minor mistake of Einstein led to the greatest
scientific mistake of the past century
When developing his theory, Einstein introduced
the Lorentz contraction with which he
unwittingly revived the aether theory. The
concept of curved space must be considered a
version of the aether theory. A meticulous
repetition of his derivation of the Lorentz
transformation formula for time leads to the
same result, but Einstein made a mistake in the
derivation of the transformation formula ξ
= γ (x
the X-coordinate. We will point out the
mistakes of Einstein and show that these make
the Lorentz contraction for moving objects
unnecessary. It turns out that all phenomena
that up to now have been considered a
combination of time delays and the Lorentz
contraction can be fully attributed to the time
The interpretation of the Lorentz transformation
formulas must be revised and the term ‘travelled
distance’ must be given a key role. All
results regarding the dynamics proposed by
Einstein with his general theory of relativity
can be acquired easily with the amended special
theory of relativity presented here.
test in a moving system
and time in the moving system
of the integration constant
of the slower time speed
Einstein created the Lorentz contraction
Time and location in moving systems
Einstein's theory of relativity is still
standing proud after over a hundred years.
However, famous scientists regularly lament
that our human mind is incapable of imagining
the four-dimensional 'spacetime' that plays an
important role in the theory. Consequently,
Einstein's genius is highly praised and any
scientists that ‘fails
to understand’ can consider themselves
lucky to be normal. Einstein was an exceptional
The issues scientists are struggling with result
from the fact that mainstream science still has
one foot in the aether theory. Here is why:
Einstein assumed that the velocity of light has
the same consistent value for each observer,
regardless of his movement speed relative to
the source. This assumption makes aether as a
transmitter for the movement of light in space
unnecessary. He could use the constant velocity
of light to explain the results of Michelson
and Morley but also of Fizeau and others.
This convinced Einstein that he had dealt the
aether theory the death blow, but he
unwittingly invited it back in through the back
door. When developing his theory, he introduced
the contraction of the 'space’ of a moving
system. The contraction does not only concern
the space but also all physical objects located
in this moving space. This is called the
Lorentz contraction. This contraction serves as
the foundation of the term ‘curved space’.
Einstein first removed the extremely rarefied
substance of ‘aether’ from space to
subsequently assign physical properties to
space itself. He filled space with a substance
that was able to contract or expand.
This substance is an extremely rigid material
that only measurably vibrates during great
cosmic events such as colliding stars. As
described by a professor (lit
1): “the stiffness of this spacetime is
comparable to that of a thick steel plate”
This is simply a new form of the aether theory.
Even though persons interested in the theory of
relativity expressed and still express numerous
comments about the physical incomprehensibility
of the Lorentz contraction, established science
considers each critical sound as a base attack
on Einstein's genius theory which can only be
haughtily contested by pointing out the
mathematical complexity of the theory.
In an article on the Lorentz contraction (lit 2), I set out why the Lorentz
contraction must be incorrect on philosophical
In continuation of this conclusion we will
indicate in the present article the mistakes
Einstein made deriving in 1905 the special theory of relativity (lit
3). These mistakes forced him to introduce
the Lorentz contraction to make the theory
Einstein attempted to provide a philosophical
foundation for his theory of relativity
multiple times. He referred particularly to the
principle of causality (cause and effect) to
support his general theory of relativity (lit
4, page 772). This is somewhat sparse for a
theory which has dramatically changed our
worldview. We will set out some
nature-philosophical thoughts that must precede
the physical theory in the next article.
We will start with our principle
of relativity: there is only one physical reality. We can define this as
a consistent description of all observers of a
physical event taking place somewhere.
For example, an event
such as the toppling of a row of dominoes with
the last stone activating a switch which makes
a glass water fall, causing a puddle on the
floor, will be described in the same manner by
each observer. A passing hiker, a train
passenger or a person in a roller-coaster, any
observer who can freely observe the event from
beginning to end will describe the event to an
outsider in the same manner, including the
puddle. If there is an observer who claims that
part of the event has not taken place like the
others describe it, he will be asked to explain
how the puddle ended up on the floor. If he
denies that there is a puddle, he will not be
taken seriously as an observer: “Everyone can
see that there is a puddle on the floor!”
It is essential for physics that various
observers of a physical event give the same
However, this agreement also has its downsides.
If established science claims to ‘perceive’
that the earth is flat, an observer who
disagrees will be ridiculed. He will be
required to convince others to adopt his
position. He will need to present the facts and
bombard them with arguments. Only persons who
can do this successfully will contribute to the
development of science.
It took Einstein every effort to start his
“Dialogue” at the start of the last century
to convince the “Criticasters”, as he
called them, of his theory of relativity.
We will attempt to convince the “Deniers”
with the same gusto in this article that based
on the physical reality a small improvement to
the theory of relativity is necessary. The
small improvement – rejecting the Lorentz
contraction – has major implications for our
ideas of ‘spacetime’, however.
We will define a physical
event as a change during a certain
period from a recognizable state into a new recognizable
state of a collection of material
objects. 'Reconcilability’ means that all
eligible observers can see the same distinctive
elements of a state.
A special physical event is the ‘duration’.
