TIME TRAVEL ON EARTH IS FEASIBLE

40 Danish Scien i ic Jou nal No100, 2025
PHYSICAL SCIENCES
TIME TRAVEL ON EARTH IS FEASIBLE
An ono A.
PhD, HonDSc, H.P o Sci,
Independen esea che , Kie , Uk aine
h ps://doi.o g/10.5281/zenodo.17249786
Abs ac
The a icle p o es ha he e sion o he special ela i i y heo y (SRT) ha is augh in all physics ex books
is inco ec , since he ela i is ic o mulas ob ained in i a e inco ec and hey a e inco ec ly explained using he
inco ec p inciple o no exceeding he speed o ligh . They also d aw inco ec conclusions abou he physical
un eali y o imagina y numbe s and he exis ence in na u e o only ou isible uni e se.
A co ec ed e sion o he SRT is p esen ed and i is explained ha he a gumen ‘speed’ in he co ec ed
ela i is ic o mulas is, in acco dance wi h New on’s i s law, he ou h spa ial dimension. The p inciple o he
physical eali y o imagina y numbe s is expe imen ally p o en, which e u es he p inciple o no exceeding he
speed o ligh . I is shown ha he SRT, on he one hand, and adio enginee ing, elec ical enginee ing and com-
pu e enginee ing, on he o he hand, mu ually e u e each o he . I is explained ha in na u e, in addi ion o ou
isible uni e se, he e a e many mu ually in isible, since hey a e in di e en dimensions, uni e ses and an i-
uni e ses, which a e da k ma e and da k ene gy. This explains he well-known p ope ies o da k ma e and da k
ene gy - hei in isibili y and he absence o co puscula con en . The e o e no s udies a he La ge Had on Collide
can explain he phenomena o da k ma e and da k ene gy.
I is explained also ha in he an i-uni e ses o such an in isible Mul i e se he e is an i-ma e and an i- ime.
The e o e, ime a el is possible in i . Time a el is also a ailable o people on Ea h.
Keywo ds: special ela i i y heo y, ela i is ic o mulas, Mul i e se, an i-uni e se, an ima e , an i- ime,
a ow o ime, in e nal ime, ex e nal ime, ime zones o Ea h, ime a els
1.In oduc ion
The 20 h cen u y in physics was ich in new in e -
es ing scien i ic ideas. Bu some o hem, al hough hey
we e called heo ies, ha e no ye ecei ed expe i-
men al con i ma ion. And one o hem is he special el-
a i i y heo y (SRT) [1]-[3], which was nomina ed o
he Nobel P ize 66 imes. Howe e , due o he lack o
expe imen al con i ma ion, she ne e ecei ed i .And
he Nobel Commi ee u ned ou o be igh , since in he
21s cen u y, i s indispu able expe imen al e u a ions
we e published.Ne e heless, his e sion o SRT is
now s udied in all physics ex books used in he educa-
ional p ocess e en in he mos p es igious uni e si ies.
2. The e sion o SRT augh in all physics ex -
books is inco ec
The gene ally accep ed e sion o SRT is inco ec
because he ela i is ic o mulas ob ained by i s c ea-
o s – Joseph La mo [4], Nobel lau ea e Hend ik An-
on Lo en z
1
[5], Jules Hen i Poinca é [6], Nobel lau e-
a e Albe Eins ein
2
[7] and o he ou s anding scien is s
– a e inco ec :
Fig 1. G aphs o unc ions m( ), Δ ( ), l( ), co esponding o he exis ing and co ec ed e sions o SRT in he
subluminal < c and hype luminal > c anges
1
Who ecei ed his Nobel P ize in 1902 o explaining he
Zeeman e ec .
2
Who ecei ed his Nobel P ize in 1921 o s udying he pho-
oelec ic e ec .
Danish Scien i ic Jou nal No100, 2025 41
𝑚=𝑚0 /√1−(𝑣
𝑐)]2 (1)
𝛥𝑡=𝛥𝑡0√1−(𝑣
𝑐) 2 (2)
𝑙=𝑙0√1−(𝑣
𝑐)]2 (3)
Mo eo e , he c ea o s o SRT could no e en ex-
plain hese o mulas. And he e o e much o wha hey
did la e was done inco ec ly:
• Fi s , hey did no unde s and ha he alue in
hese o mulas, in acco dance wi h New on's i s law,
is he ou h spa ial dimension, in addi ion o leng h,
wid h, and heigh . The e o e, ela i is ic o mulas had
o be explained no only in he subligh < c ange, bu
also in he hype ligh < c ange. Howe e , his was
no done.
• Second, no unde s anding he physical meaning
o he imagina y alues o he quan i ies m( ), ( ), l( )
in he hype ligh > c ange o speeds, he au ho s o
STR, in o de no o explain hei ela i is ic o mulas
in his ange, in oduced in o STR a pos ula e called he
p inciple o no exceeding he speed o ligh . And based
on his pos ula e, i is now some imes e en claimed ha
Albe Eins ein unde s ood ha no hing in he Uni e se
can mo e as e han he speed o ligh . And ha he
speed o ligh is no jus a numbe , bu a physical limi .
The same as, o example, absolu e ze o a a empe a-
u e o minus 273.15 deg ees Celsius.
