Following
previous studies on the nature of the forces in physics within the
universe, a pattern of mathematical unity between complimentary
quantities has become apparent.This becomes most apparent when energy
and its fields are expressed in space-time (S-T) units of measure as
outlined in a previous paper entitled 'Theoria Omnia – A work in
Progress'.
An
analysis, initially aimed at a more comprehensive understanding of
inertia in an earlier paper, has carried past those mathematical
conclusions to suggest a wider application of the results therein.
The following is a summary of the case of unity between acceleration,
a, and inertia, ί.
Inertia and
Acceleration
“There
does not appear to be any meaningful quantification of inertia in the
current or past physics literature, however inertia is easily
quantified from Newton's Laws. The relationship between acceleration
caused by gravity or any acceleration, a,
and inertia can be quantified mathematically from Newton's Second Law
of Motion, F = ma, in combination with the Equivalence Principle,
which establishes an invariable mathematical product between the two,
given that different masses accelerate at the same rate in the same
gravity field. Let the Greek lower case letter iota,
ί,
be assigned to inertia for algebraic purposes and avoid confusion
with other quantities using I or i .
From
F = ma, a = F/m from which SI units a
evidently has units Newtons per Kilogram, (N/kg in addition to the
more commonly used m/sec2)
. From the Equivalence Principle, a
is proportional to ί
,
and that proportionality is apparently a simple reciprocal
relationship a
= 1/ί
and ί
= 1/a
. ί
has the units kg / N. The following examples demonstrate the above
relationship:
if
a mass of 20 kg has an acceleration of a
=
10 N/kg, from F = ma, the force is 200 N. As a = F/m, the inertia
ί
= m/F = 20/200 = 0.1 kg/N. a
x ί = 1
if
a mass of 15 kg has an acceleration of a
=
1 N/kg, force is 15 N and the inertia ί
= m/F = 15/15 = 1 kg/N.
a x ί = 1
if
a mass
of 40 kg has an acceleration of a
=
0.1 N/kg, the force is 4 N and the inertia, ί
= m/F = 40/4 = 10 kg/N.
a
x ί = 1
The
lower the acceleration the higher the inertia and vice versa. The
force per unit mass determines the acceleration, and the mass per
unit force determines the inertia.
Regardless
of mass, a ί
= 1, which is why different masses accelerate at the same rate in the
same gravitational field.
Scientific experiment has so far never been able to disprove the
Equivalence Principle.”
The
General Equation for the Equivalence Principle
of
acceleration and inertia is a
ί
= 1
The
above analysis of the alternative unit of measure for acceleration
from a = F/m, newtons per kilogram, opens the way for the expression
of Newtonian physics equations in a different form:
Newtonian
Equations expressed using Acceleration units as N/kg instead of m/s2
“An
alternative unit of measure for acceleration also offers another set
of Newtonian equations. They represent an alternative approach to
calculating quantities seen in Newtonian physics.
For
example, given the alternative measures for acceleration N
kg
-1
= ms-2,
then s-2
= N kg-1
m-1,
therefore s2
= kg m N
-1
and s = √
(kg.m / N) which in English says that time equals the square root of
(mass times length divided by force).
Symbols
used are F = force, m = mass, a = acceleration, ί (iota) = inertia,
t = time, v = velocity, r = length, M = momentum, n = dimension
number, c = the speed of light, g = gravity field, E = mass-energy
and k denotes a constant. Symbols in SI units are force (N) newtons,
mass (kg) kilograms, time (s) seconds, length (m) metres. Symbols in
S-T units are s = space, t = time.
Quantity
Equation
SI
Unit
Space-Time
Unit
(derived
from these equations)
Time
t
= √
( m r / F )
( kg m / N )½
t
Acceleration
a = F / m
( N / kg) s/t2
Velocity
v
= Ft /m
( N s / kg) s/t
Length
r
= Ft 2
/ m
( N s2
/ kg) s
Mass
m
= F t 2
/ r
( N s2
/ m ) t3/s3
Force
F
= m r / t 2
( kg m / s2
) t/s2
Momentum
M
= F 2
t 3
/ m r
( N2
s3
/ kg m ) t2/s2
Energy
E
= k m v2
( kg m s-1)
t/s
Space-Time
Units show complete consistency in these modified Newtonian
Equations, indicating that both the standard and modified Newtonian
Equations and the Space-Time Units are correct and consistent, as
predicted. It
also verifies that the space-time unit for mass, t 3/s
3
is correct.
This
is key evidence supporting the interpretation of Mass and Gravity by
Theoria Omnia and this paper.”