This event can be observed on a clock. Because
the duration is a physical event, the presence
of an object in relation to the duration must
be a physical event in itself. A stone lying in
the countryside in peace represents a physical
event as long you observe it!
A system is defined as all material
points that do not move or experience a
different acceleration in relation to each
A stationary system is defined as the
system from which a moving system is observed.
system is a system with a certain speed
(or acceleration) relative to the stationary
You may wonder why only
material objects are indicated, while
numerous forces and fields also play
in physics. This is because the role they
play only becomes recognizable based on the
effect on the
material with which they
Based on symmetrical considerations, we must
state that the amount of the speed
is mutually equivalent between the stationary
system and the moving system.
velocity of light means that a clock in a
moving system – depending on the speed with
which the system
moves – is slower than the clocks of the
observers looking at the moving system. The
fascinating thing is that the trailing clock
should be moving faster if we stand next to
this clock. This means that we have changed
systems. We will discuss this extensively
We will always work with identical
clocks that if placed next to each
other work at the same speed.
Because these identical clocks in the moving
system move slower, the events in the moving
system take place at a slower time
speed. The Lorentz factor (gamma) γ ≥ 1 is linked to this: the
time in the moving system runs γ
sec/sec slower compared to the
stationary system. We limit ourselves to v
<< c to ensure γ
is close to one.
The physical event – like a full rotation of
the large hand of a clock – will take longer
according to the clocks of different observers
with different velocity's relative to the
clock. It is a comparable event but at the
moment the observer finds that the long hand of
clock has made one full rotation, the
long hand of the observed, moving clock has not
yet reached this point. An event in a moving
system takes place at a slower time speed.
An enlightening concept is the point-event.
This is an event taking place at one location
at one moment in the system of an observer. A
collision or flash of light. A point-event will
take place at another moment and another place
in the system of an second observer relatively
moving related to the first observer.
If an observer sees an object pass by with a
speed of v
m/s, the corresponding 'event' after t
sec will according to him be a duration
sec on the clocks in his system and a travelled
v.t meters in his system. The clock on
the moving object shows a time of t*
= t/γ sec at that moment. The
covered distance according to the moving system
is equal to v.t* = v.t/γ meters. This is
ostensibly less than stated by the first
observer. How is that possible? We will discuss
What identical event must the (moving)
observer located near the object assign to
this? He is standing still relative to the
object. Nothing happens there besides the
ticking of the clock. The duration t*
is the only thing the observer can assign to an
Because t and
t* differ, the observers see different
events. The moving observer can call it the
same event as the observer in the stationary
system only if t*
= t. This means that the moving system
must move γ.t sec before the observer in
that system experiences the identical event.
The mutual event has a special position.
This is the travelled distance of the moving
system in the stationary system. This is
accompanied by a travelled distance of the
stationary system in the moving system. The
duration of an identical event must be the same
length according to the own clock. We will see
that the travelled
distance in the stationary system for
an identical event according to the moving
system must be γ2
greater than the distance travelled in
accordance with the stationary system. This
surprising result is derived in section 7.
Clock test in a moving
At the start of his article on the special
theory of relativity (lit
3, page 894), Einstein emphasised the
importance of synchronized, identical clocks.
He gave us a method to test whether two clocks,
A and B, work at the same speed in a system.
The fixed distance between the clocks is AB.
The two clocks will work at the same speed if
the duration AB/c
for the light to travel one way is equal to the
duration BA/c sec
of the way back.
This gives us three point events.
moment the pulse is sent from A) and
the moment tB
on which the pulse is reflected in B, and the
on which the pulse arrives back at A (fig
1), have the following relationship:
tA = tA' –
Moment tB takes place on the
synchronised clocks exactly halfway between the
times of arrival and departure at A.
This clock test may seem self-evident but is of
paramount importance for understanding the
special theory of relativity. Einstein proved (lit
4, page 902) that a clock on a moving
object has a slower time speed.
The way Einstein came up with the relativity
theory is often highly praised. He
mathematically found the
coordination-transformations based on the
assumption of the constant velocity of light.
He carried out as a thought experiment the
clock test with two clocks moving at a constant
velocity of v
m/s. An example is two clocks in a
moving train (fig 1).
A light pulse is sent from A to B and reflected
back to A from B. For an observer located in
the train, this takes 2.AB/c
This is the time he can see on his clock.
The duration is determined by both the observers
on the train and the observers on the ground
using the clocks of their own system. For the
observers on the ground that watched the
experiment in the moving system, the light
pulse also moves with speed c from A to B and back, but they see
point B move with velocity v
in the meantime. The distance travelled
by the pulse on the way there is greater than AB.
We can calculate at what place B must be when
the pulse catches up to it but taking the value
for the speed of the pulse relative to points A
and B is sufficient.
distance on the way back that must be travelled
by the pulse is smaller than AB.
To determine the length of time on the way
back, we can use the expression (c
+ v) m/s for the same mathematical
The analysis in the following sections shows
that the duration of the movement to and fro on
the clocks for the observers on the ground is
greater than the duration on the clocks of the
observers on the train! The time speed of the
clocks of the observers on the ground must have
been faster than that of the clocks of the
observers on the train.