• Thi dly, in he 21s cen u y, despi e he ac ha
he a emp o disp o e he STR by he OPERA expe -
imen [8] a he La ge Had on Collide was unsuccess-
ul, i was ne e heless expe imen ally p o en ha im-
agina y numbe s a e physically eal [9]-[20], and he e-
o e he p inciple o no exceeding he speed o ligh
and he STR i sel a e inco ec [21]-[49].
• Fou hly, i u ned ou ha o mula (1) in he hy-
pe ligh >c ange co esponds o a physically uns able
p ocess ha canno exis in na u e a all.
The e o e, he conclusions made in he gene ally
accep ed e sion o he SRT om hese inco ec o -
mulas using he inco ec p inciple o no exceeding he
speed o ligh a e also inco ec :
• abou he exis ence o ou only isible uni e se
in na u e;
• abou he physical un eali y o imagina y num-
be s. And, ul ima ely, his inco ec e sion o he SRT,
as a esul o he s uggle o su i al, ins ead o being
co ec ed in he u u e, ended up being canonised – a
con ic ion o med in he communi y o ela i is ic
physicis s and in public opinion abou i s in allibili y,
3
In he Uni ed S a es, he Ins i u e o Elec ical and Elec on-
ics Enginee s (IEEE) has es ab-lished an annual awa d in his
name.
4
In i s o iginal in e p e a ion, his law o di ec cu en elec-
ical ci cui s was o mula ed by Geo g Simon Ohm in 1826
a e nine yea s o expe imen al esea ch, a a ime when no
abou he inadmissibili y o i s c i icism and any subse-
quen co ec ions. The e o e, o example, in he
USSR, c i icism o he SRT was p ohibi ed h ee imes:
in 1934 by a esolu ion o he Cen al Commi ee o he
All-Union Communis Pa y (Bolshe iks) on he dis-
cussion o ela i i y, in 1942 by a esolu ion o he P e-
sidium o he Academy o Sciences o he So ie Union
on he heo y o ela i i y, and in 1964 by a sec e es-
olu ion o he P esidium o he Academy o Sciences o
he So ie Union, which p ohibi ed any c i icism o Al-
be Eins ein's heo y. This ban has no been li ed o
his day.
Un o una ely, p ohibi ing c i icism o ce ain sci-
en i ic heo ies is no a new phenomenon. Fo example,
Nicolaus Cope nicus, who spen 40 yea s in he 16 h
cen u y de eloping his heliocen ic model o he uni-
e se, p uden ly chose o publish his heo y ‘On he
Re olu ions o he Celes ial Sphe es,’ which e u ed
Claudius P olemy's geocen ic model, a e his dea h,
so as no o all oul o he Inquisi ion. Bu Gio dano
B uno and Galileo Galilei, who unwisely suppo ed Co-
pe nicus' heo y, had al eady deal wi h he Inquisi ion.
Gio dano B uno was e en bu ned ali e a he s ake.
The e o e, he common-sense p ocess o c ea ing sci-
en i ic heo ies by iden i ying ce ain sho comings in
hem as a esul o expe imen al esea ch and subse-
quen ly co ec ing hem does no always go smoo hly.
3. E idences o he physical eali y o imagi-
na y numbe s
And so as no o be un ounded, we will p o ide
one o he p oo s o he physical eali y o imagina y
numbe s wi h using he in e p e a ion o Ohm's law o
linea al e na ing cu en elec ical ci cui s p oposed by
Cha les P o eus S einme z
3
in 1893 [50]. This o mula-
ion o Ohm's law
4
p oposed e en be o e Eins ein and
Poinca é published he now uni e sally accep ed e -
sion o he special heo y o ela i i y in 1905. And
now, millions o elec ical and adio enginee s a ound
he wo ld use his o mula ion o Ohm's law in
S einme z's in e p e a ion in hei daily wo k. This, o
cou se, p o es i s alidi y. Howe e , physicis s, unable
o e u e his p oo , con inue o igno e i .
To unde s and whe he physicis s a e igh , le 's
ake a close look a his si ua ion. In S einme z's o -
mula ion o Ohm's law, i is s a ed ha no only esis-
o s ha e elec ical esis ance, bu also capaci o s and
induc o s (also called induc ance coils). Bu he e-
sis ance o esis o s is measu ed by eal numbe s R,
while he esis ance o capaci o s C and induc o s L is
measu ed by imagina y numbe s -1/jωC and jωL.
The e o e, linea elec ical LCR-ci cui s o any
elec ical measu ing ins umen s exis ed. In 1828, Ohm was
dismissed om his job by o de o he Minis e o Educa ion
o publishing his esea ch. A high- anking o icial a he ime
belie ed ha he use o ma hema ics in physics was unac-
cep able.
42 Danish Scien i ic Jou nal No100, 2025
Fig. 2. Fo se e al decades now, e e y adio enginee ing labo a o y has had ins umen s called equency e-
sponse me e s, which by hei e y exis ence p o e he physical eali y o imagina y and complex equencies,
and he e o e o any o he imagina y and complex numbe s. And hus, hey ende ed he OPERA expe imen un-
necessa y.
con igu a ion ha e esis ance measu ed by com-
plex numbe s. Consequen ly, i s alue and he alue o
he cu en lowing h ough such a ci cui , acco ding o
Ohm's law as in e p e ed by S einme z, depend on he
equency ω o he ol age applied o his elec ical ci -
cui ..
