The Lorentz Factor

            The Lorentz Factor:
                                             Lorentz Factor Formula
My initial reaction to the formulas for relativistic mass/time/length/energy was "here we go again with c-square".
It is materially impossible to reach the speed represented in c-square, as c itself is defined as a fixed, maximum limit. It is materially impossible to materially weigh a mass when it is in motion; it can only be theoretically computed. In fact, given the constancy of the motion of a light photon, this event is referred to as massless in the science literature.
The simplest of tests for mass in motion are impossible to effect, as in placing a scale or balance under a bird in flight or, even a runner scampering across a weigh-station for trucks.

The Cheetah, the Fastest land animal on Earth: 70 mph
How much does a Cheetah weight when it is running full speed ahead?
Please, don't tell me," its mass divided by g".

            The problem with theoretical special relativity is its being tied to the observers and their reference frames. In fact, there can be no changes in the spacetime/motion event "observed", yet relativistic measurements abound for the observation. In that sense, even the concept of "rest mass" is questionable as it is defined as of the relationship to the observer.
           The very notion of motion denies the concept of mass at that point, for such events represent mass in motion and are by definition countering the effect of gravity as such.
            Weighing mass in motion represents a near contradiction of terms, as it is lighter or even in free-fall when in motion, counteracting the gravitational pull on its mass.
           Self-consistency field theory for relativity means that all observers observe the same spacetime event without changes, etc. But there is another problem of self-consistency: that concerns being consistent or not in the mathematical application of the four formulas.
            The purpose of this analysis is to answer the question as to whether the terms and proposed equations for special relativity are consistent as stated in their mathematical design.

equation_lorentzis the Lorentz Factor. "So, according to Lorentz's theory, no body can reach the speed of light because the mass becomes infinitely large at this velocity." [Source:]

            This statement reflects one of the numerous statements regarding changes that bodies undergo in their internal structure according to special relativity theory when approaching the speed of light.
           These statements entail a change in mass increase, a change in energy, a change of time dilation, and a change in length contraction, among others. The Lorentz factor appears in all of the formulae regarding the changes of the internal structure of the bodies concerned.

Factor Lorentz equation


However, what is the spacetime/motion reason for creating a huge number as in c-square, 8.987551787E16, then reduce the ratio of v-square divided by c-square, by subtracting it from unit 1.0, and then reduce it even further by finding its square root.
            In fact, when v is 299790.0, then the ratio obtains 0.9999836 producing final result as 0.0040496, whereby this value is 246.9 times smaller than the 0.9999836 ratio value. The reduction of a 246.9 numerical value requires a material explanation. However, there is none in the literature.
            One could also suggest employing a distinct procedure. For example, the question may be asked, why subtract unit 1.0? One could propose a subtraction based on units 2.0, 3.0…etc. There is no explanation of the  material function of unit 1.0.
1 - 0.9999836 = 0.0000164
1 - 0.00000000009999836 = 0.999999999
            One may also question why the use of c-square, and why not use c-cube [c³]? There is no apparent material need or explanation to propose c-square in the Lorentz Factor.
One could obtain a ratio without using the squared terms.
c = 299792.458 kms/sec
1/ 299792458 = 0.333564
c-square = 299792458.0 meters/sec
1/8.987551787 = 0.111265
 v/c  ~   v-square/c-square
There exists a theoretical need to explain why use c-square and not simply c.
There exists a theoretical need to explain why use v-square/c-square and not v/c.
            Therefore, the ratio v-square/c-square is reduced numerically twice: a) by subtracting it from unit 1.0; and b) by finding its square root.  One would need, then, to explain why the original ratio of v-square/c-square needs to be reduced by hundreds of times. What does that prove? Plus, one would have to explain how and why the original ratio is reduced differently for each different numerical value assigned to v.
           Is there some kind of material relationship that exists in spacetime/motion that determines the hundreds-times reduction need?   I do not know of any. So, why reduce the v-square/c-square ratio differently for each gradation variation of v, as though spacetime/motion actually obeyed this reduction?
            The v/c relationship is raised to ridiculously high numbers as in v-square/c-square only to be ridiculously reduced to lower math values [subtracted from unit 1.0 and use of the square root].
            There is in fact a third reduction that is contradictory from the start.
v/c = 299,792,450.0/299792458.0  =  0.999999973
Reduction of ratio:
v² / c² = 299792450.0 / 8.987551787E16 = 0.999999946
Reduction subtraction from unit 1.0:
1 - 0.999999946 =  0.000000053
Reduction by square root:
√0.000000053 = 0.000230217
Finally, 0.999999946 / 0.000230217  = 4343.72764 final value of Lorentz Factor is 4343.7 times smaller than original v² / c² ratio.
Consider, accordingly:
If original ratio percentage:
m0 = 1 = 1 / 0.999999946 = 1.000000054 = mass in motion
If reduced ratio percentage:
m0 = 1 = 1 / 0.000230217 = 4343.727874 = mass in motion

