MATHEMATICS & NATURE
Mathematics, Physics, Mechanics & Astronomy
Random Vol. 1 Sn: 202101
https://mathnature.github.io
c
⃝ Mathematics & Nature–Free Media of Eternal Truth, China, 2021 https://orcid.org/0000-0002-3644-5170
.
Article
.
Physics
On the Relativity of the Speed of Light
X. D. Dongfang
Orient Research Base of Mathematics and Physics,
Wutong Mountain National Forest Park, Shenzhen, China
Einstein’s assumption of constant speed of light is regarded as a basic principle of modern physics
and has a great and far-reaching influence. However, the nature and scope of application of the
constant speed of light hypothesis have not been discussed by relativity theory, which has led to
readers’ misunderstanding of relativity, especially special relativity, for more than 100 years, and has
b een deeply rooted. Here I introduce the Dongfang unitary principle, which has a wide application
prosp ect in the logic self consistency test of mathematics, natural science and social science. Based on
this, I propose the complete space-time transformation including the Lorentz transformation, clarify
the definition of relative velocity of light and the conclusion that the relative velocity of light is variable,
and further prove that the relative variable light speed is compatible with Einstein’s constant speed
of light. The specific conclusion is that the propagation speed of light in vacuum relative to the
observer’s inertial reference frame is always the constant c, but the propagation speed of light relative
to any other inertial reference frame which has relative motion with the observer is not equal to the
constant c; observing in all inertial frame of reference, the relative velocity of light propagating in the
same direction in vacuum is 0, while that of light propagating in the opposite direction is 2c. The
essence of Einstein’s constant speed of light is that the speed of light in an isolated reference frame is
constant, but the relative speed of light in vacuum is variable. The assumption of constant speed of
light in an isolated frame of reference and the inference of relative variable light speed can be derived
from each other.
Keywords: Dongfang unitary principle; Lorentz transformation; Dongfang Complete space-time
transformation; Light velocity invariant illusion; Relative variable light speed.
PACS number(s): 03.30.+p—Special relativity
1 Introduction
Because of relativity, the speed of light in vacuum
has a very special position in modern physics. Although
the hypothesis of invariance of light speed
[1, 2]
and the
principle of relativity
[3]
, which are the basis of special
relativity, are regarded as the two basic principles that
can stand the test of experiment
[4-10]
and the demon-
stration of logical completeness
[11-13]
, the essences of the
hypothesis of constant speed of light and the inferences
of Lorentz transformation are not always clear to al-
l physics readers. This is because the relevant experi-
mental results can have different or even contradictory
explanations
[14, 15]
. Of course, the so-called superluminal
and slow light speed phenomena
[16-24]
are not variable
light speed phenomena in the usual sense, while various
superluminal and variable light speed theories
[25-30]
are
only limited to formal reasoning.
The conclusions of theoretical physics often come from
mathematical deduction. We know that from different
angles, the same mathematical physics problem can have
completely different formal solutions, and each formal so-
lution can have different interpretations. A mathemati-
cal physics problem is meaningful only when its real solu-
tion conforms to the natural law, and the real solution of
the mathematical physics problem should be unique. If
we discuss the transformation of time and space parame-
ters from the perspective of the existence and uniqueness
theorem for the solution of mathematical physics prob-
lems, the essences of the hypothesis of invariable light
speed and the inference of Lorentz transformation will
be clear. At this time, it is very important to put forward
the relevant mathematical and physical problems. There
is a universal principle to test the self consistency of nat-
ural science theory: There is a definite transformation
relationship between different metrics, and the natural
law itself will not change due to the selection of different
metrics. When the mathematical expression form of nat-
ural law under different metrics is transformed into one
metrics, the result must be the same as the inherent for-
m under this metrics, 1 = 1, which the transformation
is unified. This principle is called the Dongfang unitary
principle.
The Dongfang unitary principle can be widely used to
test the logical self consistency of mathematics, physics
and even philosophy. Using the Dongfang unitary prin-
ciple to test the physics hypotheses and inferences that
Citation: Dongfang, X. D. On the Relativity of the Speed of Light. Mathematics & Nature 1, 202101 (2021).
