Quantum Physics has so far been about the very small,
the minimum values. This Paper exposes for the first time the other
side of the quantum coin – maximum values, and the entanglement
between the minima and maxima ; the reason behind the maximum value
which governs the speed of light ; the fundamentals behind Planck's
quantum calculations and behind the constants ; the physical
embodiment of the Planck Constant and some other issues which have
vexed modern physics.
Warning: contains mathematics and may not be easy to understand for some people.
Quantified
and Quantum Space-Time
Paper
3
M.J. Bull 2015
Abstract
:
Quantum Physics has so far been about
the very small, the minimum values. This Paper exposes for the first
time the other side of the quantum coin – maximum values, and the
entanglement between the minima and maxima ; the reason behind the
maximum value which governs the speed of light ; the fundamentals
behind Planck's quantum calculations and behind the constants ; the
physical embodiment of the Planck Constant and some other issues
which have vexed modern physics.
Contents
Introduction
The
Revised Fundamentals
The
Motions
Table of
Motions
Velocity
Acceleration
Magnetic and
Mass Currents
The
Energies
Table of
Energies
Inertia and the
Planck Constant
Summary
The
quanta of length
and time
are the only truly fundamental quantities, and they define all other
physical quantities, constants and the minima and maxima of Quantum
Physics.
That is why Space-Time units of measure are the
fundamental units of measure. Unlike SI units of measure, they make
the relationship between quantum minima and maxima clear, and define
and quantify all quantities including those which are still unknown
in physics.
The Energies are the
minimum quantum values, and as such are not new. It is the
recognition that they define the reciprocal maximum values, the
Motions, that is new.
Introduction
Papers 1 and 2
preceding this Paper 3 do provide a background to clarify
understanding of the Space-Time (S-T) units of measure which form the
subject of this Paper.
(
Paper
1,
detailing the experiments, mathematics and theory can be found in the
blog titled 'New Physics - The Relationship between Gravity, Mass,
Magnetism and Electricity' at michaeljbull.blogspot.com or published
at http://independent.academia.edu/MichaelBull1
as a downloadable PDF file under the author's name, titled “Mass,
Gravity and Unity”. Paper
2,
examines the quadrants of Motions and Energies about which some
things are known as well as speculates on the S-T interpretation of
matter and anti-matter. It is titled 'Complex Space-Time' and is
published as detailed above for Paper 1.)
The
Revised Fundamentals
The work on quantum
values done by Max Planck in the early 20th
century are values which he expressed in SI units of measure (the MKS
system). The equations which he used to calculate these quanta made
use of the constants ћ,
G, c, t. The basic Planck units are the quanta of length, mass, time,
electric charge and temperature. There are many others derived from
these. The use of SI units for their expression masks the fundamental
relationships between Motions and Energies.
The reciprocity of
the Motions and Energies was discussed in the previous two Papers.
If
the quantum of length (or distance as space in 1 dimension) is
denoted Sq
and the quantum of time denoted Tq
, it can be shown that the velocity ( v = Sq/Tq
) is exactly equal to the velocity of light in free space, c.
(1.616199x 10-35
/ 5.39106x 10-44
= 2.997924x 108
m/s = c,
exactly)
These are two quanta
calculated by Planck from the constants including c
which actually themselves define c
rather than vice versa. The quanta are both minimum
values and they define the maximum
value for velocity. It is therefore Sq
and Tq
which are fundamental to the constant, c.
It was shown in the
previous papers that any physical ratio (quantity) can be expressed
in units of S and T only. Also from Paper 1, section 2, an
alternative set of equations derived by using the SI unit of
acceleration (normally m/s2
) as N/kg, proved the S-T unit for mass is T3/S3
. In SI parlance that would mean sec3/metre3
as the unit of measure for the quantum of mass. It is shown
mathematically below under the section headed 'Motions' that that
unit can be converted to kg and the quantum value then agrees with
Planck's calculation for the quantum of mass. The constant, c,
can also be used in the expression of the physical ratios for both
the Motions and the Energies and each ratio can be assigned a
numerical value from the fundamental Sq
and Tq
,
or mathematically more simply from c.