And his makes i possible o pe o m a simple bu
e y impo an expe imen ha will allow us o con i-
den ly answe he ques ion o whe he imagina y num-
be s a e physically eal. A e all, i he imagina y e-
sis ances o capaci o s and induc o s, since hey a e
measu ed by imagina y numbe s, a e physically un eal,
hen hei inclusion in elec ic ci cui s should no a ec
he esul s o measu ing he esis ance o he LCR-
ci cui in any way. The esis ance o he LCR-ci cui in
his case will always be measu ed by eal numbe s and
will no depend on he equency. And ice e sa, i he
imagina y esis ances -1/jωC and jωL a e physically
eal, hen when he equency o he ol age applied o
he LCR-ci cui changes, he alue o he cu en low-
ing h ough i will change due o he change in i s e-
sis ance.
And all enginee s know ha he esis ance o LCR
ci cui s always depends on he equency o he ol age
applied o hem, which is why he cu en alue in such
an expe imen will always change. The e o e, de ices
o eco ding such measu emen s ha e long been c e-
a ed and a e mass-p oduced – oscilloscopes, equency
esponse me e s, spec um analyze s, e c. E en many
adio ama eu s ha e he simples o such de ices – a
es e (also some imes called a mul ime e ). And his
ci cums ance, i.e. he abili y o measu e imagina y pa-
ame e s o elec ical ci cui s wi h such de ices, i e u-
ably p o es hei physical eali y. A e all, i is possi-
ble o measu e only wha eally exis s in na u e. The e-
o e, mos o wha we know abou he wo ld a ound us,
we lea ned p ecisely wi h he help o de ices – in phys-
ics, and in biology, and in chemis y, and in all o he
sciences.
Consequen ly, i he e sion o SRT s udied in
physics ex books we e co ec , hen nei he elec ical
5
And his iend William Whis on, in he a mosphe e o he
omnipo ence o he Inquisi ion, was s ipped o his p o esso -
ship and expelled om Ox o d Uni e si y o some o his
ca eless e-ma ks.
enginee ing, adio enginee ing, no compu e enginee -
ing should exis , since hese sciences use Ohm's law as
in e p e ed by S einme z. Bu hese sciences and he
co esponding elec ical and adio enginee ing p od-
uc s do exis . Mo eo e , elec ical enginee ing and a-
dio enginee ing exis ed e en be o e he c ea ion o
SRT.
O he p oo s o he physical eali y o imagina y
numbe s ha e also been published [51]-[54].
4. Re ised e sion o SRT; in isible uni e ses
and an i-uni e ses, hid-den Mul i e se
Since, as has jus been p o en, imagina y numbe s
a e physically eal, he ela i is ic o mulas o SRT,
aking his ci cums ance in o accoun , need o be ex-
plained in ull, since he c ea o s o his heo y ex-
plained hem only in he ange o subligh speeds <c,
in which he alues m, Δ and l ook alues measu able
by eal numbe s. Bu in he ange o hype ligh speeds
>c, hese alues m, Δ and l al eady ook alues meas-
u able by open [55] Scipione Del Fe o, Niccolò Fon-
ana Ta aglia, Ge olamo Ca dano, Lodo ico Fe a i
and Ra aele Bombelli 400 yea s be o e he c ea ion o
SRT as imagina y numbe s, he physical meaning o
which, howe e , was incomp ehensible o hem and
was no explained. And pe haps e en ea lie han hem,
imagina y numbe s we e disco e ed by Paolo Valmes
[56], who was bu ned ali e a he s ake o his by o de
o he inquisi o Tomás de To quemada. E en Isaac
New on, in o de o a oid ouble, p e e ed no o use
imagina y numbe s a ha ime
5
.
Howe e , in o de o explain he physical meaning
o imagina y numbe s, ela i is ic o mulas mus i s
be co ec ed so ha hey co espond o physically ea-
sible p ocesses. To do his, ela i is ic o mulas (1)-(3)
in he ange > c mus be such ha he g aphs o he
unc ions m( ), Δ ( ), l( ) (Fig. 1d,e, ) a e simila o he
g aphs o he same unc ions m( ), Δ ( ), l( ) (Fig.
1a,b,c) in he ange < c. To do his, we need o in o-
duce he unc ion iq in o o mulas (1)-(3) iq
Danish Scien i ic Jou nal No100, 2025 43
Fig. 3.
G aphs o unc ions 𝑞(𝑣) and 𝑤(𝑣), illus a ing he meaning o he ‘ loo ’ unc ion in disc e e ma hema ics
𝑚(𝑞)=𝑚0𝑖1
𝑞 / √1−(𝑣
𝑐−𝑞)]2 (4)
𝛥𝑡(𝑞)=𝛥𝑡0𝑖1
𝑞√1−(𝑣
𝑐− 𝑞) 2 (5)
𝑙(𝑞)=𝑙0𝑖1
𝑞√1−(𝑣
𝑐−𝑞)]2 (6)
whe e 𝑞(𝑣)=⌊𝑣/𝑐⌋ – he ‘ loo ’ unc ion o dis-
c e e ma hema ics om he a gumen /c (i s g aph is
shown in Fig. 3a), which is he ou h spa ial dimen-
sion; 𝑤=𝑣−𝑞с – local eloci y in all uni e ses (i s
g aph is shown in Fig. 3b).
