!on3 momentum3 s2!n> e!n4 'esc(!e'

$n' $''s non-2(!m!t!e m$t%em$t!c$" $(!$"es :con84u($t!on s2$ce3

%!"e(tH!"e(t s2$ce3 2(o)ect!e %!"e(tH!"e(t s2$ce>3 /%!c% $(e #-2(o'ucts

o1 t%e m$t%em$t!cs t%$t !s e!n4 use' to 'esc(!e t%e 2%#s!c$" s#stem One

s%ou"'n9t con1use t%e m$t%em$t!c$" o)ects $n' o2e($t!ons t%$t $(e e!n4

use' to 'esc(!e t%e 2%#s!c$" s#stem /!t% $ctu$" 2(o2e(t!es o1 t%e 2%#s!c$"

s#stem T%!s !s $ (e2(esent$t!on$" 2(o"em Es2ec!$""# /%en one !s 'e$"!n4

/!t% m$t%em$t!c$" 2(o2e(t!es o1 t%e /$e-1unct!on3 /%!c% e,!sts !n # !(tue

o1 t%e st$te $1te( ose($t!on o1 t%e .u$ntum s#stem Fo( e,$m2"e3 4!en t%e

'!st!nct!ons '!scusse' et/een m$t%em$t!c$" o)ects $n' 2%#s!c$" o)ects

2(e!ous"#$oe3 !t c$n e su(m!se' t%$t e"e$t!n4 6N-con84u($t!on6N-

con84u($t!on s2$ce to $ 2%#s!c$" s2$ce !s "!*e e"e$t!n4 t%e nume(s !n t%e

*e"!n Xe"!n tem2e($tu(e sc$"e to e (e$" 1e$tu(es o1 t%e 2%#s!c$"

2%enomen$ o1 tem2e($tu(e Fun'$ment$""#3 t%e nume(s on t%e *e"!n

tem2e($tu(e sc$"e $(e on"# (e2(esent$t!e 2(o2e(t!es o1 t%e 2%#s!c$"

2%enomen$ o1 t%e(m$" ene(4# A"t%ou4% .u$ntum con84u($t!on s2$ce %$s $

4(e$te( ut!"!t# t%$n c"$ss!c$" con84u($t!on s2$ce !n (es2ect to .u$ntum

mec%$n!cs3 !t c$n e s$!' t%$t t%e ut!"!t# o1 t%e 6N-con84u($t!on6N-

J



con84u($t!on s2$ce !n .u$ntum mec%$n!cs "!es !n !ts $!"!t# to

m$t%em$t!c$""# (e2(esent t%e eo"ut!on o1 t%e 2%#s!c$" st$tes3 $"e!t t%(ou4%

$ %!4%e( %!4%e(-'!mens!on$" s2$ce T%!s (e2(esent$t!on3 %o/ee(3 !s !n t%e

1o(m o1 $ s2$ce t%$t 'esc(!es t%e st$te o1 $"" 2oss!!"!t!es Fu(t%e(mo(e3

s!nce 6N-con84u($t!on6N-con84u($t!on s2$ce (e2(esents t%e st$te o1 $""

2oss!!"!t!es o1 t%e .u$ntum s#stem3 !t !s not me$n!n41u" to $ss!4n $ not!on o1

‘distance ’ $s !t !s me$n!n41u" 1o( $ met(!c s2$ce T%e 2%$se-s2$ce n$tu(e o1

6N-con84u($t!on6N-con84u($t!on s2$ce !s '!5e(ent 1(om met(!c s2$ce !n t%$t

!n met(!c s2$ce t%e(e !s $ 2%#s!c$" not!on o1 '!st$nce /%e(e$s !n t%e 1o(me(

$ss!4n!n4 $ not!on o1 distance '!st$nce’ 'oes not 2(o!'e $n# 2%#s!c$""#

(e"e$nt 2(o2e(t!es It !s not c"e$( /%$t t%e not!on o1 distance '!st$nce’ !n $

2%$se-s2$ce "!*e 6N-con84u($t!on6N-con84u($t!on s2$ce /ou"' co((es2on'

