/--------------------------------------------------------------------*
| --------------| A COLLECTION OF IDEAS | by Raheman Velji |
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* * * [must use a fixed-width font to view diagrams properly] * * *

CONTENTS:

(1) Inventions
Two inventions which use "self-sufficient propulsion" as a mode
of transportation. The term "self-sufficient propulsion" will be defined
and it will be realized at the end of the section that "self-sufficient
propulsion" will have a lasting effect on transportation (especially in
space exploration).

(2) Law of Conservation of Energy
Two examples which clearly demonstrate that the Law of
Conservation of Energy is wrong.

(3) Absolute Frame of Reference
First, this section will demonstrate that special relativity is
wrong. Then, it will amend special relativity by introducing the concept of
an "absolute frame of reference". This section also discusses a possible
method for determining the "absolute velocity" of an object.

(4) Work
This is a continuation of the previous section. The discussion
thus follows by considering "absolute velocity" (that is, velocity measured
relative to the "absolute frame of reference"). Dark matter is shown to be
a result of the fact that relative velocity can surpass the speed of light.
An explanation as to why our Universe is expanding is hypothesized.

(5) Extras:

(1) Absolute Velocity:
This section discusses a different method for determining
the absolute velocity of an object.

(2) Electricity:
This section analyzes the idea of electricity using
"impulses". This section isn't revealing like the previous ones. Instead,
the only reason I am including this section is because at the end we derive
the correct equation for the change in time between electron collisions.

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-|-|-| (1) INVENTIONS -|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-
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Inventions:
1) The Seesaw Newton Motor
2) The Simple Newton Engine

Devices that use "self-sufficient propulsion" work on Newton's law that
"every action has an equal and opposite reaction." The idea is to harness
the "action" and eliminate the "reaction", or convert the "reaction" into
useable energy. Thus, within the device, the "reaction" is lost allowing
the "action" to propel the device. All devices that use "self-suffiecient
propulsion" work without affecting the environment. That is, they don't
need a road to push off of like cars, they don't have to push air like
planes or spew out gases like space shuttles. Thus, they get the name
"self-sufficient propulsion" because they are self-sufficient. In other
words, you can put a box around the entire device and the box would move,
and nothing would enter or exit the box, and the device itself wouldn't
react with the environment that comes inside the box. It only reacts to the
environment in the box, which it creates, which it uses to propel itself.
(I propose that any device that uses self-suffiecient propulsion should have
the name "Newton" added to its full-name so that we remember how it relates
to Newton's third law. Whether this convention should be followed is
debatable.)

Whether the Seesaw Newton Motor or the Simple Newton Engine are feasible is
uncertain. However, the idea of "self-suffiecient propulsion" will have a
lasting effect on transportation (especially in space exploration).

* [must use a fixed-width font to view diagrams properly]

-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
=-=-=-1) The Seesaw Newton Motor=-=-=-=-=-=-=-=-=-=-=-=-=
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

Top view:


M1a---M2a <--front
electromagnets
m1
\
\ /\
\ ||
o <--seesaw ||
\ forward
\
\
m2

M1b---M2b <--back
electromagnets


Ideally, "M1a", "M1b", "M2a", "M2b", "m1", "m2" are all electromagnets.
(Some of the electromagnets can be changed into permanent magnets where it
is deemed fit.) "M1a", "M1b", "M2a", and "M2b" are fastened to the base,
while "m1" and "m2" are connected to a "seesaw" whose pivot ("o") is
connected to the base. (It is possible to construct this without the back
electromagnets.)

The way this invention works is somewhat hard to explain. Here is a
simplified version:

When "M1a" and "m1" are nearly touching an electric current is sent through
"M1a", "M1b", and "m1". "M1a" should repel "m1" while "M1b" should attract
"m1". Thus, both "M1a" and "M1b" will experience a force in the forward
direction, while the seesaw swings around bringing "m2" close to "M2a". As
"M2a" and "m2" are close now, an electric current will pass through "M2a",
"M2b", and "m2". "M2a" should repel "m2" while "M2b" should attract "m2".
Again, the electromagnets connected to the base, "M2a" and "M2b", will
experience a force in the forward direction while the seesaw swings back to
its starting position to repeat the cycle. Since all the electromagnets
that are connected to the base experience a force in the forward direction,
the entire device will be propelled forward as the seesaw keeps swinging
about. Notice that the seesaw does *not* rotate, it simply moves back and
forth, like a seesaw.

It should be noted that as the seesaw swings about, a bit of the "backward"
energy of the electromagnets on the seesaw will be conveyed to the base via
the pivot, thus slowing down the entire device. That loss of speed, though,
is negligible.

The above explanation of the workings of the Seesaw Newton Motor is
incomplete. One must understand the following:

Every action has an equal and opposite reaction. The main idea of the
Seesaw Newton motor is to harness the "action" by converting the "reaction"
into useable energy. When the front electromagnets, back electromagnets and
the electromagnet on the seesaw are activated, the front and back
electromagnets experience a "positive" force by being forced forward. The
electromagnet on the seesaw, however, experiences a "negative" force as it
moves in the backward direction. One must get rid of the "negative" energy
of the electromagnet on the seesaw. If the "negative" energy is not rid of,
then it will somehow be transferred to the entire device, thus not allowing
the device to gain velocity. The Seesaw Newton Motor does not only get rid
of the "negative" energy, it in fact uses it to propel the device further.
Consider the following scenario: a Seesaw Newton motor at rest, and set-up
similar to the diagram above. Now, let us initiate a current through "M1a",
"M1b", and "m1". The electromagnets on the base ("M1a" and "M1b") will
experience a "positive" force by being forced forward. The electromagnet on
the seesaw ("m1"), however, will experience a "negative" force by being
forced backward. However, at the other end of the seesaw, the electromagnet
("m2") seems to be approaching the front electromagnet ("M2a") and receding
from the back electromagnet ("M2b"). Thus, at the other end of the seesaw,
when those electromagnets are activated, the repulsive force between the
electromagnet on the seesaw and the front electromagnet will be greater,
thus propelling the device further forward. Also, at the other end of the
seesaw, when those electromagnets are activated, the attractive force
between the electromagnet on the seesaw and the back electromagnet will be
greater, again propelling the device further forward. The fact that both
magnets ("M2a" and "M2b") experience a greater forward force is due to the
the initial "negative" energy of the electromagnet on the seesaw ("m1").
Thus, both the "action" and the "reaction" are harnessed to propel the
entire device forward. Thus, in a sense this invention is more effective
than a space shuttle because it harnesses both the "action" and "reaction",
unlike a shuttle which only uses the "action".

