Correcting
some Fundamentals in Physics.
The Case for Space-Time Units of Measure
Michael J. Bull 2018
With reference to published work by D.B.Larson
Abstract:
This Paper examines the validity of Space-Time (S-T) units of
measure. It uses them to identify errors in current Physics, often
induced by the misunderstandings caused by SI units of measure. SI
units do not always make clear the dimensions of the physical
quantities they represent. The conclusions validate this author's
interpretation of mass and gravity which have already been supported
by experimental evidence as outlined in the Paper 'Mass and Gravity'.
(Refer to the author's website https://michaelbull.academia.edu
for further details.)
Contents
Scalar Motion
The
existence of scalar motion has now been widely accepted within
Physics, and it is appropriate to examine the consequences of its
existence. Some of the most significant consequences are related to
the dimensions of this previously unrecognised type of motion. The
word 'dimension' is used in several different senses, but in the
sense in which it is applied to space it signifies the number of
independent magnitudes that are required for a complete definition of
a spatial quantity.
It
is generally conceded that space is three-dimensional. Thus three
independent magnitudes are required for a complete definition of a
quantity of space. Throughout the early years of science this was
taken as an indication that the universe is three-dimensional.
Currently, one of the favoured hypotheses is that of a
four-dimensional universe, in which the three dimensions of space are
joined to one dimension of time. In other hypotheses there are four
dimensions of space, a conceptual image of which is barely within our
mental capability.
There
does not appear to have been much critical examination of the
question as to the number of dimensions of motion that are possible.
Most of the scientific community has simply taken it for granted that
the limits applicable to motion coincide with those of the spatial
reference system. On reviewing this situation it can be seen that
this assumption is incorrect.
The
relation of any one of the three space dimensions to a quantity of
time constitutes a scalar motion. Thus three dimensions of scalar
motion are possible. But only one dimension of
motion can be accommodated within the conventional spatial reference
system. The result of any motion within this
reference system can be represented by a vector (a one-dimensional
expression), and the resultant of any number of such motions can be
represented by the vector sum (likewise one-dimensional). Any motions
that exist in the other two dimensions cannot be represented.
This
is a shortcoming of the reference system. In
examining the nature of scalar motion it can be seen that this type
of motion cannot be represented in the reference system in its true
character.
The
magnitude and direction attributed to such a motion in the context of
the reference system are not specifically defined, but are wholly
dependent on the size and position of the object whose location
constitutes the reference point. Now it is found that there are
motions which cannot be represented in the reference system in any
manner. It is therefore evident that the system of spatial
coordinates that is used in conjunction with a clock as a system of
reference for physical activity give a severely limited, and in some
respects inaccurate, view of physical reality. In order to get the
true picture one needs to examine the whole range of physical
activity, not merely that portion of the whole that the reference
system is capable of representing.
Gravity
and Mass
For
example, gravity has been identified as a scalar motion, and there is
no evidence that it is subject to any kind of a dimensional
limitation other than that applying to scalar motion in general. It
must therefore be concluded that gravity can act in three dimensions.
Furthermore, it can be seen that gravity must act in all of the
dimensions in which it can act. This is a necessary consequence of
the relation between gravity and mass. The magnitude of the
gravitational force exerted by a material particle or aggregate (a
measure of its gravitational motion) is determined by its mass. Thus
mass, m, is a measure of the inherent scalar motion content of the
matter. It follows that motion of any mass is a scalar motion. To
produce such a compound motion, a positive scalar motion v (measured
as speed or velocity) must be applied to the mass. The resultant is
“mv,” now called momentum, but known earlier as “quantity of
motion,” a term that more clearly expresses the nature of the
quantity.
In
the context of a spatial reference system, the applied motion v has a
direction, and is thus a vector quantity, but the direction is
imparted by the coupling to the reference system and is not an
inherent property of the motion itself. This motion therefore retains
its scalar status irrespective of the vector direction.
In
the compound motion mv, the (negative) gravitational motion acts as
a resistance to the (positive) motion v. The gravitational motion
must take place in all three of the available dimensions, as any one
of the three may be parallel to the dimension of the reference
system, and there would be no effective resistance in any vacant
dimension.
Gravitational motion may therefore be identified as
three-dimensional speed, which can be expressed as s3/t3,
(s/t) x (s/t) x (s/t), where s and t are space (length) and time
respectively.