2 X. D. Dongfang On the Relativity of the Speed of Light
have not been proved can transform the controversial
problems into the definite solution problems of mathe-
matical physics, so as to find the real solution of the
problem under the condition of definite solution and dis-
tinguish it from the formal solution, and the problem
will have a clear answer. The unitary principle test
of quantum mechanics has promoted the discovery of
many important problems and conclusions from mod-
ern physics to common quantum theory.
[31-34]
. Here, I
use the Dongfang unitary principle to test the concept
of space-time in the meaning of special relativity, and
propose a complete space-time transformation that in-
cludes the Lorentz transformation and thus conforms to
the meaning of special relativity. From it, we can find
the existence of the definition of relative speed of light,
which is no longer constant, and then we can prove that
the relatively variable speed of light is compatible with
Einstein’s constant speed of light.
2 Complete transformation of time and s-
pace parameters
Let the relative speed of two inertial reference frames
Σ and Σ
′
be v, and the unitary principle test of the logic
self consistency of the hypothesis of constant light speed
in vacuum contains the following four metrics: (a) the
speed of light measured on reference frame Σ relative to
reference frame Σ; (b) the speed of light measured on
reference frame Σ
′
relative to reference frame Σ
′
; (c) the
speed of light measured on reference frame Σ relative to
reference frame Σ
′
; (d) the speed of light measured on ref-
erence frame Σ
′
relative to reference frame Σ. According
to the unitary principle, the result of the transformation
of light speed between different metric must be the same
as the inherent speed of light under this metric, and the
transformation is unitary.
It should be pointed out that the self consistent log-
ic must satisfy the unitary principle, and the logic that
violates the unitary principle must not be self consisten-
t and implies many contradictions, while the physical
logic with local self consistency may not be the natural
law. Logical self consistency is only a necessary condi-
tion but not a sufficient condition for the theory of nat-
ural science. With regard to the space-time coordinates
of the so-called event P , the concept of special relativity
description is as follows:
i) The time-space coordinate (x, y, z, t) of event P
measured on reference frame Σ relative to refer-
ence frame Σ;
ii) The time-space coordinate (x
′
, y
′
, z
′
, t
′
) of event P
measured on the reference frame Σ
′
relative to the
reference frame Σ
′
;
There are actually two other concepts:
iii) The spatiotemporal co ordinate (ξ, ζ, η, τ) of event
P measured on reference frame Σ relative to refer-
ence frame Σ
′
;
iv) The spatiotemporal coordinate (ξ
′
, ζ
′
, η
′
, τ
′
) of
event P measured in the reference frame Σ
′
rel-
ative to the reference frame Σ.
It can be seen that for two inertial reference frames, an
event has four sets of space-time concepts. The special
theory of relativity based on the Lorentz transformation
only describes the first two sets of space-time concepts
(x, y, z, t) and (x
′
, y
′
, z
′
, t
′
).
y
y
c
o
o
c
, , ,y y
9
9
c c
, , ,
K
K
c c
z z
,
[
c
x
,
[
c
x
,r
ȡ
P
c
¦
¦
,
c
x x
,
c
c
r
ȡ
z
c
z
Figure 1 Four sets of spatiotemporal concepts of the same
event relative to two inertial reference frames
On reference frame Σ, measuring the time and space
parameters of event P relative to reference frame Σ and
to reference frame Σ
′
, the clock used is the clock on ref-
erence frame Σ, and the concept of time belongs to ref-
erence frame Σ, so τ = t. Similarly, on reference frame
Σ
′
, measuring the time and space parameters of event
P relative to reference frame Σ
′
and relative reference
frame Σ, the clock used is clock on reference frame Σ
′
,
and the concept of time belongs to the reference frame
Σ
′
, so τ
′
= t
′
.
τ = t, τ
′
= t
′
(1)
The above equations show the characteristics of isolated
reference frame of time, that is, in all inertial reference
frame, the observer can measure the motion law of an
object relative to its own frame and relative to other in-
ertial frames, but the clock used can only be the clock of
that reference frame. The meaning of time here accord-
s with Einstein’s definition, that is, when the reading
t = t
′
= 0 of the calibrated synchronous clocks resting
in the reference frame Σ and Σ
′
respectively, the coor-
dinate origin points of the two inertial frames coincide
exactly.
