Natural Science Forum / Physics / Relativity / October 2005

Dimensional Analysis and Relativity

    Over the years the writer has received E-mails which strongly assert
that the techniques of Dimensional Analysis ARE OF NO BENEFIT in the study
of relativistic phenomena without any  justification for that strong
statement. Such an assertion can only have be provided by individuals whose
inborn ability to think has been severely repressed by excessive education.
This repression of intelligent thought is characteristic of the process by
which PhD candidates acquire their degrees. They are well taught the
accepted truth at the expense of their ability to question that truth. They
become, in other words, priests of a religion rather than true scientists.

    The fact that the relativistic phenomena involve processes in which the
units of measurement are affected by the processes themselves (e.g.;- The
Lorentz Transformations of Special Relativity and the Time Dilation of
General Relativity) means that an intelligent approach to an understanding
requires a technique which enables one to keep track of these effects in a
logical manner. This technique is well known and goes by the name of
Dimensional Analysis.

    Dimensional Analysis is a technique which recognizes the fact that
every term in a physical equation MUST have the same dimensional content
(i.e.- length, time, force, mass, etc.) if one is not to become involved in
the foolish exercise of equating apples and oranges. It has become readily
apparent over the years that only three dimensional entities are required.
All other dimensional entities can be derived from those three using
accepted physical equations. (This conclusion is based upon over a century
of observation but, like the fact that only four colors are required to
produce a map without color interference at boundaries, has not been
rigorously proven to the writer's knowledge.)

    It is common in the physical sciences to use the dimensional entities
of Mass(M), Length(L) and Time(T) as fundamental (others might be used in
their stead without error). The writer, however, chooses to substitute the
dimensional entity of Force (F) for the dimensional entity of Mass as being
more fundamental. Unlike Force, Length, and Time, Mass is not directly
observable. It can only be observed in terms of the force which results when
velocity is changed or which results when it is in the proximity of another
mass (weighing). The dimensional content of various physical quantities are
provided below:

    Dimensional
Quantity   Symbol Content

Force  (F)   F F
Length (L)   L L
Time   (T)   T T
Energy    E F*L
Charge    Q L
Momentum   U F*T
Angular Momentum  J F*L*T
Planck's Constant  H F*L*T
Velocity   V L/T
Acceleration   A L/T^2
Mass    M F*T^2/L
Incremental Mass  Mi F*T^2/L
  (This is the mass observed during an incremental velocity change.
Gravitational Constant  G L^4/(F*T^4)
Ergo-gravitational Constant D 1/F
  (This term is identical to Dr. Einstein's Cosmological Constant)
Temperature   t' F*L
Dielectric Constant of Space e' F
Permeability of Space  u' F*T^2/L^2

    The relativistic transformations for these quantities are readily
apparent:

  Parallel Transverse
Quantity  Velocity Velocity Gravity

Force   1  Bv  1
Length   1/Bv  1  1/Bg
Time   Bv  Bv  Bg
Energy   1/Bv  Bv  1/Bg
Charge   1/Bv  Bv  1/Bg
Momentum  Bv  Bv^2  Bg^3
Angular Momentum 1  Bv^2  1
Planck's Constant 1  Bv^2  1
Velocity  1/Bv^2  1/Bv  1/Bg^2
Acceleration  Bv^3  1/Bg^2  1/Bg^3
Mass   Bv^3  Bv^3  Bg^3
Incremental Mass Bv^3  Bv^3  Bg^3
Gravitational Constant 1/BV^8  1/Bv^5  1/Bg^8
Ergo-Gravitational
  Constant  1  1/Bv  1
Temperature  1/Bv  Bv  1/Bg
Dielectric Constant 1  1/Bv  1
Permeability  Bv^2  1/Bv^3  Bg^4

Bv = (1-V^2/C^2)^0.5; Bg = Actual Radius/Horizon Radius;
Velocity Transformations modified by (1-Va*Vb/C^2) in denominator.

Note:- The Lorentz Transformation for Transverse Force is the reciprocal of
that given in texts. The conventionally accepted expression is in error
because of the foolish use of Maxwell's Equations in its derivation.

    Applying these transformations to the relativistic phenomena provides
results which are consistent with ALL observations and allows the Universe
to be explained from before and through the big bang and its eventual
expansion to an infinite radius. It does this in terms of 3 dimensional
Euclidean space and is consistent with the ABSOLUTE validity of the Law of
Conservation of Energy. Most important, it is consistent with Quantum Theory
and does not require the hare-brained ideas associated with Superstring
Theory.

    The source material for this posting may be found in
http://einsteinhoax/hoax.htm ("The Einstein Hoax" {1997});
http://einsteinhoax/gravity.htm; ("Gravity" {1987}); and
http://einsteinhoax/relcor.htm ("Corrections to Special Relativity" {1997}).
EVERYTHING WHICH WE ACCEPT AS TRUE MUST BE CONSISTENT WITH EVERYTHING ELSE
WE HAVE ACCEPTED AS TRUE, IT MUST BE CONSISTENT WITH ALL OBSERVATIONS, AND
IT MUST BE MATHEMATICALLY VIABLE. PRESENT TEACHINGS DO NOT ALWAYS MEET THIS
REQUIREMENT. THE WORLD IS ENTITLED TO A HIGHER STANDARD OF WORKMANSHIP FROM
THOSE IT HAS GRANTED WORLD CLASS STATUS.

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    E-mail:- einsteinhoax@isp.com

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