So the observed event requires more time
according to the clocks of the ground team than
to the clocks of the team on the train. You can
justify this based on the fact that more than
one event takes place for the persons on the
ground: the travelling light beam to and fro
and the travelled distance of the train.
Time plays an unfathomable role here as both
clock teams do not experience any faster or
slower passage time, they simply experience the
time of the event.
Place and time in the
The relationship between time and place of the
own clock in the stationary system and the time
and place of the passing clock in the moving
system was found by Einstein in the following
manner. He used two coordinate systems:
the coordinate system in the
stationary system with coordinates (x, y, z, t), and
the coordinate system of the
moving system with coordinates (ξ, η, ζ, τ).
Each point in space is always in both systems at
once and a moving object will also always be in
both systems simultaneously. Each place where
the object may be at any time will have a
different set of four coordinates in the two
The trick is finding formulas that enable you
to find the four coordinates (ξ, η, ζ, τ) from
the set of coordinates (x, y, z,
This is called a coordinate
Because the constant movement takes place along
the X-axis, we assume – together with
– without proof that the values of the
coordinates in the Y-direction and the
Z-direction do not change, η
= y and ζ
To find place ξ
and time τ
in the system moving with v
, if time t and place x
in the stationary system are known, Einstein
used the clock test on two clocks A and B in
the moving system. We will follow and examine
his calculation scrupulously .
When the origin A of the moving system passes
origin O in the stationary system (fig 1) a light pulse departs from A to
point B. The initial
conditions in the stationary system x = 0
= 0 and in the moving system ξ
= 0 and τ = 0
apply to this moment. Point A is the origin of
the moving system and ξB
= AB = ℓ meters
applies to point B.
We will also call the stationary system: system O
, and the moving system: system A.
At what point of time t
does the pulse reach point B according to an
observer in the stationary system? Einstein
assumed that the (moving) distance AB for the observer in the stationary
system may not have the length ℓ. He calls this length x'.
The following formula applies to place B in the
stationary system: xB
= x' + v.t.
We also write this as x'
= xB – v.t
= x' meters.
In the moving system A, the formula (1) for synchronized clocks will be
expressed in the time τ
of the system A:
The time coordinate τ
is a function of the coordinates (x,
y, z, t)
of the stationary system. This makes sense,
as we want to know the time at a place in
system A if we know the coordinates including
the time of that place in system O.
To determine the formula, we must use the time
and place of the three point–events in the stationary
system. We find the following three points of
The 1st time in the stationary
system when the light pulse left A is tO = 0 sec.
The 2nd moment on which the
pulse arrives at B is equal to: sec.
The 3rd time, the return to
At those times, the three places in the
stationary system are also known:
The 1st place in the
stationary system is the origin O at xO
= 0 meters, because the pulse left O at
The 2nd place is point B after
meters, as that was the time the pulse was reflected
back in B.
The 3rd place is point A'
, because this is the moment the pulse arrived
back at A.
can be written down as:
We can now enter the found coordinates (x, t)
of the 3 point–events:
This expression can be found as a total
differential if x'
is not too great:
The meaning of this expression is found in:
We can now expand the equation (3)
using partial differentiations.
The first term in the left part gives:
The term in the right part gives:
When entered in (3),
which means that
This leads to
If x' is small, we can look at the right
term to find the derivative for x in point (0,0):
If we delve into this, we find the solution:
In this formula
a is an integration constant.
is important that the length x'
is used to find the derivative of τ in
the point (0,0).
In this way it does not matter what value the
has. So there is no need to assume the length
the integration constant.
We calculate a just like Einstein by considering the
behaviour of time in the Y-direction. We will
have to calculate this again because of our
We use the clock test, but now for clocks along
½(τA' + τA) = τB
We let a light pulse move along the Y-axis from
point A to point B – located at a distance of
– and back. According to the observers in
both systems, the distance between A and B is
equal to y0
meters. For the observers in the moving system,
the pulse moves perpendicularly up and down.
For the observers in the stationary system, the
light pulse moves in a triangle (fig 2). We can use the formula for the
According to the observers in system A, the
duration for the way there is τB
and the same for the way back. The return time
Looking from system O, the pulse travels in a
diagonal line from O to B. The component of the
speed in the Y-direction is equal to
The time the pulse needs to reach point B is
The duration to A' is equally great.
The return time will be
So the return time in the Y-direction is γ
times as long in the stationary system compared
to the moving system. We will use this result
to calculate a.
Note: Here we introduce the
≥ 1 applies.
By considering the Y-direction, we now have 3
coordinates in the stationary system (x, y, t) and in the moving system (ξ,
We will use the initial values t
= τ = 0 and x =
ξ = 0 and y
= η = 0 when the origins of O and
The function for the time
τ is now
will then look as follows:
The total differential for the three variables x, y and
The meaning of this can be found as follows:
The first term in the left part of (3A)
can now be written as:
The right part will be:
When using this and
the fact that τ (0,0,0)
, we will get:
The conclusion is that
, which means that τ
= constant in a direction perpendicular
movement direction. This in contrast to
the time along the X-axis, which is linear.