Mathematics & Nature (2021) Vol. 1 3
There is a class of basic facts that have a potential im-
pact on physical theory. For example, when the moon is
on the line between the sun and the earth, measuring the
distance between the sun and the earth on the earth can
be divided into two parts: the distance between the sun
and the moon and the distance between the moon and
the earth; When the moon is not on the line between the
sun and the earth, measuring the position vector of the
sun relative to the earth on the earth can be decomposed
into two parts: the position vector of the sun relative to
the moon and the p osition vector of the moon relative
to the earth. This kind of fact is abstracted as an axiom:
the position vector of an object relative to other inertial
reference frames in all inertial reference frame obeys the
operational rule of vector superposition. We call it the
principle of the relative position vector superposition.
The above problems (iii) and (iv) can now be solved.
As shown in Fig. 1, according to the agreement of spe-
cial relativity, the two inertial reference frames Σ and
Σ
′
have a common x axis. When the moment of refer-
ence frame Σ is t, the distance between the coordinate
origins of the two coordinate frames is oo
′
= vt. Since
the distance between an object measured in all inertial
reference frame relative to other inertial frames can be
divided, then x = oo
′
= vt + ξ, therefore ξ = x − vt. Be-
cause ζ = y, η = z, then the transformation relationship
between the spatiotemporal coordinates (x, y, z, t) rela-
tive to reference frame Σ and the spatiotemporal coor-
dinates (ξ, ζ, η, τ) relative to reference frame Σ
′
of event
P measured in reference frame Σ is as follows
ξ = x − vt, ζ = y, η = z, τ = t (2)
Similarly, observed in the reference frame Σ
′
, the
transformation relationship between the spatiotemporal
coordinate (x
′
, y
′
, z
′
, t
′
) of event P at time t
′
relative to
the reference frame Σ
′
and the spatiotemporal coordi-
nate (ξ
′
, ζ
′
, η
′
, τ
′
) of the relative reference frame Σ is as
follows
ξ
′
= x
′
+ vt
′
, ζ
′
= y
′
, η
′
= z
′
, τ
′
= t
′
(3)
The meaning of Einstein’s constant speed of light hy-
pothesis is that the speed of the observed light relative
to the reference frame in any inertial frame is c, which
is expressed as
dr
dt
=
dx
dt
2
+
dy
dt
2
+
dz
dt
2
= c
dr
′
dt
′
=
dx
′
dt
′
2
+
dy
′
dt
′
2
+
dz
′
dt
′
2
= c
Therefore, the invariance of light speed in special relativ-
ity belongs to the constant speed of light in an isolated
reference frame. Einstein derived Lorentz transforma-
tion according to the principle of constant light speed in
isolated reference frame and relativity principle
x
′
=
x − vt
1 − v
2
c
2
y
′
= y, z
′
= z
t
′
=
t − vx
c
2
1 − v
2
c
2
(4)
The inverse transformation is
x =
x
′
+ vt
′
1 − v
2
c
2
y = y
′
, z = z
′
t =
t
′
+ vx
′
c
2
1 − v
2
c
2
(5)
Obviously, Lorentz transformation in the sense of special
relativity describes the relationship between space-time
parameters of isolated reference frame between two iner-
tial reference frames.
Now we can determine the relations among various
defined spatial parameters. By substituting the first for-
mula of the set of relations (2) into the first formula of
Lorentz transformation (4), or the first formula of the set
of relations (3) into the first formula of Lorentz inverse
transformation (5), new transformation and correspond-
ing inverse transformation are obtained respectively
x
′
=
ξ
1 − v
2
c
2
x =
ξ
′
1 − v
2
c
2
(6)
After substituting the equivalent form x
′
= ξ
′
− vt
′
of
the first formula of (3) into the first formula of formula
(6), or substituting the equivalent form x = ξ + vt of the
first formula of (2) into the second formula of formula
(6), we get the following results
ξ =
1 − v
2
c
2
(ξ
′
− vt
′
)
ξ
′
=
1 − v
2
c
2
(ξ + vt)
(7)
These transformations are different from both Lorentz
transformation and Galileo transformation.
