

Completed (24 days) Completed (57 days) Completed (26 days) Completed (47 days) Completed (19 days) PROJECT 5 Completed (14 days)  Critical analysis of the main premises of special relativity: Lorentz & Minkowski Completed on 14Jun2015 (14 days) NOTE: the text below refers to what was written by A. Einstein in "relativity: The Special and General Theory" (you can download a copy from http://www.gutenberg.org/ebooks/30155). All the redcoloured numeric references are directly taken from that book .The current section is mainly focused on Appendix I SIMPLE DERIVATION OF THE Lorentz transformation (SUPPLEMENTARY TO SECTION 11). The derivation is started from the following system of equations:
After performing some minor modifications, the aforementioned system is converted into:
At a first sight, it seems that (5) is not better than (1) : the searched relationship (i.e., x' & t' related to x & t ) has been artificially provoked by relying on two unknown constants (i.e., a & b ); nevertheless, the original requirement of bringing further information into picture remains unaltered (i.e., previously, it had to explain the intended relationship; now, the meaning of the new constants).Before analysing the next steps, I will clarify various issues whose misunderstanding is precisely the responsible for most of the subsequent errors:
(5) , the derivation follows with:For the origin of K' we have permanently x' = 0 Such an assumption is wrong for various reasons. Firstly, it goes against the alreadyexplained fact that x' (better: Δx' ) may not be zero. Otherwise, no velocity might have been considered; or, alternatively, the associated velocity (c ) would be zero, what is impossible on account of its essence (i.e., constant value much bigger than zero). In fact, this clarification denotes a second error: forgetting about the unbreakable relationship between x' & t' (equivalently to what happens with x & t ) through the constant c , what avoids these variables to be independent upon each other (i.e., x' might take any value above zero, but only as far as t' would also be equal to x'/c ). There is a third error in the aforementioned statement: even in case that x' = 0 would be valid, it would have been a very bad choice on account of its extremely limited applicability; that is: the conclusions outputted for x' = 0 (e.g., x = bct/a ) wouldn't work when such a condition is not met (i.e., when x' ≠ 0 , x ≠ bct/a ).After all the aforementioned errors, the resulting formula x = bct/a is converted into:
Such a conversion occurs by creating a new variable (the velocity v ) from the fraction x/t . That is: the author started from a fraction being equal to a constant and, after performing some formal replacements (i.e., not bringing any new information into picture), created a new variable defined by this same fraction. That is: x/t = c & x/t = v & c ≠ v (?!).Afterwards, Einstein writes: [...]we only require to take a "snapshot" of K' from K; this means that we have to insert a particular value of t (time of K), e.g. t = 0. This "snapshot" represents a more intuitive way to understand the confusion between x (spatial coordinate) and Δx (variation between two spatial coordinates; what the x in v = x/t is actually referring to): it is impossible to take a snapshot of a spatial variation or a velocity, it would rather be a video.I will stop my analysis of this document here, because of not seeing the point in continuing. The aforementioned errors are so clear and "unfixable" that I cannot think of a better way to transmit the intended ideas. Lastly, I want to highlight an issue which, unlikely what some people seem to think, I consider very relevant: better making sure that everything works fine before bringing the more elegant/magical/cool ideas in. That is: any experienced person should have assumed that this development was faulty just after having quickly skimmed through it. More specifically, after having noticed the starting conditions (i.e., a system of two interindependent equations, each of them inversely relating two variables to the same constant), the additional information being accounted (i.e., none) and the final results:
Even by ignoring the new v (where could a new variable come from?), it should have been clear that, without accounting for additional information, the proposed system cannot be solved. 