Note about on-line relativistic calculators: On-line Data sets

The following data computations present selective percentages for v of c, the speed of light: 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, 90%, 99%….99.9999999%.
Given the fact that the four formulas present the same design, one would expect all four to produce the same numerical values. As may be observed on the lists below, the three categories relativistic mass, time and energy produce the same incremental numerical values. This is what one would expect given the fact that their symbolic formulas are the same.

For v = x c, m = x m0
For v = 0.1c, m = 1.005037815259212m0                Lowest value on scale
For v = 0.2c, m = 1.0206207261596576m0
For v = 0.3c, m = 1.0482848367219182m0
For v = 0.4c, m = 1.0910894511799618m0
For v = 0.5c, m = 1.1547005383792515m0
For v = 0.6c, m = 1.25m0
For v = 0.7c, m = 1.4002800840280099m0
For v = 0.8c, m = 1.666666666666667m0
For v = 0.9c, m = 2.294157338705618m0
For v = 0.99c, m = 7.088812050083353m0
For v = 0.999c, m = 22.366272042129374m0
For v = 0.9999c, m = 70.71244595191452m0
For v = 0.99999c, m = 223.60735676962474m0
For v = 0.999999c, m = 707.1069579492319m0
For v = 0.9999999c, m = 2236.0680339452942m0
For v = 0.99999999c, m = 7071.067813726424m0
For v = 0.999999999c, m = 22360.68009119951m0                        Highest value on scale

For v  =  0.1c, T = 1.005037815259212T0              Lowest value on scale
For v  =  0.2c, T = 1.0206207261596576 T0
For v  =  0.3c, T = 1.0482848367219182T0
For v  =  0.4c, T = 1.0910894511799618T0
For v  =  0.5c, T = 1.1547005383792515T0
For v  =  0.6c, T = 1.25T0
For v  =  0.7c, T = 1.4002800840280099T0
For v  =  0.8c, T = 1.666666666666667T0
For v  =  0.9c, T = 2.294157338705618T0
For v  =  0.99c, T = 7.088812050083353T0
For v  =  0.999c, T = 22.366272042129374T0
For v  =  0.9999c, T = 70.71244595191452T0
For v  =  0.99999c, T = 223.60735676962474T0
For v  =  0.999999c, T = 707.1069579492319T0
For v  =  0.9999999c, T = 2236.0680339452942T0
For v  =  0.99999999c, T = 7071.067813726424T0
For v  =  0.999999999c, T = 22360.68009119951T0                       Highest value on scale


For v = x c, E = x E0
For v = 0.1c, E = 1.005037815259212E0     Lowest value on scale
For v = 0.2c, E = 1.0206207261596576 E0
For v = 0.3c, E = 1.0482848367219182 E0
For v = 0.4c, E = 1.0910894511799618 E0
For v = 0.5c, E = 1.1547005383792515 E0
For v = 0.6c, E = 1.25m0
For v = 0.7c, E = 1.4002800840280099 E0
For v = 0.8c, E = 1.666666666666667 E0
For v = 0.9c, E = 2.294157338705618 E 0
For v = 0.99c, E = 7.088812050083353 E0
For v = 0.999c, E = 22.366272042129374 E0
For v = 0.9999c, E = 70.71244595191452 E0
For v = 0.99999c, E = 223.60735676962474 E0
For v = 0.999999c, E = 707.1069579492319 E0
For v = 0.9999999c, E = 2236.0680339452942 E0
For v = 0.99999999c, E = 7071.067813726424 E0
For v = 0.999999999c, E = 22360.68009119951 E 0                       Highest value on scale

Rest mass m0 = 1 kg
Relative velocity v = 29979.2458 km/s < c or = to c
Rest mass energy E0 89,875,517,873.682 MJ
Relativistic mass energy E 90,328,294,129.055 MJ
For v = 0.1c, m = 1.005037815259212m0  = Mass energy rate E/E0
Velocity ratio to light v/c = 10%
But, the same does not hold true for length contraction. As may be observed from the list below, the numerical values corresponding to the same percentages for v of c for length contraction derive in a decremental fashion progressively lower values, instead of progressively higher values as in the other three formulas.