Equations (2), (3), (4) and (5) describe the transfor-
mation relations among four groups of space-time pa-
rameters of two inertial reference frames with relative
4 X. D. Dongfang On the Relativity of the Speed of Light
velocity v. The form of the equations is as follows,
x
′
=
x − vt
1 − v
2
c
2
y
′
= y = ζ = ζ
′
z
′
= z = η = η
′
t
′
=
t − vx
c
2
1 − v
2
c
2
⇔
x
′
=
ξ
1 − v
2
c
2
ξ
′
= x
′
+ vt
′
τ = t, τ
′
= t
′
ξ
′
=
1 − v
2
c
2
(ξ + vt)
(8)
The corresponding inverse transformation relation is
x =
x
′
+ vt
′
1 − v
2
c
2
y = y
′
= ζ
′
= ζ
′
z = z
′
= η
′
= η
t =
t
′
+ vx
′
c
2
1 − v
2
c
2
⇔
x =
ξ
′
1 − v
2
c
2
ξ = x − vt
t = τ, τ
′
= t
′
ξ =
1 − v
2
c
2
(ξ
′
− vt
′
)
(9)
The above transformation relations (8) and (9) conform
to the sp ecial relativity meaning, and are called complete
space-time transformation. According to the complete
space-time transformation, the complete transformation
relations between the intrinsic quantity and the relative
quantity of the corresponding physical quantity such as
momentum and energy between different inertial refer-
ence frames can be derived, which is omitted here. We
also need to give priority to discovering the deeper spa-
tiotemporal parameter transformations
3 Variability of relative speed of light
The Lorentz transformation is essentially a speed pre-
serving transformation, which stipulates that the speed
of light in the vacuum of two isolated reference frames is
constant, thus defining the transformation relationship
of the space-time parameters of the two inertial reference
frames. Since the speed of the experimental observation
light relative to the laboratory reference frame in the
vacuum is constant c, Einstein proposed the hypothesis
that the speed of light does not change. In turning, he de-
rived the Lorentz transformation and established special
relativity
[35]
. Now that we have a complete space-time
transformation, we have a clear definition of the relative
speed of light. According to the complete space-time
transformation, the relative speed of light is variable,
and the relative variable light speed is compatible with
the constant speed of light in an isolated reference frame.
It is assumed that when the coordinate origin o of
the inertial reference frame Σ coincides with the coordi-
nate origin o
′
of the inertial reference frame Σ
′
, the light
source at the common origin emits a photon to the pos-
itive direction of the x axis. According to the complete
space-time transformation, the two inertial frames of ref-
erence contain four definitions of light speed, namely:
a) The isolated speed of the photon relative to the
reference frame Σ measured on reference frame Σ,
|dr/dt| = c;
b) The relative light speed of the photon relative to
Σ
′
measured on reference frame Σ, |dρ/dτ| =?
c) The isolated speed of the photons relative to
reference frame Σ
′
measured on reference frame
Σ
′
,|dr
′
/dt
′
| = c;
d) The relative light speed of the photon relative to
Σ measured on reference frame Σ
′
, |dρ
′
/dτ
′
| =?
The constant speed of light in an isolated frame of refer-
ence is well known, and the results are written directly
above.
Now let’s calculate the two relative speeds of light
|dρ/dτ| and |dρ
′
/dτ
′
|. According to the transformation
formula (2), one obtains
dξ
dτ
=
d (x − vt)
dt
=
dx
dt
− v
dζ
dτ
=
dy
dt
,
dη
dτ
=
dz
dt
The isolated light speed |dr/dt| = c on the reference
frame Σ will be used in the calculation. Therefore, the
results of the relative light velocity dρ/dτ of photons rel-
ative to the reference frame Σ
′
measured on the reference
frame Σ satisfy the relationship
dρ
dτ
=
dξ
dτ
2
+
dς
dτ
2
+
dη
dτ
2
=
dx
dt
− v
2
+
dy
dt
2
+
dz
dt
2
=
dx
dt
2
+
dy
dt
2
+
dz
dt
2
− 2v
dx
dt
+ v
2
=
c
2
− 2v
dx
dt
+ v
2
̸= c
(10)
If the light propagates along the common x axis of the
two inertial reference frames, that is, the velocity of light
relative to the reference frame Σ measured on the refer-
ence frame Σ is dx/dt = ±c, dy/dt = 0 and dz/dt = 0,
then the speed of light relative to the reference frame Σ
′
measured on the reference frame Σ is,
dρ
dτ
= |c ∓ v| (11)
If the reference frame Σ
′
is also a photon, v = ±c. There-
fore, the relative velocity of light propagating in the same
direction is 0 while that of light propagating in the op-
posite direction is 2c measured on the reference frame
Σ.
