Related Special-Relativity Equations

            Four special relativity formulas are commonly cited in the physics literature for relativistic mass, time dilation, length contraction and relativistic energy. The particular theses propose that when spacetime events near the speed of light then mass increases, time dilates/increases, length contracts, and energy increases.
            One thing is certain. The four formulas for special relativity, given the importance of motion (Lorentz Factor) propose a direct relationship not only between mass and velocity. But, they propose a direct relationship among time and velocity; length and velocity; and, energy and velocity. The very procedural division and multiplication of terms against motion (the Lorentz Factor) establishes this belief in said direct relationships.

"It is not good to introduce the concept of the M = m /m of a moving body for which no clear definition can be given. It is better to introduce no other mass concept than the 'rest mass' m.  Instead of introducing M it is better to mention the expression for the momentum and energy of a body in motion."
                                    -Albert Einstein in letter to Lincoln Barnett, 19 June 1948. (quote from L. B. Okun (1989). Cfr., L.B. Okun (1989), "The Concept of Mass", Physics Today, 42(6):31-36. [Source: Wikipedia.com, "Mass in special relativity".]

            In that sense, it is not so much the correctness or incorrectness of the formulas that must be addressed, but rather an explanation is required as to why relativists perceive such a direct relationship on all levels of matter-energy in spacetime/motion. They offer no such admission in their work.
            The four formulas basically obey the same mathematical procedure, where their main term [at rest] is divided by the Lorentz Factor [motion thesis].
Various special-relativity equations exist.

* Relativistic Mass

relativistic Mass

* Time Dilation

time dilation

* Length Contraction

Length Contraction

A mass m moving with speed v has relativistic energy E and momentum p, given by

* Relativistic Energy

Relativistic Energy

[Source: Relativity for Dummies.]

            When observing the four formulas for special relativity, one may think that the four symbolic formulas yield the same numerical results since they contain the same algebraic/mathematical procedure: a term divided by the Lorentz Factor. In the Lorentz Factor three terms refer to the same mass [m, mο, v], and one term c refers to a distinct mass, that of a photon.
            It is generally stated that as the light photon approaches the speed of light, its mass increases. I find it suspect that relativistic mass, time dilation, length contraction and relativistic energy reflect the same relationship to the same denominator, the Lorentz Factor:  (1 - v² /c²) 1/2. Note the changes to internal structure vary: increase mass (greater speed infinite mass increase); time dilation (slower/faster clocks); length contraction (greater velocity smaller length); relativistic energy (increase).
            A conceptual deficiency concerns the fact that length represents a feature of mass. The analysis of the word-concepts/terms to be used is the first step in carrying out a theoretical spacetime/motion analysis. The four concepts in terms of a spacetime/motion analysis relate in the following manner:

Space          =          mass increase, length contraction [missing are width and height dimensions]
Time           =          time dilation
Motion       =          relativistic energy motion/relationship

            One significant contradiction between the formulas and the theses proposed concerns that between mass increase and length contraction. Why are the four formula the same mathematically, yet the numerical results are different. The mass formula produces incremental values and the length formula produces decremental values.
            If the mass of an electron/photon increases as it approaches the speed of light in vacuum, one would expect correspondingly that the time dilation, length, and energy values might increase as well ---given the presence of the same denominator in the different equations and similar terms in the formulae.
            Given the presence of the same denominator [Lorentz Factor], I would expect the number range for the unknown terms [mο, tο, Eο, Lο], would necessarily be the same, the same numerical values being produced. For the four special-relativity formulae [mο, Δtο, Lο, mv] reflect the same basic design with the same denominator; each one divided by the Lorentz factor:
[m, Δt, L, E]  =  [mο, Dtο, Lο, Eο]
  Lorentz factor



Therefore, it makes little sense to me that one of the terms [length contraction] would produce decremental results, while the other three [mass increase, time dilation and relativistic energy] would produce incremental results.  The four theses appear to represent a contradiction in the theoretical interpretation of special relativity.
contradiction in the theoretical interpretation of special relativity

            The numerical values for the terms mass and length are progressively positive from zero to infinitely large [0 - ∞], and should therefore produce the same kind of progressive results as in increase of mass and an increase of length [not its contraction or decrement]. The question is how can the same basic design produce opposing greater|lesser structural results in this regard.
            The theoretical problem involves postulating a pre-conceived idea while employing a different mathematical procedure for length contraction.
            If one divides the Lorentz factor into mο [mass at rest], then a large number for m will result [increase mass]. If one multiplies L by the Lorentz factor, then a small number for Lο [length contraction] will result [diminished length]. At first glance, the difference in mathematical procedures explains the apparent contradiction between increase of mass and contraction of length.
            How can the same Lorentz Factor in the four special relativity formulas produce opposing theses in terms of quantities [increase/decrease, more/less] in numerical values?
Three of the special relativity formulas employ the incremental numbers and one category [length] employs the reciprocals of those same incremental numbers.
Consider the selected data that I obtained from the on-line calculators about the four special relativistic categories.

Note about on-line relativistic calculators:
 :          www.ultimate-theory.com [Special relativity; length contraction calculator.]
:           http://Keisan.casio.com calculates the length contraction of a body moving same relative velocity with respect to the observer. L = Lογ 
:           www.1728.org Relativistic calculator.
:           http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/tdil.html

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