to 2%#s!c$""#3 s!nce !t !s $ s2$ce o1 $"" 2oss!"e st$tes In ot%e( /o('s3 !t /ou"'

not e c"e$( $s to /%$t !t me$ns to c$"cu"$te /%$t t%e distance '!st$nce’

et/een t/o 4!en st$tes o1 2os!t!ons /ou"' e!s !n $ s2$ce t%$t (e2(esents

on"# t%e s2$ce o1 $"" 2oss!"e st$tes Fo( e,$m2"e3 t%!s /ou"' e $*!n to

$ttem2t!n4 to c$"cu"$te /%$t t%e distance '!st$nce’ et/een t/o 2o!nts !n $

m$t%em$t!c$" s2$ce /%!c% (e2(esents $(!ous tem2e($tu(es o1 $ 4$s

enc"ose' !n $ o, T%!s s2$ce (e2(esents t%e co""ect!on o1 $"" 2oss!"e

tem2e($tu(es o1 t%e 4$s Ho/ee(3 $ttem2t!n4 to $22e$" to t%e 2(o2e(t# o1

'!st$nce !n t%!s “t emperature G m$t%em$t!c$" s2$ce 'oes not me$n t%e s$me

t%!n4 $s !t 'oes /%en !t !s /!t% (es2ect to $ met(!c s2$ce I1 $ c$"cu"$t!on o1

B



t%e distance '!st$nce’ et/een t/o 2oss!"e tem2e($tu(es /e(e to e m$'e3

t%e distance '!st$nce’ c$"cu"$te' /ou"' on"# me$n t%e '!st$nce et/een

t%ose t/o 2o!nts !n t%!s s2$ce /!t% (es2ect to t%e tem2e($tu(e 2%$se-s2$ce

T%!s /ou"' not co((es2on' to $ 2%#s!c$""# (e"e$nt 2(o2e(t# $out t%e s#stem

tem2e($tu(e s!nce t%e m$t%em$t!c$" 1o(mu"$t!on o1 2%$se-s2$ce !sn’t t%e

s$me $s !t !s 1o( $ met(!c s2$ce In Euc"!'e$n o( M!n*o/s*! met(!c s2$ces3 !t

!s 2%#s!c$""# (e"e$nt to c$"cu"$te t%e '!st$nce et/een t/o 2o!nts !n t%ese

s2$ces $s !t !s $ 2%#s!c$""# (e"e$nt o2e($t!on $n' $ 1un'$ment$" o2e($t!on

1o( t%e !'e$ o1 $ c%$n4e !n 2os!t!on. +try to ma,e this !oint stronger $y

oering more eam!les and distinctions (or !hysical s!ace and ho'

'e use distance to defne change in motion/ In 6N-con84u($t!on6N-

con84u($t!on s2$ce t%!s so(t o1 c$"cu"$t!on /ou"' e unc"e$( $n' not

2%#s!c$""# (e"e$nt T%us3 t%e not!on o1 e"e$t!n4 6N-con84u($t!on6N-

con84u($t!on s2$ce oe("oo*s t%e 1$ct t%$t 6N-con84u($t!on6N-con84u($t!on

s2$ce !s 1un'$ment$""# $ 2%$se s2$ce $n' not $ met(!c s2$ce3 s!nce '!st$nce

!s not $ 2%#s!c$""# (e"e$nt 2(o2e(t# !n $ 2%$se s2$ce

Fu(t%e(mo(e3 $not%e( 2(o"em /!t% $n $(4ument "!*e A"e(t9s

$(4ument3 !s t%$t suc% $(4uments%e uses t%e m$t%em$t!c$" o)ects $n'

2(o2e(t!es o1 t%e /$e-1unct!on $n' 2(esumes t%em to e "!te($" e"ements o1

ou( (e$"!t# $n' 2%#s!c$" /o("' T%ese T%!s $(4uments $ssumes t%$t t%e

$ns/e( to t%e .uest!on 3 Is ou( m$t%em$t!cs o1 .u$ntum mec%$n!cs !s

(eecte' one-to-one !n t%e 2%#s!c$" /o("'?3 !s #es T%!s !s not t%e c$se



ec$use m$t%em$t!c$" o)ects 'o not %$e $n# c$us$" 2o/e(s !n t%e 2%#s!c$"