The
mass (the
resistance that this negative gravitational motion offers to the
applied positive motion) is then the
inverse of this quantity, or t3/s3.
(The
SI equations for mass, m = F/a and
m
= F t 2
/ r
, when
converted to S-T units also yield t3/s3,
refer to the Paper 'Mass and Gravity' by this author.)
Since only one dimension of motion can be
represented in a three-dimensional spatial coordinate system, the
gravitational motion in the other two dimensions has no directional
effect, but its magnitude applies as a modifier of the magnitude of
the motion in the dimension of the reference system.
The
'hidden' dimensions of gravitational motion may account for the lack
of progress in mainstream physics in understanding the nature of
gravity.
The
Mechanical System
Consider now a different kind of 'dimension'. When
physical quantities are resolved into component quantities of a
fundamental nature, these component quantities are called
dimensions. The currently accepted systems of measurement express
the dimensions of mechanical quantities in terms of mass, length,
and time, together with the dimensions (in the first sense) of these
quantities.
Now
that mass has been identified as a motion, a relation between space
and time, all of the quantities of the
mechanical system can be expressed in terms of space and time only.
For
purposes of the present discussion the word “space” will be used
instead of “length,” to avoid implying that there is a some
dimensional difference between space and time. On this basis the
'dimensions', or 'space-time dimensions' of one-dimensional speed
are space divided by time, or s/t.
As
indicated above, mass has the dimensions t3/s3.
The
product of mass and speed (or velocity) is t3/s3
× s/t = t2/s2.
This is “quantity of motion,” or momentum.
The
product of mass and the second power of
speed is t3/s3×
s2/t2
= t/s, which
is energy.
Acceleration,
the time rate of change of speed, is s/t × 1/t = s/t2.
Multiplying
acceleration by mass, obtained is t3/s3
× s/t2 = t/s2,
which is force, the 'quantity of
acceleration', it could be called.
The
dimensions of the other mechanical quantities are simply
combinations of these basic dimensions. Pressure,
for instance, is force divided by area, t/s2
× 1/s2 = t/s4.
Angular
Motion
When
reduced to space-time (S-T) terms in accordance with the foregoing
identifications, all of the well established mechanical relations
are dimensionally consistent. To illustrate this agreement, consider
the relations applicable to angular motion, which take a different
form from those applying to translational motion, and utilize some
different physical quantities. The angular system introduces a
purely numerical quantity, the angle of rotation, ς
(sigma). The time rate of change of this angle
is the angular velocity ω (omega), which has the dimensions ω =
ς/t = 1/t. Force is applied
in the form of torque, L, which is the product of force and the
radius, r. L = Fr = t/s2
× s = t/s (energy). One other quantity entering into the angular
relations is the moment of inertia, symbol I, the product of the
mass and the second power of the radius. I = mr2
= t3/s3
× s2 = t3/s.
The following equations demonstrate the dimensional consistency
achieved by this identification of the space-time dimensions:
energy
(t/s) = L
ς
= t/s × 1 = t/s
energy
(t/s) = ½Iω2 =
t3/s × 1/t2=
t/s
power
(1/s) = Lω = t/s × 1/t = 1/s
torque
(t/s) = ½Iω2 =
t3/s × 1/t2=
t/s
The
Gravitational Force Equation
The
only dimensional discrepancy in the basic equations of the
mechanical system is in the gravitational force equation, which is
expressed as F = G
mm'/d2
, where G is the gravitational constant and d is the distance
between the interacting masses.
Although this equation is correct mathematically, it
cannot qualify as a theoretically established relation. As one
physics textbook puts it, this equation 'is
not a defining equation... and cannot be derived from defining
equations. It represents an observed relationship.'
The reason for this inability to arrive at a theoretical explanation
of the equation becomes apparent if examined from a dimensional
standpoint. The dimensions of force in general are those of the
product of mass and acceleration. It follows that these must also be
the dimensions of any specific force. For instance, the
gravitational force acting on an object in the earth’s
gravitational field is the product of the mass and the 'acceleration
due to gravity'. These same dimensions must likewise apply to the
gravitational force in general. When looking at the gravitational
equation in this light, it becomes evident that the gravitational
constant represents the magnitude of the acceleration at unit values
of m' and d, and that these quantities are dimensionless ratios. The
dimensionally correct expression of the gravitational equation is
then F = ma, where the numerical value of
'a' is Gm'/d2
.
