Dimensions
and Scalar Motion.
Paper
6
Michael
J Bull, 2016.
Abstract:
This
6th
Paper looks at the full spectrum of quantum numerical values up to
and including the 4th
dimension and explores the rather more complex mathematical nature of
the calculated quantum values. The Paper clarifies the meaning of
dimensions and considers the angles of scalar motion of the different
dimensions, which in itself may be an insight to assist the mind to
comprehend beyond the third spatial dimension.
Sections
1. Space-Time Measure and the Reference System
2. Tables of Motions and Energies – Quantum Numerical
Values
3. Analysis of the Patterns from the Tables of Motions
and Energies
4. Clarification of 'Dimensions'
5. Scalar Motions, Angles and Comprehension
Summary:
The
discussion of a variation of angles between scalar motions according
to dimension does allow some resolution of the conceptual impasse
most people experience beyond the 3rd
dimension, however the effects of the different angles and numbers of
possible scalar motions are not known. It is likely a prerequisite
that some comprehension of the possible precedes its successful
study, as evidenced by science fiction which evolves into science
fact over time.
Space-Time
Measure and the Reference System
(This Section is an edited shortened version of DB
Larson's discourse on Space-Time units of measure, editing is in
italics.)
The existence
of scalar motion has been demonstrated (in
prior work by others), and it is appropriate
to examine the consequences of this existence. Some of the most
significant consequences are related to the dimensions of this 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, the favoured hypothesis is
that of a four-dimensional universe, in which the three dimensions of
space are joined to one dimension of time. Strangely enough, there
does not appear to have been any critical examination of the question
as to the number of dimensions of motion that are possible. 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
magnitudes 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.
Here again
is a shortcoming of the reference system. In an examination of 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 is not specifically defined, but is
wholly dependent on the size and position of the object whose
location constitutes the reference point. It is then 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 gives 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.
For instance,
gravitation 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 gravitation can act three-dimensionally.
Furthermore, it can be seen that gravitation must act in all of the
dimensions in which it can act. This is a necessary consequence of
the relationship between gravitation 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 negative scalar motion content of the
mass (as distinct from matter). (Larsen
perpetuates the misunderstanding of mainstream physics between mass
and inertia, however his logic remains valid.)
It follows that motion of any mass m
is a motion of a negative 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 positive scalar status irrespective of the vectorial direction.
In the
compound motion mv,
the negative gravitational motion acts as a resistance to the
positive
motion v.
The gravitational motion must therefore 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.
One may
therefore identify the gravitational motion as three-dimensional
speed, which can be expressed as s3/t3,
where s and t
are space and time respectively.
The inertial
mass (the resistance that this negative gravitational motion offers
to the applied positive motion) is then the inverse of this quantity,
or t3/s3.
Since only one
dimension of motion can be represented in 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 S-T
unit for mass was derived in Paper 1 by this author, independently of
Larson's logic above, from another equation for mass, m = Ft
2/r,
yielding the same S-T result, t 3/s
3.
Newton's F =
ma yields the same result for mass also. m = F/a = t/s2
/ s/t2
= t3/s3
.)
Now to 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.
But 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 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.
(By
extension, the product of mass and gravity, t3/s3
x s3/t3
equals unity.)
Acceleration, the time rate of change of speed, is s/t × 1/t =
s/t2.
Multiplying acceleration by mass, obtains t3/s3
× s/t2
= t/s2,
which is
force,
the “quantity of acceleration,” it might be called.
(That
is Newton's Second Law of Motion, F = ma (or t/s2
= t3/s3
x s/t2
=
t/s2)
The
dimensions of the other mechanical (and
electro-magnetic)
quantities are simply combinations of these basic dimensions.
(
This section is edited and modified from published work by D.B.
Larson. For further detail and original text by Larson refer Paper 1,
Appendix 2, 'Mass, Gravity and Unity' at michaeljbull.blogspot.com.au
or independent.academia.edu/MichaelBull1)
Motions
and Energies Quantum Values
M.J. Bull 2015
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 (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
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 1053
m/s2
|
S/T
velocity
electric
current
c
= m/sec
=
2.997924x108
m/s
|
S
length
electric charge Q capacitance C
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
|
Minimum Values
MOTION
Maximum 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
6.187356x 1034
|
T/S
potential energy
electric
energy
sec/m
1/c
=3.335643x 10-9
|
T2/S
inertia
ί
t/c = s2/m
1.798266 x 10-52
|
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
Analysis
of the Patterns from the Tables of Motions and Energies
The S-T values in
the Table
of Motions
are expressed in metres per second (S/T) from index powers 1 to 4,
each combination representing a different quantity, for example S/T
is velocity while S/T2
is acceleration. The S/T configuration is related directly to SI
units (MKS system) of measure and require no conversion, because
metres/second already exist in SI units.
The S-T values in
the Table
of Energies
are expressed in seconds per metre, T/S, which is not a unit of
measure recognised in SI units. They are similarly differentiated by
the index powers. Experimentation with the mathematics indicates that
there is a difference factor between SI units and sec/metre of
approximately 1018
regardless of the varying index powers. For example the quantum of
inertia, T2/S,
is 1.798 x 10-52
sec/m and in SI units is 6.629 x 10-34
J.sec, a difference of 3.686 x 1018.
Other energies have a very similar difference between sec/m and their
SI unit.
The values in darker yellow in the Motions table are
minima and have their reciprocal maxima in the darker yellow in the
Energies table. The lighter yellow values are the converse of the
darker yellow values, so that the Motions and Energies each contain
both minimum quantum and maximum quantum values. The pattern is clear
if both tables are viewed in conjunction. The darker yellow values
have their reciprocals in the other table's darker yellow areas, and
similarly but conversely in the lighter yellow areas.
