Money and Math

            The relativistic formulas for mass increase and length contraction are two aspects that supposedly occur together in the observation of a relativistic event. Notice the math procedures: division and multiplication.

Mass Increase:
mass in motion = mass at rest divided by γ
m  = m ο / γ
Length Contraction:
length in motion = length at rest times γ
L = Lο (γ)
            Let us assign the numerical value of $1.00 to mο (and to Lο ), and $9.00 to γ. We do not assign any numerical value to m or L because these are the unknown quantities according to the mathematical formulas that we want to know.
What can you do with one and nine dollars mathematically? The question arises, then, what can be done with $1.00 and $9.00 in reality (as existing matter-energy events in spacetime/motion). You only have $1.00 and your friend has $9.00 (or vice versa, whichever).
            Which of the following mathematical equations/transactions are possible with the total money that you and your friend have?

$1.00 | $9.00  = m, L

Addition:
$1.00 + $9.00 = $10.00                                 =          possible total $10.00
                                                                                   Exists potentially
Subtraction:
$1.00 - $9.00 = $8.00                                    =         possible difference of $8.00
                                                                                  Exists potentially
Multiplication:
$1.00 x $9.00 = $90.00                                 =       impossible to produce $90.00
                                                                                  you both only have $10.00
                                                                                  Non-existent
Division:
$1.00 / $9.00 = 0.111111111111  times =    abstracted number, [times]
Non-existent
$9.00 / $1.00  = 9 times                           =    abstracted number, [times]
                                                                      Non-existent

Now, meanings can be rearranged. Division can be inverted by the number of times represented by the amounts of money.

Division:
$1.00 / 9 times = 0.11111111111 cents in nine parts
$9.00 / 0.111111111111 times  = 8.1000000081 dollars in one part as a
                                                                      percentage of nine
                                                                      and so on, infinitely so.

            In other words, the $1.00 and the $9.00 can be divided by the number of times/parts one may choose, from infinitely low to infinitely high. But, the results from those divisions/denominators have nothing to do with dollar amounts, but rather abstracted numbers of mathematical divisions made in the procedure. The 9 times and the 0.1111111111 are abstracted numbers, not dollar amounts.
            In the theory of special relativity and the formulas to derive numerical values for m, t, L, E, γ, two different mathematical procedures are proposed for use: division and multiplication. In terms of our money example, these would be:
Multiplication:
$1.00 x $9.00 = $90.00                                 =          impossible to produce $90.00
                                                                                  you both only have $10.00
                                                                                  Non-existent
Division:
$1.00 / $9.00 = 0.1111111111111 times   =  abstracted number, not money
                                                                                  Non-existent 

$9.00 / $1.00 = 9 times                                       = abstracted number, not money
                                                                                  Non-existent

            In other words, the mathematical procedures chosen to derive numerical values for the terms of the formulas correspond to abstracted mathematical procedures that do not exist in terms of our money examples.
            In order for our money example of $90.00 to exist, we know that some other conditions and circumstances would have to change in order to be able to obtain $90.00, given that our funds only add up to $10.00. With regard to money, we would know how to derive $90.00 from the economic reality around us. For example, we would have to have eight more pairs of people who have $10.00 between them; or any other combination of $80.00 dollars to add to our $10.00.          
            And, by dividing mο or Lο ($1.00) by g ($9.00) or inversely, we know that we are simply deriving a multiplicand (0.1111111111 and/or 9) for these numbers. We are not actually deriving a numerical value for L or M [dollars and cents]as per the level of the numerical values for mο or Lο.   
            Now, remember the mathematical procedures and their terms must relate to actual matter-energy events that exist for them to be taken into consideration as methods for deriving those matter-energy event relationships in spacetime/motion.
            Let us consider now the examples with an automobile and their related speeds.
            Remember, the physicists state that L, length contraction, occurs at all levels of spacetime/motion for all forms of matter-energy. They state that the fact of length contraction occurs with an automobile and its variable speeds, only that we as observers cannot notice the changes in perceived length of the automobile.
            Substituting the examples of mathematical procedures given above in dollars and cents, now look at these procedures regarding a car and its speeds. It must be emphasized again: even though the formulas for special relativity say "mass increase" and "length contraction" they actually mean to say "perceived mass increase" and "perceived length contraction", meaning a perception by the observer of the cited mass|length event.
Mass Increase:
mass in motion = mass at rest divided by γ
m  = mο / γ 
Car Mass Increase:
car mass in motion = car mass at rest divided by γ
carm  = carο / γ 
Length Contraction:
length in motion = length at rest times γ
L = Lο (γ)
Car Length Contraction:
car length in motion = car length at rest times γ
carL = carLο (γ)
            Car = mass | Perceived car measurement length = L