This unc ion iq in o mulas (4)-(6), which de ines
he essence o each uni e se, o in ege alues
6
q( ),
equal o 0,1,2,3,4,5, akes he alues +1, +i, -1, -i, +1,
+i, … e c. And he alue q( ) = 0 in o mulas (1)-(3) o
he subligh speed ange < c co esponds (since i0 =
Fig. 4. S uc u e o he hidden Mul i e se co esponding o he p inciple o physical eali y o complex numbe s
6
And o non-in ege alues o q, i is unde ined.
44 Danish Scien i ic Jou nal No100, 2025
1) o ou isible uni e se, which we will call he
a dion
7
uni e se o he sake o cla i y. The alue q( )
= 1 in he hype ligh speed ange 2c > > c co e-
sponds (since i1 = i) o some o he in isible uni e se,
since i is beyond he e en ho izon. Fo cla i y, we will
he e o e call i he achyonic
8
uni e se. Then he alue
q( ) = 2 in he speed ange 3c > > 2c will co espond
o (since i2 = -1) an in isible a dion an i-uni e se, and
he alue q( ) = 3 in he speed ange 4c > > 3c will
co espond o (since i2 = -1) an in isible achyonic an i-
uni e se, he alue q( ) = 4 in he speed ange 5c >
> 4c will co espond (since i4 = +1) o ano he (and
he e o e also in isible) a dionic uni e se, he alue
q( ) = 5 in he speed ange 6c > > 5c will co espond
(since i5 = +i) o ano he achyon uni e se. And so on.
Tha is, acco ding o o mulas (4)-(6), he e is no
one isible uni e se, as claimed in he gene ally ac-
cep ed e sion o SRT, bu also a mul i ude o mu uall
in isible o he uni e ses and an i-uni e ses, o ming a
Mul i e se, which we will he e o e call hidden. Such a
hidden Mul i e se, whose s uc u e is winding, is
shown in Fig. 4. And in his s uc u e o he hidden
Mul i e se, he dis ibu ion o ma e ial con en in each
h ee-dimensional pa allel uni e se and an i-uni e se
will be de e mined by i s unc ion 𝑓𝑞(𝑥,𝑦,𝑧), and he
alue iq will be he coo dina e o hese uni e ses. Tha
is, he hidden mul i e se will be desc ibed by he o -
mula q(x,y,z)+iq .
5. Analysis o da a ob ained by he WMAP and
Planck spacec a
Bu ha ing p o en he exis ence o mu ually in is-
ible pa allel
9
uni e ses and an i-uni e -ses, necessa y
o ind ou how hey a e placed in he hidden Mul i-
e se. O , in o he wo ds, wha is he s uc u e o his
hidden Mul i e se? I is also necessa y o unde s and
wha da k ma e and da k ene gy a e, so named be-
cause o hei incomp ehensibili y, since no chemical
elemen s ha e been ound in hem, and also because
hey do no abso b, emi , e lec o e ac any elec o-
magne ic adia ion, and a e he e o e in isible.
Mo eo e , da k ma e and da k ene gy accoun
o mo e han 95% o all mass-ene gy in he cosmos.
Mo e p ecisely, acco ding o da a ob ained by he
WMAP spacec a [57], he mass-ene gy o ou isible
uni e se (ac ually a hidden Mul i e se) consis s o
4.6% ba yonic ma e , 22.4% da k ma e , and 73.0%
da k ene gy. And acco ding o mo e ecen da a ob-
ained by he Planck spacec a [58], he en i e uni e se
(again, in ac , he en i e hidden Mul i e se) consis s o
4.9% ba yonic ma e , 26.8% da k ma e , and 68.3%
da k ene gy.
The e o e, na u ally, he eliabili y o o he
knowledge in mode n physics, which is unab-le o ex-
plain he phenomena o da k ma e and da k ene gy, is
ques ionable. And since i has been p o en beyond
doub ha na u e does no consis o a single uni e se,
7
Ta dyon uni e se is a e m used by Isaak Asimo in his sho
s o y ‘Take a Ma ch’.
8
Tachyon uni e se is a e m used by Isaak Asimo in his
sho s o y ‘Take a Ma ch’
9
Since hey do no in e sec
10
Con ucius was an ancien Chinese philosophe and s a es-
man who li ed mo e han wo housand yea s ago and emains
bu a Mul i e se, hen, in addi ion o he s ill unsuccess-
ul sea ch in he mic ocosm o he na u e o da k ma -
e and da k ene gy phenomena a he La ge Had on
Collide , i is necessa y o begin sea ching o hei ex-
plana ion in he mac ocosm o ou hidden mul i e se.
A e all, Albe Eins ein himsel w o e: ‘I is meaning-
less o keep doing he same hing and expec di e en
esul s’. The ancien Chinese philosophe Con ucius
10
said he same hing: ‘The mos di icul hing is o ind
a black ca in a da k oom, especially i i is no he e’.
