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On he ca ie o ine ia
G ahn, Pa ick; Annila, A o; Kolehmainen, E kki
G ahn, P., Annila, A., & Kolehmainen, E. (2018). On he ca ie o ine ia. AIP
Ad ances, 8(3), A icle 035028. h ps://doi.o g/10.1063/1.5020240
2018
On he ca ie o ine ia
Pa ick G ahn, A o Annila, and E kki Kolehmainen
Ci a ion: AIP Ad ances 8, 035028 (2018); doi: 10.1063/1.5020240
View online: h ps://doi.o g/10.1063/1.5020240
View Table o Con en s: h p://aip.sci a ion.o g/ oc/ad /8/3
Published by he Ame ican Ins i u e o Physics
AIP ADVANCES 8, 035028 (2018)
On he ca ie o ine ia
Pa ick G ahn,1,aA o Annila,2,band E kki Kolehmainen3,c
1COMSOL, FI-00560 Helsinki, Finland
2Depa men o Physics, Uni e si y o Helsinki, FI-00014 Helsinki, Finland
3Depa men o Chemis y, Uni e si y o Jy ¨
askyl¨
a, FI-40014 Jy ¨
askyl¨
a, Finland
(Recei ed 21 Decembe 2017; accep ed 21 Ma ch 2018; published online 29 Ma ch 2018)
A change in momen um will ine i ably pe u b he all-emb acing acuum, whose eac-
ion we unde s and as ine ia. Since he acuum’s physical p ope ies ela e o ligh , we
p opose ha he acuum embodies pho ons, bu in pai s wi hou ne elec omagne ic
ields. In his physical o m he ee space houses ene gy in balance wi h he ene gy o
ma e in he whole Uni e se. Likewise, we eason ha a local g a i a ional po en ial
is he acuum in a local balance wi h ene gy ha is bound o a body. Since a body
couples o he same acuum uni e sally and locally, we unde s and ha ine ial and
g a i a ional masses a e iden ical. By he same oken, we in e ha g a i y and elec o-
magne ism sha e he simila unc ional o m because bo h a e ca ied by he acuum
pho ons as pai ed and unpai ed. © 2018 Au ho (s). All a icle con en , excep whe e
o he wise no ed, is licensed unde a C ea i e Commons A ibu ion (CC BY) license
(h p://c ea i ecommons.o g/licenses/by/4.0/). h ps://doi.o g/10.1063/1.5020240
I. INTRODUCTION
How does mass ou he e in luence mo ions he e? The ques ion calls o he ca ie o ine ia.
In con as , he cause o ine ia is known. Ine ia is he g a i a ional eac ion due o he o al mass o
he Uni e se.1–4The a gumen o he cause o ine ia is i ial. The uni e sal g a i a ional po en ial
expe ienced he e builds up wi h dis ance om he bodies ou he e because he numbe o bodies
inc eases as 2and g a i a ional po en ial alls as 1/ . Thus, he mos dis an ma e in he Uni e se
con ibu es mos o ine ia. I is puzzling only how he eac ion due o he bodies ou he e ac s a
once he e.
The ac ion a a dis ance oubled New on: “Tha g a i y should be inna e, inhe en and essen ial o
ma e , so ha one body may ac upon ano he a -a-dis ance, h ough a acuum, wi hou he media ion
o ... om one o ano he , is o me so g ea an absu di y ha I belie e no man, who has in philosophical
ma e s a compe en acul y o hinking, can e e all in o i .”5F om his pe spec i e gene al ela i i y
is an excellen ma hema ical model o g a i a ion bu no an explana ion o ine ia when wi hou he
ca ie o g a i a ion. Cu ed space ime wi hou subs ance canno eac agains a physical ac ion.
Despi e being ins an aneous, ine ia has all he hallma ks o a adia i e in e ac ion ha p opaga es
a he ini e speed o ligh . In o he wo ds, g a i y and elec omagne ism ha e he same o m o o ce.6
Thus, i is pe plexing how he eac ion can display he same cha ac e is ics as ligh and s ill appea as
i i we e an ac ion a a dis ance. Pu di e en ly, how ine ia can esul om he mos dis an bodies
ou he e and s ill mani es i sel ins an aneously he e, jus like a local ield. Pieces o he puzzle do
no i each o he , o do hey?
