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Relativity vs. absolute simultaneity:

Varying flow of time or varying frequency?

Avril Styrman

a)

Physics Foundations Society, Vasamatie 25, 02630 Espoo, Finland and The Finnish Society for Natural

Philosophy, Kirkkokatu 6, 00170 Helsinki, Finland

(Received 10 January 2018; accepted 23 May 2018; published online 3 July 2018)

Abstract: The General Theory of Relativity (GR) and the Dynamic Universe (DU) are evaluated

in how they explain frequencies of atomic clocks. DU and GR predict the frequencies with equal

accuracy, but their explanations, the postulates they apply in the explanations and the word-views

that come along with them are entirely different. The central argument is that if uniﬁed and under-

standable physics is appreciated, then DU deserves to be taken as a viable alternative to GR. In GR

different frequencies of identical atomic clocks are explained by letting rates of the ﬂow of time in

their frames of reference vary as functions of the clocks’ states of motion and gravitation. The GR-

based world-view is nonunderstandable because GR violates absolute simultaneity, and disuniﬁed

because quantum mechanics is built on different postulates than GR. In DU different frequencies of

identical atomic clocks are explained by letting their frequencies vary as functions of their states

of motion and gravitation. As DU commits to absolute simultaneity and as the postulates of DU

sufﬁce as the ontological ground of quantum mechanics at least partially, DU provides an under-

standable and uniﬁed scientiﬁc world-view . V

C2018 Physics Essays Publication.

[http://dx.doi.org/10.4006/0836-1398-31.3.256]

Re´sume´: La the´orie de la relativite´ge´ne´rale (RG) et de l’univers dynamique (UD) sont e´ value´s

sur la fac¸on dont ils expliquent les fre´ quences des horloges atomiques. La RG et l’UD pre´disent les

fre´quences avec une pre´ cision e´gale, mais leurs explications, les postulats qu’ils appliquent aux

explications et les visions du monde qui les accompagnent sont entie`rement diffe´rents. L’argument

central est que si l’on reconnaıˆt la physique uniﬁe´ e et compre´hensible, alors l’UD me´rite d’eˆtre

conside´re´ comme une alternative viable a` la RG. En RG, diffe´rentes fre´quences d’horloges

atomiques identiques sont explique´es en faisant varier les vitesses de l’e´coulement du temps dans

leurs cadres de re´fe´rence en fonction des e´tats de mouvement et de la gravitation des horloges. La

vue du monde base´e sur la RG est incompre´hensible parce que la RG viole la simultane´ite´ absolue,

et est de´suniﬁe´ e parce que la me´canique quantique est construite sur des postulats diffe´rents de

ceux de la RG. Dans l’UD, diffe´rentes fre´quences d’horloges atomiques identiques sont explique´es

en laissant leurs fre´quences varier en fonction de leurs e´tats de mouvement et de gravitation.

Comme l’UD s’engage a` la simultane´ite´ absolue et que les postulats de l’UD sufﬁsent, au moins en

partie, comme fondements ontologiques de la me´canique quantique, l’UD fournit une vision du

monde scientiﬁque compre´hensible et uniﬁe´e.

Key words: Atomic Clocks; Absolute Simultaneity; Proper Time; Coordinate Time; Cosmic Time; Theory of Relativity;

Time Dilation; The Dynamic Universe; Uniﬁcation; Grand Uniﬁed Theory.

I. INTRODUCTION

Atomic clocks are the most accurate means of measuring

time. An atomic clock contains atoms whose oscillating elec-

trons run the clocks. The frequency of a clock is the number

of oscillations an electron completes between two quantum

states within one second, i.e., the dimension of frequency is

1/s. Numerous tests

1

reveal that identical atomic clocks

in different states of motion (b) and gravitation (d) have

different frequencies. The Dynamic Universe (DU) and the

General Theory of Relativity (GR) agree that the gravita-

tional potential and the velocity of a clock affect its fre-

quency as follows:

The greater the velocity of a clock, the smaller is

its frequency. The smaller the velocity of a clock,

the greater is its frequency.

The greater the clock’s distance from the

barycenter of the system where the clock resides,

the greater the gravitational potential of the clock.

In tests committed in the Earth Centered Inertial

(ECI) frame, altitude from the sea level on Earth

determines the clock’s distance from the

barycenter. It suffices here to concentrate on the

a)

Avril.Styrman@gmail.com

ISSN 0836-1398 (Print); 2371-2236 (Online)/2018/31(3)/256/9/$25.00 V

C2018 Physics Essays Publication256

PHYSICS ESSAYS 31, 3 (2018)

The greater the gravitational potential of a clock, the greater is its frequency;

the lower the gravitational potential of a clock, the lower is its frequency.

ECI frame, which is the frame where the available

test data has been gathered.

Both DU and the Schwarzschild solution of GR give correct

predictions of the frequency fby Eq. (1) and Eq. (2), or the

differences in their predictions in the ECI frame are so small

that empirical tests cannot determine which theory is more

accurate.