The
Electrical System
The
space-time dimensions of the quantities involved in electricity can
easily be identified in the same manner as those of the mechanical
system. Most of the measurement systems currently in use add an
electric quantity to the mass, length and time applicable to the
mechanical system, bringing the total number of independent base
quantities to four. However, the new information developed in the
foregoing paragraphs enables expressing the electrical quantities of
this class in terms of space and time only, in the same manner as
the mechanical quantities.
Electrical
energy (watt-hours) is merely one form of
energy in general, and therefore has the energy dimensions, t/s.
Power
(watts) is energy divided by time, t/s × 1/t = 1/s.
Electrical
force, or voltage
(volts) is equivalent to mechanical force, with the dimensions t/s2
.
Electric
current (amperes) is
power divided by voltage. I = 1/s × s2/t
= s/t. Thus current
is dimensionally equal to speed.
Electrical
quantity(coulombs) is current multiplied by
time, and has the dimensions Q = I t, = s/t × t = s
.
Resistance
(ohms) is voltage divided by current, R = t/s2
× t/s = t2/s3.
This is the only one of the basic quantities involved in the
electric current phenomenon that has no counterpart in the
mechanical system. Its significance can be appreciated when it is
noted that the dimensions t2/s3
are those of mass per unit time.
The
dimensions of other electrical quantities can be obtained by
combination, as noted in connection with the mechanical quantities.
As
can be seen from the foregoing, the quantities involved in the
current electricity are dimensionally equivalent to those of the
mechanical system. It could be described as the mechanical aspects
of electricity. The only important difference is that mechanics is
largely concerned with the motions of individual units or
aggregates, while current electricity deals
with continuous phenomena in which the individual units are not
separately identified.
The
validity of the dimensional assignments in electricity, and the
identity of the electrical and mechanical relations, can be verified
by reducing the respective equations to the space-time (S-T) basis.
For
example, in mechanics the expression for kinetic energy is W = ½mv2,
the dimensions of which are t3/s3
× s2/t2=
t/s.
The
corresponding equation for the energy of the electric current is W
=I2Rt. As
mentioned above, the product Rt is equivalent to mass, while I, the
current, has the dimensions of speed, s/t. Thus, like the kinetic
energy, the electrical energy is the product of mass and the second
power of speed, W = I2Rt
= s2/t2
× t2/s3×
t = t/s.
Another expression for mechanical energy is force times
distance, W = Fd = t/s2
× s = t/s.
Relations between electric and mechanical systems
are equivalent in S-T units of measure. Electric resistance, t2/s3,
equates to mass per second, t3/s3
x 1/t = t2/s3
in the mechanical system.
Electric
Charge and Electric Quantity
Identification of the space-time dimensions of
electrostatic quantities, those involving electric charge, is
complicated by the fact that in
present-day physical thought electric charge
is not distinguished from electrical quantity.
As can be seen in the previous section, electric
quantity is dimensionally equivalent to space, s.
On the other hand, it can deduced from the points brought out in the
preceding section, that electric charge is a
one-dimensional analogue of mass, and is therefore dimensionally
equivalent to energy, t/s.
This
can be verified by consideration of the relations involving electric
field intensity, symbol E. In terms of charge, the electric field
intensity is given by the expression E = Q/s2
. But the field intensity is defined as force per unit distance, and
its space-time dimensions are therefore
t/s2
× 1/s = t/s3.
Applying these dimensions to the equation E = Q/s2
, obtained is Q = Es2
= t/s3 × s2
= t/s.
As
long as the two different quantities that are called by the same
name are used separately, their practical application is not
affected, but confusion is introduced into the theoretical treatment
of the phenomena that are involved. For
instance in the relations involving capacitance (symbol C), Q = t/s
in the basic equation C = Q/V = t/s × s2/t
= s. The conclusion that capacitance is
dimensionally equivalent to space is confirmed observationally, as
the capacitance can be calculated from geometrical measurements.
However, the usual form of the corresponding energy equation is W =
QV, reflecting the definition of the volt as one joule per coulomb.