Ma hema ically i is possible o combine wa es ha p opaga e o wa d in ime wi h hose ha
p opaga e backwa d in ime o make up an ins an aneous e ec .7Howe e , his solu ion by symme y
appea s in a logical con adic ion wi h ime’s asymme y, ha is, wi h he uni e sal a ow o ime
esul ing om he Uni e se’s dilu ing expansion.8–10 The u u e is no he pas . The e o e, i is ha d
aEmail: [email p o ec ed]
bCo espondence: P o . A o Annila [email p o ec ed]
cEmail: [email p o ec ed]
2158-3226/2018/8(3)/035028/13 8, 035028-1 ©Au ho (s) 2018
035028-2 G ahn, Annila, and Kolehmainen AIP Ad ances 8, 035028 (2018)
o us o imagine how he pos ula ed pai ing o g a i a ional wa es o ins an aneous e ec s could
possibly be uni e sally pe ec .
The p oblem is no me e i e e sibili y bu also pa h-dependence. The Uni e se displays his-
o y. The p esen acc ues along he uni e sal e olu iona y cou se om all he pas s a es in a
non-de e mina e manne . Today is no dic a ed de e minis ically and solely by he ini ial s a e.
Al eady he mos dis an obse a ion o uni e sal e olu ion, namely cosmic mic owa e backg ound
CMB adia ion11,12 e eals ha low mul ipoles o angula decomposi ion a e no independen bu
anomalously co ela ed.13–15 In gene al, subsequen s a es a e co ela ed along he pa h o a non-
holonomic p ocess.10,16,17 When his o y ma e s, he ime- and pa h-dependen ajec o ies a e a
a iance wi h cons an -ene gy equa ions o mo ions ha can, a leas in p inciple, be ans o med o
ime-independen ames.18
Then again, he pu a i e local ield, as a means o he immedia e eac ion, ough o be physical
and ha e i s sou ces, jus like any o he ield. This implies some subs ance ha embodies he uni e sal
g a i a ional po en ial in balance wi h i s sou ces, ha is, wi h all bodies in he Uni e se. The pos u-
la ed physical acuum seems o in i e a e u n o he e he , which, in u n, has been abandoned since
Michelson-Mo ley expe imen and ad en o gene al ela i i y.19,20 To a oid his con lic , a ious
ansien and i ual ields ha e been sugges ed.21–24 In his way he acuum is pic u ed o possess
epheme al ene gy densi y abou nJ/m3, ye wi hou any eal subs ance.25 The p e ailing pe cep ion
o acuum appea s o be inconsis en in one way o he o he .
The success o mode n physics, howe e , does no exclude ha he acuum is some ela i is ic
physical subs ance whose e ec s a e modeled wi h g ea p ecision.26 This is unde s ood. Fo example,
quan um g a i y assumes ha space has disc e e s uc u e.27 To ind a way ou o he deadlock we
b ing o wa d he ecen ly econside ed possibili y ha he acuum is, a e all, a physical medium,
no sus aining pho on p opaga ion, bu being he pho ons hemsel es.28–31 Ou p oposal complies
wi h mode n physics ye embodies he acuum wi h he physical ca ie . When he e is no appa en
disag eemen wi h con empo a y calcula ions, we see no ob ious oppo uni y o p opose clea -cu
p edic ions o es ou physical pe cep ion o he acuum agains ma hema ical modeling o da a.
Ins ead, we examine a ious phenomena o look o obse a ional e idence agains ou p oposal and
o logical laws.
II. THE PHOTON-EMBODIED PHYSICAL VACUUM
We p opose ha he pho ons in ee space do no p opaga e exclusi ely in he o m o single
quan a o ligh , bu in pai s whe e he wo pho ons a e comple ely ou -o -phase (Fig. 1). Then
elec omagne ic ields o he wo pho ons sum o ze o. The exac cancella ion is amilia om an
an i- e lec ion coa ing. A hin ilm does no ac ually p e en he pho ons om e lec ing bu combines
e lec ed ays o des uc i e in e e ence. A coa ed lens appea s anspa en , bu in ac , no all pho ons
a e ansmi ed h ough.32 In he exac ou -o -phase con igu a ion, he pai ed pho ons ca y ene gy
densi y wi hou a ne elec omagne ic ield. This na u al ee ene gy minimum s a e o acuum, known
also as space, is da k and ine as obse ed.