DU :f¼f0ð1dÞﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

1b2

q:(1)

GR :f¼f0ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

12db2

q:(2)

f

0

is the frequency of a hypothetical reference clock at rest far

enough from the barycenter of the ECI frame, i.e., at state

b¼0 and d¼0.

b)

b¼v/c characterizes the effect of the clock’s

state of motion on fwhere vis the clock’s velocity in the ECI

frame, and cis the velocity of light. d¼Gm/rc

2

characterizes

the effect of the clock’s gravitational state on f,whereGis the

gravitational constant, mis the central mass of the system deﬁn-

ing the gravitational frame where the test is committed, and ris

the clock’s distance from the barycenter of the system.

2

Although the predictions of DU and GR in the ECI

frame are very close, their explanations are entirely different.

This article popularizes how GR and DU explain the fre-

quencies in terms of their postulates, why the GR explana-

tion violates absolute simultaneity and renders nature

nonunderstandable, and how the DU explanation sustains

absolute simultaneity and applies Quantum Mechanics (QM)

in its explanation. This is done in order to bring forth the

notion that there has been an economically uniﬁed and

understandable alternative to GR for some time now.

A brief historical overview of the development of rela-

tivistic physics and the Special Theory of Relativity (SR)

and GR explanations are given in Section II. It is shown why

GR’s violation of absolute simultaneity renders nature

nonunderstandable, and it is pointed out that neither the

GR-based cosmology model’s (FLRW’s) cosmic time nor

variations of SR provide a way out of the dilemma (Section

III). The DU explanation is given and it is shown how it is

uniﬁed with QM in Section IV. It is emphasized that the

selection between constancy and variability of the velocity

of light in vacuum is a matter of selecting between two

mutually exclusive metaphysical commitments (Section V).

The concluding remarks are given in Section VI, with the

focus on how indoctrination into relativistic physics effec-

tively prevents the forthcoming of alternatives and the uniﬁ-

cation of physics. The basic structure of DU is presented in

the Appendix.

II. THE SR AND GR EXPLANATIONS

Newtonian physics was unable to explain certain phe-

nomena that were observed in the late 19th and the early

20th centuries. This resulted in extending and modifying

Newtonian physics by SR in 1905. SR was extended into GR

in 1915, and GR was gradually extended into FLRW. Obser-

vations on atomic phenomena triggered the development of

QM mainly in 1920s which completed the empirical cover-

age of theories of physics.

The postulates of SR are constancy of the velocity of

light, coordinate transformations and the relativity principle.

Consider how these postulates are applied in explaining fre-

quencies of atomic clocks A and B that move relative to

each other at a constant velocity at ﬁxed gravitational poten-

tial.

c)

The following abbreviations are used.

F

A

and F

B

: The frames of reference where clocks

A and B reside.

f

A

and f

B

: The frequencies of clocks A and B.

The relativity principle states that the laws of physics are

the same in all inertial frames of reference. In this sense

every clock in an inertial frame is at the state of rest: A is at

rest from the aspect of F

A

, B is at rest from the aspect of F

B

,

and an arbitrary clock is at rest from the aspect of its own

frame. As every clock is at rest from the aspect of its own

frame, also the ﬂow of time is identical for every clock from

the aspect of its own frame. This can be abbreviated by say-

ing that all clocks in inertial frames of reference have identi-

cal proper time.

In addition to considering clocks from the aspects of

their own frames, we can consider A from the aspect of F

B

,

and B from the aspect of F

A

. In such comparison, we can

freely select the rest frame and the frame that moves with

respect to the rest frame. Let us select F

A

as the rest frame

and F

B

as the moving frame. A coordinate transformation

speciﬁes how the ﬂow of time in F

B

relative to F

A

changes

as a function of the velocity of B relative to A, namely, how

much slower or dilated is the ﬂow of time in F

B

relative to

F

A

.

d)

This can be abbreviated by saying that when measured

in coordinate time of F

A

, B has a slower ﬂow of time than A.

The SR equation for predicting f

B

relative to f

A

is derived

from the coordinate transformations

fB¼fAﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

1ðv=cÞ2

q:(3)

The relativity principle allows considering that A and B

are both at the state of rest, even though they are at different

relative states of motion. As they are at an identical state of

rest, also the characteristic emission and absorption frequen-

cies of atoms in A and B are identical:

e)

the frequency of A

from the aspect of F

A

is f

A

; the corresponding frequency of

B from the aspect of F

B

is f

B

;f

A

¼f

B

. Even though f

A

¼f

B

when measured in proper time, numerous tests show that the

b)

Due to Earth’s rotational velocity and its gravitation, we do not have con-

ditions b¼0 and d¼0 anywhere on Earth. Therefore, in practice we must

determine f

0

with the aid of a clock with known rotational velocity and grav-

itational state.

c)

SR and GR were not designed for explaining frequency readings of atomic

clocks. The ﬁrst atomic clocks were built in the 1950’s and applied in testing

SR in the 1970’s. This raised the need for speciﬁc physical explanations of

clock frequencies.

d)

A coordinate transformation also speciﬁes how much the magnitude of

meter in F

B

grows relative to F

A

as a function of the velocity of B relative to

A, and how much B proportionally contracts relative to A.

e)

An atom has several characteristic frequencies; we are dealing here only

with a speciﬁc quantum transition in A and in B.