Mathematics & Nature (2021) Vol. 1 5
Similarly, according to the transformation formula (3),
one obtains
dξ
′
dt
′
=
d (x
′
+ vt
′
)
dt
′
=
dx
′
dt
′
+ v
dζ
′
dτ
′
=
dy
′
dt
′
,
dη
′
dτ
′
=
dz
′
dt
′
In the calculation, the isolated light speed |dr
′
/dt
′
| = c
of the reference frame Σ
′
is used again, so the results of
the relative light velocity dρ
′
/dτ
′
of photons relative to
the reference frame Σ measured in the reference frame
Σ
′
satisfy the relationship
dρ
′
dτ
′
=
dξ
′
dτ
′
2
+
dς
′
dτ
′
2
+
dη
′
dτ
′
2
=
dx
′
dt
′
+ v
2
+
dy
′
dt
′
2
+
dz
′
dt
′
2
=
dx
′
dt
′
2
+
dy
′
dt
′
2
+
dz
′
dt
′
2
+ 2v
dx
′
dt
′
+ v
2
=
c
2
+ 2v
dx
′
dt
′
+ v
2
̸= c
(12)
For the light propagating along the common x axis of
the two inertial reference frames, the velocity of the
light measured on the reference frame Σ
′
relative to the
reference frame Σ
′
is dx
′
/dt
′
= ±c, dy
′
/dt
′
= 0 and
dz
′
/dt
′
= 0, while the speed of the light measured on
the reference frame Σ
′
relative to the reference frame Σ
is
dρ
′
dτ
′
= |c ± v| (13)
If the reference frame Σ is also a photon, v = ±c. There-
fore, the relative velocity of light propagating in the same
direction is 0 while that of light propagating in the op-
posite direction is 2c measured on the reference frame
Σ.
Formulas (10) and (13) show that when the velocity
between two inertial reference frames is not zero, the two
relative light velocities are related to the relative veloci-
ties of inertial reference frames. Obviously, the relative
velocity of light propagating in the same direction is 0
and that of light propagating in the opposite direction
is 2c when observed in any inertial reference. Under the
complete space-time transformation, the relative speed
of light is variable, and the Einstein’s constant speed of
light in isolated frame of reference is a necessary condi-
tion for the relative variable speed of light.
4 Compatibility between relative light
speed and solitary light speed
Now we know that Einstein’s constant speed of light
hypothesis means that the speed of light in an isolated
frame of reference is constant, while the relative speed
of light is variable. The unitary principle requires that
the result of the transformation of the relative speed of
light in vacuum into the isolated speed of light in vacu-
um must be the constant c, otherwise it will constitute
a negative result of 1 ̸= 1. Therefore, the constant E-
instein speed of light must also be able to be derived
from the variable relative speed of light. The proof is as
follows.