FIG. 1. When wo pho ons, whose elec omagne ic ields shown in blue and ed, co-p opaga e exac ly ou -o -phase, he e is
no ne elec omagne ic ield, and hence he pho on pai ca ies me e ene gy densi y (a). When he phase con igu a ion depa s
om he comple e des uc i e in e e ence, e.g., nea a cha ge, elec omagne ic ields mani es hemsel es (b).
035028-3 G ahn, Annila, and Kolehmainen AIP Ad ances 8, 035028 (2018)
FIG. 2. Two iden ical pho ons (a ows) p opaga e a igh angles owa d each o he and s ike concu en ly a beam spli e (g ay
ba ). A single pho on may wi h equal p obabili y ei he pass h ough o e lec , bu when wo pho ons a i e simul aneously,
he cou se o e en s is di e en . The wo pho ons when comple ely ou -o -phase will pai o co-p opaga ion as in (a) and (b)
because he esul ing pho on pai wi hou a ne elec omagne ic ield (des uc i e in e e ence) is lowe in ene gy han wo
dis inc pho ons. In o he wo ds, i would be ene ge ically un a o able i he wo coinciden pho ons we e bo h o e lec (c)
o ansmi (d).
The pai ing o pho ons o co-p opaga ion was demons a ed, as i now seems o us, by Hong,
Ou, and Mandel in 1987.33 In he amous HOM-expe imen , wo iden ical pho ons p opaga e a
igh angles owa d each o he and hi a beam spli e simul aneously (Fig. 2). When one pho on
e lec s and he o he ansmi s h ough, we conclude ha he wo pho ons pai . The obse ed signal,
known as he Hong-Ou-Mandel dip34 sums he elec omagne ic ields o he wo pho ons wi hin hei
cohe ence leng h. When he pai ing is pe ec ly ou -o -phase, he signal is a a minimum, i.e., no ligh
is obse ed.
The pho on pai ing is ene ge ically a o able since he opposi e phenomenon whe e pho ons a e
gene a ed om he acuum, consumes ene gy.35 Consis en ly, we eason ha i bo h pho ons we e
ei he e lec ed o ansmi ed h ough, hey should be isible. Bu since no ligh is de ec ed, we
conclude ha he co-inciden pho ons canno bu pai o he ene ge ically a o able s a e.
Ou physical in e p e a ion o he HOM-expe imen di e s om he ma hema ical accoun by
quan um mechanics whe e all ou op ions o he e lec ion and ansmission a e summed o ma ch
he measu ed ou come o no ligh . On he o he hand, we main ain jus as quan um mechanics ha he
des uc i e in e e ence, i.e., he pai ing will happen, only i he wo pho ons a e indis inguishable
om each o he wi hin Heisenbe g’s unce ain y when hey a i e a he beam spli e .
Mo eo e , he HOM-expe imen exempli ies ou implici pos ula e: he pho on is indi isible and
e e nal basic cons i uen o na u e. This a omis ic ene lea es no oom o addi ions o excep ions. I
could be alsi ied by an expe imen whe e he pos ula ed pho on conse a ion is iola ed. O cou se,
ou s ance may seem all ou da ed, because in mode n physics he pho on numbe is no conse ed.
This u h we wish o ques ion. We simply main ain ha he pai ed pho ons ha e inconspicuously
gone by, ye hei e ec s, in ac , ha e been de ec ed o deduced bu no p ope ly explained.
Ou po ayal o he acuum in e ms o he pai ed pho ons makes sense o bo h adia i e
and seemingly ins an aneous a ibu es o ine ia. The acuum’s adia i e cha ac e was o malized
by Maxwell in he uni a y condi ion c2εoµo= 1. I ela es he speed o ligh o he ee space
pe mi i i y εoand pe meabili y µo. Al hough he pho on, as he o ce ca ie , has a ini e speed,
he eac ion appea s ins an aneous, because he acuum in he physical o m o pai ed pho ons is
all-a ound.