Physics Essays 31, 3 (2018) 257

corresponding frequencies of A and B are different when

measured in coordinate time of the other frame. They are

explained as follows.

When measured in coordinate time of F

A

, the ﬂow of

time in F

B

is slower relative to the ﬂow of time in F

A

, i.e.,

when a period of time has passed in F

A

, a shorter period of

time has passed in F

B

relative to F

A

. When measured in coor-

dinate time, f

B

is lower relative to f

A

, because the ﬂow of

time in F

B

is slower relative to F

A

: when A has completed n

oscillations within a period of time, B has completed a fewer

number of oscillations because a shorter period of time has

passed in F

B

and therefore B has had less time oscillate.

Thereby, SR does not in fact predict clock frequencies, but

differences in ﬂow of time which cause different frequency

readings. The same holds for GR.

SR is insufﬁcient because it covers only cases where

clocks move relative to each other at constant velocities

at ﬁxed gravitational potential. GR extends the relativity

principle to include frames in accelerating motion. GR also

postulates the equivalence principle which equalizes gravita-

tional acceleration and inertial acceleration, and therefore

allows taking into account how a clock’s state of gravitation

affects the ﬂow of time in its frame. Near space experiments

with atomic clocks are performed in the ECI frame. These

can be analyzed by applying the Schwarzschild solution of

GR, where the frequencies f

A

and f

B

of clocks A and B at dif-

ferent states of motion and gravitation are compared to the

frequency f

0

of a hypothetical clock 0 at rest, far enough

from the barycenter of the system where the test is commit-

ted.

f)

Once we have obtained f

A

and f

B

relative to f

0

by

Eq. (4) and Eq. (5), we can calculate their proportions,

fA¼f0ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

12db2

q¼f0ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

12Gm=rc2ðv=cÞ2

q:(4)

fB¼f0ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

12db2

q¼f0ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

12Gm=rc2ðv=cÞ2

q:(5)

Again, when measured in proper time, A and B and 0

have identical frequencies, but when measured in coordinate

time of one frame, the two other clocks have different fre-

quencies. Gravitation and velocity affect the ﬂow of time in

F

A

and F

B

relative to the ﬂow of time experienced by the

hypothetical reference clock in F

0.

The effect of gravitation

is related to the distance from the barycenter: the greater the

distance of A (B) from the barycenter, the faster is the ﬂow

of time in F

A

(F

B

); the smaller the distance of A (B) from the

barycenter, the slower is the ﬂow of time in F

A

(F

B

). There-

fore, when 0 has completed noscillations within a period of

time, A and B have completed a smaller number of oscilla-

tions, because a shorter period of time has passed in F

A

and

F

B

(which are nearer to the barycenter), and therefore A and

B have had less time to oscillate. While the effect of the rela-

tive velocities of A and B is called time dilation, the effect of

the relative gravitational states of A and B is called gravita-

tional redshift/blueshift: from the aspect of a clock on a

mountain, a clock in a valley experiences gravitational

redshift; from the aspect of the clock in the valley, the clock

on the mountain experiences gravitational blueshift.

g)

III. VIOLATION OF SIMULTANEITY AND THE

RESULTING DILEMMA

It was pointed out in Section II that in SR and GR, when

measured in coordinate time of one frame, another frame has

a different ﬂow of time. This means that objects in different

states of motion and gravitation do not exist at the same time.

For example, the Earth, the Moon, and the Sun do not exist

simultaneously, and neither do the center of the Earth and its

surface, nor your lower lip and your upper lip. Chou et al.

3

have tested that a 33 cm difference in altitude sufﬁces for the

difference in coordinate time, but GR informs that any differ-

ence sufﬁces. Reinhardt et al.

4

conclude that this “abolishes

the notion of absolute time”

h)

and Chou et al. conclude that

“we have to give up our notions of simultaneity.” Absolute

simultaneity must go if GR stays, and if absolute simultaneity

stays GR must go. The violation of absolute simultaneity

leads into the basic relativistic dilemma.

Absolute simultaneity is implicit in basic human concep-

tualization where houses, trees, mountains, star systems,

planets, and galaxies are wholes whose parts exist at exactly

the same time. Absolute simultaneity is supposed to hold on

the left side of Fig. 1. The process of perception yields a

mental image of a whole house in your consciousness. As all

parts of the house exist simultaneously, your mental image

of the house corresponds to the house.

GR is supposed to be true on the center of Fig. 1. Your

mental image of the house is exactly the same as on the left,

but it does not correspond to a whole house, as the top and the

bottom exist in frames F

1

and F

2

with different ﬂows of time.

This is a simpliﬁcation, for as GR informs that any difference

in altitude results into a different ﬂow of time, the house con-

sists of millions of parts with different ﬂows of time.

The right side of Fig. 1aims to represent reality as it is

according to GR, where the top and the bottom have differ-

ent ﬂows of time. But this is completely different from how

people conceptualize reality. In effect, a proponent of GR

can only keep on applying basic human conceptualization,

while believing that it conveys a false picture of reality.

