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1  Introduction
Many experiments, like the MichelsonMorley
and Sagnac experiments and others, are testing the fundamental
nature of light. It is conflicting to observe that the velocity
of photons is measured as a constant, when the observer moves
away from that light source. Since all other particles are
measured with additive velocities (Vv) or (V+v) with respect to
a moving frame, why can photons not obey that same rule? Since
Newton's mechanics has shown that all relative velocities
produce a Doppler frequency shift, we must expect that some
special phenomena prevent us from detecting the real change of
relative velocity. It is quite incorrect to believe that this
phenomenon cannot be explained using physical reality and Newton
physics. As required by the principle of massenergy
conservation ^{[1]}, the atoms (nucleus and electrons) forming the local
standard reference meter and the moving clock have acquired some
extra mass due to the materialization of kinetic energy. Quantum
mechanics shows^{ }^{[1]} that this increase of energy changes the de Broglie
electron wavelength and consequently, the Bohr radius and the
clock rate. It is surprising to find new hypotheses like
spacetime distortion, and even more, the suggestion of "new
logic" to explain these observations, while it is not taken into
account that the rate of the moving clock is naturally modified
due to the increase of mass (following the absorption of kinetic
energy). The simple application of the principle of massenergy
conservation explains naturally all these experiments.
We
must recall that an empirical equation used to predict the
outcome of a physical system is not an explanation.
When there is no physics underneath these mathematical
equations, they give empirical predictions of what will happen
to the system. Mathematical equations generally deal with
symbols, but they never explain "why". A real
explanation must answer the question of causality, which is
asked by why? An equation is never the "cause" of
a phenomenon.
2  Switching between Frames of Reference
Let
us
consider
the
frame
of
reference
of
a
small
stars
cluster,
with
stars
having
all
the
same
velocity,
as
illustrated
on
figure 1. One of those stars is our Sun, which is surrounded by
the Earth moving around it. In this star frame, an observer
measures that the photons are emitted at velocity c with respect
to the star system. That light (hn,
on figure 1) travels toward the Earth, but the Earth moves away
at velocity v_{E} with respect to
the star system as illustrated on figure 1.
Figure 1
Figure 2
1 
2 
3 
4 
3  Einstein's Clock Synchronization Technique
On
the
station
frame,
an
observer
calculates
the
velocity
of
light,
using
his
proper
units
[s]
and
the
standard
method
used
by
Einstein. A pulse of light is emitted from location A toward B
(see figure 2). The station observer measures the velocity of
light, calculating the quotient of the length L_{v},
divided by the difference of local time between light emitted
from A and received at B (see figure 2). Since the train is in
motion, for the station observer, the distance L_{v}
between A and B is represented by _{v}[s] and not _{s}[s], because the train is
really longer when in motion. Measuring the "time interval"
means only, that the station observer records the displays shown
respectively on both clocks, at the instant light is at location
A (CD_{A}) and later B (CD_{B}). This experiment
gives c.
5 
4

Synchronization of Moving Clocks a
and ß, with a Third Clock µ
We
have
seen
above,
that
there
are
two
perfectly
equivalent
methods
to
synchronize
clocks.
Method
#1
uses
a
twoway
reflected
beam
of light on a mirror, while method #2 is carrying a third clock
µ on the moving frame between a
and ß. Of course, due to their kinetic energies, both
clocks a and ß on the train,
run at a slower rate. As a consequence of that slower clock
rate, we show that when all three clocks A and B and a are all synchronized at zero, at the
same instant, the fourth clock ß cannot show a Clock
Display equal to zero, due to the Einstein's synchronization
technique described above. This phenomenon does not seem to have
been noticed directly previously. However, we will see that it
is the "cause" of the Sagnac effect. This deficient
synchronization of clock ß with respect to the others has
been demonstrated in a previous paper ^{[1]}. We use here
method #2, which is mathematically equivalent. The result
is identical.
We consider that clock µ starts moving from clock a to clock ß, at the moment clock a passes besides clock A (see left hand
side of figure 2). Since clock µ moves at the additional
velocity e[s] (with respect to
v[s]), the Difference of Clock Displays (DCD[s])
is recorded on clock A, while clock µ
travels across the distance _{v}[s]
with
respect to the moving frame: This gives:
6 
7 
8 
9 
10 
11 
12 
13 
5  Table of Clock Synchronization
We have shown above that the synchronization of clocks on a
moving frame is such that clocks a
and ß must necessarily be synchronized with a different
display "at the same instant". This is required even if both
clocks a and ß are located on
the same frame. However, both clocks (A and B) at each extremity
of the station frame show the same display at the same instant.
