A Spacetime/Motion Analysis of the Terms in the Formulas for Special Relativity for Mass, Time, Length and Energy
Consider the terms of the equation proposed for the theory of relativistic mass.
mο = mass at rest
m = mass in motion
Δtο = time at rest
Δt = time in motion
Lο = length at rest
L = length in motion
mv = energy at rest
E = energy in motion
mο = mass at rest = exists and may be known
m = mass in motion = exists; directly incommensurable; unknown
Δtο = time at rest = exists and may be known
Δt = time in motion = exists; directly incommensurable; unknown
Lο = length at rest = exists and may be known
L = length in motion = exists; directly incommensurable; unknown
mv = energy at rest = exists and may be known
E = energy in motion = exists; directly incommensurable; unknown
One of the main problems with the theory of relativity may be observed in the wordconcepts employed in the four cited relativistic formulas.
The first question is whether the terms reflect spacetime/motion events that exist and are capable of being known.
v = velocity of mass = exists and may be known
c = velocity of light photon in vacuum = exists and may be known
v/c = possible relationship exists as of existing terms
v² = squaring of velocity of mass = no material existence; exists only as an abstracted idea
c² = squaring velocity of light photon in vacuum = no material
existence; exists as an abstracted idea
v² / c² = dividing square of velocity of mass by square of light speed = no material existence; exists only as an abstracted idea
1  v² / c² = the proportion of dividing the square of mass by the square of
the velocity of lightspeed subtracted from unit 1.0 = no material existence;
exists only as an abstracted idea
√ 1  v² / c² = the square root of the proportion of dividing the square of
mass by the square of the velocity of lightspeed subtracted from unit
1.0 = no material existence; exists only as an abstracted idea
mο / √ 1  v² / c² = a mass at rest divided by the square root of the
proportion of dividing the square of mass by the square of the
velocity of lightspeed subtracted from unit 1.0 = exists only as an abstracted idea
m = mο / √ 1  v² / c² = a mass equals a mass at rest divided by the
square root of the proportion of dividing the square of mass by the
square of the velocity of lightspeed subtracted from unit 1.0 = no
material existence; exists only as an abstracted idea
In first considering the consistency of a mathematical formula, a relationship of equivalency of material terms of matterenergy, one must consider whether the terms and relationships proposed in the equation exist in terms of spacetime/motion. In other words, the question to be determined is whether the terms and their relationships exist as forms of matterenergy and whether they actually occur in spacetime/motion {in reality}.
One must explain each computational step in the mathematical procedure proposed in terms of spacetime/motion coordinates. In my view, in the four cited formulas they mean nothing; as no matterenergy event in spacetime/motion can be found that relates to each computational step. Undoubtedly numerical values are derived as of the equation, but the question is whether they represent what the proponent of the equation determines.
For example, the squares of the terms v and/or c do not exist in spacetime/motion. The vmass cannot attain the square of its velocity. It is impossible to multiply the purported limit maximum speed of a light photon times 2, much less by 299792458 times. The light photon cannot attain the square of its 299792458 k/s velocity.
Further, it is physically and/or chemically impossible to divide v by c, much less divide vsquare by csquare. It is physically and/or chemically impossible to subtract the proportional ratio of v/c from the abstracted unit 1.0, much less to do so with vsquare divided by csquare.
In addition, the square root of the resulting numerical value derived from the previously cited [materially impossible] computations simply has no physical and/or chemical meaning in spacetime/motion events.
To involve the previous impossibly derived numerical computations with the concept of mass at rest [m0] and/or mass in motion [m] has no physical and/or chemical meaning.
If a single term in the equation does not materially exist, if it is in fact immaterial, then the entire equation is nonconsistent, nonexistent as of the terms and relationships being proposed.
In fact, forget about considering the possibility of measuring the mass of a moving form of matterenergy in spacetime, the equation is inconsistent as it proposes the idea of csquare, squaring the proposed limit of the velocity of a light photon [c] [299792458 m/s]. The measured velocity of light in vacuum exists [299792458 m/s]; the square of that material event does not exist in spacetime/motion and merely represents an abstracted idea.