If both "action" and "reaction" are to be harnessed, one must ensure that
the electromagnets on the seesaw should not hit either the front
electromagnets or the back electromagnets. That is because any collision
will slow the forward motion of the entire device. It may seem that if the
seesaw swings so hard that "m1" hits "M1a" or "m2" hits "M2a" then the force
of the collision will cause the base to experience a force in the forward
direction. This is wrong. Only the "forward momentum" of the seesaw will
"push" the base forward. However, when the seesaw electromagnet hits the
front electromagnets, the entire seesaw will stop moving and the "backward
momentum" of the electromagnet on the seesaw will be conveyed to the base
via the pivot. Thus, any collisions are undesirable.

One must avoid collisions by ensuring that the electromagnets are activated
such that the seesaw never has a chance to collide. Thus, input sensors
would need to be used to calculate the speed of the seesaw so that the
electromagnets can be perfectly timed to avoid collisions. By avoiding
collisions, both "action" and "reaction" are harnessed.

Notice that for this invention to actually move the electromagnets must be
very strong and the entire device must be light. Otherwise, the device will
stay in the same spot and just wiggle about instead of moving. In any case,
this invention can definetely compete with devices that use ion propulsion.

Also, the entire Seesaw Newton Motor can (with a battery) be put into a box
and the box would move without interacting with the environment outside the
box. Thus, it moves using "self-sufficient propulsion".

-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
=-=-=-2) The Simple Newton Engine-=-=-=-=-=-=-=-=-=-=-=-=
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

The Simple Newton Engine works using "self-sufficient propulsion".

The engine is a cylinder with a piston in it. The piston may require wheels
to move inside the cylinder.


\-----------\-----------\-----------\-----------\
Every action has an equal and opposite reaction. The main idea of the
Simple Newton Engine is to harness the action by getting rid of the
reaction. How do we get rid of the momentum of the reaction? One way is by
using friction, which is discussed in "Step 3".

The idea is to force the piston in the backward direction, down the
cylinder. Since every action has an equal and opposite reaction, the
cylinder will then experience a force in the forward direction. This force
is ideally created by using electromagnets. Let us say that there is an
electromagnet on the piston ("#") which repels the magnet ("X") that is
connected to the front of the cylinder. (Also, one could make this similar
to a Linear Induction Motor, with the piston as the projectile.)

Side-view (cross-section):

| ___cylinder
| ||
| \/
|/-------------
|| #X| <--magnet ("X") forward -->
|\-------------
| /\
| ||__piston ("#")
|
|<--start
/-----------/-----------/-----------/-----------/

STEP 1:
\-----------\-----------\-----------\-----------\
Now, activate the electromagnet on the piston. So the piston, which is
repelled by the magnet, moves down the cylinder as the magnet and the
cylinder accelerate forward.

| ___ The magnet and the cylinder
| || move forward...
| \/ -->
| /-------------
| | # X|
| \-------------
| /\ <--
| ||__ ...as the piston moves backward
| through the cylinder
|<--start
/-----------/-----------/-----------/-----------/

STEP 2:
\-----------\-----------\-----------\-----------\
In fractions of a second, the piston will have arrived at the back of the
cylinder. The piston must be stopped before it slams into the back of the
cylinder because, if it does then the energy of the piston will cancel out
the forward velocity that the cylinder has gained. So, the energy of the
piston must be removed (by friction, e.g. brakes on the wheels) or harnessed
(a method which converts the "negative" energy of the piston into something
useable).

If friction is used to stop the piston, the friction must cause the piston
to lose velocity in decrements; should the brake make the piston stop
abruptly, then the "negative" momentum of the piston will be transferred to
the cylinder. Consider the following analogy: if I'm on a bike and I stop
abrubtly by pushing down hard on my brakes, I (my body) will go hurtling
forth until I hit a wall. In the presence of gravity, I might hit the
ground before I hit a wall, but the point remains the same. However, if I
push on my brakes and slowing come to a stop, I can avoid being thrown
forward. And moreover, by coming to a stop slowing, the momentum of me and
the bike is dissipated as heat, and perhaps sound. Thus, in the Simple
Newton Engine the "reaction" is lost due to friction (as heat and possibly
sound) while the "action" is harnessed to propel the cylinder forward.

|
|
|
| /-------------
| | # X|
| \-------------
| /\
| ||__The piston must be stopped before
| it hits the back of the cylinder
|<--start
/-----------/-----------/-----------/-----------/

STEP 3:
\-----------\-----------\-----------\-----------\
When the piston has reached the end, and has been brought to a stop, it must
then be moved to the front of the cylinder, perhaps by hooking it to a chain
which is being pulled by a motor. Perhaps the piston can slowly move back
on its wheels towards the front of the cylinder. Or perhaps the piston can
be removed from the cylinder when it is being transferred to the front, and
thus leave the cylinder free so that another piston can "shoot" through the
cylinder.

|
|
|
| /-------------
| |# X|
| \-------------
|
|
|
|<--start
/-----------/-----------/-----------/-----------/

Return to STEP 1:
\-----------\-----------\-----------\-----------\
The piston has been returned to the front. Overall, the engine has moved
and gained velocity. Now it is ready to restart at STEP 1.

|
|
|
| /-------------
| | #X|
| \-------------
|
|
|
|<--start
/-----------/-----------/-----------/-----------/

Also, like the Seesaw Newton Motor, the entire Simple Newton Engine can
(with a battery) be put into a box and the box would move without
interacting with the environment outside the box. Thus, it uses
"self-sufficient propulsion".