/o("'3 !n t%e sense t%$t t%e# 'o not !nte($ct /!t% 2%#s!c$" s#stems One

c$nnot t$*e t%e m$t%em$t!cs $s "!te($" t%e m$t%em$t!cs o1 2%#s!cs !s me(e"#

$ (e2(esent$t!on$" too" use' to 'esc(!e t%e (esu"ts o1 e,2e(!ments t%$t %$e

een e(!8e' 1o( $ 4!en t%eo(# o1 t%e 2%#s!c$" /o("' T%e m$t%em$t!cs /e

use to 'esc(!e t%e /$e-1unct!on :H!"e(t s2$ce> $s $ s2$ce3 !s $

m$t%em$t!c$" 1o(m$"!sm t%$t !s conen!ent to use to 'esc(!e ou( 2%#s!c$"

/o("'3 o( mo(e 2(ec!se"#3 ou( 2%#s!c$" e,2e(!ment$" (esu"ts I1 A"e(t9s

$(4ument /e(e t(ue3 t%en /e /ou"' e $"e to ose(e e,2e(!ment$""# t%$t

/e "!e !n $ 6N 6N-'!mens!on$" /o("' %o/ee(3 t%$t !s #et to e con8(me'

Re"$t!!t# s$#s /e "!e !n $ =D =-'!mens!on$" m$n!1o"' o1 s2$ce-t!me $n' t%$t

%$s/e %$e some e,2e(!ment$" e!'ence 1o( !tt%!s A"e(t9s t%es!s 'oes not3

to m# *no/"e'4e A"e(t $22e$"s to t%e met$2%#s!c$" $s2ects o1

m$t%em$t!c$" o)ects to 1u(t%e( %!s c$se t%$t t%e /o("' !s 6N ut once

$4$!n33 %o/ c$n one t$*e o)ects t%$t %$e no 2%#s!c$" 2(o2e(t!es3 no c$us$"

2o/e(s3 $n' 'o not e,!st !n ou( s2$ce-t!me to "!te($""# !m2ose t%e !e/ t%$t

/e "!e !n $ 6N- '!mens!on$" /o("'? T%us3 A"e(t9s $(4ument t%$t 6N 6N-

'!mens!on$" s2$ce !s t%e (e$" '!mens!on$"!t# o1 t%e s2$ce /e "!e !n !s $ !t

m!s4u!'e' As c$n e !n1e((e'3 I $m t$*!n4 $ (e$"!st $22(o$c% to t%!s 'e$te

1(om t%e onset

We s%ou"' not un'e(m!ne t%e 2(esu22os!t!ons o1 6D 6-'!mens!on$"

s2$ce /e t$*e !n ou( e,2e(!ments /!t% t%e met$2%#s!c$" c"$!ms /e m$*e

L



1(om 2u(e"# "oo*!n4 $t t%e m$t%em$t!cs A 2%#s!c$" t%eo(# $ssumes3 o( t%e

'$t$ o1 $ 4!en e,2e(!ment $ssumes 6D-s2$ce $n' t%en $ sc!ent!8c $n'

m$t%em$t!c$" mo'e" !s m$'e 1(om !t T%!s mo'e" 2(esu22oses t%e not!on o1 $

6-'!mens!on$" s2$ce Ou( e2!stem!c $ccess !s 'e8ne' $n' "!m!te' # suc% $

2(esu22os!t!on Fo( e,$m2"e3 $n# .u$ntum mec%$n!c$" e,2e(!ment t%$t !s

'one %$s $ ‘builtin’ $ssum2t!on t%$t !t !s e!n4 'one !n 6D6-'!mens!on$"

-s2$ce s!nce ou( me$su(ement 'e!ces $(e $ssume' to e !n 6-'!mens!on$"