Now, supposedly the terms of mο and m represent two different states/moments of the same mass as expressed in the formula. And, the term v, velocity of a mass, also represents the velocity of that same mass [as term m]. The theoretical idea proposed is to compute the moving mass [as term m]. But, in order to achieve that computation, the formula employs the velocity of a distinct mass from the mass being proposed [ terms m, mο and v]; the distinct mass being that of a light photon [c].
Setting aside for a moment the impossibility of squaring the speed of m [any mass] and the velocity of c [a light photon], there is no material basis in spacetime for dividing velocitym by velocityc, other than to derive a comparison of velocities between two distinct spacetime events.
Further, if it were materially possible to weigh the moving mass of any mass, one would simply need to weigh it. The need for this particular formula arises from the theoretical propositions regarding the supposedly distinct behavior of matterenergy within the selfperceived idea of relativity of matterenergy in spacetime/motion, which is part of the theoretical problem at hand.
The impossibility of measuring exactly the position of mass while in motion is a wellrecognized fact in physics. In fact, the massless state of a photon is defined generally as of its motion. Since the photon is in constant motion, it has no materially recognizable mass, due to its infinite counterreaction to gravity, which is the reason the photon is said to be massless.
In order for the proponent of the mathematical equation/formula to be relevant, several questions in this particular case would require being stated and answered.
Why and how does one measure a moving mass in reality?
Why propose measuring a moving mass by way of a numerical value in comparison to its own rest mass?
Why employ the square root symbol where it appears in the denominator?
Why employ the unit 1.0 as shown in the equation within the square
root expression?
Why divide the velocity of a mass by the velocity of a light photon?
Why square the velocity of a mass?
Why square the velocity of a light photon?
Why divide the square of the velocity of a mass by the square of the
velocity of a light photon?
Why subtract the result from the division of the square of the velocity
of a mass by the square of the velocity of light speed from unit
1.0?
Why derive the square root of the subtraction of the result from the
division of the square of the velocity of a mass by the square of
the velocity of light speed from unit 1.0?
Why divide the result of the square root of the subtraction of the result
from the division of the square of the velocity of a mass by the
square of the velocity of light speed from unit 1.0?
Each particular term of the equation, together with the terms' modifications and use must be explained and reasoned for the formula to make any sense in spacetime/motion. And these explanations must have a material basis regarding the forms of matterenergy in spacetime/motion. The previous questions have no material answer for the cited equation.
From my reading of the literature in physics, it appears that because the cited formula/equation derives a particular numerical value then it is purported to be consistent with the proponent's idea about relativity, meaning then that the formula/equation is correct. Yet, there is no stepbystep explanation of the computational derivations proposed and required in order to derive a numerical value for the equation.
Generally, there is merely a statement of "fact", as though it were a fact that the formula is selfconsistent because that is the way relativity behaves. The general proposition is usually stated as "more mass is required in order for a particular mass to achieve the speed of light".
Yet, with regard to contraction of length, greater speeds means a decrement in length. The same basic formula proposes an increment in mass, but a decrement in length.
The mathematical design of the formula proposed as such derives a relationship of more/less mass in relation to velocities of mass/photon proposed. The initial design of the formula presents that proposition as of the computational steps designed into the formula.
The question remains, however, from the mathematical design of the relationship of more/less mass to less/more velocity whether the theoretical statement is correct from that numerical derivation, or whether the numerical result actually means what the proponents of the formula say it means. Is more/infinite mass required to achieve the speed of light, when the opposite is obvious: the near massless light photon itself achieves the maximum speed known for matterenergy? In spacetime/motion, matterenergy [the light photon] appears to suggest that the less mass, the greater the speeds are possible; and, the more mass [too many examples available], the lesser speeds are present.
There appears to be a trick involved in the presentation of the formula for relativistic length contraction. [Better argue the theme of reciprocals.]
Although the formula for length contraction, L, follows the same design as the other three categories, the term Lο is expressed as reciprocals of the numerical values of the other three formulas.
The formula for length contraction is making the same algebraic and mathematical statement as the three formulas for mass, time and energy:
However, in the case of length contraction, what is actually being stated is:
I would suggest that, in fact, it is impossible to compute the formula as it stands in order to derive the reciprocals of the other data sets. But, this is not what is being stated.
