This article explains how "pi", "e", the "impedance of space", time, space, and the other physical properties arise from simple standing waves, and how the "wave function" relates to the physical properties.
Reality is basically observed, and measured, in terms of "time intervals" and "time periods". Time intervals are most fundamentally associated with radii, and time periods are most fundamentally associated with circumferences. Both of these times are quantized by counting external reference cycles from such sources as atomic clocks. Historically, "day cycles", "month cycles", "year cycles" and the cycles of spring/mass systems and pendulums have been used to quantize times.
Time periods come about when two bodies interact about a common point, in a
common "period".
The time period is the physical property that is common to both parties to an
interaction.
A time period can be defined as:
time period(system) = cycle-count(reference) / cycle-count(of
system)
A time period is a count of the reference cycles, between each cycle of a system under observation. Cycles are observed against an assumed stable background, which is needed to determine when cycles are complete.
A separate time interval exists for each party to an interaction. This time
interval is a count of the reference cycles, between when a cause is observed in
a body, and when a casual effect is observed in the system the body is
associated with. A time interval or distance ( X = Ct
), is associated with each party to an interaction, whereas the time
period is shared by both parties.
A time interval can be defined as:
time(interval) = cycle-count(reference) / interval(cause to
effect)
A constant k1, associated with an isolated entity, can be defined as:
k1 = cycle-count(reference) / cycles(period) *
interval(cause to effect) / cycle-count(reference)
In the case of a perfectly symmetrical, isolated entity, k1 is equal to "2 pi".
A constant k2, associated with an isolated system, can be defined as:
k2 = exp(k1)
In the case of a perfectly symmetrical, isolated system, k2 is equal to exp(2 pi) or 535.488....
The physical expression of k1 is "2 pi", the ratio of two
distances", circumference and radius.
The physical expression of k2 is also the ratio of two distances, a small and a
large circumference. An easy to visualize physical representation of k2 would be
the two circumferences ( or radi or diameters) of a coaxial transmission line.
A transmission line with a charactistic impedance of 376.733.. ohms matches the
impedance of space. The physical condition that satisfies the "impedance of
space" can be defined as:
Z = k * ln(exp(2 pi)) / 2 pi
Now it is obvious that ln(exp(2 pi)) equals "2 pi" but this
equation is more familiar to electrical engineers as:
Z = k * ln( outer diameter / inner diameter)
where the ( outer diameter / inner diameter) for a 376 ohm transmision line
equals 535.488, and k equals ( Z0 / "2 pi") or 59.959.. This is
commonly expressed as:
Z = 59.959 ln( outer diameter / inner diameter)
As far as I know, this is the first explanation of how these two constants arise. ( 59.959 and 535.488) Note that k is simply a constant used to scale the numeric value of impedance, and if Z0 were set equal to 2 pi, then the electrical properties could be defined from the equation: Z0 = ln(exp(2 pi)), or 2 pi, for pure space, and Z = ln( outer diameter / inner diameter) otherwise.
Distance is fundamentally an interaction time which is multiplied by a
constant to differentiate it from period time. This constant is of course
"C", which serves no purpose other than to differentiate between the
two fundamental kinds of time, and set the units.
distance(x) = time interval(x) * C
Mass is simply a property used to differentiate between two interacting
bodies. Humans perceive conserved "objects" having mass, varying in
homogenous "media" such as time, space and magnetic flux. In the
simplest case, we perceive the object Earth varying in media without considering
that the Earth's media is an expression of the Sun's mass. ( And vice versa.)
In fact, the media associated with objects is a more complete and fundamental
expression of objects than mass. This can be expressed as:
mass(A) * G = (time(interaction B)*C)^3 / ( time(period) / 2
pi)^2
mass(B) * G = (time(interaction A)*C)^3 / ( time(period) / 2 pi)^2
Note that "C" is used to express interaction time as a distance, while "G" is a constant used to differentiate between object A and object B, or more fundamentally between media A and media B, such media fundamentally being standing waves.
All other physical properties can be defined in terms of the time, distance
and mass thus defined, but the most fundamental expression of the physical
properties is:
property(X) = tan(A)^L * tan(B)^M * time(period)^N * C^(L+M) /
G^O
where:
L, M, N and O are integers
C = the speed of light
G = the universal gravitational constant
tan(A) = orbital velocity(A) / C
tan(B) = orbital velocity(B) / C
In other words, what we perceive as velocities are basically tangent functions associated with what we perceive as interacting bodies. Note that when "C" and "G" are set equal to one, that the simple elegance of reality becomes apparent.
To understand how these fundamental principles relate to the "wave function" and quantum mechanics read some of the other articles under "Random Thoughts". In these articles, I assert that Special Relativty is basically the addition of tangents:
and that spectrum of hydrogen-like ions is basically a trig identity: sin(A)^2
+ sin(B)^2 = 1
which after a little juggling is expressed as: v = Rydberg's
constant * ( 1/M^2 - 1/N^2)
The bottom line is that all this stuff ( reality) is just standing waves and geometry. The physical constants "Z0", "C" and "G" are unnecessary, and should be discarded as they complicate reality by creating a plethora of unnecessary properties. This makes people look at the properties as separate things, rather than as a part of a simple matrix.
I might mention that the issue of setting the impedance of space equal to one
or "2 pi" depends upon whether the standard of measurement should be
based on circumferences ( 2 pi) or radii ( radians). Currently we measure time
in cycles, while we measure most of the other properties, including distance,
mass, etc. in radians. Radians have to do with "bodies" and
interaction times, while cycles have to do with systems and period times. I, of
course, opt for cycles, as ultimately, even interaction times are measured in
cycles, and determining the coincidence of "cause" events, and
"effect" events have an "uncertainty" about them. ( Cycles
can be "zero beat", intervals cannot.)