The dilemma has raised reactions for more than a

100 years now. Often the criticism is targeted at SR.

5

FIG. 1. The basic relativistic dilemma.

f)

GR as such is not involved with a hypothetical rest frame. The Schwarzs-

child solution applies it. There are no other known GR solutions that incor-

porate gravitation.

g)

Sometimes the term ‘time dilation’ is used to denote also the effects of

gravitation.

h)

Although absolute simultaneity is implicit in Newtonian absolute time,we

do not have to couple absolute simultaneity with the Newtonian idea that

time and space are independent of objects in space. Instead, we can couple

absolute simultaneity with the Leibnizian idea that time is merely a derived

concept: when objects in space change, time goes forward. See Leibniz’s

Letters to Clarke III.4. and IV.41.

258 Physics Essays 31, 3 (2018)

However, as GR is an extension of SR and FLRW is an

extension of GR, the dilemma bothers each of these individ-

ually and all of them together. Robb reminds that the viola-

tion of simultaneity renders our basic picture of reality false

and that we still cannot escape simultaneity, whereas Geach

reminds that simultaneity belongs to logic that should be the

same for all science:

This seemed to destroy all sense of the reality of the

external world and to leave the physical universe no

better than a dream, or rather, a nightmare. If two

physicists A and B agree to discuss a physical

experiment, their agreement implies that they

admit, in some sense, a common world in which the

experiment is supposed to take place.

6

“at the same time” belongs not to a special science

but to logic; … Our practical grasp of this logic is

not to be called into question on account of

recondite physics; for without such a practical

grasp we could not understand even elementary

propositions of physics, so a physicist who casts

doubt upon it is sawing off the branch he sits upon.

7

The dilemma catches philosophers between the devil and

the deep blue sea: the paradigmatic role of relativistic physics

forces philosophers of science into making sense of it, but

arguably, one cannot make sense of a world-view that is espe-

cially nonunderstandable, due to the postulates of relativistic

physics. Tooley,

8

Craig,

9

and many others have sought a way

out of the dilemma by reconciling SR with absolute simulta-

neity. Their solutions include adding a privileged reference

frame in SR, which functions as the ground for simultaneity.

The privileged reference frame requires changing the relativ-

ity principle which especially states that the laws of nature

are the same everywhere, i.e., that there especially is no privi-

leged frame. Even if their modiﬁed versions of SR would

work, their challenge would be to expand them into modiﬁed

GR and FLRW, which they have not attempted to do. This

underlines that relativistic physics as a whole certainly oper-

ates without simultaneity and suffers from the dilemma.

Cosmic time does not provide simultaneity either. FLRW

was built by complementing GR by parameters that extended

it into the scale of cosmology. According to FLRW’s cosmo-

logical principle the distribution of matter in the Universe is

homogeneous and isotropic in large enough scales. Given the

homogeneous and isotropic scales by the cosmological princi-

ple, the relativity principle and the coordinate transformations

allow them to exist at the same cosmic time. According to

Wu¨ thrich,

10

“two events are FLRW-absolutely simultaneous

just in case they … occur at the same cosmological time t.”

The following abbreviations are used.

T: a temporal stage of the Universe whose all parts

exists absolutely simultaneously, including every

individual particle.

T

F

: an FLRW-based temporal stage of the Uni-

verse whose largest cosmological-scale parts exist

absolutely simultaneously.

Cosmic time is needed for talking about the age and the

expansion rate of the Universe, for saying that a T

F

has a

total energy, average density, diameter, total mass, and so

forth. The difﬁculty here is that the expression “large

enough” of the cosmological principle leaves open just what

kind of “simultaneity” we are dealing with. It is certain that

aT

F

is not equivalent with a T, for their equivalence would

contradict GR which violates absolute simultaneity. In GR,

e.g., no planet in the Solar System exists simultaneously but

it is not known just where the cosmological principle starts

to apply. On the other way around, it may be safely supposed

that two halves and four quarters of a Tare large enough to

qualify as parts of a T

F

, but it is not known what is the limit

of division after which two parts of a Tno longer qualify as

parts of a T

F

. It can be conjectured that T

F

denotes large-

scale parts which exist simultaneously, but not small-scale

parts. This is disconcerting for a person whose logic indi-

cates that the existence of a large-scale composite at time t

entails the existence of all its interrelated parts at t, including

its small-scale parts. But as FLRW inherits the postulates of

GR, this logic is violated: T

F

cannot denote small-scale parts

with different ﬂows of time.

In sum, cosmic time has two central problems. First, it is a

creation of imagination. Popper

11

did not like the cosmological

principle: “I dislike making of our lack of knowledge a princi-

ple of knowing something.” Second, it is intended to provide

simultaneity but it reveals the basic relativistic dilemma from

another angle: cosmic time is applied only in the largest cos-

mological scale, but the concept of a whole-but-no-parts can-

not be digested by human capabilities. Dorato

12

maintains that

“the contingency of cosmic time and its statistical nature have

led logicians and philosophers to object to the possibility of

using it to ground the existence of an objective now.” Cosmic

time cannot function as the ground of the existence of an

“objective now” because it does not answer what “now” or

“point of time” are supposed to mean.