The sea ch o a solu ion o his p oblem in he
hidden Mul i e se allows us o assume ha [59]-[72]:
 da k ma e and da k ene gy a e mos likely
he es o ou hidden Mul i e se, apa om ou isible
uni e se, a dion and achyon uni e ses and an i-uni-
e ses, which a e in isible o us because hey exis in
o he dimensions;
 and since he uni e ses and an i-uni e ses o
da k ma e and da k ene gy a e ac ually ou side ou
isible uni e se, hey mani es hemsel es in i only as
phenomena (p esumably in he o m o g a i a ional
shadows) gene a ed by he exis ence o o he in isible
pa allel uni e ses and an i-uni e ses o he hidden Mul-
i e se
11
;
 da k ma e is a phenomenon caused by he ex-
is ence o in isible pa allel uni e ses and an i-uni-
e ses in he hidden Mul i e se neighbou ing ou isi-
ble uni e se.
 da k ene gy is a phenomenon gene a ed by he
exis ence o o he uni e ses besides ou isible uni-
e se and i s neighbou ing in isible uni e ses and an i-
uni e ses, o he in isible pa allel uni e ses and an i-
uni e ses o he hidden Mul i e se.
The e o e, da k ma e and da k ene gy ha e no
co puscula con en
12
.. And hey will ne e be de ec ed
a he La ge Had on Collide .
This explana ion o he phenomena o da k ma e
and da k ene gy also p o ides
in o ma ion abou he s uc u e o he hidden Mul-
i e se. Indeed, gi en ha he mu ually in isible uni-
e ses and an i-uni e ses o he hidden Mul i e se a e
connec ed o each o he by nume ous po als h ough
which hey exchange hei ma e ial con en s, i can be
a gued ha o e billions o yea s o hei exis ence, in
acco dance wi h he law o communica ing essels,
hei mass-ene gy has p ac ically comple ely equalised.
And hen:
• acco ding o expe imen al da a ob ained by he
WMAP spacec a , he en i e hidden mul i e se con-
sis s o 100% / 4.6% = 21.8 pa allel uni e ses, and ac-
co ding o da a ob ained by he Planck spacec a , i
consis s o 100% / 4.9% = 20.4 pa allel uni e ses;
• da k ma e , acco ding o expe imen al da a ob-
ained by he WMAP spacec a , consis s o 22.4% /
he mos amous Chinese pe son o his day. Fo a long ime,
Con ucianism was as impo an in China as Buddhism. I
o ms he basis o mode n s a e ideology.
11
Simila ly, o example, you may sea ch unsuccess ully o
a inging elephone in he oom you a e in, when i is ac ually
in he nex oom.
12
Like shadows on a sunny day.

Danish Scien i ic Jou nal No100, 2025 45
4.6% = 4.9 pa allel uni e ses, and acco ding o da a ob-
ained by he Planck spacec a , consis s o 26.8% /
4.9% = 5.5 pa allel uni e ses;
• acco ding o expe imen al da a ob ained by he
WMAP spacec a , da k ene gy consis s o 73.0% /
4.6% = 15.9 pa allel uni e ses, and acco ding o da a
ob ained by he Planck spacec a , i consis s o 8.3% /
4.9% = 13.9 pa allel uni e ses.
6. Co ec ed e sion o SRT, explana ion o he
phenomena o da k ma e and da k ene gy
As can be seen, he expe imen al da a ob ained by
he WMAP and Planck spacec a did no con i m he
abo e conclusions abou he s uc u e o he hidden
mul i e se, since ou isible uni e se in his s uc u e
has no wo neighbou ing in isible pa allel uni e ses –
one achyon uni e se and one achyon an i-uni e se –
bu i e o six.
The e o e, i is ob ious ha he e was some e o
in he p e ious easoning. And i u ns ou ha we we e
w ong in assuming ha he e is only one addi ional di-
mension q in he hidden Mul i e se and, consequen ly,
i s co espondence o physically eal complex numbe s
con aining only one imagina y uni . In o de o six
13
o he pa allel uni e ses – h ee achyon uni e ses and
h ee achyon an i-uni e ses – o coexis wi h ou isi-
ble uni e se in he ac ually exis ing hidden mul i e se,
i is necessa y o ha e h ee addi ional dimensions q, ,
s and he ela i is ic o mulas mus be co ec ed again
as ollows [73]-[81]
0 1 2 3
2
( , , ) 1 [ ( )]
q s
m i i i
m q s q s
c
   
(7)
2
0 1 2 3
( , , ) 1 [ ( )]
q s
q s i i i q s
c
      
(8)
2
0 1 2 3
( , , ) 1 [ ( )]
q s
l q s l i i i q s
c
    
(9)
whe e 𝑞(𝑣)=⌊𝑣𝑞/𝑐⌋ – he ‘ loo ’ unc ion o dis-
c e e ma hema ics om he a gumen 𝑣𝑞/𝑐 , which is
one o he o hogonal coo dina es q o he ou h spa ial
dimension ;
𝑟(𝑣)=⌊𝑣𝑟/𝑐⌋ – he ‘ loo ’ unc ion o disc e e
ma hema ics om he a gumen 𝑣𝑞/𝑐, which is ano he
o hogonal coo dina e o he ou h spa ial dimension
; 𝑠(𝑣)=⌊𝑣𝑠/𝑐⌋ – he ‘ loo ’ unc ion o disc e e
ma hema ics om he a gumen 𝑣𝑞/𝑐, which is one
mo e o hogonal coo dina e s o he ou h spa ial di-
mension ;
q, , s – p ojec ions o he eloci y ec o on o
he o hogonal coo dina es q, ,s (see Fig. 5).