An observer on the station frame could observe that clocks a and ß do not show an identical
display at the same instant. However, the observer on the train
could not detect any difference when synchronizing his local
clocks, because both methods of synchronization using light, or
carrying clock µ, agree with the above Einstein's
discordant synchronization, between a
and ß. Since this phenomenon has not been discussed
previously (except in ^{[1]}), and in
order to give a nonambiguous description, we present a table of
Clock Displays appearing simultaneously on the four clocks A, B,
a and ß as a function of the
apparent time on clock A, for each successive second [s] as
given in equation 13.
Seconds [s] 
Seconds [s] 
Seconds [v] 
Seconds [v] 




















Respective Clock Displays on each Clock at the
Same Instant.
Table 1
6 Velocity of Light in a Moving Frame
Let us calculate the distance "L_{2}" (see figure 2) traveled by the beam of light emitted
at the velocity c, from location A, at rest on the station,
during the time light passes from a
to ß located in the moving frame. Using Galilean
coordinates, we calculate the velocity of the photons moving at
velocity (cv) with respect to the moving train. The
photons must travel across the moving distance L_{v}[s]
when we consider the relative velocity (cv) before passing from
a to ß. Consequently, the
time T_{L}_{2}[s] (or DCD_{v}[s]) taken to pass from a to ß, at the relative velocity
(cv), is equal to:
14 
15 
16 
17 
18 
19 
20 
21 
7  Experimental Confirmation of the Discordant Einstein's
Synchronization Method with the GPS
There
are
direct
measurements
proving
that
the
velocity
of
light
in
one
direction
is
c±v
with
respect
to
the
moving
observer.
This discordant synchronization given in equation 13 has been
measured in the world system of clock synchronization with the
Global Positioning System. It is then observed experimentally
that the Einstein's method of synchronization using the "half
time interval" taken by a reflected beam of light is inadequate
to determine the correct time. A correction (which is the Sagnac
effect) has to be added.
As an example, let us assume that clock a
(from figure 2) is in New York (N.Y.), and clock ß is in
San Francisco (S.F.) as illustrated on figure 3. The velocity v
is the velocity of rotation of the Earth around the pole axis,
at the location where the experiment is done. The distance is the distance between New York and
San Francisco (dotted line on figure 3).
Clock Synchronization on the Rotating Earth.
Figure 3
22 
23 
24 
8  Synchronizing Clocks with the GPS
Other
experiments
can
be
realized
to
test
the
difference
of
synchronization
(time)
between
clocks.
Experiments,
with
northsouth
displacements
of
clocks,
have
also
been
verified
experimentally. Instead of exchanging directly the radio signals
or moving clocks between New York (N.Y.) and San Francisco
(S.F.) as illustrated on figure 3, let us assume that a radio
signal is sent from New York to a station at the North Pole
(N.P.) of the Earth before being reflected (or reemitted)
toward San Francisco. This can be done using a satellite located
above the North Pole. In this case, in agreement with the GPS,
we observe that the simultaneous exchange of radio
synchronization between a and
ß, does not show the difference of 14 ns, since light
never travels across meridians, as illustrated on figure 3.
Then, light never has to move directly against the Earth
velocity of rotation. The projection of the light path on the
area A, defined above (equation 23) is zero, because light
travels along the meridians, via the North Pole. Of course,
there is a higher order correction related to the transverse
velocity of light with v that can be considered elsewhere, but
this is clearly not observable experimentally.
A
similar
result
is
obtained
when
we
carry
an
atomic
clock
µ,
at
constant
geodesic
altitude
in
the
northsouth
direction
from
New York to the North Pole (N.P.). Of course, in that case,
clock µ might increase its rate because of the decrease of
tangential velocity of Earth rotation at higher latitudes.
However, it has been demonstrated that the flatness of the Earth
is such that the gravitational potential at the pole compensates
exactly for the loss of rotational velocity v. Since no
meridians are crossed, the GPS correctly calculates a zero
correction on clock µ, at its arrival at the North Pole.
For the same reason, a null correction is also calculated on
clock µ by the GPS when it is moved from the North Pole
(N.P.) to San Francisco (S.F.).