The mathematical
reciprocity between Motions and Energies indicates that the Energies
are derived from the quantum minima
and the Motions express the reciprocal maxima.
The
other side of the quantum coin is that the minima, or quanta, define
the maximum values also,
as pointed out above with the maximum value for velocity, c.
The
summary of all the S-T ratios and products is reproduced below in the
interests of convenience for the reader.
MOTION
SPACE
EXPANSION
MATTER
|
S4/T4
?
|
S4/T3
?
|
S4/T2
?
|
S4/T
?
|
S4
?
|
↑
S4
|
S4
?
|
TS4
gluon
|
T2S4
photon
|
T3S4
Z-boson
|
T4S4
W-boson
|
|
S3/T4
?
|
S3/T3
mass
current
GRAVITY
|
S3/T2
?
|
S3/T
?
|
S3
volume
|
S3
|
S3
volume
|
TS3
top quark
|
T2S3
bottom quark
|
T3S3
tau
|
T4S3
tau neutrino
|
|
S2/T4
?
|
S2/T3
?
|
S2/T2
magnetic
current
|
S2/T
?
|
S2
area
|
S2
|
S2
area
|
TS2
charm quark
|
T2S2
strange quark
|
T3S2
muon
|
T4S2
muon neutrino
|
|
S/T4
?
|
S/T3
Δ
accel,
|
S/T2
Δ
speed,
accel.
|
S/T
speed,
elec
current
|
S
distance,
elec charge capacitance C
|
S1
|
S
distance,
elec charge
capacitance C
|
TS
up quark
|
T2S
down quark
|
T3S
electron
|
T4S
electron
neutrino
|
|
1/T4
?
←
|
1/T3
?
contraction
|
1/T2
?
of
time
|
1/T
frequency
|
S0/T0
= 1
Unity
MOTION
|
S0
|
T0
S0 = 1
Unity
MATTER
|
T
time
|
T2
?
expansion
|
T3
?
of
time
|
T4
?
→
|
|
← T -
4
|
T - 3
|
T - 2
|
T - 1
|
T0
|
O
|
T0
|
T1
|
T2
|
T3
|
T4
→
|
|
1/T4
?
|
1/T3
?
|
1/T2
?
|
1/T
frequency
|
1/T0
S0 = 1
Unity
ANTI-MATTER
|
S0
|
T0/S0
= 1
Unity
ENERGY
|
T
time
|
T2
?
|
T3
?
|
T4
?
|
|
1/T4S
anti electron
neutrino
|
1/T3S
anti electron
(positron)
|
1/T2S
anti down quark
|
1/TS
anti up quark
|
1/S
power
|
S-1
|
1/S
power
|
T/S
energy
electric
energy
|
T2/S
inertia
|
T3/S
moment of inertia
|
T4/S
?
|
|
1/T4S2
anti muon
neutrino
|
1/T3S2
anti muon
|
1/T2S2
anti strange
quark
|
1/TS2
anti charm
quark
|
1/S2
?
|
S-2
|
1/S2
?
|
T/S2
force,
elect potential V
|
T2/S2
momentum
magnetic
energy
elec resistivity σ
|
T3/S2
?
|
T4/S2
?
|
|
1/T4S3
anti tau
neutrino
|
1/T3S3
anti tau
|
1/T2S3
anti bottom
quark
|
1/TS3
anti top quark
|
1/S3
?
|
S-3
|
1/S3
?
|
T/S3
elect field intensity E
|
T2/S3
elec resis R
magnetic potential
|
T3/S3
MASS
energy
|
T4/S3
?
|
|
1/T4S4
anti W-boson
|
1/T3S4
anti Z-boson
|
1/T2S4
anti photon
|
1/TS4
anti gluon
|
1/S4
?
|
S-4
↓
|
1/S4
?
|
T/S4
pressure
|
T2/S4
magnetic intensity H
|
T3/S4
mag resist μ
|
T4/S4
?
|
ANTI
– MATTER
SPACE
CONTRACTION
ENERGY
The Motions
The
above mentioned definition of the maximum possible velocity, c,
carries the same logic to all of the other Motions, both identified
and unknown, because the reciprocal relationship with the Energies
remains the same as for c.