Fig. 5. Six-dimensional space o he hidden Mul i e se, whe e q, , s a e he coo dina es o in isible pa allel uni-
e ses, and x, y, z a e he coo dina es o he ma e con en in each pa allel uni e se
Consequen ly, he space o such a hidden mul i-
e se will be six-dimensional (see Fig. 5). And i s s uc-
u e will co espond o he qua e nions σ + i1ω1 + i2ω2
+ i3ω3 , i.e. hype - complex numbe s [82] con aining
p ecisely h ee imagina y uni s i1, i2, i3, which a e e-
la ed o each o he by he ollowing ela ions
13
O less. Then some pa allel uni e ses o ou hidden Mul-
i e se may be absen and eplaced by uni e ses o neighbou -
ing Mul i e ses.
222
1 2 3 1iii   
(10)
1 2 3 2 3 1 3 1 2 1ii i i i i i ii   
(11)
1 3 2 2 1 3 3 2 1 1ii i i ii i i i
(12)
46 Danish Scien i ic Jou nal No100, 2025
Fig. 6. Possible qua e nion s uc u e o he hidden Mul i e se con aining wen y- wo pa allel uni e ses, includ-
ing six in isible uni e ses adjacen o ou isible uni e se
In such a qua e nion s uc u e o he hidden Mul-
i e se [83], [84], unlike i s s uc u e conside ed ea lie
(in Fig. 4), he dis ibu ion o ma e ial con en in each
h ee-dimensional pa allel uni e se will be de e mined
by a unc ion 𝑓𝑞,𝑟,𝑠(𝑥,𝑦,𝑧), and he coo dina es o hese
uni e ses will be de e mined by he alues i1q, i2 и
3
is
. Tha is, he hidden Mul i e se will be desc ibed by he
o mula 𝑓𝑞,𝑟,𝑠(𝑥,𝑦,𝑧)+𝑖1𝑞+𝑖2𝑟+𝑖3𝑠. This is ex-
ac ly wha Lisa Randall p edic ed: ‘We could be li ing
in a h ee-dimensional pocke o highe dimensional
space.’
And om o mulas (7)-(9) i ollows ha such a
hidden Mul i e se s ill has a winding s uc u e. In his
case, i is possible o mo e om a a dion uni e se o a
a dion an iuni e se and om a a dion an iuni e se o
a a dion an iuni e se in di e en ways, bu no in an
a bi a y way, bu only in such a way (see Fig. 6) ha
he alue o iq will successi ely ake he alues +1,
+i1⨁+i2⨁+i3 , -1, - i1⨁ -i2⨁- i3 , +1, … and so on,
whe e ⨁ is he symbol o he logical ope a ion o dis-
c e e ma hema ics ‘exclusi e OR’. In his case, di e -
en ajec o ies o mo emen om one uni e se (o an-
iuni e se) o ano he can di e only due o he eplace-
men o some achyon uni e ses om i1, i2, i3 wi h
o he s and some achyon an iuni e ses om i1, i2, i3
wi h o he s. The e o e, he achyon uni e ses i1, i2, i3 in
he hidden Mul i e se a e loca ed pa allel o each o he .
The achyon an iuni e ses i1, i2, i3 a e also loca ed pa -
allel o each o he o he same easons. And he e o e,
in he hidden Mul i e se, when mo ing om any a -
dyon uni e se o a a dyon an iuni e se and hen o an-
o he a dyon uni e se, pa allel uni e ses and an iuni-
e ses mus al e na e in he ollowing sequence – ‘ a -
dyon uni e se’, ‘one o he achyon uni e ses’,
‘ a dyon an iuni e se’, ‘one o he achyon an iuni-
e ses’, ‘ a dyon uni e se’, ‘one o he achyon uni-
e ses’, e c.
One o he simples explana ions o such possible
qua e nion s uc u es o he hidden mul i e se is shown
in Fig. 6. I di e s om he s uc u e shown in Fig. 4 in
Danish Scien i ic Jou nal No100, 2025 47
ha i con ains se e al pa allel achyon uni e ses and
an i-uni e ses co esponding o he h ee imagina y
uni s i1, i2, i3 . Ano he di e ence is he p esence in such
a mul i e se s uc u e no only o bidi ec ional po als
co esponding o o mula (7) and ma ked wi h double-
headed a ows, bu also o unidi ec ional po als
14
, co -
esponding o o mulas (8) and (9) and ma ked wi h sin-
gle-headed a ows.
Mo eo e , na u ally, he mo emen om ou a -
dyon uni e se o he a dyon an iuni e se h ough some
achyon uni e se – o example, i1 – does no neces-
sa ily ha e o p oceed u he h ough he achyon an i-
uni e se i1.I can p oceed u he h ough he achyon
an iuni e ses i2 and i3. The same ese a ion applies o
he si ua ion i he mo emen om he a dyon uni e se
o he a dyon an iuni e se begins h ough he achyon
uni e ses i2 and i3. All hese ansi ions a e shown in
Fig. 6. Mo eo e , since he da a ob ained by he WMAP
and Planck spacec a co espond o open helical s uc-
u es o ou hidden Mul i e se, uni ed h ough he co -
esponding po als wi h o he Mul i e ses, hen all o
hem oge he o m he Hype uni e se.
