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Gregor L. Grabenbauer 1/5

D

ID

E

INSTEIN

C

OMPILE

P

ERFECT

N

ONSENSE

?

Gregor L. Grabenbauer

gg@grabenbauer,de

February 2016

(revised 8. September 2016)

Anatoli A. Vankov[1] presented in his paper “On Controversies in Special Relativity” (2006) his

profound doubts on Einstein’s principle that spherical waves are to be described from a moving

frame of reference as a spherical wave too. He argued that despite all the popular presentations

in course books the shape of a spherical wave cannot be discovered from the moving frame

because of the aberration of light: “

The truth is that the problem of shape of light front is,

indeed, tightly related to the aberration and Doppler effects.”

THE LOR E N T Z T RA N S F O R MA T I O N AP P L I E D

In his in 1905 Einstein stated that by applying the Lorentz transformation the shape of a

sphere would hold in the moving frame too.

„Zur Zeit = ‘ = 0 werde von dem zu dieser Zeit gemeinsamen Koordinatenursprung

beider Systeme aus eine Kugelwelle ausgesandt, welche sich im System mit der

Geschwindigkeit ausbreitet. Ist (, , ) ein eben von dieser Welle ergriffener Punkt, so

ist also

² + ² + ² = ²².

Diese Gleichung transformieren wir mit Hilfe unserer Transformationsgleichungen

und erhalten nach einfacher Rechnung:

′² + ′² + ′² = ²′².

Die betrachtete Welle ist also auch im bewegten System betrachtet eine Kugelwelle von

der Ausbreitungsgeschwindigkeit . Hiermit ist gezeigt, dass unsere beiden

Grundprinzipien miteinander vereinbar sind.“

The translation of Einstein’s 1905 Electrodynamics paper states for the last paragraph

2

:

„The wave under consideration is therefore no less a spherical wave with velocity of

propagation when viewed in the moving system. This shows that our two

fundamental principles are compatible.”

The equations of the Lorentz transformation applied herein are given as follows:

=

(

−

)

=

(

+

′

)

′

=

(

−

/

²

)

=

(

+

′

/

²

)

Given a spherical wave by the equation above

Gregor L. Grabenbauer 2/5

² + ² + ² = ²²

we have to show that by applying the Lorentz transformations a secondary equation will be

produced having the same form. The same algebraic form turns out to give the same geometrical

shape.

As the vector takes the direction parallel to the equations and were supplied.

The calculation steps are given in detail as follows:

Obviously we have the same form within the moving frame of reference S’

which seems to indicate that all frames of reference have the same spherical shape to observe.

HOW TO P R O V E EI N S T E I N ’S SPHE R I C A L EQ U A T I O N?

The Einstein’s starting equation was:

As the left hand side and right hand side must have the same value, we get:

The so-called Minkowski metric is presenting the same equation as follows:

Hence, what Einstein showed to be equal was:

Summarizing the lines above we see that for all transformations of the Lorentz kind the

transformed values itself are restricted to

and the proof of any invariant is limited to

Gregor L. Grabenbauer 3/5

Einstein did prove that there is a sphere-like formula for every point to describe. What he

omitted was to define some unique radius for all points of the same shape. To understand the

fundamental nonsense of Einstein’s ‘proof’ it’s important to outline that only points that share

the same x-value will be mapped to the same shape. As Einstein introduced the t-coordinates as

not only arbitrary but rather as some real time values the conventional reception of his ideas, i.e.

to assume that his kind of thinking would go logically straight, did cause the major part of this

error. There are given no constraints for pairs of symbols like ’²~², ’² < ² or

!

=

"

,

therefore the variables of ’ are not tightly bound against . According to Einstein’s idea to

show the compatibility of his principles every point is mapped to its very own shape and one

spherical shape ends up in as many different shapes as points exist along the x-axis.

#$%&'($%)$)%*'+,*-('./'/00+*$%'&*1&*2(

&+.(,(

3

/,(2/++()'*'.(&/2(&+.(,(

3

The notion of time in motion that takes different values out of the same time at rest is quite

unknown. Do different time values indicate different times to take place or do all points of the

coordinate system in motion share the same time but have different constant delays? The

interpretation of an indefinite number of different times –like Wolfgang Pauli gave it– produces

an indefinite number of different shapes out of one shape at rest. To show that basic principles

hold just by demonstrating that there may be drawn a sphere through any point - this is

completely impossible. In order to prove that all points of 3 are mapped to 3 one has to assure

that the formulae of all points of some sphere share the same radius:

4

5

5

5

567

7

The constraints above directly forbid different times within the same shape. When fulfilling

these constraints all attempts to introduce some relativity of simultaneity in order to cope with

manifold shapes are to be rejected immediately. To allow non-simultaneity as some valid kind of

simultaneity would perturb the right hand side of the equation above and enable us to proclaim

nonsense by highly sophisticated means.