From the complete inverse space-time transformation
(9), one obtains the following relationships
dx
dt
=
dξ
dt
+ v =
dξ
dτ
+ v
dy
dt
=
dς
dt
=
dς
dτ
dz
dt
=
dη
dt
=
dη
dτ
First, substituting theses relationships into the calcula-
tion formula |dr/dt| of the speed in isolated reference
frame of
, and then using relative light speed
dρ
dτ
2
=
dξ
dτ
2
+
dς
dτ
2
+
dη
dτ
2
= c
2
− 2v
dx
dt
+ v
2
given in equation (10), we have
dr
dt
=
dx
dt
2
+
dy
dt
2
+
dz
dt
2
=
dξ
dτ
+ v
2
+
dς
dτ
2
+
dη
dτ
2
=
dξ
dτ
2
+
dς
dτ
2
+
dη
dτ
2
+ 2v
dξ
dτ
+ v
2
=
c
2
− 2v
dx
dt
+ 2v
dξ
dτ
+ 2v
2
=
c
2
− 2v
dξ
dτ
+ v
+ 2v
dξ
dτ
+ 2v
2
= c
(14)
Similarly, from the complete inverse space-time transfor-
mation (8), one obtains the relationships
dx
′
dt
′
=
dξ
′
dt
′
− v =
dξ
′
dτ
′
− v
dy
′
dt
′
=
dς
′
dt
′
=
dς
′
dτ
′
dz
′
dt
′
=
dη
′
dt
′
=
dη
′
dτ
′
By substituting theses relationships into the into the
calculation formula|dr
′
/dt
′
| of the speed in isolated ref-
erence frame of
′
, and using again the relative light
6 X. D. Dongfang On the Relativity of the Speed of Light
speed
dρ
′
dτ
′
2
=
dξ
′
dτ
′
2
+
dς
′
dτ
′
2
+
dη
′
dτ
′
2
= c
2
+ 2v
dx
′
dt
′
+ v
2
given by formula (12), the following result is obtained,
dr
′
dt
′
=
dx
′
dt
′
2
+
dy
′
dt
′
2
+
dz
′
dt
′
2
=
dξ
′
dτ
′
− v
2
+
dς
′
dτ
′
2
+
dη
′
dτ
′
2
=
dξ
′
dτ
′
2
+
dς
′
dτ
′
2
+
dη
′
dτ
′
2
−2v
dξ
′
dτ
′
+v
2
=
c
2
+ 2v
dx
′
dt
′
− 2v
dξ
′
dτ
′
+ 2v
2
=
c
2
+ 2v
dξ
′
dτ
′
− v
− 2v
dξ
′
dτ
′
+ 2v
2
= c
(15)
It can be seen that according to relative light speed in
the complete space-time transformation, constant light
speed in isolated reference frame can be derived. It can
be said that the relative variable light speed is also a
necessary condition for constant light speed in isolated
reference frame.
The calculation results of (10) - (15) above show that
there are definitions of constant solitary light speed and
variable relative light speed under the complete space-
time transformation. Einstein’s invariance of light speed
belongs to the constant speed of light in isolated refer-
ence frame. The constant speed of light in isolated frame
of reference is compatible with the relative variable speed
of light, and they do not constitute a seemingly opposite
negative basis on the surface. All these calculations are
elementary, but elementary does not mean that the cor-
responding problems and conclusions are of little impor-
tance. Often, the discovery of primary problems is more
difficult than the discovery of higher problems, and the
impact of primary problems is more profound.
5 Conclusions and comments
In this paper, Dongfang’s unitary principle, which
is widely applicable to the logical test of natural and
social sciences, is used to test the space-time transfor-
mation of special relativity, and based on the thought
of special relativity, a complete space-time transforma-
tion is proposed, from which a new conclusion in line
with the meaning of special relativity is drawn. That
is, within the framework of special relativity, the rela-
tive speed of light is still changing, and the change of
the relative speed of light is compatible with the con-
stant speed of light in Einstein’s hypothesis. Einstein’s
invariable speed of light belongs to the constant speed
of light in isolated reference frame, that is, the speed
of light in vacuum relative to that reference frame mea-
sured on any isolated inertial reference frame is c, which
is the real meaning of constant light speed. In fact, the
concept of ”event” in special relativity defines the char-
acteristics of isolated reference frame of space and time
concepts used to describ e physical laws. The mapping re-
lationship between space-time concepts of each isolated
reference frame is determined by the Lorentz transforma-
tion. From the laboratory reference system, if the light
moves in the opposite direction with other reference sys-
tems, the vacuum light speed relative to that reference
frame is greater than c; if the light moves in the same
direction with other reference systems, the vacuum light
speed relative to that reference frame is less than c.
The condition of an inertial reference frame is very
special because there is no real inertial reference frame
in nature. Even if the inertial reference frame conditions
are satisfied, if the speed of a particle relative to other
inertial reference systems measured in the laboratory ref-
erence frame is greater than the speed of light in vacuum,
the isolated speed of a particle measured on that iner-
tial reference frame will always be less than the speed of
light in vacuum. This is the essence of the speed limit
of special relativity. The Lorentz transformation deter-
mines that the velocity of the isolated reference frame of
matter motion is less than that of light in vacuum. How-
ever, this sp eed limit theory does not apply to relative
velocity. The observer cannot stand on photons, and the
relative velocity of light to light in the vacuum observed
in the laboratory is actually distributed between 0 and
2c. It should be stated again that the length of an object
measured in the same inertial frame is separable, that is,
the length of straight lines observed in all inertial refer-
ence frame can be added or subtracted. In a broad sense,
the position vectors between moving objects observed in
the same inertial frame obey the rule of vector superpo-
sition. Because of this, if the relative variable speed of
light is negated, the constant speed of light in Einstein’s
isolated reference frame is also denied. However, there
may be no causal relationship between the relative vari-
able speed of light and the constant speed of light in an
isolated reference frame, although the relative variable
speed of light and the constant speed of light in isolated
reference frame can be derived from each other in the
sense of complete space-time transformation.