For v  =  0.1c, L =   0.99498743710662L0               Highest value on scale
For v  =  0.2c, L = 0.9797958971132712L0
For v  =  0.3c, L = 0.9539392014169457L0
For v  =  0.4c, L = 0.916515138991168L0
For v  =  0.5c, L = 0.8660254037844386L0
For v  =  0.6c, L = 0.8L0
For v  =  0.7c, L = 0.714142842854285L0
For v  =  0.8c, L = 0.5999999999999999L0
For v  =  0.9c, L = 0.4358898943540673L0
For v  =  0.99c, L = 0.14106735979665894L0
For v  =  0.999c, L = 0.04471017781221601L0
For v  =  0.9999c, L = 0.014141782065918275L0

For v  =  0.99999c, L = 0.004472124774634615L0
For v  =  0.999999c, L = 0.0014142132088478148L0
For v  =  0.9999999c, L = 0.0004472135842108574L0
For v  =  0.99999999c, L = 0.00014142135620009053L0
For v  =  0.999999999c, L = 0.000044721358917592574L0 Lowest value on scale

            Immediately, one wonders how can the same symbolic formula, for four different categories, produce three categories with incremental numerical values, and one category with decremental numerical values. The only way that can happen if some other unrecognized procedure is being followed not stipulated in the formula.
The data for the first three categories [mass, time, energy] reflect the same progressively increasing numerical values for the percentages of v of c.
The fourth category [length] reflects progressively decremental numerical values that at first sight appear unrelated to the other three incremental sets. However, the decremental data for length contraction are simply the reciprocal numerical expressions for the incremental data of the other three categories.
            This fact is unexpected since the formula for length contraction is presented exactly in the same manner as the formulas for the previously three cited categories.
            Yet, obviously, because of the data being presented by the on-line calculators for special relativity length, there is evidently another procedure being followed:

            * Length Contraction

Length Contraction

In other words, the incremental|decremental data are relational as reciprocals for 1/L. Obviously the reciprocals are derived for length contraction simply because the worded statement of its thesis is that there is contraction, a decrease in length.
This being the case, there is no consistency in the supposed thesis-building for the four formulas of special relativity.  By stating that the categories of mass, time dilation and relativistic energy reflect increments, and the length category reflects decrements, but only one basic design is offered for the four categories is evidently a mistake.
No where in the science literature do I find a clarification regarding a distinction in mathematical procedure for the different categories. No where is it stated that the length contraction requires finding the reciprocals of the specific incremental numerical values of the other three categories in order to substantiate the thesis about length contraction [a decremental series].
            It would appear that the proponents of special relativity simply chose the reciprocal values of the other three categories as an obvious attempt to prove contraction. That's why they chose reciprocals, over say, multiplying L by the Lorentz Factor in order to obtainL0
  The four special relativity formulas are designed alike in order to produce incremental values. Therefore, choosing reciprocals for L, without indicating the reasoning behind such a choice, is completely arbitrary and biased, without any theoretical meaning or mathematical substantiation. 
            In fact, it is superfluous to present the four special relativity formulas. As mentioned earlier, one could present one basic formula
[m, Δt, L, E, etc.]        =         [m0, Δt0, L0, E0, etc.]

                                               relativistic category obeys this formula

and, then simply state that any relativistic category obeys this formula. However, for decremental numerical values, as in length contraction, it is necessary to further find the reciprocal of the cited basic formula, as in 1/L.
            However, given the fact that the category of length contraction theoretically implies decremental numerical values, such a practice cannot be followed. One must demonstrate and explain which particular mathematical procedure is being followed for length contraction as distinct from the other incremental categories.
However, in my view, still there is no theoretical consistency in choosing three incremental data sets and one decremental data set. They could have chosen time as decremental and the other three dimensions of space [mass, length, energy] as incremental data sets.
The theoretical problem is not simply the fact that the specificity of length contraction goes unexplained, but that the basic formulas for specific relativity based on the common denominator of the Lorentz Factor make no material sense. They do not reflect how matter-energy behave as forms of  spacetime/motion.
They chose the categories of incremental mass and decremental length, well-knowing that length, width & height are reflective of mass.