In this equation, Q = W/V = t/s × s2/t
= s. Because of the lack of distinction between the two usages of Q
the quantity CV, which is equal to Q in the equation C = Q/V is
freely substituted for Q in equations of the W = Q/V type, leading
to results such as W =C/V2,
which are dimensionally incorrect.
Such
findings emphasize the point that the ability to reduce all physical
relations to their space-time dimensions provides us with a powerful
and effective tool for analysing physical phenomena.
Magnetism
The
usefulness of S-T units is clearly demonstrated when it is applied
to an examination of magnetism, which has
been the least understood of the major areas of physics.
The currently accepted formulations of the various magnetic
relations are a mixture of correct and
incorrect expressions, but by using those
that are most firmly based it is possible to identify the space-time
dimensions of the primary magnetic quantities.
This
information then enables correcting existing errors in the
statements of other relations, and establishing dimensional
consistency over the full range of magnetic phenomena.
In
carrying out such a program it is found that magnetism is a
two-dimensional analogue of electricity. The effect of the added
dimension is to introduce a factor t/s into the expressions of the
relations applicable to the one-dimensional electric system. Thus
the magnetic analogue of an electric charge,
t/s, is a magnetic charge, t2/s2.
The existence of such a charge is not recognised in present-day
magnetic theory, probably because there is no
independent magnetically charged particle,
but one of the methods of dealing with permanent magnets makes use
of the concept of the 'magnetic pole', which is essentially the same
thing. The unit pole strength in the SI system, the measurement
system now most commonly applied to magnetism, is the weber, which
is equivalent to a volt-second, and therefore has the dimensions
t/s2 × t =
t2/s2.
The
same units and dimensions apply to magnetic flux, a quantity that is
currently used in most relations that involve magnetic charge, as
well as in other applications where flux is the more appropriate
term. Current ideas concerning magnetic potential, or magnetic
force, are in a state of confusion. Questions as to the relation
between electric potential and magnetic potential, the difference,
if any, between potential and force, and the meaning of the
distinctions that are drawn between various magnetic quantities such
as magnetic potential, magnetic vector potential, magnetic scalar
potential, and magneto-motive force, have never received definitive
answers.
Now,
however, by analysing these quantities into their space-time
dimensions one is able to provide the answers that have been
lacking.
It
is found that force and potential have the same dimensions, t/s2,
and are therefore equivalent quantities. The term “potential” is
generally applied to a distributed force, a force field, and the use
of a special name in this context is probably justified, but is
should be kept in mind that a potential is a
force.
On
the other hand, a magnetic potential (force) is not dimensionally
equivalent to an electrical potential (force), as it is subject to
the additional t/s factor that relates the two-dimensional magnetic
quantities to the one-dimensional electric quantities. From the
dimensions t/s2
of the electric potential, it follows that the correct dimensions of
the magnetic potential
are t/s × t/s2 =
t2/s3
. This agrees with the dimensions of magnetic vector potential. In
the SI system, the unit of this quantity is the weber per meter, or
t2/s2
× 1/s = t2/s3
. (The corresponding cgs unit is the gilbert, which also reduces to
t2/s3
).
The
same dimensions should apply to magneto motive force (MMF), and to
magnetic potential where this quantity is distinguished from vector
potential. But an error has been introduced into the dimensions
attributed to these quantities because the accepted defining
relation is an empirical expression that is dimensionally
incomplete. Experiments show that the magneto motive force can be
calculated by means of the expression MMF = n I, where n is the
number of turns in a coil. Since n is dimensionless, this equation
indicates that MMF has the dimensions of electric current. The unit
has therefore been taken as the ampere, dimensions s/t. From the
discrepancy between these and the correct dimensions we can deduce
that the equation MMF
= n I, from which the ampere unit is derived, is lacking a quantity
with the dimensions t2/s3
× t/s = t3/s4
.
There
is enough information available to make it evident that the missing
factor with these dimensions is the permeability,
the magnetic analogue of electrical resistance.
The permeability of most substances is unity, and omitting has no
effect on the numerical results of most experimental measurements.
This has led to overlooking it in such relations as the one used in
deriving the ampere unit for MMF. When we put the permeability
(symbol μ) into the empirical equation it becomes MMF
= μnI, with the
correct dimensions, t3/s4
× s/t = t2/s3.
