Apples and​​ Pears

Dan Romalo

While I was 7 or 8 years old, I was intently taught not to add​​ apples with pears! I didn’t agree, in fact I protested vehemently, yet eventually I've had to finally yield to the adults' might. I conformed without conviction because I was wondering why three apples and four pears might not, by simple cipher’s power, signify seven; or the trick otherwise done by extending the significance of apples and pears towards the larger significant of fruits?​​ 

Grown up at high school level I met the dimensional analysis rigor, and was again taught that, more or less by might of the apples and pears principle, both members of any well-founded physical equation must be, dimensionally, identically composed.​​ 

After that, all along an incredibly long-life span — experienced step by step — I endeavored to comprehend how the world runs.​​ 

Essentially, I fought very hard trying to understand how electromagnetism, by permeating the entire universe, determines its evolution. At a certain moment I submitted to the presumption that it’s the theory of relativity which is the most natural way to approach physics from its philosophic side. And when approaching this way the problem I was driven to conclude that the theory of Relativity’s fundamentals situates themselves not at the approaching level, yet one level deeper, essentially where the strong physical nature of the Relativity concept imposes that all symbols involved when working on such a subject shall be strictly physically defined, meaning by this not virtually defined. Or, trying a more precise description: mathematics, operating conjointly with physics by means of specific symbols interacting in a virtual common space, configures complex theories.​​ 

It happens yet that the symbols used distribute themselves into two classes’ that are clearly distinct. Factually, one meets the class of mathematical symbols on one part and that of symbols of true physical nature on the other.​​ 

While the class of mathematic symbols is one of items definable at will — their logic coherence being ensured by the logic of the subject worked on — physics’ symbols are bound to be strict representations of physical individual truths. From this results that: while mathematical theorems may be built somehow at will — on the condition that the symbols used are strictly coherently defined — Physics’ equations shall be built exclusively from pure physically defined symbols. This is so simply because physics’ truths may not be decided by will. One may oppose that physics also uses inhomogeneous relations, yet those are only descriptive works without any power of physical statement. They may express a physical truth yet only under the control of a specific reformulation.​​ 

The in-perspective drawings are an example at hand of the procedure: exact physical truths may be extracted from them means of adequate transformation rules.​​ 

A more elaborate example of the same kind of implication may be found looking into STR.​​ 

Essentially, STR’s roots originate in Poincare and Lorentz works. Those, originally, did not intend to be more than a change of coordinates equations set. A. Einstein, formally, adopted the idea and, by upgrading the so assumed Lorentz-transform-set into a supposed physical truth, imposed it as a Principle of physics. Yet so doing hides a bug: the STR can’t satisfy a symbol-homogeneity test because it imposes, arbitrarily and by principle, “c” as an absolute constant presumed of being of a pure physical nature. Yet this can’t be true at least because by no means the one-way speed value of c could be, instrumentally certified.