The table of the Motions quadrant below summarises those quantities.
Table
of Motions (4th
Quadrant)
|
S4/T4
?
c4
=
8.077602x 1034
|
S4/T3
?
sc3
|
S4/T2
?
s2c2
|
S4/T
?
s3c
|
S4
?
6.823x 10-140
m4
|
↑
S4
|
|
S3/T4
?
c3/t
|
S3/T3
mass
current (gravity)
c3
=
2.694398x
1025
|
S3/T2
?
sc2
|
S3/T
?
s2c
|
S3
volume
4.2217x 10-105
m3
|
S3
|
|
S2/T4
?
c2/t2
|
S2/T3
?
c2/t
|
S2/T2
magnetic
current
c2
=
8.957548x
1016
|
S2/T
?
sc
|
S2
area
2.6121x 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
velocity
electric
current
c
=
2.997924x108
m/s
|
S
length
electric charge Q capacitance C
Sq
= 1.616199x 10-35
m
|
S1
|
|
1/T4
?
1.183866x 10174
←
|
1/T3
?
6.385696x 10129
contraction
|
1/T2
?
3.440734x 1087
of
time
|
1/T
frequency
1.854921x
1043
|
MOTION
Maximum Values
|
S0
|
|
← T -
4
|
T - 3
|
T - 2
|
T - 1
|
T0
|
O
|
Each value of the motions can be
calculated from the quanta Sq and Tq
. Some are entered on the Table to demonstrate that they are all
large numbers and represent maximum values for each quantity.
Velocity
The
velocity ( v = Sq/Tq
) is exactly equal to the velocity of light in free space, c.
(1.616199
x 10-35
/ 5.39106 x 10-44
= 2.997924 x 108
m/s = c,
exactly), which is the maximum value for velocity.
Acceleration
a = Sq
/(Tq)2
= 1.616199 x 10-35/ 2.906356 x 10-87
= 5.506912 x 1051 m/s2
= a max = c/t,
which is the maximum value for acceleration.
Magnetic and Mass
Currents
Both
are represented by the 2nd
and 3rd
power of velocity c
respectively.
Magnetic current is represented by a flow of electric charge in two
orthogonal directions simultaneously. Mass current similarly by a
flow in three orthogonal directions. For detailed further explanation
refer to Paper 1, section 4.
The
quantum of mass calculated by Planck is mp
= 2.17651 x 10-8
kg. In S-T units that same
quantum
of mass, Tq
3/
Sq
3
= 3.711404 x 10-26
sec3/
metre3
. To convert s3/m3
to kg it is necessary to divide 2.1765 x 10-8
by 3.711404 x 10-26
to obtain the conversion factor from s3/m3
to kg. The conversion factor is 5.864384 x 1017.
Multiply the s3/m3
quantum by the conversion factor which yields 2.17651 x 10-8
which equals mp
,
the quantum of mass in kg. (The same result is obtained by working
from the fundamental Sq
and Tq
.) This conversion process is needed for all of the minima in the
Energies (2nd
Quadrant) to revert to Planck values, however, the maxima in the
Motions quadrant are measured directly by SI units.
The
reason for this is that Motions are a ratio of distance/ time,
whereas the Energies are
time/
distance, which has no equivalent in SI units.
It
can be noted from the Motions table above that c
has been used as an alternative expression with S-T units (the
expressions in red ink) because c
is a ratio of the quanta of space and time. The same notation can be
used in the Energies table but note that the c
factor is reciprocal, i.e. 1/c.