The variables of Einstein’s formula were given without any indexes. Being aware of the idea that

time coordinates of are limited to single points of space, Einstein would have had to write

down3:

4

5

5

5

567

5

Gregor L. Grabenbauer 4/5

This example shows the application of the Einstein criterion for circular shapes. The shapes

occur as 2D-projection of spherical waves originating at point Q and expanding with . The

Points 8 and 9 are transformed to 8and 9 using the Lorentz transformation. Equations of the

form

are fulfilled by any of the four points, but the points 8 and 9 are dedicated

to different circles. As all points show the constraint

would be sufficient to

prove. Taking into account that is a variable and is obliged to be a variable there remains

nothing to be checked. The equations

can take different -values if and only if the

values of :;< are allowed to differ. There was no principle to enforce or indication to be read

that the moving system may encounter point 8 and point 9 at different times

!

=

"

.

The picture above shows a simulation at rest with two different circles (light gray) for the given

time value . As the radius of circles is a linear function of time even in moving states for

any small circle through 8at time >

?

with @8

A

A

A

A

A

A

>

?

there exists some even larger circle

through 9’ with @9

A

A

A

A

A

A

>

B >

?

.

The gradients along C@D

!

E and C@D

"

E indicate the time needed to expand the

circles that start in @. The idea to deploy different times would cause the theory to create as

many circles as different points are given by the original shape. This would end up in stupidity as

the self-imposed principle of covariance cannot hold: Producing an infinite number of shapes out

of one shape will give an indefinite set of tasks of transformations. Finally, if the shapes are

intended to occur at different times and there is not given a final time to stop further

occurrences no retransformation may ever be completed. This is a consequence of the switch

from implicit timing in the frame a rest to explicit timing convention.

The Einstein idea to slice the time by creating non-simultaneous events in the moving system

drags severe bugs. The system at rest is thought to be static because there is no time index for

the objects, no time index at the points. All objects within the system at rest share the same time.

As any point of the system in motion may have some different time to indicate its specific time

dependency the system carries as many static subsystems as different times occur. The system

Gregor L. Grabenbauer 5/5

in motion has all the features needed to record each object at its very own point of time.

Moreover, the static system may be described synchronously whereas the dynamic system is

given by asynchronous description, each object taking its time index explicitly. It seems quite

impossible that there exists a valid transform from the moving system to some static system

because the information of so many static systems cannot be stored into one system without loss

of precision or uniqueness.

CONCLU S I O N

Einstein seemed to believe that the shape of a spherical wave is given in the moving

System S' if the observer of S' is able to describe it by some spherical equation. Einstein mixed

up two elements successfully. He never used the common intension of “it” as holistic structure

referenced by “to describe it” but he thought that giving some point the same formula, i.e. time

slicing the shape into points that may be viewed as part of some sphere, would match the

intension of “it”.

Being able to describe something using a specific form is nothing to proof anything. If an

algebraic form is equivalent to some geometrical shape the presentation of it may be concerned

as some evidence which geometrical constructions have in general. But practical applications

need a lot more of constraints to be checked in order to get some evidence.

#$%&'($%&*FG(H'$-(I/&'*J$-(,$&('*&*2((-$)(%H(FK'.((LM$-/0(%H(*1

'.(1*,2M0/$%*,)(,'*1M01$0.$&J(%(,/0H*-/,$/%H(+,$%H$+0(

If we are able to paint a ball of diameter N within a coordinate system using the equating

principle N and if we have painted a ball then we would have done it if and only

if N B . But if we teach to paint a ball by applying a rule like N the most

important constraint may be refrained. If the Lorentz transformation cannot be used to establish

some equivalence of diameters of balls for what is it useful then?

If we take into account that any observer can see shapes only by apparent simultaneous

events (i.e. simultaneously incoming photons) the situation described by Einstein is drastically

flawed with errors. Did Einstein actually kidding someone as he wrote his Elektrodynamik-

paper?

[1] http://arxiv.org/pdf/physics/0606130.pdf,

Vankov, Anatoli Andrei:“On Controversies in Special Relativity”, 06/14/2006

[2] http://www.fourmilab.ch/etexts/einstein/specrel/www/

[3] The other idea so cope with the mismatch is left untouched: Einstein could have thought that common

time is not different of kind to time which is related to single points of space. To enforce this idea

variable would have to be replaced by and the constraint , given by Einstein for the ‘slow

running clocks’ only, would have to hold throughout Lorentz transformation as interpreted by

Einstein.