Then again, he balance be ween he acuum, as he uni e sal g a i a ional po en ial, and he
o al mass Mis gi en by he enowned ze o-ene gy p inciple Mc2–GM2/R= 0.36,37 I can also be
w i en as he uni a y condi ion GM/c2R= 4πGρ 2= 1, whe e he uni e sal mass Mis wi hin adius
R=c o he Uni e se a i s cu en age = 13.8 billion yea s, and Gis he g a i a ional cons an . The
a e age densi y o ma e ρ= 6.12×10-27 kg/m3in he Uni e se co esponds o he a e age ene gy
densi y 0.55 nJ/m3.25 I co esponds o he cosmological cons an Λ≈10

122 in Planck uni s and
o he ecip ocal o he age o he Uni e se squa ed by he uni a y condi ion. We eason as ea lie 38
ha he acuum is e ol ing so ha Λ∼

2 h oughou he his o y o he uni e se. In he e ol ing
Uni e se cand Gcanno be cons an s bu unc ions o he dec easing uni e sal ene gy densi y.39,40
In he o he wo ds, p ope ies o he dilu ing acuum a e changing, jus as p ope ies o any o he
e ol ing subs ance.
The idea o pho on-embodied acuum en ails ha he quan um o ligh is an indes uc ible
en i y.41,42 O he wise, he acuum could collapse o anish al oge he o eme ge om no hing.

035028-4 G ahn, Annila, and Kolehmainen AIP Ad ances 8, 035028 (2018)
The conse a ion o quan a means by Noe he ’s heo em43 ha in o al he e a e n=Mc2 /h=c5 2/Gh
≈10121 quan a.30 Acco dingly, when a subsys em opens up o adia i e emission, a leas one bound
quan um o ac ion as an in eg al pa o he ma e will become a ee quan um as an in eg al pa o
he su ounding space.29,31,44 Con a ywise, quan a a e abso bed om adia ion o ma e .
We emind igh away ha his iew o he pho on as he elemen a y cons i uen was abandoned
sho ly a e as i s in oduc ion.42 A ha ime he a omis ic no ion was hough o be a a iance wi h
adia i e decay ia wo o mo e al e na i e pa hs. Namely, he conse a ion o quan a seems o be
iola ed when an ini ial s a e decays o one and he same g ound s a e ei he di ec ly by a single pho on
emission o ia wo in e media e s a es yielding h ee pho ons in succession. Howe e , o ejec he
conse a ion o quan a on hese g ounds does no appea o us ull p oo , because he quan a in
he o m o pai ed pho ons a e no conside ed and coun ed. The e o e, we hink i is o in e es o
see wha can be explained and unde s ood by he pho on-embodied acuum – and e en ually wha
canno .
Ou examina ions a e no exhaus i e, and ou e e ences a e no comple e, bu we belie e ha
he p oposal would be comp ehensi e enough o ins iga e also o he a emp s o alsi y he physical
acuum ha embodies ains o pai ed pho ons. Mo eo e , we mo i a e in e es in ine ia jus as he
pionee s and con empo a ies. Namely, ine ia in ol es he whole Uni e se, and hence i s comp e-
hension may hold he key o p oblems o cosmology ha mani es hemsel es mos no ably as da k
ene gy and da k ma e .
III. PERCEPTION BY THE PHYSICAL VACUUM
The acuum is in ol ed in many phenomena. Mos no ably, i exe s o ces as elec omagne ic
and g a i a ional ields. The essence o acuum en ails also explana ion o i s o igin and e olu ion.
The e o e, we ind wo h inspec ing he basics a he han engaging in in icacies and con o e sies.
A. Radia i e and ins an aneous ine ia
The e is no dilemma wi h ins an aneous eac ion despi e he ini e speed o ligh , p o ided ha
he pai ed-pho on ene gy densi y is a hand e e ywhe e. The omnip esen subs ance will eac o any
ac ion a once.