The
error in the dimensions attributed to MMF carries over into the
potential gradient, the
magnetic
field intensity. By definition, this is the
magnetic field potential divided by distance,
t2/s3
× 1/s = t2/s4
.
But
the unit in the SI system is the ampere per
meter, the dimensions of which are s/t ×
1/s = 1/t is incorrect. In
this case, the cgs unit, the oersted, is derived from the
dimensionally correct unit of magnetic potential, and therefore has
the correct dimensions, t2/s4
.
The
discrepancies in the dimensions of MMF and magnetic field intensity
are typical of the confusion that exists in a number of magnetic
areas. Much progress has been made toward clarifying these
situations in the past few decades both active, and sometimes
acrimonious, controversies still persist with respect to such
quantities as magnetic moment and the two vectors usually designated
by the letters B and H. In most of these cases, including those
specifically mentioned, introduction of the permeability where it is
appropriate, or removing it where it is inappropriate, is all that
is necessary to clear up the confusion and attain dimensional
validity.
Correction of the errors in electric and magnetic
theory that have been discussed in the foregoing paragraphs,
together with clarification of physical relations in other areas of
confusion, enables expressing all electric and magnetic quantities
and relations in terms of space and time, thus completing the
consolidation of all of the various systems of measurement into one
comprehensive and consistent system.
An
achievement of this kind is, of course, self-verifying, as the
probability that there might be more than one consistent system of
dimensional assignments that agree with observations over the entire
field of physical activity is negligible.
Electric
Current Theory
Straightening out the system of measurement is only a
small part of what has been accomplished in the development of
Space-Time units of measure. More importantly, the
positive identification of the space-time dimensions of any physical
quantity defines the basic physical nature of that quantity.
Consequently, any hypothesis with respect to a physical process in
which this quantity participates must agree with the dimensional
definition. The effect of this constraint on theory construction is
illustrated by the findings with respect to the nature of current
electricity that were mentioned earlier.
Present-day theory views the electric current as a
flow of electric charges. But the dimensional analysis shows that
charge has the dimensions t/s, whereas the moving entity in the
current flow has the dimensions of space, s.
It
follows that the current is not a flow of
electric charges. Furthermore, the
identification of the space-time dimensions of the moving entity not
only tells us what the current is not, but goes on to reveal just
what it is.
According to present-day theory, the carriers of the
charges, which are identified as electrons, move through the spaces
between the atoms. The finding that the moving entities have the
dimensions of space makes this kind of a flow pattern impossible. An
entity with the dimensions of space cannot move through space, as
the relation of space to space is not motion.
Such an entity must move through the matter
itself, not through the vacant spaces.
This
explains why the current is confined within the conductor, even if
the conductor is bare. If the carriers of the current were able to
move forward through vacant spaces between atoms, they should
likewise be able to move laterally through similar spaces, and
escape from the conductor. But since the current moves through the
matter, the confinement is a necessary consequence.
The
electric current is a movement of space through matter, a motion
that is equivalent, in all but direction, to movement of matter
through space. This is a concept that many
individuals will find hard to accept. But it should be realised that
the moving entities are not quantities of the space which is
familiar, extension space, it may called. There are physical
quantities that are dimensionally equivalent to this space of
ordinary experience, and play the same role in physical activity.
One
of them, capacitance, has already been mentioned in the preceding
discussion. The moving entities are quantities of this kind, not
quantities of extension space.
Here,
then, is the explanation of the fact that the basic quantities and
relations of the electric current phenomena are identical with those
of the mechanical system. The movement of
space through matter is essentially equivalent to the movement of
matter through space, and is described by the same mathematical
expressions.
Additionally, the identification of the electric charge
as a motion explains the association between charges and certain
current phenomena that has been accepted as evidence in favour of
the “moving charge” theory of the electric current.
One
observation that has had considerable influence on scientific
thought is that an electron moving in open space has the same
magnetic properties as an electric current. But it can now be seen
that the observed electron is not merely a charge. It
is a particle with an added motion that constitutes the charge.
The
carrier of the electric current is the same particle without the
charge. A
charge that is stationary in the reference system has electrostatic
properties. An uncharged electron in motion within a conductor has
magnetic properties. A charged electron moving in a conductor or in
a gravitational field has both magnetic and electrostatic
properties.
It
is the motion of physical entities with the dimensions of space that
produces the magnetic effect.
