In several scientific disciplines that involve mathematics an imaginary
number is used in the calculations to make the numbers come out right. That
should mean that there really is something acting on the physical world that
is represented by that imaginary number, since it makes the math come out
correctly in real world calculations.
An example of this is voltage = current x impedance
The number used for impedance is a complex number composed of a real number
plus an imaginary number.
V=I*(R+J) voltage =current times impedance J is an imaginary number to make
the math come out right.
Current is plotted horizontally on a graph and an imaginary vertical axis is
used for j; a2 +b2 = c2 pythagorean theorem is used to calculate a value for
the current. Showing that the imaginary number represents another dimension
acting on the current. This imaginary axis, for the imaginary number, on the
graph, is at a right angle to the real axis for the current. So the
imaginary number is acting, mathematically, as another dimension.
Einstein's general relativity theory, to explain gravity, (which has been
proven experimentally correct) uses time as a 4th dimension. In the real
world the 3 dimensions, length, width, and depth are each one at a right
angle to the other two dimensions. Time, being a 4th dimension, should be at
a right angle to the 3 physical dimensions, to qualify as a 4th dimension.
The imaginary number, used in calculating current and other things, has an
imaginary axis on a graph that is at a right angle to the real axis, and it
is therfore acting as a 4th dimension. Since the only proven 4th dimension
is time:
I recommend that time should be substituted for the imaginary number in all
calculations, in scientific disciplines, that use an imaginary number to
make the math come out correctly.
This could lead to all sorts of new equations in all of these fields, and
show how time itself is entering into the function of the real world in
these scientific disciplines.
Could lead to seeing how time influences every science that uses imaginary
numbers. Could (maybe) give a mathematical link between general relativity,
[gravity] and electromagnetism, through substituting time symbols that
represent time in each discipline into the other discipline.  Perhaps
leading to a way of using electromagnetism to influence gravity.
Might even lead to a unified field theory that works.
Complex imaginary number applications [Only registered users see links. ]
This substitution for the imaginary number being time is already done in
relativity theory:
Relativity
In special and general relativity, some formulas for the metric on spacetime
become simpler if one takes the time variable to be imaginary.
Since the universe is uniform I recommend:
SUBSTITUTE TIME FOR THE IMAGINARY NUMBER, IN EVERY SCIENTIFIC DISCIPLINE
THAT USES AN IMAGINARY NUMBER TO MAKE THE MATH COME OUT CORRECTLY.
See what new equations that it leads to and do experiments to verify if
those equations accurately show what happens in the real world.
Website showing example of use of imaginary or complex numbers: [Only registered users see links. ]
Since complex numbers provide a system for finding the roots of polynomials,
and polynomials are used as theoretical models in various fields, complex
numbers enjoy prominence in several specialized areas. Among these
specialized areas are engineering, electrical engineering and quantum
mechanics. Topics utilizing complex numbers include the investigation of
electrical current, wavelength, liquid flow in relation to obstacles,
analysis of stress on beams, the movement of shock absorbers in cars, the
study of resonance of structures, the design of dynamos and electric motors,
and the manipulation of large matrices used in modeling. While many of these
applications are beyond the scope of the Math B curriculum, an introductory
glimpse of the application of complex numbers to electrical circuits can be
easily understood and manipulated by students.
Application to Electrical Engineering:
First, set the stage for the discussion and clarify some vocabulary.
Information that expresses a single dimension, such as linear distance, is
called a scalar quantity in mathematics. Scalar numbers are the kind of
numbers students use most often. In relation to science, the voltage
produced by a battery, the resistance of a piece of wire (ohms), and current
through a wire (amps) are scalar quantities.
When electrical engineers analyzed alternating current circuits, they found
that quantities of voltage, current and resistance (called impedance in AC)
were not the familiar onedimensional scalar quantities that are used when
measuring DC circuits. These quantities which now alternate in direction and
amplitude possess other dimensions (frequency and phase shift) that must be
taken into account.
In order to analyze AC circuits, it became necessary to represent
multidimensional quantities. In order to accomplish this task, scalar
numbers were abandoned and complex numbers were used to express the two
dimensions of frequency and phase shift at one time.
In mathematics, i is used to represent imaginary numbers. In the study of
electricity and electronics, j is used to represent imaginary numbers so
that there is no confusion with i, which in electronics represents current.
It is also customary for scientists to write the complex number in the form
a + jb.
Introduce the formula E = I • Z where E is voltage, I is current, and Z is
impedance.
Possible Student Questions:
The impedance in one part of a series circuit is 2 + j8 ohms, and the
impedance in another part of the circuit is 4  j6 ohms. Find the total
impedance in the circuit. Answer: 6 + j2 ohms
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"stone" <[Only registered users see links. ]> schrieb im Newsbeitrag
news:[Only registered users see links. ]...
That
that
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__________________________________________________ __________________________
___ [Only registered users see links. ]
<><><><><><><><>
You say that as if the use of SQRT(1) is an ad hoc 'fudge factor.'
It isn't.
It arises because related physical phenomena often can be expressed in
a single mathematical relationship if the underlying mathematics is
sufficiently powerful.
Complex numbers are more 'powerful' at expressing concepts than simple
real numbers.
For example, if you want to describe simple harmonic motion you can use
separate real variables for position, velocity, acceleration, and such,
but each needs to be evaluated separately. Using one simple wave
function (with complex values) only one amplitude and one frequency
need to be evaluated and *all* the variables of interest from position
and velocity and acceleration to snap and crackle and pop and their
phase relationships can be found by simple differentiation of the wave
function.
Complex numbers appear in the physical theory of the complex refractive
index [Only registered users see links. ]
where dispersion and absorbtion are linked through the use of complex
numbers, with no 'time' component to the relationship at all.