            The Lorentz Factor, in this case causes the term mass in motion [mο]  to be 4343.727264 times greater than the original ratio.
            Einstein once commented that when the mathematicians took over the theory of relativity, he no longer understood it. I have the impression that the Lorentz Factor is the result of physicists or the mathematicians as Einstein called them, fiddling with the numbers. It appears to be the result of fiddling with the formulas in order to produce the pre-conceived numbers. Regarding increases in mass in motion, time in motion and energy in motion, they fiddled with the numbers in order to produce large numbers, very large numbers. And, in the case of the pre-conceived idea of length contraction, they produced smaller numbers by simply using the reciprocals of the largest numbers.
There appears to be no reason to raise a physical limit to the motion of matter-energy [c] by 299,792,458 times; nor to relate that then to v-square of the mass under consideration, and then subtract that ratio from unit 1.0. Only to then find the square root of that number, ---especially when square roots derive two possible fractal answers depending upon whether the terms are expressed in meters or kilometers.
            The Lorentz Factor gives the appearance that there is only one answer to the equation, when square root procedures produce two possible distinct numerical answers.
                      √299792.458 kilometers = 547.53305                    
                      √299792458 meters = 17314.51582
           The Lorentz Factor, as with all root computations, generates at least two distinct answers, as shown by the data sets.
For v = 0.9c,
m = 2.294157338705618mο
                                                                  For v = 0.99c,
                                                                  m = 7.088812050083353mο
For v = 0.999c,
m = 22.366272042129374mο
                                                                  For v = 0.9999c,
                                                                  m = 70.71244595191452mο
For v = 0.99999c,
m = 223.60735676962474mο
                                                                  For v = 0.999999c,
                                                                  m = 707.1069579492319mο
For v = 0.9999999c,
m = 2236.0680339452942mο
                                                                  For v = 0.99999999c,
                                                                  m = 7071.067813726424mο
For v = 0.999999999c,
m = 22360.68009119951mο

            Obviously, all previous answers are numerically correct. The point is to understand how square roots produce two fractal number expressions; cube roots produce three possible fractal answers; and so on.
           The formula has a pre-determined range of increments and decrements designed into its algebraically expressed denominator:

                                                               formula has a pre-determined range of increments and decrements

           The Lorentz Factor first increases the velocity of the mass in motion and the photon mass by squaring their numerical values (by 299,792,458 times or fractals thereof). And, then, the Lorentz Factor decreases or reduces those incremental values by subtracting their ratio from unit 1.0 and then furthering reducing that numerical value by finding the corresponding square root.
           It is difficult for me to understand the logic behind defining incremental ranges from 1.0 to 299,792,458 times/multiples (for terms v and c). Then take their corresponding ratio values [v/c] only to decrease them a few hundred times by subtracting the ratio from unit 1.0 and then finding its square root. Even less logical in my view is to observe how all of this will ultimately serve as a divisor (increment/decrement) for rest mass or a multiplicand (decrement/increment) for mass in motion ---depending on the analytical perspective.
           The range is pre-determined by the lesser values expressed in the v-term from unit 1.0 through 9.9 (theoretically), just for the sake of example, not for exactness (specifically, from 1.0 - 299,792,458 kms/sec). When the lowest speed of the v-term is a small number [as in 1.0], then the result derived as of the entire the equation will be the highest moving mass [m]. The formula yields an obvious event that the lowest speed of mass gives highest numerical value for moving mass. And, heavy mass events have lowest subluminal speeds.
           When the highest speed of the v-term is a large number [as in 9.9], then the result derived as of the entire equation will be the lowest moving mass [m]. The formula yields an obvious event that the highest speed of mass gives lowest moving mass. Near massless photon has highest speed limit. Yet, in spite of this relationship designed into the equation, somehow the scientists find that these numbers, this numerical range, means that infinitely high mass is required to reach near light speed.
           The formula appears to be redundant, and in that it is self-consistent. The formula represents a redundant statement that highest speeds correspond to lowest moving mass. The less mass, the faster speeds possible in spacetime/motion. A light photon, near massless, represents the highest maximum speed attained by matter-energy; their statement, not mine.
           And, the lowest speeds of mass [at rest] correspond to the highest amounts of moving mass: the ore mass, the slower the speeds in spacetime.
           The cited formulas for special relativity, as they are often called, entail a pre-determined mathematical design and structured outcome in their possible computations.

formulas for special relativity


formula represent a lesser/greater range of numerical values

           Remember, the minus, the square root and the division procedures in the formula are also mandatory, fixed terms. You must subtract from unit one, you must divide factors, and you must derive square root. The symbolic formula demands these steps.
           In other words, irrespective of the play on variable terms, the numerical values that may be derived from the cited formula represent a lesser/greater range of numerical values…, always below the fixed limit of the speed of a light photon in vacuum.
           The apparently self-consistent conclusion is designed in the terms of the formula. Therefore, the formula represents no particular relationship with matter-energy in spacetime/motion, other than a preconceived notion of mass at rest [mο]  and mass in motion [m].
           But, since all matter-energy, all spacetime/motion are in constant flux, the concept of mass0 is relational, as well as mass at rest, which is also in motion [as its internal structure].

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