7. How o see in isible uni e ses and an iuni-
e ses
Bu o e i y ha hese in isible uni e ses eally
exis , we need an app op ia e expe imen ha allows us
o see hem [85]-[98]. And o unde s and wha his ex-
pe imen migh be like, we need o emembe ha in
o mulas (7)-(9), he pa ame e s q, , s a e o hogonal
coo dina es o he ou h spa ial dimension , in which
mu ually in isible pa allel uni e ses somehow d i el-
a i e o each o he . The e o e, hey ouch each o he
and e en sligh ly imme se in o each o he , o ming co -
esponding ansi ions h ough which hei ma e ial
con en s a e exchanged. These ansi ions a e usually
called po als [99],[100]. And he en ances o hem ap-
pea o be, a leas , some o he anomalous zones, o
which he e a e mo e han wo hund ed housand on
Ea h. [101]-[104].
And since in o he uni e ses he cons ella ions in
he sky ine i ably di e om he cons ella ions in ou
ea hly sky, when a elling h ough a po al om Ea h
o a neighbou ing uni e se o an i-uni e se, he map o
he s a y sky in he po al will g adually ans o m in o
a map o he s a y sky o ha neighbou ing uni e se o
an i-uni e se. And i a elescope is placed in such a po -
al (o a leas a i s en ance in he anomalous zone),
hen by compa ing he posi ion o he s a s in he sky in
he po al and ou side he po al, changes in he posi ion
o he s a s can be de ec ed. And i hese di e ences
u n ou o be oo small, hen he elescope will ha e o
be mo ed deepe in o he po al. A e all, Si A hu
S anley Edding on mo ed his elescope much u he
o his amous expe imen in he ea ly 20 h cen u y –
om England o he island o P incipe in he A lan ic
Ocean [105].
Fig. 7. Scheme o an as onomical expe imen o de ec in isible uni e ses
These o he cons ella ions in he s a y sky in he
po als will se e as expe imen al p oo o he exis ence
o in isible uni e ses and an i-uni e ses ou side he
po als. The co esponding expe imen s (Fig. 7) a e
e y inexpensi e and easy o implemen . Mo eo e ,
some obse a o ies a e al eady loca ed in anomalous
zones. Fo example, he Main As onomical Obse a-
o y o he Na ional Academy o Sciences o Uk aine is
loca ed 12 km om he cen e o i s capi al, Kie , in he
Holosii skyi Fo es .
8. An ima e and an i- ime, ex e nal and in e -
nal ime
Ha ing con inced ou sel es ha he exis ence o
he hidden Mul i e se can be p o en expe imen ally, le
14
Why in such po als mo emen is possible only in one di-
ec ion - om he en ance o he exi - is di icul o us, li -
ing in a space in which mo emen in na u e is possible in any
di ec ion, o imagine. The p ocesses ha de e mine he possi-
bili y o such mo emen in na u e a e ye o be unde s ood.
us con inue o ex ac new knowledge om he e ised
e sion o SRT.
Fi s , he s uc u e o he hidden Mul i e se al-
eady allows us o explain a p oblem ha is cu en ly
inexplicable wi hin he amewo k o physics ex -
books: whe e is an ima e loca ed [106]? I is clea ha
i canno be ound in ou isible uni e se, since i s an-
nihila ion wi h ma e would cause ou uni e se o
cease o exis . Bu he ac ha an ima e does exis has
been p o en expe imen ally. In 1995, a sensa ional e-
sul was ob ained a CERN – scien is s managed o ob-
ain nine a oms o an ihyd ogen, which exis ed o
abou o y billion hs o a second. And jus one g am o
Bu o isi o s who ind hemsel es in such one-way po als,
hey a e mo e dange ous han wo-way po als, since i is im-
possible o e u n om hem o you uni e se. Al hough in he
me o wi h one-way mo emen on escala o s we s ill encoun-
e . Bu he me o is no na u e.
48 Danish Scien i ic Jou nal No100, 2025
such an ihyd ogen would cos 662.5 illion (i.e. a hou-
sand billion) dolla s. Thus, he exis ence o an ima e
has been expe imen ally p o en.
This expe imen can also be conside ed p oo ha ,
in acco dance wi h o mulas (7)-(9), an ima e can ex-
is in na u e, bu only in he in isible a dion and ach-
yon an i-uni e ses o he hidden Mul i e se and Hype -
uni e se. (see Fig. 6), since hey a e he an ipodes o
in isible a dion and achyon uni e ses.
Secondly, he exis ence in he hidden Mul i e se
o no only a dion and achyon uni e ses, bu also an i-
uni e ses, makes i possible o a el no only in space,
bu also in ime [107]-[127]. This e u es he claim o
physicis s who, al hough hey ecognise he hypo he -
ical possibili y o ime a el in ce ain exo ic si ua ions
in special
15
and gene al
16
ela i i y and in quan um
physics
17
, bu deny he possibili y o human ime a el
e en in he dis an u u e.
