bperet wrote: ↑
Thu Jun 28, 2018 10:45 am
A common resistance acts like a membrane, limiting flow through it. Both permeability and permittivity do the same. I will explore this further.
L = Rt, inductance is resistance for a period of time (i.e. energy suddenly appears from a "potential" stored in a magnetic field -- 2D counterspatial)
In other words, inductance IS mass is resistance for a period of time (L = m = Rt)... if there was no mass, there'd be no resistance!... and oh, look mass and inductance have the same dimensions of motion: t3
Conversely, C = Gt, capacitance is conductance for a period of time (i.e. energy suddenly appears from a "potential" stored as a dielectric field -- 1D counterspatial)
Conductance (G) and Resistance (R) by definition have in themselves a reciprocal relation (G = 1/R)
R = μI, resistance is permeability of current, i.e inductance
G = εI, conductance is permittivity of current, i.e. capacitance (s3
* easy to miss the true scalar reciprocal relationship of capacitance (s3
/t) to inductance (t3
) as the cross-product does not yield 1 (unity) but rather 1/t2
. This is because what we call inductance... the linear "lines of force" (net push/pull of scalar motion, 1D) is on the same side of the unit speed boundary as our observation (time-space i.e. same reference frame of time to time)... the capacitance is counter-spatial... the rotational "lines of force" or the net "imaginary" (scalar motion we call magnetic, 2D) and is on the other side of the unit boundary within the Time Region (TR) of the atomic rotation and so our observance is limited to the NET rotation as we cannot observe locations in 3D time directly but we can
observe how time effects space (as a NET scalar push/pull PLUS net scalar rotation, real + 1D imaginary = complex). The NET effect of three dimensions of time are reduced to the affect on one dimension in the inverse aspect -- and space is one-dimensional too, as every point in space can be related to every other point using one dimension [distance] -- the difference being the well-known 1/c2
transform. Look here it is: E = mc2
... energy (one-dimensional motion in time) is scaled to mass (three-dimensional motion in time) using the 1/c2
transform directly (naked proof). OK, here it is again in the electrical world: P = IV (axiomatically) and V = IR (Ohm's law) → P = I2
R → P = E/t = I2
R → E = I2
Rt → E = I2
m (mass IS resistance for a period of time) → E = c2
m (current IS motion at the speed of light, c) → E = mc2
... looks familiar. In furtherance of demonstration, note that when crossing the unit speed boundary speed (s/t) becomes 1/t2
: substitute 1/t for s (as s/t = 1; this IS motion) and the result is 1/t2
In natural units
that makes μεI2
= 1 or μ0
Fully reduced (taking both 1 = c and I = c as current IS a speed of +1): μ = 1/ε
Doesn't get any more obvious than that.
bperet wrote: ↑
Sun Feb 03, 2019 4:52 pm
When the rotation extends into the 2nd rotational plane, j, you get intermediate speed (2-x) motion. Now this is interesting because unlike the low-speed plane, it has NO projection onto the real axis--it is always zero, regardless of angle, as it is orthogonal to the real axis. This makes things appear "instantaneous" (infinite speed). And two-dimensional "electric" rotation is what we call "magnetism." So your magnetic fields arise with [1 ai bj 0k]--and why electromagnetism requires electricity to produce it.
We're talking about the natural datum on the j
axis... the one with no dependence on clock time... cause... effect... it's up to you. Whether the voltage
(overall inductive) or voltage
(overall capacitive) and the magnitude of the phase angle separating them in clock time simply depends on the NET reactance ("imaginary" i.e. rotational
resistance) -- scalarly rotationally inward
or scalarly rotationally outward
-- as a function of the circuit's SUM capacitance and SUM inductance -- which are themselves governed by inverse laws of relation -- for a given switching frequency... we're talking AC here or nothing's changing. Here we see instantaneous
effect in time for a given period as a phase angle (clock time!) with difference in phase angle (180-θ) expressed as a constant wavelength ("angle") in clock time!
In electric power flow, it is important to know how much current is leading or lagging because it creates the reactive power in the system, as opposed to the active (real) power. It can also play an important role in the operation of three-phase electric power systems.