You are making the mistake of associating too much reality to a common
mathematical treatment.
Spacetime's use of "imaginary time" is simply a device to turn
hyperbolic spacetime into something that looks more like Euclidean
time. This only serves to futz with the mathematics and does nothing to
change the fact that our 4D universe *does in fact* have hyperbolic
geometry.
Top posting:
Well let's do the substitution and see:
v = i x (r + J) j is the imaginary number
substituting time (t) for the imaginary number
v = i x (r+t); substituting i for charge/time [coulombs/time]
v = ch/t x (r + t); v = ch/t x r + ch/t x t; t's cancel
v = i x r + charge. For alternating current.
That equation that I derived from substituting j with t makes sense after
considering it.
v = i x r + charge [substitution was made for i = charge/time (or
coulombs/t)
That equation makes sense for alternating current.
Current goes from max to 0 then back to max in the opposite direction and
then to 0. When the current is at 0 and ready to change direction the charge
(built up at both ends of the wire) is at a maximum, so the potential
difference has reversed and ready to push the current back in the opposite
direction. So, the value of the voltage (potential difference stays
constant) throughout the cycle. As I x r increases the charge moves away
from the ends of the wire, in current, and charge at ends of wire goes down
while current goes up, still keeping voltage value v, constant. That
equation does describe what is happening with alternating current. The
substitution of j for time worked.
Also, v  (i x r) = charge is valid. When v = i x r then the charge built
up at the end of the wires is 0. V = i x r in direct current, and with
direct current there is never a charge built up at the end of the wire
because the charge is flowing constanly in one direction through the wire.
It's easy to derive new equations doing this. Start substituting time for
the imaginary number, in science fields that use imaginary numbers, and you
could be the first to derive your own equations.
I truly believe this is a valid substitution, based on the argument below.
stone wrote in message <[Only registered users see links. ]>...
that
is
for
the
at
spacetime
polynomials,
motors,
these
current
found
and
____ [Only registered users see links. ]
<><><><><><><><>
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WTF is *this* supposed to be? Until you *define* your terms all you
have is a spoonful of AlphaBits (TM).
Do you have any idea what you are talking about? I doubt it or you
could express yourself a little more clearly.
Is "v" the scalar we call "potential"? Is it measured in 'volts'?
Does the 'x' represent 'vector product' or just thirdgrade
multiplication?
Does 'r' stand for 'resistance' or 'radius' or 'displacement'?
If 'j' is 'the imaginary number' (presumably SQRT(1)) is 'J' something
else like 'current density': [Only registered users see links. ]
or is it just bad typography for 'j'?
If you really understood WTF you are talking about you would use
*standard* nomenclature (you would *know* it), or at least define *all*
the terms you use in your alleged 'equations.'
A more explicit use of parentheses would make your errors more
apparent.
The mathematical operation you call 'cancel' is illdefined.
....until you check your units. Then it turns into an *obvious* pile of
crap.
v = voltage or potential difference (charge difference); i = current, r =
resistance, J = imaginary number
Well let's do the substitution and see:
v = i x (r + j) substituting t (time) for j (the imaginary number)
v = i x (r+t); substituting i for charge/time [coulombs/time]
v = charge/t x (r + t); v = charge/t x r + charge/t x t; t's cancel
v = i x r + charge. For alternating current.
That equation that I derived from substituting j with t makes sense after
considering it.
v = i x r + charge [substitution was made for i = charge/time (or
coulombs/t)
That equation makes sense for alternating current.
Current goes from max to 0 then back to max in the opposite direction and
then to 0. When the current is at 0 and ready to change direction the charge
(built up at both ends of the wire) is at a maximum, so the potential
difference has reversed and ready to push the current back in the opposite
direction. So, the value of the voltage (potential difference stays
constant) throughout the cycle. As I x r increases the charge moves away
from the ends of the wire, in current, and charge at ends of wire goes down
while current goes up, still keeping voltage value v, constant. That
equation does describe what is happening with alternating current. The
substitution of j for time worked.
Also, v  (i x r) = charge is valid. When v = i x r then the charge built up
at the end of the wires is 0. V = i x r in direct current, and with direct
current there is never a charge built up at the end of the wire because the
charge is flowing constanly in one direction through the wire.
This is easy to do as you see. Go to any scientific discipline that uses an
imaginary number (as another dimension) to make the math come out correctly
and substitute t (time) for the imaginary number and then derive your own
equations.
The imaginary number may be simply there to handle capacitance and
inductance, but the important thing is that to use it to calculate current
it is plotted on a graph using the imaginary number on a vertical imaginary
axis at a right angle to the real axis for current. That means the imaginary
number is acting like a fourth dimension. That means t for time can be
substituted for it. Time is the only thing proven in general relativity
theory to act like a fourth dimension and act on the physical world
producing a warped spacetime metric which is used to explain gravity.
(General relativity theory was proven experimentally correct accurately
predicting the angle a star passing near a solar eclipse would appear to
move as light passed by the sun, and was bent by the sun's gravity.) So time
is proven to act as a fourth dimension. The imaginary number with its
imaginary axis acts as a fourth dimension. The time substitution for the
imaginary number is therefore valid. There is no dimensional inconsistency.
The imaginary axis is at a right angle to the real axis for current, and the
pythagorean theorem is used to calculate current. Another dimension is at a
right angle to the other three dimensions, length, width and height, which
are each one at a right angle to the other two. The imaginary axis qualifies
as another dimension, and so does the imaginary number plotted along it.
Summary: You may substitute that kind of imaginary number for time.
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"Josef Matz" <[Only registered users see links. ]> wrote in
news:43a951cd$0$9652$[Only registered users see links. ]:
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