The uni e sal g a i a ional po en ial is highly in a ian because i sums g a i a ional po en ials o
all bodies ou he e. Only a massi e dema e ializa ion, e.g., ou a a dis an galaxy could momen a ily
pe u b ine ia he e. Such a pe u ba ion would a i e he e a he speed o ligh , and hence could,
a leas in p inciple, be de ec ed by measu ing i s eac ion o ce on a body, no only by means o
in e e ome y. The pe u ba ion on ine ia would be minu e since he powe o he p opaga ing
po en ial2will dec ease in e sely o he squa ed op ical dis ance, and di ec ly o he equency which
shi s down along i s way h ough he expanding Uni e se.45,46
Likewise, when an ac ion pe u bs he pho on-embodied acuum he e, he ensuing eac ion as
an ene gy densi y wa e will begin o p opaga e he Uni e se o e . E en ually, i will each dis an
bodies ou he e. By he same oken, when he acuum is egaining i s balance a e he pe u ba ion
he e, a body ou he e will be ossed ha dly a all.
A change in momen um d pwill ine i ably en ail some dissipa ion, i.e., in ol e wo k, and hence
una oidably couple o he uni e sal acuum. Fo ins ance, ou mo ion along wi h he Milky Way is
inescapably somewha asymme ic, i.e., non-ine ial ela i e o bodies in he es o he Uni e se.
The e o e, he cosmic mic owa e backg ound adia ion has a dipola empe a u e g adien ac oss he
sky. Likewise, accele a ion ela i e o he physical acuum will mani es i sel as Un uh e ec .47 In
ac , no mo ion along a piece o an open ajec o y is uly non-dissipa i e because he mo ing body
will in a iably keep changing i s s a e ela i e o some o he bodies whose dis ibu ion is asymme ic,
albei iso opic on he la ges scale. Con e sely, when he o bi o a body closes exac ly, he e is no
ne dissipa ion because hen he ini ial and inal s a es a e one and he same s a e.
B. Ro a ional ine ia
In ex book physics, cen i ugal o ce is e e ed o as a ic i ious o ce, bu i eels e y eal on
a ca ousel. The physical acuum esol es he disc epancy be ween he doc ine and own expe ience.
035028-5 G ahn, Annila, and Kolehmainen AIP Ad ances 8, 035028 (2018)
When he body mo es along a cu ilinea ajec o y, i s s a e keeps changing ela i e o he uni e sal
acuum which is he o al ield o all bodies in he uni e se. In he same way, o a ional ine ia is
unde s ood as he eac ion aken by he uni e sal acuum o balance he ac ion due o he body mo ing
along an o bi . The quad a ic dependence 2o o a ional ine ia on he dis ance om he axis o
o a ion ollows om he same easoning ha he la ge he adius o o a ion, he la ge ealm o
su ounding ene gy densi y is pe u bed.
The g a i y o dis an bodies mani es s i sel ia he physical acuum so ha a spinning body is
obla e and ha he meniscus o wa e in a spinning bucke is cu ed.48 In ques o a aining balance,
he physical acuum exe s a o ce on bodies jus as we expe ience ine ia by ou own body. Fo
example, a op is spinning s eadily, because any pe u ba ion would de ia e he acuum, ha is, he
uni e sal g a i a ional ield away om he ene gy op imum. Fo his one and he same eason, he
dwa galaxies a e o bi ing in he plane o spi al galaxies49 and no in andom o ien a ions. S ill, i
may ake eons o a celes ial sys em o a ain he he modynamic balance o plana mo ion, e.g., a e
a galaxy me ge .
The loss o ene gy and angula momen um in g a i a ional adia ion is well-known om bina y
pulsa s50 and an icipa ed by gene al ela i i y. We only o e ha he g a i a ional adia ion is in he
o m o pai ed pho ons.
C. The equi alence p inciple
The g a i a ional mass and ine ial mass a e equi alen o he g ea es p ecision, howe e , wi hou
explana ion. Since bo h he uni e sal acuum and he local g a i a ional po en ial embody he pai ed
pho ons, he e is no op ion, bu he equi alence o he local and uni e sal coupling is inescapable.