The
Energies
The
Energies are the minimum quantum values, and as such are not new. It
is the recognition that they define a reciprocal maximum value that
is new.
To date there has not been an explanation of why the speed of light
is governed to the value that it is. The reason is that it is
reciprocal to the quantum
of energy.
The S-T quantum of energy is 3.335643 x 10-9
and equals 1/c. A conversion factor needs to be applied to make that
number into that calculated by Planck because the S-T unit is seconds
/ metre and the Planck number is in Joules. That has been outlined
above in the Motions section under Magnetic and Mass Currents.
There
are more Energies known to physics than there are Motions. The table
below is a summary.
Table
of Energies
(2nd
Quadrant)
|
O
|
T0
|
T1
|
T2
|
T3
|
T4
→
|
|
S0
|
Minimum Values
ENERGY
|
T
time
Tq=5.391063x
10-44
|
T2
?
2.906356x 10-87
|
T3
?
1.566833x 10-131
|
T4
?
8.446895x 10-175
|
|
S-1
|
1/S
power
6.187356x 1034
|
T/S
potential energy
electric
energy
1/c
=
3.335643x
10-9
|
T2/S
inertia
t/c =
1.798x 10-52
|
T3/S
moment of inertia
t2/c
|
T4/S
?
t3/c
|
|
S-2
|
1/S2
?
|
T/S2
force,
electric potential V
1/cs
|
T2/S2
momentum
magnetic
energy
electric resistivity σ
1/c2
= 1.12265x 10-17
|
T3/S2
?
t/c2
|
T4/S2
?
t2/c2
|
|
S-3
|
1/S3
?
|
T/S3
elect field intensity E
1/cs2
|
T2/S3
electric resistance R
magnetic potential
1/c2s
|
T3/S3
mass
energy
1/c3
=
3.711404x
10-26
|
T4/S3
?
t/c3
|
|
S-4
↓
|
1/S4
?
|
T/S4
pressure
1/cs3
|
T2/S4
magnetic intensity H
1/c2s2
|
T3/S4
magnetic resistance μ
1/c3s
|
T4/S4
?
1/c4
|
Inertia and the Planck Constant
Inertia
is clearly not well understood in physics, often being given the same
unit of measure as mass, i.e. kg. The correction for this error is
made clear in Paper 1, section 1. It is reproduced below for the
reader's convenience.
“There
does not appear to be any meaningful quantification of inertia in the
current or past physics literature, however inertia is quantifiable
from Newton's Laws of Motion. 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
Newton's second law of motion, 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 mathematically 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 = 10 N/kg, force is 150 N and the inertia ί = m/F = 15/150 = 0.1 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
examples demonstrate that 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 this and
it is called the Equivalence Principle.”
The
general equation for the mathematical relationship
of
acceleration to inertia is a ί
= 1
It
is notable that the SI units used for the Planck Constant, h, is
joule.second, which in S-T units is T/S x T = T2/S,
an Energy reciprocal to the Motion acceleration, the joule.second is
a unit of inertia.
An
SI equivalent unit for the quantum of inertia is, from the foregoing,
therefore sec2/metre
and its value is 1.798 x 10-52.
The Planck value in joule.sec is 6.629 x 10-34
. The conversion factor from s2/m
to J.sec is 3.687 x 1018.
Multiplying 1.798 x 10-52
by the conversion factor 3.687 x 1018
, the answer is 6.629 x 10 -34,
the value of the Planck Constant in joule.seconds..
The
Planck Constant, h, is in fact the quantum of inertia.
Just
as is the case with the constant c,
the Planck constant, h,
is defined by Sq
and Tq
, and all of the constants can be defined by Sq
and Tq
.
The quanta of length and time are the only truly
fundamental quantities, and they define all other physical
quantities, constants and the minima and maxima of Quantum Physics.
That is why Space-Time units of measure are the
fundamental units of measure. Unlike SI units of measure, they make
the relationship between quantum minima and maxima clear and define
and quantify all quantities including those which are still unknown
in physics.