6D-s2$ce /%en t%e e,2e(!ments $(e con'ucte' T%!s "!ne o1 (e$son!n4

e,ten's !nto $"" t%e 2%#s!c$" e,2e(!ments t%$t $(e 'one /!t% (e4$('s to

me$su(ement 'e!ces T%us3 m$*!n4 $ met$2%#s!c$" c"$!m t%$t 6D 6-

'!mens!on$" s2$ce !s !""uso(#G $n' t%$t 6N con84u($t!on s2$ce !s t%e t(ue

(e$"!t#G !s $ !t %$2%$$(' $n' m!s"e$'!n4 $n' un'e(m!nes t%e e(# '$t$ t%$t

2(esu22ose' 6-'!mens!on$"6D s2$ce In t%$t (es2ect3 A"e(t !s /(on4

m!s4u!'e' !n m$*!n4to m$*e suc% met$2%#s!c$" $n' onto"o4!c$" c"$!ms $out

.u$ntum mec%$n!cs $se' o5 t%e 2u(e m$t%em$t!c$" 1o(m$"!sm t%$t

(e2(esents t%e e,2e(!ments t%$t %$e "e' to t%e t%eo(# o1 .u$ntum

mec%$n!cs

)gainst "ontonOntological inconsistencies o( "onton

I %$e 2(e!ous"# $4(ee' /!t% m$n# o1 Monton9s 2o!nts3 %o/ee(3

Monton 'oes not 1u""# 2(o!'e %!s /$e-1unct!on onto"o4# /!t% $ c"e$(

K



1oun'$t!on H!s $ssum2t!ons "e$e $ "ot u2 1o( 'e$te $n' $(e not .u!te c"e$(

$s to t%e!( 2%!"oso2%!c$" 4(oun'!n4s

T%e m$!n 1unct!on o1 Monton’s /$e-1unct!on onto"o4# /$s !s to

2(o!'e $ mo(e !intuitive! 4(oun'!n4 1o( t%e /$e-1unct!on9s '!mens!on$"!t# o1

2%#s!c$" s2$ce Ho/ee(3 Monton $22e$"Monton $22e$"s to $ m$t%em$t!c$"