It should be noted that the Simple Newton Engine creates a small amount of
force for a relatively minute amount of time. In my mind, it would only be
effective if many are used simultaneously. For example, I imagine that it
wouldn't be too hard for the Simple Newton Engine to have a burst of 5N for
a tenth of a second. Building a unit of ten thousand of such Newton engines
would create a combined force of 5000N, assuming that the engines can
"reload" in 0.9 seconds. The real problem is getting a good force-to-mass
ratio (acceleration); if you can get acceleration greater than 10 m/s² then
you can pretty much launch any vehicle, no matter how massive, into space.
If the vehicle is too massive, then all you need to do is add more
individual engines to the unit, and eventually it should lift off the
ground. If such high accelerations cannot be made, then I'm sure this
invention can compete with ion propulsion.

--------------------------------------------------
Magnetic Propulsion for the Simple Newton Engine:

Cross-section:

mmmmmmmmmmmmmmmmmmmm
mmmmm ____ mmmmm <-- "m" are magnets
mmmm /WWWWWW\ mmmm
mmm /W/ \W\ mmm
mm /W/ mm \W\ mm
m W mmmm W m <-- "W" is a wire coil
m |W| mmmmmm |W| m
m |W| mmmmmm |W| m
m W mmmm W m X forward
mm \W\ mm /W/ mm (into paper)
mmm \W\____/W/ mmm
mmmm \WWWWWW/ mmmm
mmmmm mmmmm
mmmmmmmmmmmmmmmmmmmm

If the magnets "m" are arranged such that the field is perpendicular to the
wire, and if a current is set up in the wire coil, then the wire coil will
either move forward or backward. This could be applied to the Simple Newton
Engine; the wire coil would be the "piston" and the magnets would be part of
the "cylinder".

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-|-|-| (2) LAW OF CONSERVATION OF ENERGY |-|-|-|-|-|-|-|-|-|-|-|-
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---------------------------------------
_________________________
| |
semi- __\ |___ _________________ |
permeable / | | | |
material | |
(dialysis | | |
tubing) | | |
| | |
| | ------*------ <--\
| | | |
| | | turbine
| | |
tube B --> | |
(contains | | | |
perfluoro- | | | |
octane) | | | |
| | | | <-- tube A
| | | | (contains
| |_________________| | water)
| | |
|____________|____________|

/|\
\_ semi-permeable
material
(dialysis
tubing)


Tube A contains 250ml of water. Tube B contains 750ml of
perfluorooctane. Tube A and tube B are connected to each other by dialysis
tubing, which is a semi-permeable material. Water can permeate through the
dialysis tubing, but perfluorooctane can't. Due to osmotic pressure, the
water in tube A will pass through the dialysis tubing entering tube B.
Since water is insoluble in perfluorooctane, and since water is less dense
than perfluorooctane, the water will rise to the top of tube B. The water
that has risen will permeate through the dialysis tubing at the top of tube
B. Once enough water has accumulated at the top of tube B, it will fall,
turning the turbine, and returning back into tube A.

Notice that this dynamo didn't require any input energy, and it will
continue to work, creating electricity by turning the turbine (and
generator, which is not shown), so long as the perfluorooctane does not seep
into tube A through the semi-permeable material. Eventually, the
perfluorooctane will seep through the dialysis tubing, and so this invention
is not a perpetual motion machine.

But how can this dynamo generate electricity without any input energy?
First, let's observe that the water at the top of tube B has a gravitational
potential energy. When it falls, the gravitational potential energy is
realized and is converted into electricity by the turbine (and generator,
which is not shown). But how did the water initially get its gravitational
potential energy? It got its gravitational potential energy by being
displaced upward in a fluid (perfluorooctane) that is more dense than it.
Thus, we must conclude that insoluble objects immersed in fluids that are
more dense gain gravitational potential energy by being displaced upwards.
However, where is that energy coming from? By the Law of Conservation of
Energy, something must lose energy so that another can gain energy. Since
we cannot find anything losing energy, we must conclude that the Law of
Conservation of Energy is wrong, and that gravity creates forces which then
create/destroy energy; in this case it created energy in the final form of
electricity.

As mentioned before, enough perfluorooctane will eventually seep
through the dialysis tubing causing the level of the liquid in tube B to
lower such that the water cannot escape through the top of the tube. And
so, the turbine will stop spinning. At such a point we can easily "unmix"
both liquids by pouring all the liquid into a tall cylinder. If we leave
the two liquids in the tall cylinder for awhile then the water will
accumalate at the top and the perflourooctane will gather at the bottom. We
know that originally there was 250ml of water. So, we need only take the
top 250ml of liquid (water) from the cylinder and put it into tube A; the
rest of the 750ml of liquid (perfluorooctane) can be dispensed back into
tube B.

Thus, this dynamo can continually produce electricity; when the turbine
stops turning because the two liquids mix, then we need only unmix the two
liquids and restart the dynamo.

Notice again that this dynamo creates electricity without using any
input energy! Some may argue that we used energy to unmix the two liquids.
That is true, *but* even though we used energy to unmix the two liquids we
did not *give* the two liquids energy. That is, two liquids in separate
beakers have the same amount of energy as the same two liquids in the same
beaker.

We can conclude by noting that energy is being created/destroyed all
around us. Gravity and magnetism are prime examples. Both create forces.
The immediate effect of the forces on the system is nothing (the vectors of
the forces cancel each other out). However, after the immediate effect, and
after a minute amount of real time, the forces will do work on the system.
If "positive work" is done, then the system will gain energy. If "negative
work" is done, then the system will lose energy. Should these forces be
sustained for a longer duration of real time, then the forces might be found
to have not done any work on the system (that is, it added the same amount
of energy that was removed). Whether "positive work" is done or "negative
work" is relative.