For a light pulse shot into the Y-direction, the
following applies: η
= c.τ meters. When we use the
we will get:
We can enter t and x,
since we know that point
y0 is reached at
so the place will be
With these results we find:
But η must at that moment be equal to y0,
which is η
= y0. If we use the formula
and divide by y0,
This results in a
= γ and with (4) the following time formula: sec.
This is the well-known Lorentz
transformation formula for time τ
in the moving system presented by
Einstein in his article on the special theory
of relativity (lit
It means that if at place x
in the stationary system at the time t
on the clocks, a clock in the moving system
which currently passes that place will show the
stated time τ
if the initial values are met.
A random clock in the moving system which on
time t = 0
is set to the same time as the clocks in the
stationary system and thus shows time τ
= 0 will on moment t reach place x = v.t
the time will correspondingly show the value:
This shows that each clock in the moving system
runs slower than the clocks in the stationary
system by factor γ.
The time in the moving system moves
slower by factor γ. The atoms move slower, cells in
plants develop slower, each identical event
moving with the moving system develops slower
than in the stationary system according to the
observers in that system.
A particular consequence of this is that two
events occurring simultaneously at two
different places in the stationary system
cannot be observed simultaneously by an
observer in a moving system.
In time formula
, this is expressed using the term
Consequences of the
slower time speed
According to the observers in the stationary
system, the time speed in the moving system is
slower by the factor gamma
to their own system.
What does this mean?
An event in the moving system that lasts T
sec on the clock in the moving system lasts γT
sec in the stationary system. The clock in the
stationary system will appear to move faster.
This is naturally hard to understand. We must
remember that these measurements also coincide
with a movement. The moving system is not
standing still! Thanks to the movement, the
observers in the moving system may actually see
that the clocks in the stationary system are
the slower clocks. We will explain this in the
If point A of a moving system, a train for
example, after t
sec travelled a distance of ℓ
meters from origin O to point P in the
stationary system, the clocks in the stationary
system will show the time t
sec, of course, but the clock of A will show
the time t/γ, as this clock is moving
slower. In the stationary system, duration t sec may concern a ball being thrown
up and falling down. If a ball was
simultaneously thrown up in system A, the ball
would not have yet returned when A passes point
P. The ball will be back when the clock in A
also shows time t. The ball will have taken γ
times as long. Point A will have moved up to γℓ
meters in the stationary system.
For reasons of symmetry, it is clear that the
velocity of the systems relative to each other
is the same. The distance travelled once the
clock shows t
sec seems to differ, however.
This difference is caused by the
‘definition’ of the stationary system. This
gives the stationary system another role in the
story than the moving system. A so-called
privileged position. In this position the
clocks in the stationary system are moving
faster than the clocks in the moving system.
This seems to introduce asymmetry for the
distance travelled by the moving system in the
stationary system after t sec shown on the clock in the
stationary system differs from the distance
travelled by the moving system in the
stationary system after t
sec on the clock in the moving system.
However, this consideration is not symmetrical.
We can return to the symmetry by looking at the
distance travelled in the moving system by the
stationary system after t
sec on the clocks in the moving system. This is
exactly the same as the distance travelled by
the moving system in the stationary system
sec on the clock in the stationary system.
It is like looking through a looking glass: if
you look from the one side, things on the other
side appear larger, but if you look from the
other side, this side is larger.
How can we describe this for the moving systems?
The solution can be found in the fact that
looking from the stationary system, the unit of time in the moving system is a
larger than in the stationary system.
This is why the clock shows fewer seconds for
the same time. We make use of a time unit which
is γ times greater than the second.
This unit only applies in a system that
actually moves, meaning that it is the time
unit that must be used in the stationary system
to describe the physical events in the moving
When expressing time in that system, I want to
call it the Lorentz
time. The accompanying unit can be
called the ‘Lorentz
second’, abbreviated to Lsec.
The following applies: 1
Lsec = γ
The time speed in the moving system has
decreased, but that is the only thing we can
say about the moving system. The velocity for
the system remains v
However, if we want to show the velocity (=
distance divided by time) in Lorentz time, the
length unit must also become γ
times as great. This is the length unit that
must be used for the travelled distance in the
direction of movement.
A distance travelled in that unit leads to a γ
times greater distance in the stationary
The greater length unit could be called the ‘Lorentz
meter’, abbreviated to Lmeter.
The following applies: 1
Lmeter = γ
This results in the following for the velocity: v
Lmeter/Lsec = v
the velocity remains mutually the same.
The distance travelled by the moving system
(Lmeter/Lsec).Lsec = v.t
The distance travelled in this unit could be
called the Lorentz
The following applies: v.t
Lmeter = γ.vt meter.
On the time t/γ Lsec for the distance
travelled by the moving system in the
stationary system we find as expected v.t
This complies with our physical intuition.
For our research, it is important to get a
deeper understanding of the meaning of the identical
event of a travelled distance in both
systems. For this identical event the duration
in the moving system expressed in Lorentz
seconds will be just as great as the duration
in the stationary system in normal seconds.
