K. Marinas' Cyclic Multiverse Hypothesis/Old Approach to Unit-Scaling

The below is the old, and now defunct, scaling law for K. Marinas' Cyclic Multiverse Hypothesis. The new scaling law, found at K. Marinas' Cyclic Multiverse Hypothesis#A Fractal Universe and Physical_Units, allows for faster-than-light-motion embedded inside normally slower-than-light matter, which could explain the origin of the astronomical quantity of energy now understood in quantum physics as vacuum energy.

A Fractal Universe and Physical Units

The Cyclic Multiverse is a self-similiar fractal which might have formed just like a snowflake would. Anything from the curvature of spacetime to the pattern of a snowflake can ultimately explained with units of measurement.

$k$ is equal to the multiple between fractal levels.

The changes of primary physical properties for the lower fractal level are as follows²:

$k^1$

Properties which are greater at the lower fractal level:

frequency

Hertz

1/s

$k^{0}$

Properties that are the same for corresponding of objects of each fractal level:

temperature	Kelvin	K
velocity	Meters per second	m/s

$k^{-1}$

Properties which are smaller at the lower fractal level:

wavelength (distance)	Meters	m
luminous intensity	Candelas	Cd

$k^{-2}$

Properties that are proportional to the amount of substance or mass at each fractal level:

charge	Columbs	C
mass	Kilograms	kg

From these assumptions, we can determine the changes that occur in other physical properties for every fractal level we go down.

The changes of physical properties for the lower fractal level are as follows:

Gravitational Phenomena

$k^1$

Properties which are greater at the lower fractal level:

angular velocity	radians/s
density	kg/m3
force/mass	m/s2
G	m3/(kg·s2)
pressure	N/m2

Material Phenomena

$k^1$

Properties which are greater at the lower fractal level:

acoustic impedance	(kg/s)/m2	proportional to the density and the phase velocity (speed of sound).
energy density	J/m3	energy / volume

$k^{0}$

Property that remains the same for corresponding of objects of each fractal level:

dynamic viscosity	(kg/s)/m	the resistance of a fluid to deformation under shear stress
surface tension	J/m2	the amount of tension that keeps a surface, especially of liquids together

$k^{-1}$

Properties which are smaller at the lower fractal level:

force	N=J/m	comes from a energetic kinetic potential produced by an impulse
power	W=J/s	rate of energy expenditure
mass flow rate	kg/s	the mass of fluid that flows past a given cross sectional area per second
kinematic viscosity	m2/s	ratio of dynamic viscosity to mass density

Correlations with substance

$k^2$

Property that is inversely proportional to the amount of substance or mass at each fractal level:

angular acceleration

radians/s2

rate of change of angular velocity

$k^{-2}$

Properties that are proportional to the amount of substance or mass at each fractal level:

area	m2	such as the area of a crossection of a specified part of a vacuum which lets photons of the lower fractal level through. Photons/area is a constant for corresponding areas of different fractal levels
impulse and momentum	N·s=kg·m/s	force * time. mass * velocity.
energy	J=kg·m2/s2	quantity of energy itself
mass	kg	equivalence of mass and energy. where there is point mass, within it are point charges.
volume flow rate	m3/s	the volume of fluid that flows past a given cross sectional area per second
torque	kg·m2/s2	force applied to a member to produce rotational motion

Light Phenomena

$k^1$

Properties which are greater at the lower fractal level:

frequency	1/s	influences the other electrical properties for this lower fractal level (Hz, cycles per second)
angular frequency	radians/s	frequency with which phase changes
spectroscopic wavenumber	1/m	the inverse of wavelength
luminosity	Cd/m2	light emission / area
light flux density	lm/m2	light incident / area

$k^{0}$

Properties that are the same for corresponding of objects of each fractal level:

luminous efficacy

lm/W

power as it appears to an observer versus the actual power

$k^{-1}$

Properties which are smaller at the lower fractal level:

wavelength distance	m	influences the other electrical properties for this lower fractal level
luminous flux	lm=Cd·sr	Candelas times Steradians (lumens, lm)
luminous intensity	Cd	power emmited by a light source

$k^{-2}$

Properties that are proportional to the amount of substance or mass at each fractal level:

luminous energy

lm·s

quantity of light. living things on the lower fractal level see photons which have $k^{-2}$ as much energy.