---------------------------------------
Suppose we have two magnets with like-charges "q" and "q0". The space
between the two charges is "r". Let the potential energy between the
charges be "U". Consulting a physics textbook we find that

1 q*q0
U = ------ ------
4*pi*E r

where "pi" equals 3.14
"E" is the permittivity of free space

As the two magnets are moved closer to each other, potential energy
will be gained and kinetic energy will be lost. As the two magnets move
away from each other, potential energy will be lost and kinetic energy will
be gained.

Say, initially, that both magnets are far apart. Now, let us do work
by moving the charges closer together. When we are done and the magnets are
close to each other, the potential energy will have increased. The increase
will be equivalent to the work we did pushing them together.

Now, let's say that we took two hammers and pounded both magnets until
they lost their magnetism. Then, the potential energy between the two
magnets will dissappear. Thus, the system has lost energy without any part
of the system gaining energy. Thus, we have demonstrated that the Law of
Conservation of Energy is wrong.

Let me recap: First, we did work to move two repelling magnets
together. Thus, we lost kinetic energy while the magnets gained potential
energy. We then destroyed the magnetism of the magnets, thus losing the
potential energy. Thus, all-in-all, we lost energy.

This idea, which works on magnetism, can also be applied to gravity.

Consider two stationary gaseous planets, both made entirely of
deutrium. Let's do work on the planets, increasing the gravitational
potential energy between the planets, by moving them apart. The increase in
gravitational potential energy will be equivalent to the amount work we did
separating the planets.

Now, let's say that the deutrium of both planets began to fuse by the
following equation:

deutrium atom + deutrium atom => helium atom + neutron + 3.27 MeV
(from http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html)

(It is true that I didn't include the initial energy to start the fusion.
However, the above equation is properly balanced, so we do not have to
consider the initial energy required.)

Now, it is obvious that mass is being converted into energy. Since the
masses of both planets are decreasing, the gravitational potential energy
between both planets will also decrease. Thus, the work we did moving the
planets apart (which is now graviational potential energy) will diminish.
We have again demonstrated that the Law of Conservation of Energy is wrong.

Let me recap: First, we did work by moving the two planets apart.
Thus, we lost kinetic energy while the planets gained gravitational
potential energy. We then converted some of the mass of the planets into
energy. Thus, we lost mass and in the process we lost gravitational
potential energy. Thus, all-in-all, we lost energy.

(One might oversimplify the above to say, "What goes up does not
*necessarily* come down.")

Or, since mass and energy are interchangeable, what if the mass of both
planets suddenly converted into energy. I don't know exactly how this could
happen, but nonetheless, it is within the realm of possibilities. Thus, the
mass of both planets would dissappear and so, the gravitational potential
energy would also dissapear.

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--------------
I will take an example out from a physics textbook and show how it is wrong,
and how its failure is due to the fact that special relativity is wrong.
(The various failures of Special Relativity are well described at the
following website: http://homepage.mac.com/ardeshir/Relativity.html)

The chapter we are considering is "Relativity of Time Intervals" in the book
"University Physics".

There are two people, Stanley and Mavis. Stanley is standing on the Earth
while Mavis is sitting on a train. Now, there is a flashlight secured on
the floor of the train and there is a mirror on the ceiling of the train.
The mirror is secured such that it will reflect the light from the
flashlight directly back down to the floor of the train. Let's do a little
experiment and have the flashlight send a flash of light towards the mirror
and time how long it takes for the light to return back to the flashlight.

*let "tM1" be the time elasped as timed by Mavis during the experiment
*let "tS1" be the time elasped as timed by Stanley during the experiment
*let "v" be the speed at which the train is
travelling at relative to the Earth
*let "d" be the distance between the flashlight and the mirror

Stanley and Mavis should both start and stop their clocks at the same time
to properly time the experiment. In order to do that in the real world is
very difficult, and perhaps it is not possible (I'm not sure). But that
does not mean in any way that we cannot consider it on paper; on paper, we
just need to assume that the light from the experiment reaches both Mavis
and Stanley instantaneously.

Now, Mavis views the light emenating from the flashlight, travelling upward
to the mirror, and getting reflected back to the flashlight.

mirror--> #### ___
| |
| |
| | "d"
| |
flash- | _|_
light--> ^^^

Thus,

(1) "tM1 = 2d/c"

Meanwhile, Stanley sees a flash of light emanate from the flashlight. It
then moves upward and to the right where it meets the mirror and gets
reflected downward and to the right. Then it hits the floor where the
flashlight is.

mirror--> #### ___
/\ |
/ \ |
"l" / \ "l" | "d"
/ \ |
/ \ |
flash- / \ _|_
light--> ^^^ ^^^
|__________|
"v*tS1"

*where "2l" is the distance that Stanley observes the light to have
travelled

Thus,

(2) "tS1 = 2l/c"
and
(3) "l² = d² + (v*tS1/2)²"

I will leave it to you to verify that using equation (1),(2) and (3) we can
derive:

(4) "tS1 = y*tM1"

*where "y" equals "1/(1-(v/c)²)^½"

That's how the physics textbook leaves the subject.

However, what if on the Earth Stanley had a contraption similar to the one
that Mavis has on his train. Let's give Stanley a flashlight which is
fastened to the ground (Earth) and a mirror that is a distance "d" from the
ground. Let's do our little experiment again except this time on Earth;
let's have the flashlight send a flash of light towards the mirror and time
how long it takes for the light to return back to the ground.

*let "tM2" be the time elasped as timed by Mavis during the 2nd experiment
*let "tS2" be the time elasped as timed by Stanley during the 2nd experiment

Notice that "d" is the same because we built both our contraptions the same
way, and "v" is the same because it is the *relative* velocity between both
the train and the Earth.

This time we will get:

(5) "tS2 = 2d/c"
and
(6) "tM2 = 2l/c"
and
(7) "l² = d² + (v*tM2/2)²"

Again, I will leave it to you to verify that using equation (5),(6) and (7)
we can derive:

(8) "tM2 = y*tS2"

Now notice that in equation (4) and equation (8) the values of the elasped
time need not have any correlation with our two little experiments! That
is, in equation (4) the value "tS1" is determined by the value of "tM1"
which could be anything. Likewise, in equation (8) the value of "tM2" is
determined by the value of "tS2" which again could be anything.