The Formulas for Special Relativity:
Terms in Vacuum and Not in Vacuum
In making such an analysis of different masses [any mass at rest; mass in motion  photon mass], and their distinct velocities [v; vsquare  c; csquare], it is necessary to explain the material relationship of dividing the velocity of a mass in Earth's atmosphere against the photon velocity in a vacuum. For the term v implied in vsquare refers to any mass in a planetary atmosphere that would supposedly achieve the speed of light.
When the theoretical proposal is made that mass at rest needs to acquire infinite mass in order to achieve the speed of light, it appears to be taken for granted that they are referencing any mass in or outside of a vacuum. For example, the term vsquare is not defined as being in vacuo, as the csquare term is so defined.
* Relativistic Mass

= unspecified in vacuum or not
= in vacuum 
It is proposed, supposedly, that the light photon travels throughout space in vacuum, or in a near vacuum, at the speed of light, 299792.458 kms/sec. As far as I can tell from the literature in physics, such computations of light travel, lightyears and such in astrophysics and astronomy are based on that proposed measurement.
The orbital speed of the planet Earth is measured then within the near vacuum of space. For the planet Earth to attain the speed of light, it would have to acquire an infinite amount of mass over and above the huge amount of mass that makes up its planetary composition. In fact, the planet Earth, as all other planets, would have to shed its mass in order to be competitive with a photon's speed. Or, it is not so much that a planetary mass would have to have infinite mass to reach c, but rather it would require an infinite force to propel it to reach c.
To expect or theoretically propose that a planet the size of Earth would require added mass in order to attain light speed simply boggles my mind and misses the point between mass and momentum, force and relativity.
If one proposes a 1:1 relationship between mass and massvelocity, then this may be worked out simply as a ratio of terms to infinity according to physicists.
A theoretical problem exists because there does not appear to be a direct 1:1 relationship between mass  velocity; between the mass and its own velocity. However, the formulas for special relativity appear to suggest implicitly (or explicitly) that a direct relationship exists between mass and speed/velocity. It is obvious that greater/lesser mass affects the speed of a body. It is not evident that velocities near the speed of a light photon affect the internal structure and composition of the mass of that body.
In all cases of matterenergy, in spacetime/motion, the relationship of massvelocity exists in relation to other spacetime/motion coordinates [medium, structure of mass, composition of mass, external factors, etc.].
One of the erroneous underlying propositions in Einstein's formula of relativity is that there is a suggestion of a direct relationship between massvelocity; be this masssubluminal velocity or, massluminal velocity.
Spacetime/motion events have their own speed limits/ranges, which are due to mass composition together with their internal structure of matterenergy, in relation to their spacetime/motion environment [entorno]. For example, you might not attempt to get a fish to swim 100 kms/hour. So, why expect some other kind of selected mass might achieve the velocity of light, of a photon?
A Sailfish, the Fastest fish on Earth: 110 km/hr = 70 mph
"The cheetah of the water".
Both the Cheetah and the Sailfish travel at 70 mph. Theoretically, you would think one might turn into the other at that speed.
Would you expect someone to write a tract as to why a fish cannot swim at 100 kms/hour? Then why entertain the idea that some selected mass might achieve the speed of light of a photon?
Other forms of radiation reach the speed of light in vacuum. But, to entertain why an airplane does not reach light speed, and miss the reason and come up with an irrelevant reason that the airplane would require infinite mass to attain that speed. An airplane cannot travel at the speed of light because it is not a photon, it is not light. Just like a whale cannot fly like a bird or, a bird cannot swim like a whale in the water. Imagine saying that a bird cannot swim like a whale because it would require more mass.
Peregrine Falcon, the fastest bird on earth: 322 km/hr = 200 mph
To offer the reason that special relativity theory offers to state why a body cannot reach light speed if irrelevant. A bodymass cannot reach light speed because, first, it is not massless like a photon, and second, it cannot shed its mass to travel at the speed of light. And, further, it is a body mass that has its own "compositional and structural limits for travel".
Imagine saying that the lamp on my desk could travel at light speed if it had infinite mass. No, the lamp could not travel at the velocity of c even with infinite mass. Stating that a body mass needs infinite mass to reach c velocity offers the false idea that if we learn how to get the lamp to take on infinite mass it might be able to travel at light speed.