In gene al ela i i y, ine ia is he g a i a ional coupling be ween ma e and space ime. Like-
wise, we unde s and ha a body couples o he acuum. We only asc ibe space wi h he pai ed-pho on
physical subs ance. The mass is a coupling cons an be ween he body and he acuum. Eule de ined
he co esponding cha ac e is ic as he o al geodesic cu a u e. I exp esses how much he pa i-
cle, as a quan ized ac ion, is mo e cu ed han he uni e sal acuum whe e he pho ons p opaga e
eely.28,51–54 The mass only appea s as he body’s in a ian a ibu e a he han he coupling cons an ,
because he iny e e ence cu a u e 1/Ro he expanding Uni e se is la ening e y slowly.
Howe e , changes in mass can be sudden and d ama ic. Fo example, when W--boson decays o
elec on and an ineu ino, he mass changes om 80 GeV/c2 o 0.511 MeV/c2. This unde lines ha
he mass is he measu e o coupling be ween he pa icle and acuum ins ead o a sole p ope y o he
pa icle. By he same oken, o dina y pa icles may ha e peculia masses in anomalous ci cums ances,
like elec ons in g aphene. Then he su ounding ield is unusual while he elec ons hemsel es a e
as usual.
I is wo h emphasizing ha he cu ed space ime is an excellen ma hema ical model o he
pho on-embodied acuum.55 Fo example, he quan a o ligh ha p opaga e om he uni e sal
acuum in o he local g a i a ional ield o a body will inc ease in ene gy densi y, i.e., blue-shi o
main ain he modynamic balance in he dense su oundings.
D. G a i y as an ene gy di e ence
Gene al ela i i y ega ds g a i y no as a o ce, bu as a mani es a ion o he cu ed space ime
due o he une en dis ibu ion o mass. In con as , when he acuum is pe cei ed as he physical
subs ance, g a i y is a o ce. I is caused by he acuum’s densi y di e ences due o he une en
dis ibu ion o mass. F om his pe spec i e, he bodies mo e in space because hey a e coupled o he
acuum which is in mo ion owa d balance.
Speci ically, he bodies a e mo ing owa d each o he , when he quan a in he dense g a i a ional
ield be ween he bodies a e escaping o spa se su oundings. The e o e, an apple alls o he g ound.
Con e sely, he bodies a e mo ing apa when he quan a a e s eaming be ween he bodies om he
su oundings. Dis an galaxies a e mo ing away om us, because hey couple o he low o quan a
ha he Uni e se shines, albei mos ly as he in isible pai ed pho ons, be ween us and he dis an
bodies.30,56,57
In his way, we unde s and ha g a i y is no exclusi ely an a ac i e o ce bu also epulsi e.
This dual cha ac e o g a i y is no di e en om ha o he elec os a ic o ce. Two cha ges o
035028-6 G ahn, Annila, and Kolehmainen AIP Ad ances 8, 035028 (2018)
opposi e sign do no ine i ably a ac each o he bu mo e also apa depending on he su ounding
ene gy densi y. “Repulsion” o anions and ca ions is ob ious when a sal c ys al dissol es in wa e .
Ou accoun o g a i y in e ms o he acuum in mo ion pa allels hough s o Riemann,
Ya ko sky, and Hea iside. They pic u ed he g a i a ional ield as a luid, including ma e as sou ces
and sinks. Howe e , he ea ly mechanical heo ies o g a i y did no explici ly speci y he sub-
s ance o acuum. Also, mode n heo ies a emp o desc ibe g a i y in e ms o quan a a he
han me e me ic. Today, jus as ea lie , he essence o space is he key o he comp ehension o
g a i y.
To p o ide oppo uni ies o alsi y he pai ed-pho on embodied g a i a ional po en ial, we main-
ain ha he g a i y is a dissipa i e phenomenon. When he ini ial and inal s a es a e dis inc om
each o he , he e ough o be some sign o dissipa ion. Fo example, he anomalous accele a ion ha
spacec a ha e acqui ed du ing lybys58 can be in e p e ed in his way.59 Also, his phenomenon has
been explained al eady ea lie as he Hubble-scale Casimi e ec .60,61
The uni e sal acuum as he g a i a ional ield o all bodies is iso opic bu no uni o m. The e is
an ene gy densi y g adien ac oss he expanding Uni e se. The con empo a y su oundings a e spa se
whe eas he dis an nascen en i on is dense in ene gy. The g adien mani es s i sel as he uni e sal
g a i a ional o ce. The esul ing accele a ion, ao=c/ =cH in e ms o Hubble cons an H, is on he
o de o 10-10 ms-2 pe cycle. I is balanced by mo ions ha display hemsel es in galaxy o a ion and
eloci y dispe sion o galaxies.30,62,63 Since he uni e sal g a i a ional ield is p esen e e ywhe e,
i mani es s i sel in a law-like manne .64 By he same oken, no da k ma e is needed o accoun
o he escape eloci ies o Milky Way and And omeda.65 Mo eo e , he g a i a ional po en ials o
galaxy g oups seem oo b oad o explain by da k ma e .66 The uni e sal po en ial, on he o he hand,
is na u ally shallow and o a wide ange.