So it is obvious that equation (4) can reduce to

(9) "tS = y*tM"

and equation (8) can reduce to

(10) "tM = y*tS"

*where "tS" is a period of time measured by Stanley
and "tM" is a "corresponding time" measured by Mavis

By "corresponding time", I mean that if Stanley and Mavis could both start
and stop there clocks at the same time, then Stanley would measure an amount
of time "tS" to have passed and Mavis would measure an amount of time "tM"
to have passed. Again, the fact that it may be difficult to get both guys
to start and stop their clocks at the same time does *not* mean in any way
that we cannot discuss it on paper.

It's obvious that equation (9) and (10) are incompatible because they both
work *only* when "v" equals zero. The general reason why the equations are
incompatible is because, despite what Special Relativity dictates, there is
an *absolute* frame of reference (some may call it a *preffered* or *unique*
frame of reference). And so it follows that there is absolute velocity;
absolute velocity is a velocity measured relative to the absolute frame of
reference.

The exact reason why both equations are incompatible will be discussed
afterward. For now you must be asking, if there is an absolute frame of
reference then how can we find out where it is? Consider the following
experiment:


--------------
(WARNING: It will be shown later that this experiment is prone to errors.)

Say we want to find the absolute velocity of a space ship. (This is very
similar to Einstein's "Train" Thought-Experiment.) In the middle of the
space ship we will have a switch. The switch is connected to two wires; one
wire leads to the front of the space ship while the second wire leads to the
back of the space ship. At the front and back of the space ship are
flashlights and timers. When the switch is activated a current will be sent
through the wire to cause both flashlights to emit a flash of light. When
they emit a flash of light the timers will commence timing. The flash of
light from the front will be directed toward the back of the ship while the
flash of light from the back of ship will be directed toward the front.
Each timer will stop when it observes a flash of light coming from the other
side of the ship.

*let "tF" be the time measured by the timer at the front of the ship
*let "tB" be the time measured by the timer at the back of the ship
*let "l" be the length of the ship
*let "v" be the absolute velocity of the ship
(assuming "v" is in the forward direction)

These two equations are obvious:

"tF*c = l + tF*v"
"tB*c = l - tB*v"

Solving the above equations we get an equation which determines the absolute
velocity of the ship:

"v = c * (tF-tB)/(tF+tB)"

Notice that the velocity "v" is in one dimension only. Supposing the area
around the space ship is Euclidean then one need only do this experiement in
two more directions to obtain the absolute net-velocity (each direction must
be perpendicular to the previous ones).

Now, as mentioned above, this experiment is prone to errors. This method of
finding the absolute velocity of an object works only assuming that during
the experiment:

(1) the space ship does not change inertial frames of reference
and
(2) the absolute frame of reference does not change inertial frames.

You may be inclined to think that so long as the space ship does not *feel*
an acceleration it will not change inertial frames of reference. You are
wrong; it is possible to change inertial frames without feeling
acceleration!

Consider a spherical ball suspended in space. From the point of view of the
absolute frame of reference the ball is moving in the right direction at a
velocity "v" and it is rotating clockwise at a velocity "v". Now, let us
say that there is an ant on the ball. When the ant is on the top of the
ball it is travelling at an absolute speed of "2v"; when the any is on the
bottom side of the ball is travelling at an absolute speed of "0".

You are changing inertial frames of reference when you experience a change
in absolute speed. Thus, the ant is changing inertial frames. But notice
that he does not *feel* accelertation. From the point of view of the
absolute frame of reference the ant is constantly accelerating and
decelerating from a speed of "2v" and "0". However, the ant does not *feel*
an accelertation.

Now, you might say that this is all good because above, during the
experiment to determine the absolute velocity, we used a space ship instead
of using, say, a train on Earth. However, this is foolish because the space
ship might be in a part of space that is "rotating" similar to the way the
Earth rotates. It is impossible for us, on Earth, to *feel* the
accelerations and deccelerations of the rotations of the Earth. Thus, it is
impossible for us to ensure that the space ship above does not change
inertial frames of reference.

And it goes without saying that we cannot ensure that the absolute frame of
reference does not change inertial frames, which is another barrier in the
determination of absolute velocity.

(On the side: Notice that the rotating Earth is nearly in perpetual motion.
Suppose we have a spherical planet made of metal rotating in space. That
planet is in pertual motion!; it will continually rotate forever, so long as
it is not disturbed. Notice that it will continually rotate because the
motion causes a force which then again causes motion, etc.)


--------------
I propose that when a velocity is measured relative to the absolute frame of
reference then we call that velocity an "absolute velocity". Also, if
acceleration, force, work, kinetic energy, time, etc., is measured from the
absolute frame of reference then it too will gain the prefix-word
"absolute".

Now, one can add the prefix-word "relative" to velocity and acceleration.
(For instance, if two objects are at rest, their relative velocity is "0".)

Absolute relative velocity and absolute relative acceleration can be
determined by making observations from the absolute frame of reference or by
using the Doppler effect. (It should be noted that the Doppler effect only
works when the absolute relative velocity is less than the absolute speed of
light. (We will discuss that fact in more depth in the next section.))

Now, I propose that when velocity, distance, time and acceleration are
measured using the equation "d=vt" or "v=at" then the term should gain the
prefix-word "apparent". The reason for the need of the prefix-word is
because the equations "d=vt" and "v=at" are false. They are false because
time dialates and, as it will be shown in the next section, acceleration
dialates.


--------------
Now let us return to the problem with Stanley and Mavis at the beginning of
this section. Remember the following equations:

(9) "tS = y*tM"
(10) "tM = y*tS"

Now, both equations ((9) and (10)) are incompatible; either one of the
equations is true or they are both invalid. This goes against the Principle
of Relativity which is "the laws of physics are the same in every inertial
frame of reference."