IV. THE DU EXPLANATION

The central postulates of DU are absolute simultaneity

and the conservation law of energy in spherically closed

space. In DU, clocks in different states of motion and gravita-

tion are interpreted to have different frequencies at the same

time. Equation (6) predicts how a clock’s state of motion b

and gravitation daffects its frequency, where Gis the gravita-

tional constant, mis the central mass of the system deﬁning

the gravitational frame where the test is committed, ris the

clock’s distance from the barycenter of the system, and vis

the velocity of the clock with respect to the barycenter.

2

f¼f0ð1dÞﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

1b2

q¼f01Gm

rc2

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

1ðv=cÞ2:

q(6)

In addition to predicting the frequencies and explaining

them in a straightforward manner, DU incorporates the

effects of band din the quantum mechanical solution of

atomic oscillators, in this case atoms that are running the

clocks. In QM, the characteristic frequencies of atomic oscil-

lators can be expressed in terms of the energy transition DE

Physics Essays 31, 3 (2018) 259

of the oscillating electrons and the Planck constant has DE/h

or in a longer form as

13

f¼mec2

hF½aDðnjÞ:(7)

Here, m

e

is the rest mass of electron eand m

e

c

2

is its rest

energy. Fis a function of the ﬁne structure constant aand the

difference D(n,j) of an electron’s quantum numbers nand j:

these characterize the states between which the electron oscil-

lates. In Eq. (7), the frequency of an atomic clock is propor-

tional to the rest energy of an oscillating electron and inversely

proportional to h.Suntola

14

shows, based on Maxwell’s equa-

tions, that hcontains cas an internal factor,

i)

and deﬁnes the

intrinsic Planck constant as h

0

¼h/c with one cremoved. By

applying h

0

in Eq. (7),itisseenthatfis directly proportional to

the electron’s rest mass m

e

and the local velocity of light c

f¼mec

h0

F½aDðnjÞ:(8)

When m

e

or cchanges, fchanges proportionally. To sus-

tain the conservation law of energy in spherically closed

space, the local velocity of light cbecomes a function of the

clock’s state of gravitation d, and m

e

becomes a function of

the clock’s state of motion b. The clock’s velocity vaffects

an electron’s rest mass m

e

as

me¼me0ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

1b2

q¼me0ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

1ðv=cÞ2

q:(9)

Here, m

e0

is the rest mass of electron ein a clock at rest

in the local frame of reference. When the test is made in the

vicinity of Earth, m

e0

denotes the electron’s rest mass when

the clock does not move with respect to the Earth. The local

gravitational state where the clock resides affects the local

velocity of light cas

15

c¼c0dð1dÞ¼c0d1Gm

rc2

0d

:(10)

c

0d

is the velocity of light in space as it were in the parent

gravitational frame, i.e., without the effect of the local mass

center.

j)

Equation (6) results from writing out m

e

and cin Eq. (8)

f¼mec

h0

F½aDðnjÞ

¼me0ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

1b2

pc0dð1dÞ

h0

F½aDðnjÞ

¼me0c0d

h0

F½aDðnjÞ ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

1b2

qð1dÞ

¼f0ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

1b2

qð1dÞ:

The discovery of cwithin the Planck constant and the

complementation of the quantum mechanical solution of

atomic oscillators by the effects of motion and gravitation

paves the way into uniﬁcation QM and DU as a theory which

incorporates the effects of gravitation and motion. This

allows calculating the frequency of a clock in any state of

motion and gravitation in the ECI frame. By complementing

the solution by the system of nested energy frames, one can

predict correct results anywhere in the Universe.

16

V. THE VELOCITY OF LIGHT: CONSTANT OR

VARIABLE?

In GR constancy of the velocity of light in vacuum cis postu-

lated, whereas in DU its variability along the change of the gravi-

tational state results from the postulated conservation of total

energy in space. We are dealing with an explanatory pay-off: cis

constant and the rate of the ﬂow of time varies; cvaries and the

rate of the ﬂow of time is constant. Neither of these options is an

empirical fact, but they are mutually exclusive metaphysical

assumptions, based on which observations are interpreted and

explained. These assumptions were applied in explaining the fre-

quencies of atomic clocks in Sections II and IV. Here, they are

applied in explaining tests depicted in Fig. 2.

k)

In all three tests, we have an atomic clock and a mirror,

and the distance between a clock and a mirror is L.Wemeasure

the time it takes from a light signal to travel from a clock to a

mirror and back to the clock. Two questions are answered in

the context of DU and GR. First, why are the results the same

in tests 1 and 2? Second, why is the result different in test 3?

TEST 1. The clock and the mirror both reside on

the sea level. Result: t.

TEST 2. The clock and the mirror both reside on

top of a mountain. Result: t.

TEST 3. The clock resides on the sea level but the

mirror resides on top of a mountain. Result: t0.t

0<t.