Either
using
simultaneous
light
transmission
or
carrying
a
clock
µ,
it
is
remarkable
that
both
methods
of
synchronization
of
clocks
between
New
York
and San Francisco, across the North Pole, give an identical zero
correction. However, when the radio signal or the moving clock,
crosses the meridians, the correction of 14 ns, as calculated by
equation 13, appears in both methods.
9  Observation of the OneWay Velocity of Light as c±v
Knowing
that the Sagnac effect, the GPS, all the related experiments
described above and also using Newton physics lead to identical
results, we can rely on the GPS data. Consequently, the GPS is a
reliable tool to measure directly the oneway velocity of light.
Let
us
start
our
experiment
with
an
atomic
clock
at
the
North
Pole
of
the
Earth.
At
this
location,
there
is
evidently
no problem with the velocity of Earth rotation (which is
nonexistent). From the North Pole (N. P.), let us initiate an
independent synchronization with the two clocks a and ß located respectively
in New York and in San Francisco. Since both methods,
(transmission of simultaneous radio signals or carrying an
atomic clock), lead to the same result, we can use the
synchronization method that we prefer. From the North Pole, and
moving along the meridians, the projection of the path on the
Earth equator A_{E} is zero.
Consequently in that case, synchronizations of the clocks in
N.Y. and S.F. with the one at the North Pole, do not need any
correction (A_{E} =0 in equation
22).
Therefore,
two
clocks
in
San
Francisco
and
in
New
York
are
now
in
perfect
synchronization.
Using
this
synchronization,
let
us
measure
the
velocity
of
light between N.Y to S.F. and also between S.F. and N.Y. Let the
observer in New York send a radio signal (across the meridians)
to San Francisco at the same time another radio signal travels
in the opposite direction. This simultaneous exchange of radio
signals can be done using the refraction of the ionosphere or
via a satellite at a low altitude above the same meridian. Since
the two clocks have been previously accurately synchronized in
the paragraph above, the absolute time of emission and reception
can be measured directly on each local clocks (a and ß). If the path length
of the radio signal is not much longer than the shortest path
(passing across the meridians), the average time interval
measured simultaneously in both directions is about 15 000
microseconds.
In
that
case,
an
accurate
measurement
of
the
time
interval
given
by
the
synchronization
above
with
the
North
Pole,
(in
agreement
with the GPS) shows that light takes an extra 0.014 microsecond
to travel eastward (from S.F. to N.Y.). Also light arrives at
the western station (from N.Y. to S.F.) 0.014 microsecond before
the average 15000 microseconds interval needed to travel a
distance of about 4500 km. Since there is a difference of 0.014
microsecond between each direction, this shows that light moves
at a different velocity eastward than westward. We calculate
that the velocity "v" of rotation of the Earth at the latitude
of those cities is about one millionth of the velocity of light.
From the above data, the time interval for light from New York
toward the approaching San Francisco is also about one millionth
shorter. Also the time interval for light to move from San
Francisco to New York (which has moved away) is about one
millionth longer. Clearly, the velocity of light with respect to
an observer resting on the Earth surface is c+v between N.Y. and
S.F. and cv between S.F. and N.Y. One must conclude
that the velocity of light is c with respect to a frame at rest.

Some
people have a restricted interpretation when the say that the
velocity of light is c with respect to the nonrotating
(zero velocity) frame.
Since the observations above had to be made using the velocity
component of the rotating Earth, some people have claimed that
the observed change of velocity is directly due to the
rotating Earth and consequently, the velocity of light is c
"only" with respect to a nonrotating frame. This
naïve conclusion is misleading, because it implies
incorrectly that the velocity of light (measured in a moving
frame) cannot be different from c when the frame moves in
straight line. We can see that the velocity c±v,
measured from a rotating frame, is a special case of velocity
c±v due to a linear motion.

We can show that logically, the velocity of light is also
c±v for an observer moving in straight line (without
any rotation).
Let
us
show
first
that
a
statement
claiming
that
light
moves
at
velocity
c,
“only”
with
respect
to
a
nonrotating
frame
is
not a physical explanation. This statement implies that
the real velocity of light cannot be c±v, if the frame
is not rotating (but just translating). The word “only”
implies that the velocity is c±v in a rotating frame
but it would not be c±v in a translating frame (even if
the velocity is the same). There exists no direct
physical mechanism capable of explaining that
light can move at velocity c±v with respect to a
rotating frame and c with respect to a translating
frame. Claiming that the velocity of light is c in a
frame translating at velocity v, and simultaneously claiming
that the velocity is c±v in a rotating frame, which is
the same phenomenon, is incoherent.