Thus, we see the need for an absolute frame of reference. I propose that
the equation for time dialation works only when the velocity is an absolute
velocity, that is, the velocity is measured relative to the absolute frame
of reference. (In all honesty I have no good reason to believe that the
rate at which time passes differs depending on your inertial frame of
reference. Nonetheless, at this point I'll assume it is true.)


--------------
Remember Einstein's "Train" Thought-Experiment? A train is travelling at a
velocity of "v" relative to the ground. One man is standing in the center
of the train and another man is standing outside. Now, when each man sees
the other standing directly in front him through the window a flash of
lightning stricks the front of the train and the back of the train.

Let's say that "v" is an absolute velocity. Now, the man on the ground will
observe the flashes of light to occur simultaneiuosly. However, the man on
the train will observe the flash of light from the front before he observes
the flash of light from the back. But from his position the light from the
front and the light from the back traversed the same distance! This means
that he will view the speed of the light from the front to be faster than
the absolute speed of light while the light from the back will be slower
than the absolute speed of light!

Relativity is right in saying that the speed of light is constant BUT it is
only constant when measured from the absolute frame of reference. If you
are in an inertial frame that is not at rest with the absolute frame of
reference then you may very well observe light not to be a constant. That
is, apparent speed of light can differ widely while the absolute speed of
light remains constant.

Einstein purports that as speed increases lengths contract and masses get
larger. This is wrong! There is no reason to believe that either is true
because one can use a similar argument like the one used above against time
dialation (as was shown in the above experiment with Stanley and Mavis).
However, it may be true that lengths *appear* to be shorter; the only way to
confirm that is by experiments. Masses, however, do not increase as speed
increases; however, momentum increases as speed increases.

-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-
-|-|-| (4) WORK -|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-
-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-

--------------
Two terms introduced in the previous section are used in this section:

-"absolute velocity": a velocity that is measured relative to the absolute
frame of reference.

-"absolute relative velocity": the relative velocity between two objects
typically measured by using the Doppler effect.

-any time "absolute" preceeds a term that means that the term was measured
from the absolute frame of reference; e.g. "absolute effective general work"
is effective general work measured from the absolute frame of reference.

This section also assumes two things:

(1)-time does dialate with respect to absolute speed

(2)-the absolute frame of reference does not change inertial frames of
reference


--------------
Once one has realized that energy is not conserved, the big question
that arises is how did something so obvious allude us, and for so long. The
answer to that has many reasons. One reason is that we did not define work
intuitively. I will now attempt to rectify that.


--------------
First, let's realize that force has two equations, or rather, that it
can be observed in two different ways. First, there is "ineffective force":

f_i = pA

where "f_i" is ineffective force
"p" is pressure
"A" is area

And then there is "effective force":

f_e = ma

where "f_e" is effective force
"m" is mass
"a" is acceleration

It should be noted that force equals mass multiplied by acceleration only
when we look at the world in Newtonian terms.

Effective force is ineffective force which is allowed to cause a change in
kinetic energy.


--------------
Consider the following scenario: two classmates, Jack and Jill, both
able to hold a one-kilogram brick. Naturally, holding that brick on Earth
is approximately equivalent to maintaining a force of 10 Newtons. Let's say
that Jack held his brick for 20 seconds, and Jill held her brick for 2
seconds. Now, without using any scientific jargon, who did the most work?
Jack obviously did more work than Jill. Thus, *intuitively*, work should
equal force multiplied by time.


--------------
Notice, that this means that work done on an object does not
necessarily have to cause a change in kinetic energy. On the contrary, even
if you placed a book on a table work is being done; the table is maintaining
a force, and likewise, the book is maintaining a force. The force of
gravity is causing stress between the two at the atomic level. Work, in
general, does not require a change in kinetic energy. Thus, I call the
following the equation for "general work":

W_i = f_i*t

where "W_i" is general work
"t" is a period of time


--------------
I propose that the real unit for work (that is, general work, which is
force multiplied by time) should be "P", for Prescott, Joule's middle name.
Thus, one prescott equals one newton second. I relegate the old,
traditional meaning for work to the term "productive work".


--------------
Now, work defined as it is today (productive work) is wrong
intuitively, but nonetheless, it is a *VERY* *USEFUL* "measuring tool". It
calculates "useful" work, where usefulness is defined as causing an object
(I use that term very loosely) to be displaced in a certain direction.
Power calculates the rate at which this "useful" work is happening. I
should make it clear that any form of work can be considered useful or
useless depending on the situation and its application.


--------------
Of course, just as force has "effective force", work has "effective
work". The term "effective" means that the work is allowed to cause a
change in kinetic energy. Thus, we can have "effective general work" and
"effective productive work"; "Effective general work" is general work that
is allowed to cause a change in kinetic energy and "effective productive
work" is productive work that is allowed to cause a change in kinetic
energy. If the work (general work or productive work) does not cause a
change is kinetic energy then the work is called "ineffective work".

To find out effective general work, take the term "f_g" and make it
effective, that is, change it into "f_e". And thus:

W_g = f_g*t
W_e = f_e*t
= ma*t

where "W_e" is effective general work

And since in Newtonian mechanics

v = a*t

where "v" is velocity

we can simplify the equation for effective general work to the following:

W_e = mv

In Newtontonian mechanics, momuntum is equal to "mv". Thus, in Newtononian
mechanics, effective general work causes a directily proportional change in
momentum.


--------------
From the previous section we know that there is an absolute frame of
reference. Allow a guy named "watcher" to inhabit the absolute frame of
reference.

Consider a space ship with a captain in it. The space ship is
travelling at an absolute velocity of "v". Then the captain turns on his
thrusters accelerating the ship in the direction of the velocity. The force
on the ship is "f_g". He leaves the thrusters on for an amount of time
"dt", an infinitesmal amount of time as measured by himself.

In the eyes of the watcher the space ship will experience a force "f_g"
(in agreement with the captain) for a period of time "dtA".

