When data mapping and data migration is part of your everyday work you don’t think about fundamental errors that may be brought in when bloody beginners start with it.
There is for example a database full of transactions and accounts each having a set of owners. Don’t even think about what to happen when twisting some of these relations. The top of the list of bugs was thought to twist all the ownerships such that every owner will get access to some foreign account. But this is not so bad as the following idea which was brought up by a student of physics few days ago: In order to check the integrity of the mapping procedures he proposed to use the method of Albert Einstein. Einstein wanted to prove his principle of covariance that the shape of a sphere remains the same after applying the Lorentz transformation.
Students of physics seem to believe that Einstein was able to prove -just by term rewriting- the conservation of the shapes which is not less than the invariance of the structure after mapping the data.
„Zur Zeit 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 x² + y² + z² = c²t².
Diese Gleichung transformieren wir mit Hilfe unserer Transformationsgleichungen und erhalten nach einfacher Rechnung:
x’² + y’² + z’² = c²t’².
Die betrachtete Welle ist also auch im bewegten System betrachtet eine Kugelwelle von der Ausbreitungsgeschwindigkeit c. Hiermit ist gezeigt, dass unsere beiden Grundprinzipien miteinander vereinbar sind.“
The translation of Einstein’s 1905 Electrodynamics paper states for the last paragraph:
„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:
Given a spherical wave by the equation above 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 v of the velocity takes the direction parallel to x the equations y=y’ and z=z’ were supplied. The calculation steps are given in detail as follows:
|ds²||=x²+y²+z² – c²t²|
|=γ²(x’+vt’)²-γ²c²(t’+ vx’/c²)² +y²+z²
=γ² (x’²+2 x’ v t’ +v²t’²)- γ²c² (t’²+ 2 t’ vx’/c² + v²x’²/c²c² ) +y²+z²
=γ² x’²+ γ² 2 x’ v t’ + γ² v²t’² – γ² c² t’²– γ² 2 t’ vx’ – γ² v²x’²/c² +y²+z²
= γ² x’² – γ² v²x’²/c² + γ² v²t’² – γ² c² t’² +y²+z²
= x’² ( γ² – γ² v²/c²) + c²t’² (γ² v²/c² – γ²) +y²+z²
= x’² γ² (1- v²/c²) – c²t’² γ² (1-v²/c²) +y²+z²
No doubt we have the same form within the moving frame of reference K’. This seems to indicate that all frames of reference have the same spherical shape to observe. The Einstein’s starting equation was: x²+y²+z²=c²t². As the left hand side and right hand side must have the same value, we get: x²+y²+z²-c²t²=0.
The so-called Minkowski metric is presenting the same equation as:
x²+y²+z²-c²t²=ds². Hence, what Einstein showed to be equal was:
Summarizing the lines above the transformations of the Lorentz type restrict the transformed values to ds²=0 and therefore the proof of any invariant is limited to 0=0.
Einstein did prove that there is a sphere-like formula for every point to be described. What he refrained was to define some unique radius for all points of the same shape, i.e. to conserve the holistic principle of the shape. Einstein gave every point of the shape its own formula. In order to comprehend the fundamental nonsense of Einstein’s ‘proof’ it is important to realize that every point may be described as part of any shape or any object – without restriction and without any proof. If Einstein had to map all the accounts of some customer from different platforms he would have created as many customers as accounts he had. Note that only points that share the same x-value will be mapped to the same shape.
Einstein introduced the t-coordinates not as arbitrary but as some real time values. There are given no constraints for pairs of symbols like x’²~x², z’²<z² or ctF=ctG, therefore the variables of the first system K are not tightly bound against the target system K’. Einstein wanted to prove the compatibility of his basic principles. So he mapped every point to its very own shape and one spherical shape ends up in as many different shapes as points exist along the x-axis.
Einstein did not prove that all points of some sphere are to be mapped to the same sphere.
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.
Einstein failed to show that his basic principles are compatible. Just by demonstrating that there may be drawn a sphere through any point nothing may be shown. In order to prove that all points of shape A are mapped to A’ one has to assure that the formulas of all points of some sphere share the same radius:
The constraints above directly forbid to have 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.
Imagine Scotty having beamed his captain that way Einstein did ‘prove’: He would have produced as many different captains as the body of his captain contained molecules.