Now, which of the following mathematical equations are possible with the car and its speed? [Car mass may be proposed either with or without drive/passengers which would affect the numerical value of its so-called mass at certain speeds. One could propose a remotely controlled car without passengers. The possibilities are infinite. In any case, car mass and car speeds are variable terms to be defined for each mathematical procedure/equation proposed.]
Addition:
Car mass + car speed = total              =          immaterial total
[kilograms] + [kilometers]                  =          Invalid math procedure
                                                                                  Non-existent
Subtraction:
Car mass - car speed = difference     =          immaterial difference
[kilograms] - [kilometers]                              Invalid math procedure
                                                                                  Non-existent
Multiplication:
Car mass x car speed = momentum   =          Possible physical concept
                                                                                  [mass times velocity]
                                                                                  Abstracted theory/concept
Division:
Car mass / car speed =  No concept   =          immaterial procedure
[kilograms] / [kilometers]                               [mass divided by velocity]
Car speed / car mass = No concept    =          immaterial procedure
[kilograms] / [kilometers]                               [velocity divided by mass]
In other words:
Division:
Car mass at rest / Car speed = Car in motion   =  abstracted number, [times]
                                                                                 Non-existent
Car speed / Car mass at rest  = Car in motion    = abstracted number, [times]
                                                                                 Non-existent
Now, the relativistic physicists wish to assign theoretical substance to these math procedures.

Division:
Car mass / car speed =  Relativity     =          Proposed physical concept
[kilograms] / [kilometers]                               Perceived Special relativity   
                                                                       Observational phenomenon
                                                                       Not physical in spacetime
Car speed / car mass = Relativity      =          Proposed physical concept
[kilograms] / [kilometers]                               Perceived Special relativity
                                                                       Observational phenomenon
                                                                        Not physical in spacetime

            In other words, the Car mass and the Car speed can be divided by the number of times/parts one may choose, from infinitely low to infinitely high. But, the results from those divisions/denominators have nothing to do with physical quantities/events, but rather the abstracted numbers of mathematical divisions made in the procedure.
            A practical suggestion to the theory of special relativity physicists would be that they need to teach the relativistic formulas at all levels of spacetime/motion for all forms of matter-energy. That would be a logical conclusion to this analysis if the theory of special relativity were true. However, there are many other observations and questions required to determine its veracity or irrelevance to spacetime.
            By employing division and multiplication procedures for the same terms [Lο and γ] two distinct values are derived for L [length in motion/contraction]. Following numbers chosen are possible arbitrary examples; may be substituted for any non-zero number.
Car Mass Increase:
car mass in motion = car mass at rest divided by γ
carm  = carο / γ 
carm = 1000 kilos / 100 kms/hr
carm in motion  = 10 times greater than carο at rest
Length Contraction:
length in motion = length at rest times γ
carL  = carLο(γ)  =  10 meters x  100 kms/hr
carL  length = 0.10 times less than carLο at rest

            The ideas expressed in the results [10 times greater than carο at rest; 0.10 times less than carLο at rest] come from knowing the theoretical theses proposed as outcomes of the equations as stated by the proponents of these special relativity formulas. They do not derive directly from the numbers or mathematical procedure themselves.
            In both cases, the terms of carm  = carL may have two distinct answers depending upon the mathematical procedures used.