Now, "dt" does not equal "dtA". That is because, due to Relativity, we
must take into account the dilation of time.

dtA = y*dt

where "y" is equal to "1/(1-v²/c²)^½"
"c" is the speed of light
"dtA" is a period of time measured by the watcher
("A" stands for "absolute")
"dt" is the period of time measured by the captain

Now, since we had a force for an infinitesmal amount of time, only an
infinitesmal amount work is accomplished. Thus, in the watcher's eyes the
thrusters are doing an amount of work equal to "dW_g":

dW_g = f_g*dtA
= y*f_g*dt

Again, let us allow general work to become effective, that is, let's allow
the general work to cause a change in kinetic energy. However, we cannot
just replace "f_g" with "f_e". This is because effective force does not
always equal "ma" in Relativity. But, we will allow "f_e" to equal "ma"
here, and it will be justified later. So,

dW_e = y*f_e*dt
= y*ma*dt

where "dW_e" is an infinitesmal amount of effective general work

Since,

a*dt = dv

where "dv" is an infinitesmal amount of velocity

Thus, we get the equation:

dW_e = yma*dt
= ym*dv

The above equation means nothing now but it will be important in the next
paragraph.


--------------
I have found the following equation in "Introduction to the Relativity
Principle" by Gabriel Barton (pg. 189):

ya = 1/m ( F - 1/c² V(V.F) )

where "F" is the vector for force
"V" is the vector for velocity

let "µ" be the angle between force and velocity measured in radians,
"0 <= µ <= pi"

The above equation can be rewritten as

ya = |F|/m ( 1 - v²/c² * cos(µ) )

Observe that "|F| = dW_g/dt",

where "dW_g" is an infinitesmal amount of general work

So,

ya = dW_g/dt/m ( 1 - v²/c² * cos(µ) )

yma*dt = dW_g ( 1 - v²/c² * cos(µ) )

In the above equation "dt" is being measured in the moving frame. So we can
use the equation in the previous paragraph. That is:

yma*dt = ym*dv = dW_e

And so,

dW_e = dW_g ( 1 - v²/c² * cos(µ) )

To be clear, in the above equation "dW_g" is an amount of general work which
is allowed to become effective as measured in the moving frame. "dW_e" is
an amount of absolute effective general work, in other words, it is
effective general work measured from the absolute frame of reference.

From the above equation, we can infer many things:

Acceleration, just like time, dialates; that is, it changes with
respect to the absolute velocity.

As absolute velocity increases and as the angle between force and
absolute velocity decreases the effectiveness of general work changes
depending on the direction of the general work. (1) If the general work is
in the direction of the absolute velocity ("0 <= µ <= pi/2") then the
general work is less effective because "dW_e < dW_g". Thus, in such a
situation we will say that the general work is "sub-effective". This means
that we cannot have an absolute velocity that surpasses the speed of light
because general work losses its effectivity when absolute velocity nears the
speed of light. (2) If the general work is in the opposite direction of the
absolute velocity ("pi/2 <= µ <= pi") then the general work is more
effective because "dW_g < dW_e". Thus, in such a situation we will say that
the general work is "super-effective". (3) If the absolute velocity is zero
or if the angle between the force and absolute velocity is 90 degrees then
"dW_g = dW_e". In such a situation we will say that the general work is
"exactly-effective". Remember that above we allowed "f_e" to equal "ma"; we
can now realize that "f_e" equals "ma" only when general work is
exactly-effective. When general work is sub-effective then

"f_e < ma"

and when general work is super-effective

"f_e > ma".

Notice that you could just as well say that as absolute velocity nears
the speed of light the effectiveness of a force to create an acceleration in
the direction of the absolute velocity diminishes. On the other hand, as
absolute velocity nears the speed of light the effectiveness of a force to
create an acceleration in the *opposite* direction of the absolute velocity
greatens. What this means is that it is easier to slow an absolute velocity
than it is to increase an absolute velocity. That is, it is easier to slow
down than to speed up.


--------------
Even though we can never have an absolute velocity greater then the
absolute speed of light, we can still have an absolute relative velocity
that surpasses the absolute speed of light. Consider two space ships both
at rest with respect to the absolute frame of reference. Let one ship
accelerate till an absolute velocity near the speed of light is reached.
Then, the other ship should accelerate in the *opposite* direction till it
reaches an absolute velocity near the speed of light. The absolute relative
velocity should now be greater than the speed of light.

Perhaps dark matter is what is observed when two objects have an
absolute relative velocity that surpasses the absolute speed of light. The
light from each body of mass would reach the other mass, however, since the
absolute relative velocity is greater than absolute speed of light, the
frequency of the light would be an imaginary number, thus making the masses
"dark". It is a well-known fact that the Universe is expanding and so there
is a lot of matter receding away from us. And so, there ought to be a lot
of matter which have a relative velocity with us higher than the absolute
speed of light, which would thus explain the fact that there is a lot of
dark matter out there.

Thus, we cannot see dark matter because the frequency of the light we
receive is imaginary.


--------------
Let us hypothesize for a moment: let us say that gravity is the result
of particles called gravitons. Also, let us assume that these gravitons
have a frequency, just like light.

Now, let us assume that the Big Bang theory is true. So, at some point
there was a huge amount of energy confined to a small point in space. Time
started and this point of energy exploded. Now, the energy will leave the
explosion in all directions.

Remember, above, that we explained that dark matter is the result of
two objects which have an absolute relative velocity higher than the
absolute speed of light. Well, now we've assumed that gravitons also have a
frequency. Thus, the frequency of gravitons between two objects which have
an absolute relative velocity higher than the absolute speed of light is an
imaginary number! Let us assume that that means that gravity's force is
ineffective between those two objects.

That may be the reason why our Universe is expanding; perhaps the
masses in the Universe are rushing away from each other so fast that gravity
is rendered ineffective because the frequency of the gravitons become an
imaginary number. Just a thought..