Electric Phenomena

$k^2$

Property that is inversely proportional to the amount of charge at each fractal level:

elastance

1/F=V/C=J/C2

potential difference for every coulomb (inverse farads)

$k^1$

Properties which are greater at the lower fractal level:

electric field strength	N/C	force / charge
current density	A/m2	current / area
charge density	C/m3	charge / volume
permeability	N/A2	allows an electric field to pass through easily, lets charge through
resistance	W/A2	higher electrical resistance at the lower fractal level (ohms Ω)

$k^{0}$

Properties that are the same for corresponding of objects of each fractal level:

applied tension	J/m2=N/m	work / area
conductivity	1/(Ω·m)	property of matter which allows an electric field to get from A to B
resistivity	Ω·m	property of matter which resists an electric field from getting from A to B
potential difference	W/A=J/C	power per unit current. energy per unit charge. current times resistance. (volt)
electric flux density polarization density	C/m2	a field which causes electric flux. electric dipole moment per unit volume.

$k^{-1}$

Properties which are smaller at the lower fractal level:

current	A	flow rate of electricity which provides a force that causes magnetic flux
permittivity	C/(V·m)	resists the flow of an electric field, contains charge
conductance	A/V	current produced / (energy / charged particle)

$k^{-2}$

Properties that are proportional to the amount of substance or mass at each fractal level:

capacitance	F=C/V=C2/J	quantity of charge stored for every volt (farads)
coulombs electric flux	C=A·s	quantity of electric charge itself

$k^{-3}$

Properties that are very small at lower fractal levels.

electric dipole moment	A·s·m	a vector due to uneven distribution of unlike charges. proportional to charge and distance.
planck's constant	J·s	the discrete quantity of action (quantum unit of angular momentum)

Magnetic Phenomena

$k^1$

Properties which are greater at the lower fractal level:

magnetic flux density

Wb/m2

magnetic flux / area

$k^{0}$

Properties that are the same for corresponding of objects of each fractal level:

inductance	J/A2	accomodation of the production of magnetic flux per current
reluctance	A2/J	resistance of the production of magnetic flux per current
magnetic vector potential	N/A=Wb/m	force per amp. magnetic flux per meter.
magnetic field strength magnetization	A/m	an auxillary field which causes magnetic flux. magnetic dipole moment per unit volume.

$k^{-1}$

Properties which are smaller at the lower fractal level:

magnetic flux

Wb=J/A=V·s

comes from an energetic magnetic field produced by a current (weber, Wb)

$k^{-3}$

Properties that are very small at lower fractal levels.

magnetic dipole moment

A·m2

a vector whose direction is normal to a loop of current. proportional to current and area.

Temperature Phenomena

$k^1$

Properties which are greater at the lower fractal level:

thermal heat transfer coefficient	(W/m2)/K	coefficient, thermal conductance
thermal resistance	K/W	index of a material's resistance to heat flow the reciprocal of conductance

$k^{0}$

Properties that are the same for corresponding of objects of each fractal level:

temperature	K	corresponding objects of the lower fractal are just as hot, or as cold, as they are in our fractal level
thermal conductivity	(W/m)/K	ability of a material to conduct heat.
thermal expansion coefficient and temperature of color	1/K	the fractional change in length or volume per Kelvin at constant pressure
velocity change with temperature	(m/s)/K	velocity increases with temperature
thermal heat capacity	J/kg	the heat stored in a given mass

$k^{-1}$

Properties which are smaller at the lower fractal level:

thermal conductance	W/K	rate of heat flow
thermal resistance coefficient	K/(W/m2)	coefficient, thermal resistance

$k^{-2}$

Properties that are proportional to the amount of substance or mass at each fractal level:

heat capacity

J/K

proportion relating the amount of energy per temperature

"Political" Properties

$k^1$

Properties which are greater at the lower fractal level:

"Political" Property	Explanation	Equal to	Physical Analogue
resistance	trouble encountered when going a distance or time	difficulty/achievement	ohms

$k^{0}$

Properties that are the same for corresponding of objects of each fractal level:

"Political" Property	Explanation	Equal to	Physical Analogue
difficulty	a measure of the problems encountered	achievement·resistance	volts

$k^{-1}$

Properties which are smaller at the lower fractal level:

"Political" Property	Explanation	Equal to	Physical Analogue
power	rate of exercising freedoms	freedoms/time	watts
achievement	the action itself	particles/time	amps

$k^{-2}$

Properties that are proportional to the amount of substance or mass at each fractal level:

"Political" Property	Explanation	Equal to	Physical Analogue
freedom	potential to do	liberties/time	joules
charge	how much has passed	achievement·time	coulombs

$k^{-3}$

Properties that are very small at lower fractal levels.

"Political" Property	Explanation	Equal to	Physical Analogue
liberty	activity	freedom·time	joule-seconds