Algebraic Computations without Squaring the terms

           Scientists in general, and physicists in particular, appear to be infatuated by the concept of powers in mathematical expressions. This appears obvious in Einstein's two famous formula regarding Energy and mass in motion. The theoretical concept of mathematical powers of numbers is misleading however in theoretical discourse as shown in this essay and in other essays about Einstein's computations. And, as seen above, it appears in the Lorentz Factor.
           It is possible to write the Einstein formulas without the concept of squared terms.  In doing so, it becomes even more obvious that said formulae propose mathematical procedures that have little to do with reality, with the different forms of matter-energy in spacetime/motion.
           Consider for example the formula that concerns us here. An alternate expression would be as follows:
           Instead of the commonly accepted algebraic expression,

algebraic expression

consider the alternate expression:

fractal numerical values

                                                                                        The same fractal numerical values are derived from the algebraic presentation as of the previous one containing the squares of the v and c terms.
In my view, it is impossible to materially reason the spacetime/motion coordinates of the matter-energy events portrayed in the denominator

=  terms exist, whose relationships
 here make no sense

of the previous equation expression. In other words, it is impossible to have the procedural steps of the equation derived as of existing matter-energy events in spacetime/motion
           Here is a stated attempt in word-concepts: "The square root of unit one [1.0] minus the velocity of a mass at rest divided by the reciprocal of the same mass at rest divided by lightspeed in vacuum divided by the reciprocal of lightspeed in vacuum".
           What has been stated here in terms of matter-energy events in spacetime/motion? Personally, I have no idea. From this expression without squares, one will obtain the same fractal values derived from the original Einstein formula employing squares. However, the terms as stated in this version without squares make more sense in terms of matter-energy events, but still make no sense at all.
             In my view, there exists no matter-energy event that derives from the simplified c-expression of the Lorentz Factor denominator.

Lorentz Factor denominator

as expressed without squares in the terms.
           Further, there exists no matter-energy event that derives from the cited denominator, referred to as the Lorentz Factor employed in the special relativistic equations, as:

Lorentz Factor employed =  terms do not exist,
      faux numbers

with squares of the terms. [Remember that the Planck constants employ powers of c to the 5th, 6th, 7th, 8th and 9th powers; even more unreal numbers.]
            These are two different fractal methods (with and without squares of terms) to skin the same cat; only the cat does not exist.
            Any (subluminal) mass at rest [m0] in relation to a luminal mass velocity in vacuum [c] does not exist as of these terms vis-à-vis unit 1.0 and their squares or square roots. Were these numerical values to reflect existing matter-energy events in spacetime/motion, one would be able to follow their computational steps in the derivations. This does not occur in the science literature.
           One need not look too far to understand that

understand that

is a non-existent ratio in terms of matter-energy in spacetime/motion. One may only contemplate the self-same thesis of special relativity that the speed of light in vacuum, c, is a physical limit to the motion of matter-energy in spacetime/motion. This self-same limit identified in the theory of special relativity denies the use of practical computations of spacetime/motion based on a multiple of c by 299792458 times ---(or, any other multiple fractal quantity for that matter) by definition.
           In order to impose a consistent set of logical statements in the algebraic notation of Einstein's two commonly cited formulas, one would need to write one as follows.
            m = E / c²
in congruence with,
            mο =  m times algebraic notation of Einstein's   or, inversely,
            E = mc²
            mο = m (algebraic notation of Einstein's )

            The problem remains, in spite of correcting the logic in presentation of the two formulas in order to improve their consistency in reasoning, both of the formulas are based on immaterial events such as c-square, among other precepts.
           From the previous analysis, it is interesting to note that two different definitions for mass at rest are being presented:
mass at rest     =          E divided by  c²
mass at rest     =             m times algebraic notation of Einstein's

           In other words, it follows that:

                                               E divided by c²  =  m times algebraic notation of Einstein's

           In my view, these two expressions make no sense, nor derive an equivalency between themselves as expressed in terms squared, or as in terms without squares.

                                         E / (c times c)  =  m times special-relativity formula

           The special-relativity formula as stated in Albert Einstein's own hand-writing as cited earlier is:
                                                   special-relativity formula    

This equation appears to entail elements of both of Einstein's now famous formulae. Its expression without squares would be then:
                                                   special-relativity formula
It is significant to note that today two distinct formulae are offered for relativistic energy, elements and terms of which are purported to be in Einstein's own hand-written formula:

                                                     E = mc²


relativists use reciprocals

            If the relativists use reciprocals for length contraction, then why not use [c/ (1/c)] instead of squares of v and c. They will say that this makes no sense, but they use reciprocals anyway.

©2014 Copyrighted. Charles William Johnson. All rights reserved.