In
physics,
an
explanation
requires
that
an
observation
is
coherent
with
respect
to
a
welldescribed
physical
mechanism.
When
we
claim
that
the
velocity
of
light is c±v, this is the direct logical consequence of
the application of the wellknown Galilean coordinates.
With the Galilean coordinates, we understand logically that
when a traveler moves in the universe at velocity v with
respect to particles moving at velocity c, the velocity of the
particles with respect to the moving frame is cv. Here
the particles are photons. This last description is a
direct physical explanation compatible with conventional logic
(without magic). Therefore the simple statement that,
the velocity of light is c, "only" with respect to a
nonrotating frame is noncoherent.

Let
us
show
now
that
the
velocity
of
light
is
c±v
with
respect
to
an
observer,
moving
in
straight
line
at
velocity
v. Let us consider two flashes of light emitted from our
Earth moving in a direction parallel to its motion, during its
orbit around the Sun. The two light beams are emitted
simultaneously in opposite directions along the Earth’s
orbit. Around the Sun, there are some stationary
stations reflecting light, which are distributed so that light
emitted from Earth can circle the Sun simultaneously in both
directions. For example, we can assume eight stationary
mirrors reflecting light and forming an octagon around the
sun. For the beam moving in the same direction as the
Earth, the moving observer will measure a longer time interval
(than in opposite direction) before light completes the
rotation around the Sun and reaches Earth again, because the
Earth has moved a small distance, during that travel time
interval of light. The velocity of light calculated is
then cv (for the Earth observer). Also, for the
observer on the moving Earth, the velocity will be calculated
as c+v for the beam of light moving in the opposite direction.
Between
each
of
the
eight
pairs
of
mirrors,
in
the
forward
direction,
when
the
observer
uses
his
proper
units
in
his
frame
and Einstein’s synchronization, the moving observer will
“believe” that the velocity of light is c. This is due
to the erroneous clock synchronization explained above.
Also, we could install a GPS around the Sun (as the one on
Earth) and we would find, just as on Earth, those clocks are
slowing down and standard meters dilated due to the kinetic
energy of the observer. The distance between a pair of
mirrors corresponds to the distance between New York and San
Francisco on Earth, as in the example above. Again, the
velocity of light moving along a straight line moves at
velocity cv with respect to the observer on Earth, if he uses
a correct synchronization method (i.e. from the Sun's pole).

The
most
remarkable
thought
experiment
is
when
the
Sun
is
completely
removed
from
the
center
of
the
system
above.
We
mean,
an
experiment done very far in empty outer space. Then
again, the observer moves at velocity v, in straight line,
along one side of the octagon. Due to the observer’s
velocity, light will take more time to complete the complete
octagonal path when he moves in the same direction as light,
than if light and the observer are moving in the opposite
direction. In fact, any mass, either the Earth or the
Sun is irrelevant. Again, this is the classical Sagnac
effect.
One
must
conclude
that
using
traveler’s
local
units,
we
always
find
the
same
number
of
local
units
for
the
velocity
of
light, due to the error in Einstein’s clock synchronization
demonstrated previously (and also in this paper). The
real velocity of light is really a constant c with respect to
an absolute frame at rest. Consequently, it is
(c±v) (and not c) with respect to a moving frame, as
measured on a real absolute clock (which takes the variation
of units into account), which would not be modified due to its
kinetic energy. The simplest way to make sure that we
always use the same time rate, is actually always looking at
the "very same clock" (with a telescope if necessary) and
correct for the delay of transmission calculated by the
observer at rest.
We
must
conclude
that
the
hypothesis
of
a
constant
velocity
of
light
with
respect
to
a
moving
frame
of
reference
is
an
illusion and therefore an error.
10  Absolute Frame of Reference
One
must
conclude
that
the
GPS
and
all
the
related
experiments
give
a
striking
proof
that
the
velocity
of
light
is
not
constant with respect to an observer, contrary to Einstein's
hypotheses. The measured velocity of light is cv in one
direction and c+v in the other. The velocity of light is equal
to c with respect to an absolute frame in space. This is now an
experimental fact. Finally, we have seen how it is apparently
constant in all frames using proper values and a correct clock
synchronization.