1o(mu"$t!on 1o( 6-'!mens!on$"6D s2$ce ut 2os!ts /!t% $ 2(o"em$t!c

c"$!m2(o"em$t!c$""# su44ests t%$t one s%ou"' "oo* $(oun'’ $(oun'G to

see’ seeG t%$t t%e /o("' /e "!e !n !s 6 '!mens!on$"6-'!mens!on$" :Monton

J=> Suc% $ c"$!m !s $ !t 2%!"oso2%!c$""# !ncom2"ete $n' con1us!n43 ec$use

/%$t 'oes "oo* $(oun'G $n' seeG ent$!"? Monton m$# %$e een

$22e$"!n4 to %!s !ntu!t!ons $n' t%en $22e$(s to $ttem2t to 4(oun' %!s /$e-

1unct!on onto"o4# # !n me(e ose($t!on Un1o(tun$te"#3 t%!s !s not %o/

t%eo(!es o1 2%#s!cs $(e 'ee"o2e' In contem2o($(# 2%#s!cs3 t%e(e !s $ 'ee2

sense o1 sc!ent!8c (!4o( !n e(!8c$t!on $n' 1$"s!8c$t!on o1 t%eo(!es !$

ose($t!on $n' me$su(ement A22e$"!n4 to !common sense! to 2(o!'e $

(eutt$" to A"e(t9s /$e-1unct!on onto"o4# !s not muc% '!5e(ent 1(om A"e(t

s*!22!n4 to t%e m$t%em$t!cs o1 t%e /$e-1unct!on to 2(o!'e %!s (e$"!sm 1o(

t%e .u$ntum /$e-1unct!on Fu(t%e(mo(e3 Monton (e1utes .u$ntum

mec%$n!cs ent!(e"# $n' c"$!ms !t !s $ 1$"se t%eo(# o1 ou( /o("' s!m2"# ec$use

!t c$nnot e (econc!"e' /!t% 4ene($" (e"$t!!t# ec$use T%!s !s ec$use %e

$ssumes 4ene($" (e"$t!!t# !s $ mo(e ‘superior ’ t%eo(# !n (e4$('s to !ts

!m2"!c$t!ons on 2%#s!c$" s2$ce s!nce !t 4ene($" (e"$t!!t# 2(o!'es 2(e'!ct!ons

60



o1 t%e n$tu(e o1 ou( 2%#s!c$" s2$ce3 !t c$n e use' $s $ 2(o,# to 'ete(m!ne

t%e $"!'!t# o1 .u$ntum t%eo(# /%e(e$s .u$ntum t%eo(# 'oesn’t cons!stent"#

2(o!'e 2(e'!ct!ons 1o( ou( 2%#s!c$" s2$ce T%!s !n%e(ent 2(esu22os!t!on !s

/%$t Monton uses to c($1t %!s o/n /$e-1unct!on onto"o4# Monton t%en

t$*es %!s 2(esum2t!on t%$t .u$ntum mec%$n!cs !s $ 1$"se t%eo(# $n' t%en

2os!ts %!s " physicalpropertybased wavefunctionontology" /%!c% 'esc(!es

st$tes t%$t t%e n$tu(e o1 s2$ce o1 t%e .u$ntum /$e-1unct!on !s

c%$($cte(!e' # $ 2%#s!c$" 2(o2e(t# /!t%!n t%e /$e-1unct!on T%!s !s $n

!nte(est!n4 2o!nt t%$t %e m$*es T%e /$e-1unct!on !n'ee' 'oes %$e $

2%#s!c$" 2(o2e(t# /!t%!n !ts 6N-con84u($t!on6N-con84u($t!on s2$ce

m$t%em$t!c$" mo'e" !1 !t c$n e some%o/ "!*ene' to met(!c s2$ce A"t%ou4%3

Monton $""u'es to t%!s physicalpropertybasedwavefunctionontology 3 %e

'oes not .u!te m$*e !t c"e$( %o/ t%!s 2%#s!c$" 2(o2e(t# c$n e use' !n %!s

/$e-1unct!on onto"o4# Fo( e,$m2"e3 t%e(e $(e m$n# 2%#s!c$" 2(o2e(t!es !n

t%e 1o(mu"$t!on o1 t%e /$e-1unct!on suc% $s t%e 6,N 1o(mu"$t!on o1 t%e

m$t%em$t!cs $s 2os!te' # Pete( Y Ze/!s3 $ P%!"oso2%e( o1 P%#s!cs $t t%e

Un!e(s!t# o1 M!$m!3 /%!c% /%o !nte(2(ets t%e 6N-'!mens!on$"

con84u($t!on s2$ce $s e!n4 $ s2$ce t%$t !s 1un'$ment$""# $ 6 '!mens!on$"6-

'!mens!on$" s2$ce ut o2e($tes !n t%!s 6,N-'!mens!on$" s2$ce Ho/ee(3

Monton 'oesn9t .u!te use t%$t so(t o1 2(o2e(t#3 %e !nste$' uses t%e 1$ct t%$t

t%e /$e-1unct!on !s (e2(esente' # $n e!4enst$te /!t% $ 2$(t!cu"$(

e!4en$"ue t%$t !s $n ose($"e oe( t%e m$t%em$t!c$""# (e2(esent$t!e 6N-

6



con84u($t!on6N-con84u($t!on s2$ce T%!s !sn9t $ ne/ 1o(mu"$t!on o1 t%e

.u$ntum mec%$n!c$" /$e-1unct!on3 !t !s )ust t%e n$tu($" !nte(2(et$t!on o1

t%e m$t(!, 1o(mu"$t!on o1 t%e .u$ntum /$e-1unct!on Monton 'oes 4o on to

c($1t %!s $(4ument $(oun' t%e not!on o1 m$t%em$t!c$" ent!t!es "!*e 6N-

con84u($t!on6N-con84u($t!on s2$ce (e2(esent!n4 ose($"es o1 $ 2%#s!c$"