In DU, the questions are answered in terms of Eq. (8)

which expresses the relation of the local velocity of light c

and the frequency of a clock. In test 1, cis lower near to

Earth’s barycenter but also the frequency of the clock at the

same distance from the barycenter is proportionally lower.

l)

In test 2, cis higher farther away from the barycenter but

also the frequency of the clock at the same distance from the

barycenter is proportionally higher. Therefore, you get the

FIG. 2. Three tests with atomic clocks.

i)

h%2p

3

e

2

l

0

c, where eis electron charge and l

0

is the vacuum

permeability.

j)

If the test is made in the vicinity of Earth where the Earth is the local mass

center, c

0d

denotes the velocity of light in space in Sun’s frame, and Earth’s

gravitational inﬂuence is taken into account by the factor (1-d). If the test is

made in the vicinity of the Moon, c

0d

denotes the velocity of light in space

in the ECI frame, and the Moon’s gravitational inﬂuence is taken into

account by the factor (1-d).

k)

The tests in the ﬁgure are thought experiments, which can however be

derived from actual experiments.

l)

The lower cnear to a mass center is observed also as the bending of light

paths and as the Shapiro delay of satellite signals.

260 Physics Essays 31, 3 (2018)

same result in both tests. In test 3, t0<tbecause cincreases

the higher the signal gets, while the clock remains on the sea

level and its frequency does not change during the test.

In GR, in test 1 the clock and the path of the light signal

are in the same frame of reference as these are at the same

distance from the barycenter. Likewise, in test 2 the clock

and the path of the light signal are in the same frame of refer-

ence. The results are the same in tests 1 and 2 because in

each case the clock and the path of the light signal are in the

same frame of reference. In test 3, when measured in coordi-

nate time of the clock at sea level, while traveling via the top

of the mountain the light signal enters frames of reference

with faster ﬂow of time than in the frame of the clock at the

sea level. When measured in coordinate time of the clock at

sea level, when a period of time such as t0has passed at

the sea level, more time has passed in frames above the sea

level. Therefore, when measured in coordinate time of the

clock at sea level, it takes only the period of time t0where

t0<tfor the light signal to travel the distance Lat constant c.

VI. CONCLUSIONS: IS UNIFICATION ALLOWED?

DU and GR explanations of tests with atomic clocks were

evaluated. In DU, clocks A and B have different frequencies

at the same time. Their frequencies are functions of their

states of motion and gravitation, i.e., relativity is expressed in

terms of the effects of motion and gravitation on the rest mass

and the local velocity of light, respectively, which saves abso-

lute simultaneity. While DU predicts clock frequencies, SR

and GR predict differences in the ﬂow of time that the clocks

experience. In GR A and B have identical frequencies when

measured in proper time, but when measured in coordinate

time of the frame of A, the rate of the ﬂow of time in the frame

of B is slower or faster; when A has completed noscillations,

B has completed a different number of oscillations, because

time has passed slower or faster in the frame of B, and there-

fore B has had less or more time to oscillate.

How could we objectively decide which explanation is

better? One way is to look at the implications of the explana-

tions. The cost of the GR explanation is violation of

absolute simultaneity which arguably makes the relativistic

world-view nonunderstandable, and the parameters that are

required in the explanation: time dilation, gravitational blue-

shift/redshift, and the dichotomy of proper time and coordi-

nate time; these are the peak of the iceberg, for FLRW alone

brings in many more parameters. In addition to its parametric

nature and nonunderstandability, relativistic physics is built

on different postulates than QM, i.e., physics about the large

scale and physics about the small scale are separated. While

DU complements the quantum mechanical solution of

atomic oscillators by the effects of motion and gravitation,

partially unifying a theory of gravitation and QM, it is very

hard to see how this could be done without letting the veloc-

ity of light vary locally, i.e., it is very hard to see how the

quantum mechanical solution of atomic oscillators could be

complemented by the effects of motion and gravitation in

the context of SR and GR, where the velocity of light is

constant. Consider the central differences between relativis-

tic physics and DU (Table I).

DU has been developed as a resolution to the problems of

relativistic physics, and it succeeds in its designed purpose.

DU replaces the mathematics and the ontology of relativistic

physics, whereas the mathematics of QM remains mainly as it

is in the context of DU; only its ontological ground is differ-

ent from typical contemporary interpretations. It is startling

that physicists have been awaiting the uniﬁcation of QM and

gravitation for a 100 years now, but when it is offered, they

reject it almost unanimously. This is because DU is different

from the theory of gravitation they are familiar with. Propo-

nents of GR who are searching for the grand uniﬁed theory

naturally wish to unify QM and GR. Although the postu-

lates of GR especially keep physics disuniﬁed, it would be

misleading to say that their faith is strong even after

100 years of failure, because the typical ideology is that GR

has been veriﬁed beyond doubt, and it is the only intelligi-

ble basis for the account of gravitation in the long-awaited

grand uniﬁed theory. In this light, it is natural that despite

the 100-year failure of unifying QM and GR, when someone

suggests different postulates that happen to succeed in the

uniﬁcation, the proponents of GR reject them just because

they are different from GR. Feyerabend saw this tendency

and Planck understood how hard it is to change one’s

habits:

Empirically minded scientists at once confront it

with status quo and announce triumphantly that ‘it

is not in agreement with facts and received

principles’. They are of course right, and even

trivially so, but not in the sense intended by them.