The mass of a photon to its own velocity as measured [299792458 m/s] is a specific case, a specific spacetime/motion event, susceptible to variations as of the variations of its surroundings, internal structure, etc.
Ultimately, one is treating the wordconcepts relating to massmotion; massrest (or mass and its absence of motion).
The very wordconcept of "relativity" distorts the concept of motion of matterenergy, more exactly understood as spacetime/motion of matterenergy.
Matterenergy events, spacetime/motion events, are relational; not relative. It is misleading to suggest that spacetime/motion events are relative to their own reference frame, or relative to other reference frames, as though there are distinct rules for different reference frames [relationships of spacetime/motion of matterenergy].
Having heard for so many decades the idea that "everything is relative" is terribly inexact and misleading. It only makes sense if one considers the theory of relativity as a relational theory about the observer to the events analyzed. Different observers have different relationships to the matterenergy events being analyzed an idea that in itself constitutes a redundancy. I say redundancy, because we already know that every spacetime/motion event is exclusive of all other spacetime/motion events (observers of spacetime/motion events being no exception).
Matterenergy in spacetime/motion is relational to the conditions of existence of matterenergy as forms of spacetime/motion. The conditions of existence of given spacetime/motion events do not necessarily undergo any changes or modifications, only the observations in different references do.
Obviously, it is inexact to think of comparisons of matterenergy events in an atmosphere with air resistance as of to matterenergy events in a vacuum. Obviously, these different velocities of different matterenergy events may be theoretically compared, but that knowledge must be stated exactly. It is theoretically without analytical procedure to propose that one may derive from/into the other without consideration of all of the relationships involved in both cases. It is theoretical without analytical procedure to propose the idea that one may possibly go from one state to the other as of a mere mathematical computation of questionably selected and little explained terms.
One may perceive theoretical relevancy to comparing the orbital velocity of planet Earth in vacuo of space with regard to the light photon traveling through that same in vacuo space. Such a comparison may be substantiated theoretically, although practically, I have my doubts as to the reach of such a theoretical proposition.
But, it appears to be highly suspect from the theoretical point of view of consistency to propose analyzing a mass within Earth's atmosphere to the comparative speed of light in vacuo in that same atmosphere.
specifically,
The numerical value employed in the cited formula/equation references the speed of a light photon in vacuo [299792458 m/s]. I have not seen any analytical cases where the numerical value for c is a variation or reduced value as the one generally cited. In other words, the cterm is never proposed to represent the reduced speed of a light photon through the air resistance of Earth's atmosphere.
Mass not in a vacuum [nonc velocity] cannot achieve c velocity; that is a tautology. Velocity is not in a vacuum so from the start the equation is wrongly posed.
Tachyons are hypothetical particles that travel faster than the speed of light.
Whatever that means theoretically.
Hypothetically a lot of things can be imagined to exist.
By definition, the term vmass will always be lower in numerical value than the term cmass, given the a priori proposition that c, the velocity of a light photon, is the maximum known limit of motion of matterenergy as it is supposedly known.
vsquare is always less than or equal to csquare in the equation [v ≤ c]
The proportion/ratio of vsquare/csquare will always be equal to or less than 0.99999999999…n. And, insofar as this less than unitone value will be subtracted from unit 1.0, the result will always be a) a lesser numerical remainder value of said ratio. Further, this lesser numerical remainder value will be expressed as its square root, still b) an even lesser value than the previously derived remainder value. Given the fact that the proportional relationship of vsquare to csquare is always a positive numerical value less than 1.0, its subtraction from unit 1.0 will always derive a positive number. This positive number will derive a positive smaller square root number that may then be divided into a moving mass or, better, multiplied times a mass at rest.
The fact, however, that c, the speed of a light photon in vacuo, is predefined as the maximum speed attainable by matterenergy in spacetime/motion, is presented as of its squared value in the equation is never treated in the "selfconsistent" discourse. It is not consistent to define the term c, for example, as a maximum limit, and then propose its square, which would represent 299,792.458 times its original value expressed in kilometers/second, or 299,792,458 times its original value if expressed in meters/second.
Just imagine if csquare appears to me to represent an impossible matterenergy event, what would it represent to higher powers. See what Einstein offers for longitudinal mass [page 6]:
©2014 Copyrighted. Charles William Johnson. All rights reserved. 