-- Leading and lagging current
(willfully incomplete) @ Wikipedia
has magnitude (absolute value) of 1 where j
is used in place of i
as 'i' has other potential meaning in EE.
This is rotation in the complex plane <1 ai
> where θ is best expressed in radians; 2π radians is one full revolution. The sign of the exponent expresses "direction" (CW or CCW) for each of the two reciprocal aspects: induction and capacitance.
The phase angle between the two varying waveforms (current and voltage) is similar to the recursive geometry of the EM spectrum in that an unbounded turn
in equivalent space (time or, if you will, counter-space) can only be represented as a bounded angle
in space -- this being due to the offset in dimensionality (x±1) required to represent equivalent
motion (how time effects space or how space effects time) in either inverse aspect -- in that the phase angle or what we call that "frequency" is the net shear
in time-space (or space-time on the cosmic side)... where only the net linear (push/pull) and net rotational motion can be transmitted across the unit [speed] boundary (the genesis being the TR of the atom)... this IS that net rotational motion.
We know this concept as dimensional reduction: two counter-rotations (each one-dimensional) can be reduced to a single dimension of linear displaced motion through a function known as Euler's Formula (for complex numbers): eiφ
= cosφ + isinφ ... flip the sign on the exponent (opposite "direction", inward → outward or vice-versa) flips the direction in one dimension only; add them together (that IS a bi-rotation) and you get eiφ
= 2×cosφ... two dimensions of motion can be reduced to a one-dimensional shear in the reciprocal aspect... unbounded bi-rotation (2D) → bounded linear [vibration] (1D). This is the basis of the concept of dimensional reduction (and its inverse, dimensional expansion) as observed in nature. For example, if combining two one-dimensional rotations results in a reduction
of dimensionality from 2 to 1, then what is the result of combining two one-dimensional linear displacements (simultaneously)?... ah ha! an area (2D) or an increase
(inverse decrease) combining
of dimensionality from 1 to 2!
To fully describe a wave (non-local) you need three things (1) [wave] magnitude, (2) frequency, and (3) phase angle (with respect to some other "reference" wave). Magnitude is obviously the net push/pull making "frequency" the net rotation (or rotational yin's shadow masquerading as rotational yang here in the material sector). This is not a shock. We've known for a long time frequency is not energy is not color is not.... It's not a lot of things we take it for in conventional, legacy science.
Changing the excitation voltage
up or down (current produced in creation of magnetic field) to the AC generator-end stator does this (varies the "lead/lag angle") in reversible AC-DC motor-generator sets. We usually set them slightly "lead" in addition to the phase angle between the AC rotor and DC stator (or vice-versa) necessary to develop the torque to keep the thing spinning (minus losses!) depending on the direction of energy transfer as most loads are inductive AC motors themselves and, well, mass IS inductance and everything's made out of mass (time, not space). Slipping a pole (too much "lead," or, if you will, too much inverse "lag") results in loss of regulation and loss of [spatial←→counterspatial] energy/speed (ah ha, motion) transfer link.
And all (electric, magnetic, kinematic motion) are at orthogonal relations to one another in 3D coordinate (extension) space. It's like a big universal dynamo where you put in one, two, or three legs of the triad and the universe gives you back the difference. Just like Faraday discovered... "dielectric" field, magnetic field, electrically-conductive medium... pick any two and they will create the missing third. Put in electric and magnetic... get motion (flow) out; put in motion and electric... get magnetic out; put in magnetic and motion... get electric out. Put in all three and you get atom building...
You'd think these guys would have figured this stuff out by now...
Choose your own direction for the "flow" of time! Fun for the whole family!
TOTAL SIDEBAR: This is why all the complexity and tapestry of thought that goes into your well-detailed explanation is reduced to the NET push/pull when it leaves you (one side of unit boundary) and is communicated to another. Only the NET effect can be felt and so emotion, or intuition (the inverse aspect of the logic of your thought) either draw that person closer to you, or push you two further apart. Consider the emotional appeal of your content even if you do not think the other party has a consideration in any regard as your message may be severely dulled otherwise. Do good for the sake of good. Like "attract" like in this speed region.