For at an early stage of development the

contradiction only indicates that the old and the

new are different and out of phase. It does not

show which view is the better one. A judgement of

this kind presupposes that the competitors confront

each other on equal terms. How shall we proceed

in order to bring about such a fair comparison?

17

A scientific truth does not triumph by convincing

its opponents and making them see the light, but

rather because its opponents eventually die and a

new generation grows up that is familiar with

it.

18

Contemporary physicists typically disregard the notion

that the cumulative structure of postulates and parameters of

relativistic physics, its nonunderstandability and its being

detached from QM are in the Kuhnian picture preludes of a

paradigm shift. This is not clearly seen when relativistic

physics is practically thought of as the truth, and when the

TABLE I. Central differences between relativistic physics and DU.

Relativistic physics The Dynamic Universe

Various parameters The number of parameters

is minimized

Proper time, coordinate time,

cosmic time

A single conception of time

Nonunderstandable world-view Understandable world-view

Gravitation and QM are disuniﬁed Gravitation and QM are uniﬁed

Physics Essays 31, 3 (2018) 261

pro-relativistic attitude is coupled with physicalist philoso-

phy of science where one looks only at mathematics. When

the outdated physicalism is left behind, it can be seen that

measuring accuracies of predictions is only the ﬁrst step in

theory evaluation, and that after this comes the evaluation of

other virtues, including metaphysical simplicity, uniﬁcatory

power and understandability.

DU gives at least as accurate predictions of all central

phenomena as relativistic physics. Once we evaluate the

other virtues of relativistic physics and DU, we get a clear

contrast between a nonunderstandable theory with diversi-

ﬁed postulates and parameters, and an understandable and

economically uniﬁed explanation of all scales in terms of

one and the same postulate base where the need of parame-

ters is minimized. Virtuousness is in the nature of a uniﬁed

theory, whereas a disuniﬁed theory extradites virtues. We

can ask: Do we want to continue with the culture of await-

ing a uniﬁed theory but not achieving it because the

untouchable postulates of GR prevent the uniﬁcation? Or

do we want to switch from waiting into working with a

uniﬁed theory?

For a proponent of DU, relativistic physics is compara-

ble to Ptolemaic astronomy which was a paradigmatic the-

ory that was kept standing by parameters (epicycles), and it

was replaced by a relatively simpler theory that explained

phenomena of that time by its basic structure without

parameters. Relativistic physics is currently a paradigmatic

theory that is kept standing by parameters. In both cases,

the proponents of a theory are not willing to admit that the

parameters are merely additional metaphysical assumptions

that are needed in matching perceptions with the basic

metaphysical assumptions of the theory, but they are seen

as empirical facts because they follow from a theory whose

basic assumptions are considered to be true. Instead of see-

ing non-understandability as a vice and understandability

as a virtue, its physicalist proponents rather think that the

theory is so ingenious that only elected few really under-

stand it, and that the function of physics is not to under-

stand reality, but only to give mathematical descriptions of

perceptions.

The physicists’ indoctrination is understandable. Well-

known theories that predict and explain all central scales of

phenomena that relativistic physics does have not been

around, not to speak of theories that manage to unify cos-

mology and quantum mechanics, and the conceptual

change away from relativistic physics is hard for an indi-

vidual as well as for the community of physicists who have

worked for a long time with relativistic concepts. But this

only underlines the importance of bringing forth viable

alternatives and investigating them without prejudice. Phi-

losophers should not sack an economically uniﬁed theory

because it is different from mind-boggling relativistic phys-

ics that keeps physics disuniﬁed. They should seriously

think if it is intelligible to invest time and efforts into the

100þyears old project of ﬁguring out what is the nature of

Minkowski spacetime, or whether it is more progressive to

shift into more advanced questions in the context of pres-

entism and absolute simultaneity, that are now backed up

by a uniﬁed system of physics.

APPENDIX: THE BASIC STRUCTURE OF DU

Introductions to DU and evaluations of DU versus rela-

tivistic physics are available.

19

The central postulates of DU

are absolute simultaneity and the zero-energy formulation of

the conservation law of energy within spherically closed

space. In DU, the three-dimensional space is the surface of a

four-dimensional sphere, whose radius is the fourth dimen-

sion. In the zero-energy formulation, zero is the sum of the

total potential energy and the total energy of motion.The

energy of motion comes in two forms: the energy of motion

of objects related to the expansion of space or rest energy; the

energy of motion of objects that move in space. The energy

of motion results primarily from the expansion of space,

and motion within space may be disregarded in the largest

cosmological scale. Likewise, gravitational energy is the

primary form of potential energy, and other forms of poten-

tial energy may be disregarded in the largest cosmological

scale. Figure 3depicts relations of the 4 D geometry and the

zero-energy balance within one contraction-expansion

cycle. When the Universe expands the radius of the sphere

increases; when the Universe contracts the radius of the

sphere decreases.

On the extreme left at the initial stage of the

contraction-expansion cycle, the Universe is ideally still,

the radius of the sphere is at the widest, the energy of

motion is minimal and the gravitational energy is maximal.