Car Mass Increase:
Carm  = Carο divided by γ 
Carm  = Carο multiplied by γ
1000 kilos divided by 100 kms/hr = 10
1000 multiplied by 100 kms/hr  = 100,000
Carm may be 10 and/or 100,000 depending upon the mathematical procedure chosen for the analysis.
The relativistic physicists have chosen 1000 kilos divided by 100 kms/hr = 10 for the formula mass increase.
Car at rest mass, Carο, is 1000 kilos and its speed is 100 kms/hr, γ, then that car in motion term, Carm, may be 10 or 100,000 numerical value ---depending upon the selected  mathematical procedure.
Length Contraction:
CarL  = Carο divided by γ 
CarL  = Carο multiplied γ
10 meters divided by 100 kms/hr = 0.10
10 meters multiplied by 100 kms/hr = 1000
CarL may be 0.10 and/or 1000 depending upon the mathematical procedure chosen for the analysis.
The relativistic physicists have chosen 10 meters multiplied by 100 kms/hr = 1000 for the formula length contraction.
Car length at rest mass, CarLο, is 10 meters and its speed is 100 kms/hr, γ, then that car in motion term, CarL, may be 0.10 or 1000 numerical value ---depending upon the selected  mathematical procedure.
Car Mass Increase:
Carm  = Carο divided by γ  = chosen by relativistic physicists
                                                                                  for mass increase formula
Carm  = Carο multiplied by γ

Length Contraction:
CarL  = Carο divided by γ 
CarL  = Carο multiplied. γ    =          chosen by relativistic physicists
                                                                       for length contraction form

            The reason why the distinct formulas have been chosen in this manner obeys the "theoretical" need to present numerical values for "mass increase", and low numerical values for "length contraction" according to the theses proposed.
Note, when Carmο is given as unit 1.0, then Carm may be 10 or 100,000 depending on the mathematical procedure chosen for the computation.
Note, when CarLο is given as unit 1.0, then CarL may be 0.1 or 1000.0 depending on the mathematical procedure chosen for the computation.
            Choosing one possible mathematical answer over another to create a fixed mathematical formula depends upon the thesis chosen for the analysis; whether one wishes to have an incremental value or a decremental value. In either case, the choices are arbitrary as the math is available in either case, either incremental or decremental values for the same term.
Carm may be equal to 10 or 100,000
CarL may be equal to 0.1 or 1000
            However, if one chooses Carmο and CarLο to be represented as Unit 1.0 for the equation, then only one answer is correct for each mathematical procedure:
            There is no given mathematical law in spacetime/motion for these "observed" matter-energy events per the definitions of special relativity. All cited terms and mathematical procedures are variables within the theory of special relativity and may be manipulated accordingly in order to derive the desired results for each case stipulated by the proponents of the particular theses.
            The terms being referenced in the theory of special relativity are all variables. There is variable mass (at rest and in motion as defined by proponents). There are variable speeds (0 to defined limit c; γ and c). And, there are variable mathematical procedures (addition, subtraction, multiplication, division; some possible to execute in matter-energy events and some impossible to execute other than as theoretically abstracted numbers).
Length Contraction:
L (length in motion) = Lο  (10, length at rest)  times γ (11, motion term)
L = Lο /(γ)       = 10 divided by 11      =          0.9090909090 (example)
L = Lο (γ)        =  11 times 10                         =          1.1 (example)

L (length contraction) will have two distinct values as shown in the previous example in relation to the mathematical procedure of division or multiplication, where the other two terms of the equation remain the same. And, this is not to speak about the two distinct answers derived in relation to the square-root procedure in the motion term (γ).
            To propose the idea that length contraction obeys the multiplication procedures as shown is erroneous, for actually according to the same terms and different math, the selected relationship is higher than the one derived from division.

            Mass Increase:
m (mass in motion) = mο  (10, mass at rest)  times γ (11, motion term)

m = mο /(γ)      = 10 divided by 11      =          0.9090909090 (example)
m = mο (γ)       =  11 times 10                         =          1.1 (example)
The physicists choose the following alternatives for their formulas for mass increase and length contraction respectively:
            Mass Increase:
m (mass in motion) = mο  (10, mass at rest)  times γ (11, motion term)
m = mο /(γ)      = 10 divided by 11      =          0.9090909090 (example)
Length Contraction:
L (length in motion) = Lο  (10, length at rest)  times γ (11, motion term)
L = Lο (γ)        =  11 times 10                         =          1.1 (example)

            In this manner, mass increase and length contraction end up representing reciprocals of their respective data sets as shall be shown below. The two choices are logical according to math procedures, as one derives higher numbers and the other derives lesser numbers.
Special Relativity Theory does not propose to add car mass and its speed, nor to subtract them from one another. They propose to divide and to multiply them times one another.

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