Derivation
of Space-Time Units and Unity
The
derivation of S-T units from SI units is self evident with a little
thought, for example: Velocity equals distance divided by time which
is expressed as s
(space in one dimension) divided by time t,
or s/t. Pressure is force divided by area, t/s2
x 1/s2
= t/s4.
Similarly acceleration is s
divided
by t
divided by
t
=
s/t2.
Acceleration can also be expressed as N/kg which in S-T units is
force, t/s2
divided by mass t3/s3
or t/s2
x s3/t3
= s/t2
which is the same S-T result as the S-T units yield for m/s2.
All
SI units consistently yield equivalent S-T unit results, indicating
that S-T units are both fundamental and verifiable.
From
the above table of physical entities and their SI and S-T units, the
mathematical reciprocal of energy (t/s), is, in the mechanical
system, velocity s/t. In the electric system, charge is also t/s and
its reciprocal is current, or electric field, s/t. This indicates that
in the mechanical system energy's field is velocity and in the
electric system electric charge's field is the electric field.
From
the S-T units it can be seen that the
product of energy and its field is unity.
It
can also be seen that momentum t2/s2,
is a two freedom analogue of energy, t/s. Magnetic charge also has
the S-T unit t2/s2,
and is the two freedom analogue of electric charge, and its
reciprocal is the magnetic field s2/t2.
The
product of these is also unity.
Mass,
t3/s3,
is the three freedom analogue of energy and its field is the
gravitational field s3/t3.
The
product of these is also unity.
The
unity result does explain why it seems impossible to extract
additional energy from electric, magnetic and gravity fields.
The
Relationship between the Electric, Magnetic and Gravity Fields
To
clarify what is meant by 'freedom', electric charge acts as a scalar
motion
attached to a particle along one axis of 3D space, magnetic charge
along two axes, and mass charge along three axes of 3D space. In a
mechanical system analogy, they equate to a line, an area and a
volume. The axes do not denote a position in space, but a relative
direction with respect to the other axes. It describes three scalar
motions acting at right angles to the others, which accounts for the
behaviour of an electric motor or generator, where the mass field
(motion) ┴
magnetic field ┴
electric field (current).
The dynamo uses motion to produce current and the motor uses current
to produce motion.
The
difference in energy between the degrees of freedom were calculated
by Einstein as mc, that is, mass to magnetic = mc, magnetic to
electric = mc, and mass to electric = mc2,
which, from the foregoing, equates to mass to energy = mc2,
or E = mc2.
Conversely, the respective fields are represented by a difference in
field intensity (per unit volume), the electric, E-field = 1/mc2
, the magnetic B-field = 1/mc and the gravity g-field = 1/m,
verifiable by their S-T units. These equations indicate the energy (=
1/field) of the E-field exceeds the B-field which exceeds g-field per
unit volume, which is indeed the case in our part of the cosmos. The
corresponding volume of effect of these three fields is highest in
the case of the g-field, followed by the B-field, then the E-field at
the same time as their effective energy intensity per unit volume
decreases. Again, the recipricosity between energy and field is
apparent in the mathematics and the physics. For example mass has the
highest energy (=mc2)
and the weakest field per unit volume with the largest volume of
effect, which is consistent with the mathematics of energy and its
field.
The
hypothesis that the above mentioned scalar motions which define
electric charge, magnetic charge and mass charge, is supported by the
operation of the dynamo and electric motor, the physics of which have
no comprehensive explanation in mainstream physics texts to date. If
an electric charge (scalar motion) in one degree of freedom were
aligned to oppose or negate one degree of the three freedoms of mass
charge scalar motion, the result would be a two freedom magnetic
charge perpendicular to the negated degree of freedom. This is the
case in the dynamo and motor. The matter which carries (i) electric
charge is the copper conductor, (ii) magnetic charge is the iron of
the stator and rotor and (iii) mass charge is carried by most matter
and manifests as the motion
of the rotor relative to the first two. The machine correctly aligns
all 3 degrees of freedom to produce the desired result, electric
charge (dynamo) or motion (motor). It is magnetism which enables the
link between electric energy and mass energy while conserving energy
input and output in that machine. The other known link between mass
and energy, nuclear fission, does not conserve the energy in the same
way and releases it to raise the entropy (disorder) of the system.
The
physics of the dynamo/electric motor above imply that motion of
electric charge (current) is the cause of the electric field, which
is in fact a potential which can move a point charge within it.