Su ely, he iny accele a ion is al eady included in modi ied New onian dynamics (MOND), bu
he model wi hou physical subs ance does no ela e he galaxy o a ion and eloci y dispe sion o
he uni e sal expansion. Mo eo e , we a e by no means o iginal by explaining he galaxy o a ion
wi hou da k ma e by quan ized ine ia ha e ol es along wi h he expanding Uni e se.67 In ac ,
ou p ima y aim he e is no o ep oduce a ious obse a ional da a by modeling bu o look o an
obse a ion ha would be in con lic wi h he p oposed pai ed-pho on acuum.
In gene al, he a ow o ime ela es o ee ene gy consump ion.8,10 F om his pe spec i e he
Uni e se does no expand wi hou cause as in he Big Bang heo y bu due o combus ion o ma e -
bound high-ene gy quan a o hose ee quan a o low-ene gy ha embody he acuum.17,57,58 The
cu en a e o expansion, i.e., on-going gene a ion o acuum om ma e , depends on mechanisms o
ans o ma ion, mos no ably nuclea eac ions in con empo a y s a s o a ious kinds including black
holes. Likewise, he nascen a e o expansion mus ha e depended on p imo dial mechanisms. They
p oduced ing edien s o ba yogenesis along wi h he dissipa ed quan a ha cons i u e he ea lies
and hence by now he coldes space.
E. Appea ance o elec omagne ic o ce ca ie s
Acco ding o he ex book physics, i seems a bi o a puzzle om whe e he pho ons o elec-
omagne ic ield appea ins an aneously, o example, when an a om ionizes. In con as , he e is no
mys e y when he pho ons a e unde s ood o be p esen bu pai ed in he ou -o -phase con igu a ion.
Elec omagne ic ields appea immedia ely when he a om ionizes and induces a phase shi away
om he pai ed-pho on minimum-ene gy con igu a ion (Fig. 1). Then, he pho ons can be de ec ed
easily. In o he wo ds, he s eng h o elec omagne ism is he measu e o he acuum’s s eng h.
I is wo h ecalling ha he ex book’s i ual pho on comes in o exis ence when i is de ec ed.
Thus, conside ing he pai ed-pho on acuum is no o mally ha di e en om pic u ing he i ual
pa icle acuum. Mo eo e , acco ding o mode n physics, acuum luc ua ions can be con e ed in o
eal pho ons.68 Al eady Maxwell conside ed ligh as undula ions o e he .69 When he wa es o
acuum a e pho ons, hen i is only logical ha he acuum is pho ons.
F. Casimi e ec
When he acuum is unde s ood o embody he pai ed pho ons, ins ead o he i ual pho ons,
hen also he Casimi e ec 70 can be desc ibed in angible e ms. The e is a ne o ce be ween adjacen
035028-7 G ahn, Annila, and Kolehmainen AIP Ad ances 8, 035028 (2018)
pla es when he e is an ene gy densi y di e ence be ween he iny slo and i s uni e sal su oundings.
In o he wo ds, he acuum in he small gap is no he same as ou side. This conclusion is o cou se
no hing new bu he e y essence o ine ia om ea ly on.23,71
Fu he mo e, we unde s and he dynamical Casimi e ec 34 so ha a high- equency pe u ba ion
will o ce he pho ons in pai s away om he pe ec ou -o -phase balance. Then he single pho ons
will eme ge o de ec ion in mic owa e band ha co e s mos o he acuum’s spec um.