Whether or not these entities—electrons or their
equivalent—are charged is irrelevant from this standpoint. Another
observed phenomenon that has contributed to the acceptance of the
“moving charge” theory is the emission of charged electrons from
current-carrying conductors under certain conditions. The argument
in this instance is that if charged electrons come out of a
conductor there must have been charged electrons in the conductor.
The answer to this is that the kind of motion which constitutes the
charge is easily imparted to a particle or atom (as anyone who
handles one of the modern synthetic fabrics can testify), and this
motion is imparted to the electrons in the process of ejection from
the conductor. Since the uncharged particle cannot move through
space, the acquisition of a charge is one of the requirements for
escape.
In
addition to providing these alternative explanations for aspects of
the electric current phenomena that are consistent with the “moving
charge” theory, the new theory of the current that emerges from
the scalar motion study also accounts for a number of features of
the current flow that are difficult to reconcile with the
conventional theory. But the validity of the new theory does not
rest on a summation of its accomplishments. The conclusive point is
that the identification of the electric current as a motion of space
through matter is confirmed by agreement with the dimensions of the
participating entities, dimensions that are verified by every
physical relation in which the electric current is involved. The
proof of validity can be carried even farther. It is possible to put
the whole development of thought in this article to a conclusive
test.
It
is found that mass is a three-dimensional scalar motion, and that
electric current is a one-dimensional scalar motion through a mass
by entities that have the dimensions of space. It is further found
that magnetism is a two-dimensional analogue of electricity.
If
these findings are valid, certain consequences necessarily follow
that are extremely difficult, perhaps impossible, to explain in any
other way. The one-dimensional, oppositely directed flow of the
current through the three-dimensional scalar motion of matter
neutralises a portion of the motion in one of the three dimensions,
and should leave an observable two-dimensional (magnetic) residue.
Similarly, movement of a two-dimensional (magnetic) entity through a
mass, or the equivalent of such a motion, should leave a
one-dimensional (electric) residue.
In
as much as these are direct and specific requirements of the theory
outlined in the foregoing paragraphs, and are not called for by any
other physical theory, their presence or absence is a definitive
test of the validity of the theory.
The
observations give an unequivocal answer. The current flow produces a
magnetic effect, and this effect is perpendicular to the direction
of the current, just as it must be if it is the residue of a
three-dimensional motion that remains after motion in the one
dimension of the current flow is neutralised.
This
perpendicular direction of the magnetic effect of the current is a
total mystery to present-day physical science, which has no
explanation for either the origin of the effect or its direction.
But both the origin and the direction are obvious and necessary
consequences of the findings with respect to the nature of mass and
the electric current.
There
is no independent magnetic particle similar to the carrier of the
electric current, and no two-dimensional motion of space through
matter analogous to the one-dimensional motion of the current is
possible, but the same effect can be produced by mechanical movement
of mass through a magnetic field, as done by a dynamo or an
equivalent process. As the theory requires, the one-dimensional
residue of such motion is observed to be an electric current. This
process is electromagnetic induction. The magnetic effect of the
current is electromagnetism.
On
first consideration it might seem that the magnitude of the
electromagnetic effect is far out of proportion to the amount of
gravitational motion that is neutralised by the current. However,
this is a result of the large numerical constant, 3 × 108
in SI
units (represented by the symbol c), that applies to the space-time
ratio s/t where conversion from an n-dimensional quantity to an
m-dimensional quantity takes place. An example that, by this time is
familiar to all, E=mc2,
is the conversion of mass (t3/s3)
to energy (t/s). In that process, where the relation is between a
three-dimensional quantity and a one-dimensional quantity, the
numerical factor is c2.
In the relation between the three-dimensional mass and the
two-dimensional magnetic residue the numerical factor is c, less
than c2 but still
a very large number.
Conclusion
The theory of
the electric current developed in the foregoing discussion passes
the test of validity in a definite and positive manner. The results
that it requires are in full agreement with two observed physical
phenomena of a significant nature that are unexplained in
present-day physical thought. Together with the positively
established validity of the corresponding system of space-time
dimensions, this test provides a verification of the entire
theoretical development described in this article, a proof that
meets the most rigid scientific standard.