Because both the Lorentz sec and the Lorentz
meter are γ times as great as the second and
the meter, the identical travelled distance (=
product of velocity and time) after t
times as great for the moving system in the
stationary system than the travelled distance
according to the observers in the stationary
system after t
If for example origin A after
t sec travelled a distance in the
stationary system of ℓ = v.t meter, the clock of A
will show a duration of τ
= t/γ. If shortly after the clock
of A shows numerically the time t,
the duration has become γ
times as great. So the time in the system at
rest will be γ.t
sec. The origin A will at that time
have travelled a distance in Lmeters that is γ times
as great: γ.v.t
Lmeter is equal to γ2.v.t
meters, A will be located at place γ2.v.t
in the stationary system.
The clocks in the stationary system will show at
that moment the time γ.t
So if we write down
which is valid for v << c, we can tell that A for
the identical event must travel a distance in
the stationary system which is
longer than the distance that has been
travelled at time t
in the stationary system
according to the observers.
summarise, these are the main three findings:
duration of an event in our stationary system
is on our clocks just as large as for the
identical event in the moving system on the
clocks of that system.
duration of an event at a fixed place in the
moving system is on our clocks always γ
times as great as on the clocks in the moving
moving system must travel a γ2
times greater distance in the
stationary system to travel the identical
distance travelled by the stationary system.
Someone can be home in 10 minutes if he leaves
now. He lingers and has only 9 minutes left. He
decides to take faster steps to get home on
time. He adjusts the rhythm of his steps by
factor 10/9th and he gets home at the time he
would have if he had left on time. Thanks to
his greater speed, his steps also increase by
10/9th. As a result, he travels not just the
needed distance during these 9 minutes but goes
even further. After these 9 minutes, he has
travelled 10/9th times the distance. While he
would usually travel 9/10th part of the
distance to his home in 9 minutes, he has now
travelled 10/9th this distance. The travelled
distance has become (10/9)2
as great. A quadratic increase.
As for the slower Lorentz time for the entire
moving system, the Lorentz distance is also a
property of the entire moving system. This
concerns the distance travelled by the entire
system expressed in Lmeters. The system itself
remains undistorted, as we will show in the
next section, and can be considered a rigid
object whose dimensions are expressed in
In the critical article (lit
7) on the Lorentz contraction, “the γ2
greater distance” is used as the baseline,
together with the influence of the acceleration
of a system on the time speed. This leads to a
transparent explanation of:
the Ehrenfest paradox with its
the bending of light in a
gravity field, and
derivation of the perihelion precession of
Mercury due to its velocity in the gravity
field of the sun.
The last two examples were used by
Einstein to demonstrate the strength of the
general theory of relativity.
In the mentioned article, we show that the
theory of relativity without Lorentz
contraction and better understanding of the
influence of the time speed lead to the same or
even better results in a clear manner.
And Einstein created the
Since we can now determine the time in the
moving system using the time and place in the
stationary system, we wonder whether we can
calculate place ξ
along the X-axis in the moving system.
To this end, we study a moving system
consisting of a train, for example, in which
both the X-direction and the Y-direction a
length of ℓ have been plotted. Light
pulses are sent in both directions
simultaneously that according to the observers
in the moving system arrive back at their
origin A at the same time after τA'
on their clocks. These are Lorentz seconds
according to the observers in the stationary
The clocks in the stationary system must show a
time of tA'
We distinguish between origin A and the place A'
because this place has changed xA' from the perspective of
the stationary system. The coordinate ξA = 0 always applies
to origin A.
The time of return in A' can be calculated from
the stationary system using time formula
. To do this, we must know the value in the
stationary system of t
in point A' at
moment of return. If we know the time t,
the value of the place x
of A’ will follow automatically from
= v.t meter.
Because in the stationary system based on the
principle of physical
reality the light pulses will meet also at
the same time just like in the moving system,
the value of t
can be determined in two ways, using the way of
the light pulse along the Y-axis (fig 2) and using the way of the light
pulse along the X-axis.
Using the Y-direction, the time tA'
upon arrival according to an observer in the
stationary system is:
The place of A' in the stationary system will
in that case.
This matches the value that can be seen by the
observers in the moving system.
The time tA' upon arrival is harder
to calculate using the X-direction.
Einstein calculated time tA'
in the following manner. He proposed to
call the length of ℓ
in the stationary system x' as long it was unknown. He
determined the return time tA'
He used ℓ = γ.x' to match results (5)
This leads to the conclusion that x' is smaller than ℓ.
This automatically leads to the conclusion that
a moving object becomes shorter along the
direction of movement.
However, this is a hasty
conclusion based on incorrect physical
The first mistake made by Einstein was
caused because he proposed calling length ℓ in the stationary system x'
p.900). He treated however this length x' not as a length in the stationary
system, but as a length in the moving system as
he let it move with speed v.
If he would have been consistent, he would have
multiplied the length again by factor x'/ℓ
etc. This means that he gained nothing from
giving the length another name.
made a second
mistake because he did not use the time
formula (6) he had derived just now. With this
formula it is easy to calculate the time of the
point B' in the stationary system where the
light pulse is reflected.