s#stem H!s 2o!nt !n us!n4 t%e physicalpropertybasedwavef unction

functionontology !s mo(e to 'e8ne t%e 'e$te $out t%e n$tu(e o1 s2$ce o1

t%e .u$ntum /$e-1unct!on H!s (e$"!st $22(o$c% to t%e .u$ntum /$e-

1unct!on !s $n outcome t%$t 4(oun's t%e onto"o4!c$" st$tus o1 t%e /$e-

1unct!on U"t!m$te"#3 %e 'oes not 2(o2e("# e4!n %!s onto"o4# /!t% c"e$(

4(oun'!n4 $n' 'oes not $''(ess %o/ t%e 2%#s!c$" 2(o2e(t# o1 t%e e!4en$"ue

$n' e!4enst$te "!n* to $""o/ %!s onto"o4# to $''(ess t%e '!mens!on$"!t# o1

2%#s!c$" s2$ce

Conclusion

A"" !n $""3 t%e onto"o4!c$" st$tus o1 t%e .u$ntum /$e-1unct!on !s 1$(

1(om sett"e' It !s $ 'e$te t%$t !s !n nee' o1 e!n4must e (e'e8ne'3 /%!c%

/$s m# $!m !n t%!s 2$2e( to 'o I e"!ee (e'e8n!n4 t%e 'e$te /!t% (es2ect

to t%e not!on o1 /%$t t#2e o1 s2$ce c$n e onto"o4!c$""# !nte(2(ete' 1(om t%e

.u$ntum /$e-1unct!on %$s $""o/e' 1o( some 2(o4(ess !n /%$t c$n e t$"*e'

$out'!scusse' !n (e4$('s to t%e n$tu(e o1 s2$ce o1 t%e .u$ntum /$e-

6



1unct!on $n' u"t!m$te"# t%e s2$ce o1 ou( (e$"!t# As %$s een s%o/n !n m#

$(4ument $4$!nst A"e(t3 t%e not!on t%$t 6N-con84u($t!on6N-con84u($t!on

"$c*s $ 2%#s!c$" not!on o1 '!st$nce $s !n t%e s$me (es2ect $s !t %o"'s !n

met(!c s2$ce !s one o1 t%e cent($" no'es t$"*!n4 2o!nts !n t%!s 'e$te

Fu(t%e(mo(e3 t%e met%o'o"o4# use' !n m# $(4ument too* !s $se' u2on t%e

*e# $s2ect $sse(t!on o1 %o/ me$su(ements !n 2%#s!cs $n' sc!ence $(e m$'e

Me$su(ements $(e m$'e # $ssum!n4 t%$t ou( me$su(!n4 !nst(uments $(e

eme''e' !n 6 '!mens!on$"6-'!mens!on$" s2$ce T%ese !nst(uments t%en

4!e us '$t$ 1(om /%!c% /e c($1t ou( 2%#s!c$" t%eo(!es3 /%!c% c$n !nc"u'e

m$t%em$t!c$" (e2(esent$t!ons o1 t%e 2%enomen$ T%en $n onto"o4# c$n e

c($1te' Ho/ee(3 $"on4 t%!s (oute o1 com!n4 u2 /!t% t%e onto"o4#3 t%e '$t$

t%$t /$s use' to c($1t t%e 2%#s!c$" t%eo(#3 !t /$s 2(esume' t%$t t%e

me$su(ement 'e!ces /e(e eme''e' !n $ 6 '!mens!on$"6-'!mens!on$"

