Re: "Dimensional Analysis and Relativity"
- From: "Vert" <avergon@xxxxxxxxxxx>
- Date: 27 Mar 2006 12:34:42 -0800
Dimensional Analysis is a technique which recognizes the fact that
every term in a physical equation MUST have the same dimensional
(i.e.- length, time, force, mass, etc.) if one is not to become
the foolish exercise of equating apples and oranges. It has become
apparent over the years that only three dimensional entities are
All other dimensional entities can be derived from those three using
accepted physical equations. (This conclusion is based upon over a
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
of Mass(M), Length(L) and Time(T) as fundamental (others might be used
their stead without error). The writer, however, chooses to substitute
dimensional entity of Force (F) for the dimensional entity of Mass as
more fundamental. Unlike Force, Length, and Time, Mass is not directly
observable. It can only be observed in terms of the force which results
velocity is changed or which results when it is in the proximity of
mass (weighing). The dimensional content of various physical quantities
Dimensional Entity Dimensional Content
Force (F) F
Length (L) L
Time (T) T
Energy (E) FL
Charge (Q) FL
Momentum (U) FT
Angular Momentum (J) FLT
Planck's Constant (H) FLT
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 (e') F
Permeability (u') F*T^2/L^2
The relativistic transformations for these quantities are readily
It's encouraging to see some intelligent discourse on this NG. I had a
professor who used to say, "What do you get when you send a bonehead to
college?" (Answer) "An edcated bonehead. This NG abounds with them.
I agree with what you say but would like to point out that there are
many roads to Rome.
In my own work I use the following:
m = mass
a = acceleration
d = distance or length
t = time
d/t^2 = acceleration
at, d/t = velocity
ma = force
mad = energy
mat = momentum
madt = Planck's constant -- which may be read as energy times time or
momentum times distance.
Momentum times distance has come handy in my theory (entitled On the
Quantum as a Physical entity).
You may be interested in my concept of dimensional analysis: (This is
from my theory also.)
The objective universe consists of matter, the space between matter and
the motion of matter through that space. That and nothing more. The
rest are concepts in the mind of man.
Man perceives matter, to quantify it he conceptualizes "mass".
Matter exists objectively, mass is a concept.
Matter resists motion or alteration of motion. Man perceives that as
"inertia" which in turn quantifies mass.
Matter moves with varying degrees of motion. Man compares all motion to
one used as a standard which is constant. This standard motion is
divided into arbitrary units. The transit of the standard through one
unit is designated as time. (The rotation of the earth is a standard
motion. One rotation is designated as a day [time] with arbitrary
subdivisions.) All other motions are then compared to a unit of time.
Thus, at base, time is the comparison of motions, nothing more.
The quantification of motion in terms of time is conceptualized as
"velocity". Ultimately this is a comparison of motions against the
The quantification of the motion of matter in terms of mass and
is conceptualized as "momentum", i.e., there is a simultaneous
determination of the quantity of matter and the quantity of motion it
Matter moves and changes that motion by interaction. Man perceives
the rate of change as "force", i.e., the change of momentum with
respect to time. Collaterally he perceives "acceleration" as the change
of velocity with respect to time.
Matter interacts with matter forming an altered configuration.
Man regards that as "energy", ultimately energy is matter (mass) in
There is space between matter. Man perceives that and quantifies it by
arbitrary standards of matter. Thus is created the concepts of
"dimension" and "distance".
So we see that dimension, space, time, mass, inertia, momentum,
acceleration, force, and energy are all subjective interpretations by
man of matter and its motion through space.
If you would care to look at the entire theory go to
http://www.wbabin.net (The General Science Journal).
find the "List of Authors" pull down and click on Vertner
- "Dimensional Analysis and Relativity"
- From: Tse
- "Dimensional Analysis and Relativity"