As follows (fig
3). In the moving system the light pulse
arrives the point B at the time τB
= ℓ/c. The location of B is ℓ
in the moving system, so the place and
the time are known quantities of the
point B in this system. With the time formula
we calculate the time of the same point but now
situated in the stationary system. This point
is indicated by B'. The resulting time tB' will have the meaning of
the time duration ΔtB'
for the light pulse to travel from O to
B'. By using the time formula we have to realize
that we transform back from the
system to the stationary system and then the
velocity of the system O is negative relative
to the system A, so –v m/s.
find the time duration for the way back from B'
to A' in the stationary system we start at the
moment that point B is passing the origin O of
the stationary system (fig
4). The clocks in B and O have been set to the
initial values t
= τ = 0.
Now the point B has become the origin of the
moving system. At the moment τ = ℓ/c
the light pulse reaches the point A at the
. We can with the time and the location of
point A in the moving system calculate the
duration ΔtA' for the return
journey of the pulse in the stationary system:
total duration back and forth in the stationary
system gives the time in point A':
tA' = ΔtB' + ΔtA'
We can interpret the difference in time
duration for the way from A to
B and the way back as a difference in the
time speed for the directions.
is an important result because it is the same
point of time as for the returning pulse in the
Remark that our principle of relativity is
satisfied. The length ℓ
between A and B however has to keep the same
value in the stationary system as in the moving
we had followed the assumption of Einstein for
the length in the moving system and had chosen
the value x'
for the length between A and B the
result would have been:
Then we find two different times (5)
for the returning light pulse:
the Y-axis and
along the X-axis.
These times must be the same because the light
pulses arrive back at A' at the same time.
This leads to the same important result
This means that the interpretation of Einstein
that an object in a moving system would shrink
due to the Lorentz contraction is incorrect.
The dimensions of an object in the moving
system are the same as the dimensions of the
same object in the stationary system.
travelled distances are affected by the time
the dimensions of the objects are not.
The Lorentz transformation formula for time
the time τ
of a clock in
moving system which just passes place x
on moment t
in the stationary system. The calculation
provides the precise time which the observers in
the moving system can observe on their clock.
This time is slower than the time in the
stationary system. This is confirmed if we return
the clock to the stationary system (like in the
twin paradox). This clock will have moved slower.
The Lorentz transformation formula for the time
is beyond all doubt.
Einstein derived the Lorentz transformation
meter for the place in the moving system. Place ξ
in the moving system can be found for a point
located at time t
on place x in
the stationary system.
For the origin of the moving system, the
following applies: x
= v.t, which means that ξ
This is correct: the origin remains the origin,
but this is the only thing that is correct!
This formula leads to
another value for the length of an object than
the observers themselves notice in the moving
system. A stick with a length of Δx
= ℓ meter between x1
= 0 and x2 = ℓ meter in the
moving system becomes by the transformation
formula the length ξ = γ(x2
The stick stretches out with a factor γ.
The observers in the
moving system are not in the ability to
determine the greater length while their unit–stick also has stretched out
with the factor γ
to a length–unit of γ
meter. So they measure a length of ℓ
while the observers in the stationary system have
calculated a length of γℓ
meter for the moving stick. If we retrieve the
moving stick, it will shrink to its original
length of ℓ
This is the way it has to be understood
according to Einstein. The stretching and
the stick by these transformations form together
an unverifiable, 'spooky' physical phenomenon.
Einstein makes an appeal to your trustfulness:
the stick has been stretched
but we cannot prove it by measurement.
In this way the phenomenon of the Lorentz
contraction of a moving object deserves no
place in physics.
Conclusion: The Lorentz transformation formula for place is
for the determination of the length of
an object in the moving system.
The question is how we can transform the length
from stationary to moving system.
We will find the solution by implicating the
travelled distance in the problem.
A travelled distance is another physical
quantity than a length. A travelled distance – the product of speed
and time –
is a physical event, closely related to
the time. A length is not a physical event, it
is a property of an object.
In section 7 we proposed as the unit for the
travelled distance the Lorentz meter.
This transformed unit is γ
meter. This is a greater unit than the
unit of 1
meter. We have reserved this greater unit for
the travelled distance. The transformation of
the length unit results in the unit for the
This is incorrect for a transformation. We
cannot transform apples into oranges. This is
why we must take a travelled distance as the
basis in the stationary system.
How can we turn length into a travelled
If we have two points x1
in the stationary system, we can describe their
in the X-direction as the products of speed and
time in the following manner as the difference
in travelled distance:
= x2 –
= v.t2 –v.
Here t2 and t1
are the times needed by the origin of the
moving system to reach the points when started
from the origin of the stationary system.
We can now transform the travelled distance Δx
and we can notice that the transformation of a
travelled distance is a transformation of the
This can be addressed using the time formula
The transformation of the length Δx=
become the transformation of Δx
for the travelled distance:
The resulting travelled distance in Lorentz
meters in the moving system has a length of
(x2 – x1)
meter. So the transformed length has in the
moving system the same value as in the
stationary system. This
is what the observers in the moving system can
interpretation takes away one shortage in the
theory of Einstein that is the observers
in the moving system do observe the time
calculated with the Lorentz transformation
formula but don't observe the calculated
length. So if we interpret the length as
a travelled distance the theory fits.