Tha is why he concep o he “a ow o ime”
[128], p oposed a he beginning o he 20 h cen u y by
Si A hu S anley Edding on, e en appea ed in phys-
ics. And he e is wha S ephen William Hawking [129]
w o e on his subjec : 'In e e yday li e, he e is a huge
di e ence be ween mo ing o wa d and backwa d in
ime. Imagine ha a cup o wa e alls o he able and
b eaks in o pieces. I you ilm his all, i will be imme-
dia ely clea when wa ching he ilm whe he he ilm is
being played o wa ds o backwa ds. I i is being
played backwa ds, we will see he sha ds lying on he
loo suddenly come oge he and, o ming a whole cup,
jump back on o he able. And you can say ha he ilm
was being played backwa ds, because in e e yday li e
his does no happen. O he wise, all he po e y ac o-
ies would ha e o be closed down."
Howe e , he exis ence o an i- ime in he hidden
Mul i e se makes he use o he concep o 'a ow o
ime' unnecessa y.
And inally, hi dly, i is easy o no ice ha in all
he ela i is ic o mulas (1)-(3); (4)-(6); (7)-(9) men-
ioned in he a icle, in addi ion o he unc ional de-
pendencies o he quan i ies m, Δ , l on he a gumen ,
he e is ano he ela i is ic dependence – he quan i y
Δ on he a gumen l
Δ = Δ 0 l / l0 (10)
Tha is, i u ns ou ha in na u e he e a e no only
he ela i is ic dependencies o physical quan i ies m,
Δ , l on he eloci y ha ha e al eady been iden i ied
and s udied in he gene ally accep ed e sion o STR,
bu also ano he ela i is ic dependency o ex e nal
ime Δ on he spa ial coo dina e l, pe pendicula o he
ime zones, gene a ed by he o a ion o he Ea h
a ound i s axis. And his ex e nal ime di e s om he
in e nal (o , in o he wo ds, biological) ime used in
e e yday li e, which canno low backwa ds and people
in i canno e u n o hei childhood. Unlike ex e nal
ime, which can low bo h in o he u u e and in o he
pas , since ai planes can c oss ime zones in bo h he
wes e n and eas e n di ec ions.
Mo eo e , unlike in e nal ime, which always and
e e ywhe e lows a he same speed, his ex e nal ime,
15
Fo example, in he ‘ win pa adox’
16
Fo example, in he egion o ul a-high g a i y nea he
e en ho izon o a black hole
measu ed by ime zones, can low a di e en speeds,
depending on he speed o he ai c a and he size o
he ime zones.
The e o e:
 a he equa o 1 ime zone is equal o Δl =
40075 km x cos 00 / 24 = 1700 km;
 a he la i ude o San iago 1 ime zone is equal
o Δl = 40075 km x cos 33.45° / 24 = =1426 km;
 a he la i ude o Buenos Ai es 1 ime zone is
equal o Δl = 40075 km x cos 34.60° /
/ 24 = 1427 km;
 a he la i ude o Melbou ne 1 ime zone is
equal o Δl = 40075 km x cos 37.82° / 24 = 1358 km;
 a he la i ude o New Yo k 1 ime zone is
equal o Δl = 40075 km x cos 40.729/ 24 = 1269 km;
 a he la i ude o Reykja ik 1 ime zone is
equal o Δl = 40075 km x cos 64.15° / 24 = 734 km;
 a he la i ude o Mu mansk 1 ime zone is
equal o Δl = 40075 km x cos 690 / 24 =
= 601 km;
 a he la i ude o Ki kenes 1 ime zone is equal
o Δl = 40075 km x cos 69.73° / 24 = = 599 km.
Then he dis ance o 1 ime zone an ai plane wi h
a speed o , o example, 800 km pe hou , will ly:
 a he equa o in Δ = 1700 km / 800 km pe
hou = 2.125 hou s o in e nal (biological) human ime;
 a he la i ude o San iago in Δ = 1426 / 800
km pe hou = 1.783 hou s o in e nal (biological) hu-
man ime;
 a he la i ude o Buenos Ai es in Δ = 1427 /
800 km pe hou = 1.784 hou s o in e nal (biological)
human ime;
 a he la i ude o New Yo k in Δ = 1586 / 800
km pe hou = 1.983 hou s o in e nal (biological) hu-
man ime;
 a he la i ude o Reykja ik o Δ = 734 / 800
km pe hou = 0.918 hou s o in e nal (biological) hu-
man ime;
 a he la i ude o Mu mansk o Δ = 601 / 800
km pe hou = 0.751 hou s o in e nal (biological) hu-
man ime;
 a he la i ude o Ki kenes o Δ = 599 / 800
km pe hou = 0.749 hou s o in e nal (biological) hu-
man ime.
This happens because ex e nal ime is he ime
ou side he plane, de e mined by p ocesses in he ex e -
nal en i onmen , and in e nal ime is he ime measu ed
by he wa ches o passenge s and c ew. And, i u ns
ou , hey a e di e en . The e o e, a e he plane lands,
passenge s ha e o change hei wa ches o local ime.
And, as you can see, in o de o a el o he pas o he
u u e, he plane's ligh du ing i s ound- he-wo ld ip
mus ake place a ound he nea es pole close enough o
i . 9. Re ised e sion o SRT; how o e i y he
easibili y o a elling o he pas and u u e
Mo eo e , e en in e nal ime i sel can a y. In e -
nal ime may o may no depend on he dis ance a pe -
17
Fo example, as a esul o elepo a ion, ins ead o in o -
ma ion, physical objec s