The maximal gravitational energy and the minimum energy

of motion are both mathematically 0. When the Universe

contracts the radius of the sphere decreases. Mathemati-

cally, when the Universe contracts the energy of motion

increases in the positive direction, and the gravitational

energy decreases, i.e., increases in the negative direction,

where their sum is always zero. The contraction continues

until the singularity, where the gravitational energy has

reached its minimum and the energy of motion has reached

its maximum. The closer the Universe is to the singularity

in the contraction stage, the faster is the contraction and

the greater the energy of motion, and the smaller the gravi-

tational energy. After the singularity, contraction turns into

expansion. Currently the Universe expands: the radius of

the sphere increases, the energy of motion decreases and

the gravitational energy increases. DU’s energy balance

equation interrelates the conservation law, the velocity of

expansion/contraction (c

4

) in the fourth dimension, the

radius of the sphere (R

4

), the mass of the Universe (M) and

the mass equivalence (M00) which is set in the center of the

sphere. (M¼M00/0.776 ¼2.3 10ˆ

53

kg. The gravitational

energy of the hypothetical homogeneous space that affects

test mass mis equal to the gravitational energy of the mass

equivalence M00.)

21

The equation states that the energy of

motion on the left side of the equation is equal to the

potential energy on the right side

c2

4M¼GMM00

R4

(11)

c

4

is the velocity of the expansion of space, i.e., the velocity

of the increase of R

4

(or the velocity of contraction in the

262 Physics Essays 31, 3 (2018)

contraction stage). As a consequence of the zero-energy bal-

ance, c

4

is the maximum velocity of any object moving in

space. Thus, c

4

is also the maximum velocity of light in

space. In hypothetical homogeneous space—where all mass

is thought to be uniformly distributed in space—the velocity

of light in space is equal to c

0

. However, in reality space is

not homogeneous, and in the vicinity of mass centers in

space, local space is tilted in the fourth dimension, making

local velocity of light csmaller than c

4

, as indicated in the

main text.

22

Thus, the velocity of light in space changes

along with the change of R

4

, and with the local gravitational

state. This is a decisive difference to relativistic physics

where the velocity of light is constant.

Again, in DU a mass object moving in space has veloc-

ity and momentum in two directions: in a space direction

and in the direction of the expansion of space in the fourth

dimension. Increase of the object’s velocity in a space direc-

tion is associated with an increase in its inertial mass (rela-

tivistic mass). The increase in its inertial mass is

counterbalanced by a decrease in its rest mass which reduces

its rest momentum (its momentum in the direction of the

expansion of space). The reduced rest momentum of

an atomic clock is observed as reduced characteristic

frequencies of atomic oscillators in the clock, as shown in

Section IV.

In DU instantaneous gravitation allows a quantitative

expression of Mach’s Principle, where the movement of a

mass object is affected by all other mass in space, in terms of

a system of nested energy frames.

16

To illustrate, e.g., an

atom on Earth is gravitationally connected to the Earth; the

Earth is gravitationally connected to the Sun; the Solar Sys-

tem is connected to the Milky Way; the Milky way is con-

nected to some cluster of galaxies; and so forth up to a

temporal stage of the Universe as a whole. Therefore, all

parts of a single temporal stage are directly or indirectly

causally connected by gravitation.

While in standard physics force is the basic quantity and

energy is derived, in DU energy is the basic quantity and

force is derived, as the local gradient of potential energy.

23

In standard physics all interactions are explained in terms of

particles/waves moving at the velocity of light at the fastest.

Consider an apple hanging from a tree. In GR/quantum ﬁeld

theory, gauge boson particles called gravitons that are emit-

ted by the Earth hit the apple and attract it toward the

ground. Also the apple emits gravitons which hit the Earth.

The apple remains in the tree as long as the gravitational

force conveyed by the gravitons is weaker than the force of

the chemical bonds of the molecules that keep the stem of

the apple attached to a branch.

DU shifts from mechanistic conveying of forces via par-

ticles into nonmechanistic recognition of the local gradient

of potential energy. In the case of gravitation, DU shifts

from mechanistic conveying of gravitation via gravitons that

move at the velocity of light, into instantaneous recognition

of the local gradient of gravitational potential. In general,

every particular aims toward its minimum potential energy

and potentiality aims to get actualized/realized into motion

which resembles Aristotle’s entelechia.

19,24

In DU, the apple

FIG. 3. The balance of the gravitational energy and the energy of motion.

20

Physics Essays 31, 3 (2018) 263

recognizes its gravitational energy and it also recognizes the

energy of the chemical bonds by which it is attached to the

branch. The gravitational energy together with the chemical

bonds create a local minimum of potential energy at the

bonding distance, i.e., at the location where the apple hangs

from the tree. When the apple hangs in a speciﬁc location,

the apple is in a local minimum, and therefore does not fall

to the ground. As the apple ripens, the chemical bonds

weaken. In effect, the location of the local minimum of

potential energy of the apple changes: the apple recognizes

its new local minimum of potential energy as the gradient of

its gravitational potential, and falls to the ground to the new

local minimum.

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16

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264 Physics Essays 31, 3 (2018)