Conclusion: the transformation ξ
a place in the stationary system into a place
in the moving system has to be considered as a
transformation of a travelled distance which is
expressed in Lorentz meter.
The Lorentz meter in the stationary system is 1 meter because γ
= 0 and in the moving system it is γ
Without the Lorentz contraction, we get a better
idea of the behaviour of the time in a moving
system. We will stick to a moving system
carrying out a constant linear movement in this
If the origin A of the moving system passes
origin O of the stationary system under the
known initial values, A will at time t be
at the place
x = v.t meters. Place and time in the
point A are then known in the stationary
system, which means that the time of the moving
clock A can be calculated using the time
Because γ >1, time
τ is smaller than time t.
The clock in the moving system is moving slower
than the clock in the stationary system.
However, the clock in the stationary system
must also move slower than the clock in the
moving system. This seems to go beyond our
imagination. The graphs used in the literature
to determine and explain this do not address
the basic problem, the issue of clocks moving
slower relative to each other.
Because this is a problem for laymen to
understand and for scholars to explain, we will
show a new manner of visualization which may be
will use a timeline
5) based on the time formula
We make use of the movement of the clocks
relative to each other. We have system O and
system A. These have a velocity of v
relative to each other. The system moves along
the X-axis. Because of the fact that we do not
need to consider the Lorentz contraction, the
entire length of the objects (e.g. trains) is
along the X-axis. The time relative to the
other system is plotted compared to the time of
the own system. According to term
, this results in a rising or declining line.
compare the time of the own system with the
time of the other system. This gives us two
sloping lines symmetrical with the X-axis.
A sloping line represents the time on the
synchronised clocks of a system at a certain
point in time. We call it the timeline
of the system at that point in time. The
timeline of system O moves from the lower left
to the upper right. The timeline of system A
moves from the upper left to the lower right.
BA represents the timeline of the moving train
B*A (in which all clocks are synchronised)
moving along the X-axis.
In the figure, point A passes point O and the
clocks have been set to the initial values
System O can represent the timeline of a
railway track, a stationary system, but can
also represent the timeline of another train, a
moving system, which moves with a different
velocity along the X-axis relative to the first
The vertical distance between the timelines
indicates the time
difference shown on the clocks located
at place x
at the same place that belongs to different
systems. If you are in a system and see the
clock in the other system show a later time
(meaning that the timeline will be higher at
that place), the clock in this first system
must be behind when looking from the later
system (meaning that the line will be lower at
The theory of relativity is a
concrete theory. Observers from different
systems will see the same event at certain
places at a time belonging to that place! The
principle of relativity.
Naturally, the timelines have the same
angle (positive or negative) relative to the
horizontal X-axis. The angle is determined by
the speed of the systems relative to each
other. The angles have been exaggerated in the
figures for the sake of clarity. The angle
between the two timelines is almost
shows the situation of the moment when origin A
of system A passes origin O of system O. System
A moves right relative to system O.
The timeline diagram is a dynamic diagram. We
can move point A from O to point P in system O.
Then we get fig
6 . We will show the timeline again for
the moment A passes point P. Point A has moved
along the X-axis.
The time of A is now below the timeline at
place P while its time was first (fig 5) equal to the timeline of system
O at point O and the time of point O is now
significantly below the timeline of system A at
the location of the point Q. We can see that
both clocks A and O are behind compared to the
The convenience of the timeline diagram is that
you can mentally move the timelines to
understand the time differences. The time
differences in simple situations can be
determined directly using some geometry.
For example, when A passed point O (fig
5), the clocks showed t
= τ = 0. At that moment, point B
showed a time of τ
– t = ≈
above the timeline of system O, with ℓ
representing the length between A to B.
If point A has moved after t
seconds (fig 6)
to point P at place x, we can see the time of A has moved
below the timeline of system O by t
The time of point B will, in that case, stay
above the timeline of system O by t
Note: In point x,
the time difference Δt
or Δτ shown on the clocks of the
stationary system respectively the moving
system does not depend on the system from which
it is observed. Seen from the stationary
system, this difference Δt
as many seconds as the Δτ
seen from the moving system in Lorentz seconds.
Example: Time and
location in the moving system
Two trains with the same length ℓ
with timelines OP and AB pass with a relative
speed of v m/s. Points O and A at the front of
the trains pass at t0
Because of the synchronicity of the clocks all
observers will find the time t
= 0 on
their own clock at that moment. Observing the
clocks in the other train they will notice a
linear path with place according to the
timelines. The timeline diagram (fig 7)
shows the initial situation of the trains with
systems are moving, so it is curious to make a
difference between a system with 'normal'
clocks and a system with 'slower' clocks. That
is why we will use in both systems the symbol t
for the time.
Observer P at the back of train OP at point +ℓ meter
will pass observer A at the front of the other
train after t
The observer at clock P can give the observer
at clock A a high five. This is important
because this makes clear that the encounter is
a physical reality, a point
event. Besides the fact that each observer
will be able to see the physical event of the
hands meeting, they will also observe the time
on the clock of both P and A. This marks the
event for all observers.
