Re: Math & physics.


"Steve Bell" <sb635@xxxxxxxxxxxx> wrote in message
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"Androcles" <Headmaster@xxxxxxxxxxxxxxxx> wrote in message
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Solar cells work, but they are not built by schoolmarms.
ISS has "almost an acre of solar panels to power its 6 laboratories"
It is up to engineers to cherry-pick the bits of theories that make
sense and leave out those that do not.
Schoolmarms write papers, engineers make the world go round.
Engineers are not too interested in prophecies. If it works, SELL it.
If it doesn't, back to the drawing board.
That's the engineering method; you can keep your prophecies,
predictions, horoscopes and palm-reading scientific methods.



I was an aerospace engineer for 22 yrs. I worked on synthetic aperture
radars (SARs). There is a mathematical development of radar theory that
relies completely on analytical (complex-valued) signals. In this theory,
a signal is mathematically represented by a complex number at a point in
time with an "in-phase" (real) component and a "quadrature" (imaginary)
component. In this theory, "point targets" reflect an EM signal
transmitted by the radar (and then the radar goes into receive mode to
receive the reflections). When a *point* target reflects the EM, the radar
maniacs I worked with (and in fact, apparently the entire "radar
community") think the analytic signal vector (complex-number) gets rotated
(phase shifted) by an amount that has nothing to do with the radar nor its
distance from the point target. Also, this is a *point* doing the
reflection, so there is nothing like "bouncing around inside and then back
out of cavities that are small relative to the wavelength," which would
lengthen the overall path the signal takes to-and-from the radar, and
cause a phase shift. A point does not have any cavities, as I pointed out
about a billion times to these insane people. And the rardar maniacs
agree, this specific phase shift is not at all "small cavity-driven." The
rotation occurs because the radar maniacs think a *point* target
(reflector) in the exterior world has an *innate* "complex-valued
reflectivity," which, when added to the incoming signal, instantaneously
rotates the incoming signal, causing a phase shift. They completely assume
the external world is innately complex-valued, just like the QM maniacs.
When I found this out, I almost puked. In fact, there is an old 1940s
paper by a man named Gabor that derives radar theory using the *exact*
same equations as QM. The paper even shows the radar theory's "uncertainty
principle," which has exactly the same form as QM's UP. The use of the
sqrt(-1) is a great mathematical tool, it can provide many mathematical
shortcuts, but *there is nothing in a real-valued physical external world
that is physically complex-valued.* I completely disagree with assuming an
innate complex-valued reflectivity exists "out there" for point targets.
Yet we can make radar images. Even though the complex-valued theory is,
imo, strictly incorrect, it comes close to what I think really happens,
close enough for us to make excellent radar images using it. I don't know
about you, but I still want to very much understand the truth, even when
an application of a theory "does well enough" to sell it.

In the Heisenberg picture of QM, position and velocity are complex-valued.
Can anyone tell me where the imaginary part of this position is at in
physical space? I know where the real part is at, but exactly where is
this "imaginary" part of a particle's position? And then please explain
what is the *physical* interpretation of the *imaginary* part of a
complex-valued velocity vector. Like I said, I know what the real part is,
but what the hell is an "imaginary" velocity? It might be quite telling
that the word "imaginary" is used - it's really refers to the made-up
nonsense of QM, all in their minds, all imaginary. All of this nonsense
happens because QM *cannot* be developed *without* the use of the
sqrt(-1). That right there should have told the original QM maniacs that
they themselves were just imagining things.

Steve Bell


You say *there is nothing in a real-valued physical external world
that is physically complex-valued.*
I'd say this: mathematics is a language, and like prose and poetry and
music, it is art. Useful art to the engineer, but art nevertheless.
When Newton wrote his laws he used Latin, the English translation
of which is:
LAW I.
Every body perseveres in its state of rest, or of uniform motion in a right
line, unless it is compelled to change that state by forces impressed
thereon.

LAW II.
The alteration of motion is ever proportional to the motive force impressed;
and is made in the direction of the right line in which that force is
impressed.

LAW III.
To every action there is always opposed an equal reaction; or the mutual
actions of two bodies upon each other are always equal, and directed to
contrary parts.

The mathematical shorthand for laws 1 & 2 (actually Galileo's laws) is:
F = dp/dt.
The mathematical shorthand for law 3 is:
Mv = mV.

We can only use the shorthand if we understand the meaning
of the symbols; F is force, m is mass, v is velocity, p is mass
multiplied by velocity, dp/dt is "alteration of motion". M is a
big mass, v is a small velocity. Beyond that, v is a vector
and is what a "right line" is all about, p we call momentum
but Newton called "motion".

Now you know that current leads voltage in a capacitor and
lags in an inductor. You also know that a magnetic field exists
around a current, and an electric field exists across the plates
of a capacitor, I don't need to tell you that. If you disagree
then there is no point in continuing.

But now I want to introduce an idea to you that will seem
strange, but think about it. Minus (-) can be thought off as a
binary operator as in 3-2 = 1, but it is really a unary operator,
as in 3 + (-2) = 1. Mathematicians love shorthand!
Algebraically, a-b=c is identical to a+b = c when b is negative.
A computer will take b, negate it and add a, storing the result
in a location called c.
On a number line, minus is the reverse DIRECTION to plus.

-2........-1.........0.........1.........2........3
<-------- ++++>

Adding 3 to -2 is VECTOR addition. Go back 2, then go
forward 3, arrive at 1.

In a real-valued physical external world I give you three apples,
take two back and you have one apple. 3 forward, 2 back.

Now... the "number" that you call i = sqrt(-1) isn't a number
at all. It's an operator, just as *, /, +,- are. It represents a vector
that is orthogonal to the number line in the complex plane.
There is '+' going to the right, '-' going to the left, 'i' going
up and, (lo and behold) '-i' going the opposite way to 'i', down.
Multiplying a number by 'i' is a rotation of 90 degrees, doing
that twice is a rotation of 180 degrees; which is the same as a
multiplying by -. It makes sense because it is CONSISTENT.
Multiplying i by - gives -i, a rotation of 270 degrees. i^2
is a rotation by 180, so 'i' is sqrt('-'). I omitted the '1' deliberately.

So where is this all going?

The physical world includes phenomena such as magnetic
and electric fields, and they are orthogonal to each other.
They are VECTORS.
IF
( we use shorthand mathematics to describe magnetic and electric fields)
THEN
there is SOMETHING in a real-valued physical external world
that is physically complex-valued.
We just need to understand the symbols. Unfortunately the
terms "real" and "imaginary" are confusing, magnetic fields
are as real as electric fields, changing one will cause the other
or motors and generators would not work.
The math is there to describe it, to provide the shorthand
so that we can manipulate phase angles and know what
component to use in a particular application. If you are
designing a microwave oven or a TV, what is the frequency,
what is the power factor? Is it different from radar? Is it safe
or will it start a fire? And the most important question for any
businessman investing capital in it: How much does it COST?

As I've already said, it is up to engineers to cherry-pick the
bits of theories that make sense and leave out those that do not.
To do that we need to cut through the hyperbole that comes
with schoolmarms trying to describe their own misunderstanding
of the real world. Those that can, do. Those that can't, teach.

--
Ref:
http://www.fourmilab.ch/etexts/einstein/specrel/www/figures/img22.gif


What kind of lunacy prompted Einstein to say
the speed of light from A to B is c-v,
the speed of light from B to A is c+v,
the "time" each way is the same?





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