Table
of Motions
Contraction
of Space
|
S4/T4
m4/s4
c4
=
8.077596x 1034
|
S4/T3
m4/s3
sc3
4.354684x 10-9
|
S4/T2
m4/s2
s2c2
2.347635x 10-53
|
S4/T
m4/s
s3c
1.265625x 10-96
|
S4
?
6.823062x 10-140
m4
|
↑
S4
|
|
S3/T4
m3/s4
c3/t
4.997898x 1069
|
S3/T3
mass
current G gravity
c3
= m3/sec3
=
2.694398x
1025
|
S3/T2
m3/s2
sc2
1.452565x 10-18
|
S3/T
m3/s
(cumecs)
s2c
7.830923x 10-62
|
S3
volume
4.221672x 10-105
m3
|
S3
|
|
S2/T4
m2/s4
c2/t2
3.092377x 10104
|
S2/T3
m2/s3
c2/t
1.667120x 1061
|
S2/T2
magnetic
current B
c2
= m2/sec2
=
8.957548x
1016
|
S2/T
m2/s
sc (=
Gί
= 1/F )
4.845242x 10-27
|
S2
area
2.612099x 10-70
m2
|
S2
|
|
S/T4
?
c/t3
=
1.914383x 10138
m/s4
|
S/T3
change
of acceleration
Δa
c/t2
=
1.031505x 1095
m/s3
|
S/T2
acceleration, Δv
c/t =
5.560912 x 1051
m/s2
|
S/T
kinetic motion KE, velocity
v,
electric
current I
c
= m/sec
=
2.997924x108
speed
of light c
|
S
length,
electric quantity Q as capacitance C
(coulomb)
Sq
= 1.616199x 10-35
m Quantum
of length
|
S1
|
|
1/T4
?
1.183866x 10174
←
|
1/T3
?
6.385696x 10129
Expansion
|
1/T2
?
3.440734x 1087
of Time
|
1/T
frequency (Hz)
1.854921x 1043
|
Maximum Values
MOTION
Minimum Values
|
S0
|
|
← T -
4
|
T - 3
|
T - 2
|
T - 1
|
T0
|
O
|
Table
of Energies
|
O
|
T0
|
T1
|
T2
|
T3
|
T4
→
|
|
S0
|
Maximum Values
ENERGY
Minimum Values
|
T
time (sec)
Tq
= 5.391063x 10-44
Quantum
of time
|
T2
Contraction
2.906356x 10-87
|
T3
of Time
1.566833x 10-131
|
T4
→
8.446895x 10-175
|
|
S-1
|
1/S
power
=VI (t/s2
x s/t)
6.187356x 1034
|
T/S
potential energy E
electric
charge Q
sec/m
1/c
=3.335643x 10-9
|
T2/S
inertia
ί
t/c = s2/m
1.798266 x 10-52
Planck
constant h
|
T3/S
moment of inertia
t2/c
= s3/m
9.694554x 10-97
|
T4/S
?
t3/c
5.226395x 10-140
|
|
S-2
|
1/S2
?
3.828338x 1071
|
T/S2
force,
electric potential V
1/cs = sec/m2
2.063880x 1026
|
T2/S2
momentum
magnetic
energy sec2/m2
electric resistivity σ
1/c2
= 1.12265x 10-17
|
T3/S2
?
t/c2
5.998367x 10-62
|
T4/S2
?
t2/c2
3.233758x 10-105
|
|
S-3
|
1/S3
?
2.368729x 10106
|
T/S3
elect field intensity E
1/cs2
= sec/m3
1.276998x 1061
|
T2/S3
electric resistance R
magnetic potential
1/c2s
6.884371x 1017
|
T3/S3
mass
energy
quantum
= 1/c3
sec3/m3
3.711404x
10-26
|
T4/S3
?
t/c3
2.000841x 10-70
|
|
S-4
↓
|
1/S4
?
1.465617x 10141
|
T/S4
pressure (sec/m4)
(1/cs3
= force/m2,
energy/ m3)
7.890828x 1095
|
T2/S4
magnetic intensity H
1/c2s2
4.253995x 1052
|
T3/S4
mag resistance μ
1/c3s
2.296378x
108
|
T4/S4
?
1/c4
1.237992x 10-35
|
Expansion
of Space Approximate
conversion of Energies quantum minima to SI units multiply S-T values
by 1018
and quantum maxima divide by 1018.