The clock of P shows a time of
= ℓ/v sec
and the clock of A shows a time of
= tP/γ sec.
Based on symmetrical reasons, we may put that
according to a neutral observer points B and O
on the other side of the trains also pass each
other at that time at a distance of ℓ
meters between the point where A and P
The neutral observer moves in
such a way that he sees the trains pass in
opposite directions at the same speed of about ½v
Lorentz contraction there is no doubt about the
The trains have been represented with solid
lines in the timeline diagram. The trains
themselves move as projections of the timelines
along the X-axis but have not been shown
because we want to focus on the times.
Observers O and B will give each other a high
five simultaneously with observers A and P
according to the neutral observer. Symmetry
determines that clock B must show a time of
tB = ℓ/v sec and clock O a time of to
We can see a range of different times at that
on clocks P and A respectively
= ℓ/v sec
on clocks B and O respectively
= ℓ/v sec and
In system O we see the times
sec and tP
= ℓ/v sec
and in the system A we see the times
= ℓ/v sec at a moment that is
simultaneously for the neutral observer. The
question is how to interpret: two indications
of time in one system. The meaning is that we
do not observe the point at the front and the
point at the back of the moving train at the
same moment in their system. If we look at the
back point the train as a whole –
because there is no Lorentz contraction –
has travelled already somewhat further than
when looking at the front point. It looks like
the train has shortened.
It is apparent from the times that in system A,
observers believe that the meetings in A and B
do not take place simultaneously and the same
applies to points O and P in the system O.
Observers in the system A believe that the
meeting at B takes place later, with a
difference of tB
= ℓ/v –(1/γ).ℓ/v
sec. In that time duration B will have
travelled the distance ½(v2/c2).ℓ
meter in the direction of A (and P).
In system P they believe that the meeting at O
took place sooner with the same time
difference. So at that moment O should also be ½(v2/c2).ℓ
meter closer to P (and A).
In this way B and O were able to give each
other a high five.
The conclusion is that we can describe this
problem clear and convincing with the time
speed alone. Once again it appears that the
concept of Lorentz
contraction has been a superfluous assumption.
The time at which point
S is halfway TS
The modifications to the special theory of
relativity presented here show that the theory
contained a minor imperfection that has not
been resolved after a hundred years. It must be
noted that the problem was tucked away deep
into some physics that many considered part of
the theory of relativity which could not be
However, we were able to find it by
meticulously repeating the derivation presented
by Einstein in his article of 1905.
We discovered that Einstein made an assumption
concerning a modified length in the stationary
system which he did not use in this system but
rather, erroneously, in the moving system. This
led to a result in which he introduced the
Lorentz contraction for the length of an object
in the moving system to gain the theory closely–reasoned.
By determining the length of a distance
travelled by a ray of light in the moving
system, we were able to show however that the
Lorentz contraction is not necessary to achieve
the correct result.
To increase the intelligibility of the theory,
we have shown that the Lorentz transformation
for the place in the movement direction does
not concern a transformation of the length but
a transformation of a travelled distance. The
dimensions of the elements that make up the
moving system are not included. We indicate how
we find the place of a point in the moving
system. The result of the place gives the same
positive confirmation by the observers in the
moving system as the transformation of the
It is interesting that an identical event of a
travelled distance by the moving system leads
to a γ2
greater distance in the stationary system
before the same event is completed. The factor γ
must be considered the factor by which time is
slower due to velocity or an acceleration
field compared to a stationary system. This
result can be easily applied to the bending of
light along a mass and when calculating the
perihelion precession of Mercury. Its clarity
gave us an improved formula for the perihelion
precession (lit 7). Our results should be the same as
given by Einstein's theory while the dilatation
of time with the factor γ
together with the shortening of the length of a
distance with the factor γ
will lead to the same greater identical
distance with the factor γ2,
but physically this part of Einstein's theory
These results are an important step for science
as the aether theory can now be definitely put
aside. Einstein did show that aether was not
necessary to explain the behaviour of light in
space, but he immediately returned to aether
for the bending of light and the behaviour of
Mercury. He did not call it aether this time,
but rather ‘curved space’. It should be
clear that assigning new properties to space
results in a new version of the aether theory.
Recently measured gravitational waves have
incorrectly been described as 'ripples in
space': they are actually ripples in
Our new insights have consequences for our
view of the universe. The supposed phenomenon
of the Lorentz contraction has resulted in an
imaginative world-view. Space is assigned
properties based on which the direction of an
object or a ray of light is directed by the
curvature of space itself. The condition of
space is in this theory determined by the mass
distribution at the actual locations. If you
remove the mass, space returns to its form in
Since we have now shown that the idea of the
Lorentz contraction is based on an error made
by Einstein the foundation of the term
‘curved space’ disappears.
This may feel as something has been lost.
The arising gap in the cosmological theories
however can be filled up if one understands the
dynamic interaction between objects and fields
in space as a result of the gradient of the
time speed at a specific location. Then the
time speed differences can be considered as the physical
cause of the movements in space.
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Elektrodynamik bewegter Körper", Annalen
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"Dialog über Einwände gegen die
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