The same
relationship applies to the greens of the space axis and magentas of
the time axis.
The units of measure
involving S, T and c
are in red ink and are reached by substituting c
for S/T, which is the speed of light. It was shown in Paper 3 that
the speed of light is defined by the quantum of velocity (a maximum
quantum value), which is itself derived from the quanta of length (S)
and time (T), which are both minimum quantum values. That is why the
speed of light is governed to what it is and is itself a maximum
quantum value. The same logic would conclude that the maximum rate of
acceleration would be 5.560912 x 1053
m/s2.
Difficult to test physically but may have significance in the study
of cosmology and the universe. Acceleration is reciprocal to inertia,
the quantum value of which is the Planck Constant. (refer
Paper 3)
There are physics
progressions to be observed, especially in the Energies Table, where
for example, electric potential, T/S2,
transfers diagonally left to right to electrical resistance, which
equates to magnetic potential, T2/S3,
and one step further left to right magnetic resistance logically
equates to mass potential, T3/S4.
Some of these quantities have not yet been contemplated by mainstream
science.
In both Tables,
The
five horizontal rows from right to left increase at each column by a
factor of 1044,
T(q).
The five vertical
columns from top to bottom increase at each row by a factor of 1035,
S(q).
All the diagonals
from top right to bottom left increase by a factor of 1079,
T(q)
x S(q).
All the diagonals
from bottom right to top left increase by a factor of 109,
T(q)
/ S(q).
1044
x 1035
= 1079
1044
/ 1035
= 109
There is a consistency between consecutive space-time
quantum values in any direction and a consistent reciprocity between
minima and maxima. This relationship only becomes visible when S-T
units of measure are used for known quantities.
In summary,
'The quantum values of Space (Sq),
1.616199 x 10-35
metres, and Time (Tq),
5.391063 x 10-44
seconds, are the fundamental quanta which together or separately
define and quantify all the quanta of all the other physical
quantities.'
These
quanta are the numerical values in the Tables above and all are
derived from T(q)
and S(q).
It
is clear from the above numerical analysis that this author's
original estimate of space
and time expansion directions was incorrect in
previous Papers, and this reversal is indicated in the above Tables.
Expansion is in the negative direction of both the X and Y axes.
Clarification
of 'Dimensions'
Larson's discourse
above on Space-Time Measure and the Reference System indicates a
blurred understanding of exactly what constitutes a dimension,
confused also by the inadequate reference system used in the case of
Space. This author's Tables above clarify the meanings. The 1st
space dimension contains all expressions which use S1
and S-1.
Similarly the 2nd
space dimension contains all expressions which use S2
and S-2
and so forth. It is clear that Time similarly has its own dimensions,
T 2
and T -2
for example, and thus does not of itself form the 4th
dimension, as is a popular conjecture in science at present. Time
exists in all space dimensions but does not have equal value in all
space dimensions, as the quantum values in the above Tables show. As
Time contracts, so the quanta of Motions and Energies decrease in
magnitude, the same result as for the contraction of Space, and vice
versa for expansion of both.
Larson's challenge
to science regarding the number of possible scalar motions is also
clarified by the Tables above. For example the number of (equal)
scalar motions in the 4th
dimension of space and time, S4/T4,
is four, just as there are three in the third dimension of space and
time, S3/T3.
It is the inadequate 3 dimensional reference system which puts the
clarity of the mathematics beyond the limits of human physical
comprehension. The Motions Table above does provide a quantum value
for the resolution of 4 scalar motions, and that is 8.077596 x 1034.
The unit of measure for that quantum maximum value is metre4
/second4.
The
difficulty most people have is resolving 4 different scalar motional
directions in a 3 dimensional reference frame,
and as Larson pointed out, they are not to be resolved as one would a
vector sum, reducing it to one dimension.
From the above
Tables it is clear that there is motion and energy in the 4th
dimension, for example, which cannot be seen, measured, resolved or
even imagined from within the current human illusion that space is
limited to 3 dimensions and time is unknowable.
(One might speculate that is where the illusive 'dark
energy' may be found, but not from within a 3 dimensional reference
frame. A problem is not solved by the same reasoning from which it
arose.)
Scalar
Motions, Angles and Comprehension
It is readily
apparent in 3 dimensions that the 3 scalar motions, ( S3/T3
), are at an angle of 90º
to each other, and that is supported by observation of
electromagnetism, where the electric current, magnetic field and the
resulting force are at 90º
to each other, as observed in an electric motor or dynamo. The
mathematics are simply 360º
divided by 4 equals 90º
between scalar motions.
Using similar logic,
the 4 scalar motions, ( S4/T4
), of the 4th
dimension are 360º
divided by 5 equals 72º
between the scalar motions. The 5th
dimension is 360º
divided by 6 equals 60º
between motions, etc.
Most people do have
trouble envisaging a dimension where a 'right angle' is 72º.
The distortion to perception is difficult to imagine.
There is, however, a
theory of reality (with quite some credibility) which uses geometry
to resolve some of the issues of mass, matter and quantum mechanics
(some of which are unsatisfactorily explained by current theories)
and which uses the 60º
angle to construct models of energy
and matter. This theory is called 'Tetryonics', and on the basis of
its use of the 60º
fundamental angle, is possibly (and unknowingly) based on 5th
dimension concepts.
(For
further details visit the community 'Tetryonics' at Google Plus, or
at independent.academia.edu)
The
discussion of a variation of angles between scalar motions according
to dimension does allow some resolution of the conceptual impasse
most people experience beyond the 3rd
dimension, however the effects of the different angles and numbers of
possible scalar motions are not known. It is likely a prerequisite
that some comprehension of the possible precedes its successful
study.