Dongfang unitary principle is the most effective log-
ical tool to deal with the tangled problems caused by
eloquence theory. This universal principle will play an
important role in the establishment of new scientific
theories. The complete space-time transformation, in-
cluding the Lorentz transformation, discovered based on
Dongfang’s unitary principle, has brought challenges to
the relativistic conclusions of kinematics and dynamics
that have been limited to Einstein’s hypothesis of con-
stant speed of light in the past. However, the impor-
Mathematics & Nature (2021) Vol. 1 7
tant and urgent problem to be solved is whether the
so-called space-time transformation is a kind of math-
ematical magic or an inevitable product of the causal
relationship of natural laws?
[1] Nerlich, G. Special relativity is not based on causality. The
British Journal for the Philosophy of Science 33, 361-388
(1982).
[2] Garrison, J., Mitchell, M., Chiao, R. & Bolda, E. Superlumi-
nal signals: causal loop paradoxes revisited. Physics Letters
A 245, 19-25 (1998).
[3] Einstein, A. Relativity: The Special and the General Theory-
100th Anniversary Edition
. (Princeton University Press,
2019).
[4] Michelson, A. A. ART. XXI. The relative motion of the Earth
and the Luminiferous ether. American Journal of Science
(1880-1910) 22, 120 (1881).
[5] M¨uller, H., Herrmann, S., Braxmaier, C., Schiller, S. & Peter-
s, A. Modern Michelson-Morley Experiment using Cryogenic
Optical Resonators. Physical Review Letters 91, 020401
(2003).
[6] M¨uller, H et al. Tests of Relativity by Complementary Rotat-
ing Michelson-Morley Experiments. Physical Review Letters
99, 50401 (2007).
[7] Haugan, M. P. and Will, C. M. Modern tests of special rela-
tivity. Phys. Today 40, 69 (1987).
[8] Zhang, Y. Z. Special relativity and its experimental founda-
tions. (World Scientific, 1997).
[9] Antonini, P., Okhapkin, M., G¨okl¨u, E. & Schiller, S. Test of
constancy of speed of light with rotating cryogenic optical
resonators. Physical Review A 71, 050101 (2005).
[10] Magueijo, J. New varying speed of light theories. Reports on
Progress in Physics 66, 2025 (2003).
[11] Mansouri, R. and Sexl, R. U. A test theory of special rela-
tivity: I. Simultaneity and clock synchronization. General
relativity and Gravitation 8, 497 (1977).
[12] Mansouri, R. & Sexl, R. U. A test theory of special relativity:
III. Second-order tests. General relativity and Gravitation 8,
809-814 (1977).
[13] Will, C. M. Theory and experiment in gravitational physics.
(Cambridge university press, 2018).
[14] Cl´ement, G. Does the Fizeau experiment really test special
relativity? American Journal of Physics 48, 1059 (1980).
[15] Wang, L-J., Liu, N., Lin, Q. & Zhu, S. Superluminal prop-
agation of light pulses: A result of interference. Physical
Review E 68, 66606 (2003).
[16] Alv¨ager, T., Kreisler, M. Quest for faster-than-light particles.
Physical Review 171, 1357-1361 (1968).
[17] Parker, L. Faster-Than-Light Intertial Frames and Tachyons.
Physical Review 188, 2287-2292 (1969).
[18] Wang, L-J., Kuzmich, A. & Dogariu, A. Gain-assisted super-
luminal light propagation. Nature 406, 277-279 (2000).
[19] Bigelow, M., Lepeshkin, N. & Boyd, R. Superluminal and s-
low light propagation in a room-temperature solid, American
Association for the Advancement of Science, 301, 200-202
(2003).