For v = 0.1c, L =  0.99498743710662L0          = reciprocal = 1.005037815259212m0
For v = 0.2c, L = 0.9797958971132712L0       = reciprocal = 1.0206207261596576m0
For v = 0.3c, L = 0.9539392014169457L0       = reciprocal = 1.0482848367219182m0
For v = 0.4c, L = 0.916515138991168L0         = reciprocal = 1.0910894511799618m0
For v = 0.5c, L = 0.8660254037844386L0       = reciprocal = 1.1547005383792515m0
For v = 0.6c, L = 0.8L0 = reciprocal                  = reciprocal = 1.25m0
For v = 0.7c, L = 0.714142842854285L0         = reciprocal = 1.4002800840280099m0
For v = 0.8c, L = 0.5999999999999999L0       = reciprocal = 1.666666666666667m0
For v = 0.9c, L = 0.4358898943540673L0       = reciprocal = 2.294157338705618m0
For v = 0.99c, L = 0.14106735979665894L0   = reciprocal = 7.088812050083353m0

Note that the categoryL0 is then the exact reciprocal of m0 [and of Δt0 and E0, whichever other incremental category one may choose].
            By the unrecognized procedure of reciprocals, the so-called theory of special relativity appears to be confirmed by the numbers produced by the symbolic formulas. The large numbers appear to prove increase mass, time dilation/increment, and increase energy. While the smaller numbers [the reciprocals], for example, appear to prove length contraction/decrement. However, it appears to me that such a "proof" is algebraically and mathematically deficient. There is no theoretical proof in fact, or even less a proof according to spacetime/motion itself as shall be illustrated below.

"Though some of these criticisms had the support of reputable scientists, Einstein's theory of relativity is now recognized as self-consistent, in accordance with many experiments, and moreover serves as the basis of many successful theories such as quantum electrodynamics."
Source: -

            From the previous analysis, the four special relativity formulas, according to the on-line calculators on the Internet, do not appear to be consistent in their statements and/or mathematical design.
           The theoretical problem with the four formulas for special relativity concerns a variation in the apparently same terms. In relativistic energy how does one rationalize mv. The four formulas employ v-square in the Lorentz Factor. Now, why does v suddenly have relevancy now in relativistic energy? Instead of writing E0 the composite term mv is used to recognize the concept of energy in motion at that level. The notation represents a prior computational step to obtaining E0.
            Ultimately, all four categories are assigned numbers that represent the same validation system of numerical values, whether they are incrementally or decrementally expressed and/or the terms and computational steps made explicit and clarified. This observation is confirmed by the fact that the data sets derived from the on-line calculators produce the same numerical values and/or the reciprocals of those numerical values.
            As illustrated above there are numerical deficiencies related to special relativity formulas for mass, time, length and energy. But, the very fact that the four special relativity formulas produce the same incremental/decremental numerical values and their reciprocals supports the inference that mass and velocity are directly related; a change in one means a change in the other.
           The idea that increased velocity necessarily means increased mass, increased time, increased energy, but decreased length also infers a direct relationship of these features of spacetime/motion to the abstracted concept of velocity of mass. Further, their inter-relationship establishes the fact that the formulas for special relativity are testimony to the idea that the internal structure of a body-mass undergoes changes as it approaches the speed of light.
            My initial reaction upon reading about these theses was to ask why would the four same mathematical procedure, based on division, produce three incremental terms [mass, time, energy increase] and one decremental term [length decrease]. The obvious reason is that the proponents of these four formulas are not being consistent in deriving the corresponding data sets.
            And, the mathematical procedure as to why this incremental/decremental contradiction occurs is because in the three incremental formulas the procedure of division is employed, while in the decremental formula the procedure of reciprocals is employed.
            The popular presentation that the data for length contraction supposedly decrease is merely a biased distraction in the theoretical interpretation of special relativity. A case could be made to present the three categories [mass, time, energy] as decremenal and the length category as incremental. One would simple derive the reciprocals of each data set.

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