We
can
consider
the
velocity
of
light
with
respect
to
a
group
of
stars
around
the
Sun.
However,
there
is
nothing
that says that that star cluster is at an absolute rest. It
probably moves around our galaxy which itself moves around the
local cluster of galaxies. From what we have seen here, we see
that the star cluster mentioned above is just another moving
frame, in which again, we have an "apparent" velocity of light
equal to c in all directions, because we do not know yet, how to
get an absolute synchronization of clocks from the absolute
frame.
A
simple
way
does
not
seem
to
exist,
which
would
enable
us
to
use
light
to
determine
the
absolute
velocity
with
respect to the fundamental frame in the universe. We have
mentioned in a previous paper ^{[9]} that there seems to be an absolute frame of reference
related to the 3Kradiation dipole in space. It exists, however,
another solution than the 3K radiation. Light seems to be
inadequate, to verify our absolute velocity with respect to an
absolute frame. It exists however another solution to locate
that absolute frame, but this is beyond the scope of this paper.
Most
physicists
believe
that
the
velocity
of
light
is
constant
with
respect
to
all
frames.
As
explained
above,
this
is
wrong.
Let
us go back to the question: The velocity of light is "c" with
respect to what? The principle of massenergy conservation
requires that light moves at a constant velocity with
respect to an absolute frame. Furthermore in all
other frames, the velocity of light is always measured
to be constant (equal to c) with respect to that moving frame,
but it is an "illusion" due to Einstein's discordant clock
synchronization.
Some
scientists
suggest
the
existence
of
an
"aether"
to
carry
light.
A
naive
"aether"
hypothesis
leads
to
a
prediction
of
the
velocity of light that could be measured "directly" as
c±v with respect to the observer. This is not that
simple. One extremely important point is that there exists
no observational justification^{[10,
11]} to assume that an aether can
possess its own energy that can be borrowed when needed. On the
contrary, all the physical phenomena are explained naturally
without having to borrow any energy or momentum from an assumed
medium. For the moment, the sole property of that assumed
aether is to establish an absolute origin to the velocityframe
of light and physical matter, because this frame of reference is
absolutely needed to comply with the principle of energy and
momentum conservation. That absolute frame might be simply
determined by the average velocity of all matter in the
universe.
One
must
conclude
that
there
exists
no
spacetime
distortion
of
any
kind.
It
is
no
longer
necessary
to
fascinate
people
with
the
magic of relativity. Unless we accept the absurd solution that
the distance between N.Y. to S.F. is smaller than the distance
between S.F. and N.Y., we have to accept that in a moving frame,
the velocity of light is different in each direction. As
mentioned above, this difference is even programmed in the GPS
computer in order to get the correct Global Positioning. This
proves that the experimental velocity of light with
respect to a moving observer is c±v.
11

References
[1] P. Marmet, Einstein's Theory of
Relativity versus Classical Mechanics, Newton
Physics Books (1997), Gloucester, Ontario, Canada K1J 7N4.
Book on the Web.
[2] P. Marmet, Classical Description of the
Advance of the Perihelion of Mercury, Physics Essays
Vol. 12. No: 4, 1999. Web page
[3] Sadeh et al. Science
162, 8978 (1968)
[4] Straumann N. General
Relativity and Relativistic Astrophysics, SpringerVerlag,
Berlin, Second printing 1991, pp. 459,
[5] CCIR Internat. Telecom,
Union Annex to Vol 7, No: 4395. Geneva 1504 (1990).
[6] CCDS Bur. Int. Poids et
Mes. 9^{th} Sess., 1417, 1980.
[7] Saburi et al. IEEE Trans.
IM25, 4737, 1976.
[8] A. G. Kelly, "The Sagnac
Effect and the GPS Synchronization of ClockStations" Ph.
D. HDS Energy Ltd., Celbridge, Co. Kildare, Ireland. Also, A. G.
Kelly, Inst. Engrs. Ireland 1995 and 1996, Monographs 1 & 2.
[9] P. Marmet, The Origin of the 3K Radiation,
Apeiron Vol, 2 Nr, 1. January 1995 Web page
[10] P. Marmet, Classical Description of the
Advance of the Perihelion of Mercury, Physics
Essays, Vol. 12, No: 3, 1999.
[11] P. Marmet, C. Couture, Relativistic Deflectionof Light
Near the Sun Using Radio Signals and Visible Light,
Physics Essays, Vol. 12, No: 1 (1999) Web page

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