[20] Bortman-Arbiv, D., Wilson-Gordon, A. & Friedmann, H.
Phase control of group velocity: From subluminal to superlu-
minal light propagation. Physical Review A 63, 43818 (2001).
[21] Kang, H., Hernandez, G. & Zhu, Y. Superluminal and s-
low light propagation in cold atoms. Physical Review A 70,
11801 (2004).
[22] Bo, F., Zhang, G. & Xu, J. Transition between superluminal
and subluminal light propagation in photorefractive Bi 12
SiO 20 crystals. Phys. Rev. A 64, 053809 (2001).
[23] Sun, H. et al. Light propagation from subluminal to superlu-
minal in a three-level Λ-type system. Physics Letters A 335,
68-75 (2005).
[24] Salart, D., Baas, A., Branciard, C., Gisin, N. & Zbinden, H.
Testing the speed of ‘spooky action at a distance’. Nature
454, 861-864 (2008).
[25] Recami, E. How to recover causality in special relativity for
tachyons. Foundations of Physics (Historical Archive) 8,
329-340 (1978).
[26] Schwartz, C. Some improvements in the theory of faster-than-
light particles. Physical Review D 25, 356-364 (1982).
[27] Gonzalez-Mestres, L. Cosmological implications of a possible
class of particles able to travel faster than light. Nucl. Phys.
B, Proc. Suppl. 48 (1996).
[28] Everett, A. Tachyons, broken Lorentz invariance, and a pen-
etrable light barrier. Physical Review D 13, 785-794 (1976).
[29] Pant, M., Bisht, P., Negi, O. & Rajput, B. Dirac spinors
and tachyon quantization. Canadian Journal of Physics 78,
303-315 (2000).
[30] Milonni, P., Furuya, K. & Chiao, R. Quantum theory of su-
perluminal pulse propagation. Phys. Rev 52, 1525 (1995).
[31] Chen, R. New Exact Solution of Dirac-Coulomb Equation
with Exact Boundary Condition. International Journal of
Theoretical Physics 47, 881-890(2008).
[32] Chen, R. Real Solution of Dirac Equation. arXiv:0908.4320
(physics.gen-ph, 2009).
[33] Dongfang, X. D. Relativistic Equation Failure for LIGO Sig-
nals, ScienceOpen, 2020.
[34] Dongang, X. D. The Morbid Equation of Quantum Numbers,
ResearchGate, 2019.
[35] Einstein, A. On the electrodynamics of moving bodies. An-
nalen der physik 17, 891-921 (1905).
Latest findings
The Morbid Equation of Quantum Numbers
The lowest standard of natural science theory is logical self consistency. Specifically, its method and inference must conform to the Dongfang unitary principle. However, relativity and quantum mechanics, as the basis of modern physics, are not so, and the problems of quantum mechanics are hidden deeper because the substantive mathematical principles of quantum mechanics have not been revealed. The quantum model of valence electron generation orbital penetration of alkali metal elements with unique stable structure is investigated. The electric field outside the atomic kernel is usually expressed by the Coulomb field of the point charge mode, and the composite electric field in atomic kernel can be equivalent to the electric field inside the sphere with uniform charge distribution or other electric fields without divergence point. The exact solutions of two Schrödinger equations for the bound state of the Coulomb field outside the atom and the binding state of the equivalent field inside the atom determine two different quantization energy formulas respectively. Here I show that the atomic kernel surface is the only common zero potential surface that can be selected. When the orbital penetration occurs, the law of conservation of energy requires that the energy level formulas of the two bound states must have corresponding quantum numbers to make them equal. The result leads to an insoluble morbid equation of quantum numbers, indicating that the two quantum states of the valence electron are incompatible. This irreconcilable contradiction shows that the quantized energy of quantum mechanics cannot absolutely satisfy the law of conservation of energy, and quantum theory violates the unitary principle. Further, I list the morbid equations composed of various eigenvalues of the angular momentum of hydrogen atom described by Bohr theory, Schrödinger and Klein-Gordon theory, and Dirac theory, and point out that there is an irreconcilable contradiction between the minimum nontrivial angular momentum eigenvalue determined by the angular momentum eigenvalue equation in quantum mechanics and the minimum nontrivial angular momentum eigenvalue of Bohr theory.