Similarly, the motion of mass charge is the cause of the gravity
field which can move a mass within it. So if mass is moving through
space relative to a given reference it creates a gravity field when
observed from that reference point. That same gravity field can cause
acceleration of another mass which is within the field, thereby
creating a secondary gravity field. If the given reference were
considered the centre of the Milky Way galaxy it can be seen why the
Sun's gravity field and the Earth's gravity field are different yet
at the same time contribute to the acceleration effect upon other
planets of the solar system. They are also a part of the sum gravity
field which belongs to the galaxy. Theoretically, one could start at
the galaxy level and using the same logic, drill down to the particle
level if the galaxy gravity field were to be analysed in detail. In
the other direction, the macroscopic view which includes all of the
galaxies would suggest that they are all in motion relative to each
other and thus have a gravitational field generated by that relative
motion. This accords with current theories of the motion of mass
charge (which is carried by most particles of matter except neutrinos
as far as we know) within the universe.
The
summed effect of the gravity field caused by mass charge in relative
motion would be simple compared to its constituent parts. The
magnitude of the mass charge and of the motion would possibly be an
analogue of that of the electric field strength and the magnitude of
the charge within it, that is, the larger the current causing the
field and the higher the point charge within it would determine the
acceleration of that point charge, which in turn creates its own
electric field by its motion. Additional complexity is added when a
charged paricle exhibits circular motion, thereby creating a magnetic
field and further electric induction effects.
It
would seem from the above that most matter is affected and
significantly connected by one or more of the three fields discussed.
The gravity field is wider in its distribution because its energy,
mass charge, is carried by most of the known fundamental particles in
the universe, whereas it is mostly the electron which carries
electric charge and photons which carry magnetic charge as far as we
know. (Photons carry momentum, which has the same S-T unit as
magnetic charge, t2/s2.)
These observations make clear why, in S-T units, acceleration is not
the same S-T unit as any of the fields.
A
common misconception is that gravity and acceleration are the same
thing, and that mass and matter are the same thing.
Similarly, it is not an electron which travels through a conductor,
but it is the scalar motion called 'charge' which does. That charge
can be observed when held on the atoms of synthetic clothing, for
example, where it is called a static charge.
S-T
units make these errors easy to detect and correct. In all
probability matter does not create the gravity field, it is mass
charge in motion which creates it. The magnitude of both mass charge
and motion affect gravity field strength. This is consistent with
the lower analogues of electricity and magnetism and consistent with
observation, the electric dynamo and motor being a good
demonstration.
Effects in
the Cosmos
S-T
units provide an insight into energies by relating the degrees of
freedom of their energies to their spatial equivalent (Refer to Table
1 and Appendix 2 in 'Theoria Omnia' for a full list of S-T units for
known quantities.) All of these are verifiable from their SI unit
equivalent.
For
example Electrical energy t/s acts in one spatial dimension, t/s
divided by s = t/s x 1/s = t/s2
which is the S-T unit for force.
Magnetic
energy acts in two spatial dimensions, t/s x t/s divided by area s2
= t/s x t/s x 1/s2
= t2/s4
which is the S-T unit for magnetic field intensity.
Gravitational
energy acts in three spatial dimensions, t/s x t/s x t/s divided by
volume s3
= t/s x t/s x t/s x 1/s3
= t3/s6
which is an unknown S-T unit.
The
above S-T units for the three phenomena have in common a product
difference between the successive degrees of freedom of t/s2
which is the S-T unit for Force.
This suggests that the multiplication of an energy of a lower degree
of freedom by force results in the next higher energy. For example
electric energy times force yields magnetic energy, and magnetic
energy multiplied by force yields gravitational energy.
Force can be expressed as Mass x Acceleration (motion).
This is consistent with the foregoing discussion of both charge and
motion together creating a field.
The
puzzle of the areas of the cosmos (observed from Earth) which appear
to have a high gravity field intensity without the commensurate
volume of matter has led to the hypothesis called 'Dark Matter' as an
explanation. This hypothesis possibly arises from the misconception
that matter is the source of the gravity field. If Mass
times Motion
is the source of the gravity field then there is no inconsistency,
keeping in mind that the relativity of the observer applies when the
observation is made.
For
example, a cluster of stars in a galaxy spiral arm on the opposite
side of the galaxy would have a higher relative motion than a similar
cluster on the same side and arm of the galaxy as the observer, with
a correspondingly higher apparent gravity field. If only the amount
of mass were considered, the strength of its gravity field would
appear inconsistently high, and lead to an assumption of additional
(invisible) mass.
This
explanation of Dark Matter is consistent with General Relativity
Theory. The only concept which is different from current thought is
the hypothesis regarding the source of the gravity field. This
hypothesis is supported by observation of the spatially related
fields of electricity and magnetism and the mathematical
relationships between them.