Mo eo e , luc ua ions in he pho on-embodied acuum we unde s and o esul in he Lamb
Shi in he same way as quan um elec odynamics a ibu es luc ua ions o he ield- heo e ic ac-
uum.72,73 The pai ed quan a luc ua e abou he ee ene gy minimum s a e, and hence hei phases
shi ansien ly away om he pe ec cancela ion. This qui e ing po en ial gi es ise o a small bu
de ec able e ec on elec on o bi s.
Ou p oposal implies ha elec omagne ism and g a i y due o hei common o ce ca ie a e
insepa able. This can be quali a i ely unde s ood o mani es , o ins ance, as a di e ence in he
measu ed p o on cha ged adius depending on whe he an elec on o a much hea ie muon is ci cu-
la ing he nucleus.74–76 The anomalous inc ease in he p o on-muon binding ene gy has al eady been
a ibu ed o a change in he su ounding adia ion.77 We eason along he same lines. The p o on
i sel emains in ac , bu i s su ounding Coulomb ield due o he muon is dense han due o he
elec on.
G. Double-sli expe imen
Concep ual conund ums o he double-sli expe imen esol e when pho ons, elec ons and o he
p ojec iles on hei way o he de ec o a e unde s ood o pe u b and in e e e wi h he pai ed-pho on
acuum. The pa icle, ha goes h ough one o he sli s, gene a es wa es o he acuum ha go also
h ough he o he sli and subsequen ly in e e e wi h he pa icle be o e i s ikes he de ec o . Pu
di e en ly, oublesome concep ual cons uc s o simul aneous ajec o ies ia bo h sli s ha e been
in oked because he physical acuum has been igno ed and he p ojec iles ha e been assumed o
p opaga e in a comple e emp iness.
Ou easoning is, o cou se, amilia om he pilo wa e heo y ha de B oglie p oposed.78
Howe e , ou pe cep ion does no en ail de e minism bu non-de e minism. The pa icle’s pa h canno
be p edic ed because i s mo ion a ec s he acuum which in u n a ec s he pa icle and so on. When
he o ce and mo ion canno be sepa a ed, he equa ion o mo ion canno be sol ed. On he o he hand,
quan um mechanics wi h he pa icle wa e unc ion is an excellen model o he pe u bed physical
acuum. Howe e , he s a is ical accoun assuming inde e minism does no desc ibe anyone pa icle
in p opaga ion, only he ou come o nume ous expe imen s.
We hink ha he pai ed-pho on acuum is consis en also wi h esul s when he p opaga ion o
elec ons h ough he sli s is moni o ed. When he elec ons a e obse ed gen ly nea he de ec o ,
he in e e ence pa e n does no anish al oge he . We in e p e his esul so ha he elec on ha
passed h ough ei he one o he sli s has al eady pa ially expe ienced he acuum wa es ha wen
h ough he o he sli . On he o he hand, when he elec ons a e moni o ed immedia ely a e he
sli s, he in e e ence pa e n is des oyed.79
Likewise, we ind he pai ed-pho on acuum consis en wi h he A sha expe imen .80 An
obs uc ing g id o wi es, when placed a he nodes o he in e e ence pa e n, does no al e he
ou come. We unde s and his so ha ma e , apa om i s mass, is anspa en o he pai ed pho ons.
The e o e, he wi e g id a he ou -o -phase nodes does no des oy in e e ence. We also hink ha he
epea ed and enowned expe imen indeed e eals ha he pa icle and he acuum wa e a e dis inc
om each o he albei complemen a y. Also, a mac oscopic body, e.g., a plane and i s g a i a ional
ield a e dis inc om each o he albei complemen a y.
The Aha ono –Bohm e ec ,81 in u n, we in e p e o demons a e ha he su ounding ene gy
densi y is a sum o an applied ec o po en ial and he omnip esen acuum po en ial. Since he
inc ease in ene gy densi y along he pa icle’s pa h o p opaga ion, displays i sel as an addi ional
phase shi , he e should be no in e e ence a all, i he acuum had no physical densi y a all.
Con e sely, we eason ha he acuum ene gy densi y could in p inciple be de e mined om he
shi ing phase e sus he applied ec o po en ial.