s2$ce3 so t%!s $se $ssum2t!on !s st!"" $ 2$(t o1 /%$tee( onto"o4# t%$t !s

c($1te' o1 t%e 4!en 2%#s!c$" t%eo(# In t%e 1utu(e3 $ met%o'o"o4# cou"' e

use' t%$t !s mo(e !n tune$"!4ne' /!t% t%e $se $ssum2t!ons t$*en 'u(!n4

e,2e(!ment$" '$t$ co""ect!on !n o('e( to 4u!'e t%e onto"o4# o1 t%e 4!en

2%#s!c$" t%eo(# T%!s /ou"' $""o/ one to $o!' t%e con1us!on o1 (e$'!n4 o5

onto"o4!es 1(om t%e m$t%em$t!c$" st(uctu(es

Z$st"#3 t%e ne,t ste2s !n un'e(st$n'!n4 t%e n$tu(e o1 s2$ce o1 t%e

.u$ntum /$e-1unct!on !s to st$(t /!t% $ 2(o2e( 1o(mu"$t!on o1 /%$t $

2%#s!c$" s2$ce 1un'$ment$""# me$ns onto"o4!c$""#3 /%$t const!tutes $s $

66



%tt22"$tost$n1o('e'u$(c%!es1$""0=ent(!es"o4!c-onto"o4#\

Resn!*3 M!c%$e" D 7et/een M$t%em$t!cs $n' P%#s!csG P+*& Proceedings of

the -iennial (eeting of the Philosophy of +cience *ssociation KK0

:KK0> 6BK]6L +/,. We J Se2t 0=

)l$ert1 2avid. Wave Function Realism. The Wave Function: Essays

on the Metaphysics of Quantum Mechanics. 4d. )l$ert1 2avid 5 and

)lyssa1 Ney. Ne' 6or,7 O(ord 8niversity &ress1 9:;3. <9-<=. &rint.

French1 teven. Wither Wave Function Realism?. The Wave

Function: Essays on the Metaphysics of Quantum Mechanics. 4d.)l$ert1 2avid 5 and )lyssa1 Ney. Ne' 6or,7 O(ord 8niversity &ress19:;3. =>-:. &rint.

@. Ae'is1 &eter. 2imension and Illusion. The Wave Function: Essays

on the Metaphysics of Quantum Mechanics. 4d. )l$ert1 2avid 5 and

)lyssa1 Ney. Ne' 6or,7 O(ord 8niversity &ress1 9:;3. ;;:-;9<.

&rint.

M$u'"!n3 T!m T%e N$tu(e o1 t%e Qu$ntum St$te he $ave %unction&

'ssays on the (etaphysics of )uantum (echanics E' A"e(t3 D$!' $n'

A"#ss$3 Ne# Ne/ o(* O,1o(' Un!e(s!t# P(ess3 06 B-J6 P(!nt

"onton1 0radley. )gainst 3N-2imensional !ace. The Wave

Function: Essays on the Metaphysics of Quantum Mechanics. 4d.

)l$ert1 2avid 5 and )lyssa1 Ney. Ne' 6or,7 O(ord 8niversity &ress1

9:;3. ;<B-;>=. &rint.

6B



Resn!*3 M!c%$e" D 7et/een M$t%em$t!cs $n' P%#s!csG P+*& Proceedings of

the -iennial (eeting of the Philosophy of +cience *ssociation KK0 :KK0>

6BK]6L We J Se2t 0=

C%!%$($3 C%$("es S A St(uctu($" Account o1 M$t%em$t!cs O,1o(' O,1o(' UP300= B P(!nt

Ho1/ee(3 T%om$s3 Zo4!c $n' Onto"o4#3 he +tanford 'ncyclopedia of

Philosophy :F$"" 0= E'!t!on>3 E'/$(' N $"t$ :e'>3 URZ

%tt22"$tost$n1o('e'u$(c%!es1$""0=ent(!es"o4!c-onto"o4#\

E!nste!n3 A3 Po'o"s*#3 73 ^ Rosen3 N :n'> C$n Qu$ntum-Mec%$n!c$"

Desc(!2t!on o1 P%#s!c$" Re$"!t# 7e Cons!'e(e' Com2"ete? Physical ,eview0

-0

He!sene(43 W :KJ0> he physical principles of the 1uantum theory :2 =>

Ne/ o(* Doe( Pu"!c$t!ons

;(!<t%s3 D :00J> Introduction to 1uantum mechanics :n' e'> U22e(S$''"e R!e(3 NY Pe$(son P(ent!ce H$""

http://plato.stanford.edu/archives/fall2014/entries/logic-ontology/

http://plato.stanford.edu/archives/fall2014/entries/logic-ontology/

raj bhakta polymathic thesis

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