--------------
Now, I would like to point out that the "rulers" we use to "measure"
various things, such as time, acceleration, velocity, force, work, energy,
etc., are subjective. For things such as time, accleration and velocity,
the way we measure the three is obvious and it is trivial to examine them.

However, force, work and energy are much different. For instance,
let's consider ineffective force. We know that as pressure increases so
does ineffective force increase. We also know that as the surface area that
is being pushed by the pressure increases, so does ineffective force
increase. Now, we say that ineffective force equals "pA" where "p" is
pressure and "A" is the affected surface area. However, we could just as
well say that ineffective force equals "3*p²A^½". We can say that because
it follows the rule that as pressure increases so does ineffective force
increase and as the affected surface area increases so does ineffective
force increase. However, the way that the equations are defined right now
makes handling them easy.

We could apply the same argument to kinetic energy and momentum.
Notice that that is why we can observe both kinetic energy and momentum as
being the result of effective work. Kinetic energy and momemtum increase as
velocity increases and as the affected mass increases. Thus, we can measure
kinetic energy as the result of effective productive work ("½mv²") or we can
measure momentum as the result of effective general work ("mv"). (To be
accurate, kinetic energy equals "½mv²" and momentum equals "mv" only when we
look at the world in Newtonian terms or when absolute velocity is near
zero.)

Also notice that velocity is relative. It is true that there is
"absolute velocity" but that does *not* mean in any way that velocity is not
relative. I should make it very clear that velocity is *always* measured
relative to some frame of reference, even absolute velocity is relative;
absolute velocity is velocity measured relative to the absolute frame of
reference.

Now, kinetic energy and momentum is what effective work accomplishes.
Both, effective productive work and effective general work, as seen above,
increase as velocity increases. But since velocity is relative, then
kinetic energy must also be relative.

Now, you can measure ineffective force, ineffective work and potential
energy from any point in the Universe and come up with the same value.
However, measuring velocity, acceleration, kinetic energy and momentum is
relative, that is, the value you get will vary. The value can vary even if
you make the measurement in the same place at the same time! To illustrate:
measuring kinetic energy depends on two things: (1) the relative velocity of
the object you're measuring and (2) the velocity at which you would say you
are travelling at. (We are assuming here that you and the object are not
changing inertial frames). Thus, if I were sky-diving and was in free-fall
such that I had reached my terminal velocity, I could say (1) that I have
kinetic energy because I am hurtling towards the Earth which is at rest and
has no kinetic energy or I could say (2) that the Earth has great kinetic
energy because I am at rest and it is rushing towards me. Both measurements
above can be made in the same position at the same time and they are both
right; it just depends on how you want to look at things. Thus, like
velocity is relative, so too is effective work (kinetic energy and
momentum).

-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-
-|-|-| (5) EXTRAS -|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-
-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-

(1) Absolute Velocity
(2) Electricity

-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
=-=-=-1) Absolute Velocity=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

--------------
Here is another way to determine absolute velocity. It is more complicated
then the method in the section titled "Absolute Frame of Reference". I
originally figured this method and I didn't have the heart to erase it and
so I left it here as an "extra".


--------------
Now, as mentioned in the above section, this experiment is prone to errors.
This method of finding the absolute velocity of an object works only
assuming that during the experiment:

(1) the space ship does not change inertial frames of reference, except for
the times the space ship intentionally moves frames
and
(2) the absolute frame of reference does not change inertial frames.


--------------
Start with two space ships. Inside one space ship is a "sender" and in the
other is a "receiver". The space between both ships should be sufficiently
large. Also, to start off with, both ships are in the same frame of
reference, that is, initially, both ships view each other as being
stationary.

Now, the sender's job is to send signals - flashes of light - to the
receiver at regular intervals. Let us say that the sender sends a signal
every "t0" seconds, "t0" being measured by the sender.

It is the receiver's job to receive the signals and observe the amount of
time elasped between signals. Initially, since the receiver and the sender
are in the same frame of reference the receiver will measure the time
between signals to be "t0", agreeing with the sender.

Now, the receiver will have to choose to either accelerate towards the
sender or away from the sender. Thus, the receiver will attain a velocity
of "v" towards the sender or away from the sender. "v" is the relative
velocity between the receiver and sender and can be measured by the receiver
by using the Doppler Effect.

Since the velocity of the receiver changed, the rate at which time passes as
observed by the receiver will also change. So now let the time that passes
between signals as observed by the receiver be "tR".

Now, we cannot simply compare "tR" with "t0". This is because the receiver
is travelling at a velocity relative to the sender and so there will be a
"lag" in the time that the receiver measures. This lag is due to the fact
that the receiver has changed positions when measuring the time between
signals. The change in the receiver's position between signals is "tR*v".
So, the time it will take the signal (which is a flash of light) to traverse
the change in position is "tR*v/c", which we will call the lag. If the
receiver is approaching the sender, then the receiver must add the lag to
"tR" to obtain the correct change in time between signals. On the other
hand, if the receiver is receding away from the sender, then the receiver
must subtract the lag from "tR" to obtain the correct change in time between
signals. We will call "t1" the corrected change in time between signals as
measured by the receiver.

Now, we can compare "t1" with "t0".

But first, let's look at the equation for Relativity's "time dialation":

"tM = 1/y * tA"

* where "tM" is the change in time measured in a "moving frame" that is
travelling at a velocity "v" ("M" stands for "moving")

* where "tA" is the change in time measured at rest with the absolute frame
of reference ("A" stands for "absolute")

* where "y" equals "1/(1-(v/c)²)^½"

Observe that when the velocity is equal to zero the rate at which time
passes is the fastest. (Thus, observers measure moving clocks to run slow.)

Thus, if "t1" is greater than "t0", the receiver is getting closer to the
spot where the velocity relative to the absolute frame of reference is zero.
On the other hand, if "t1" is less than "t0", then the receiver must turn
around and head in the opposite direction because he is getting further away
from the spot where the velocity relative to the absolute frame is zero.

To find the *exact* spot where the velocity relative to the absolute frame
of reference is zero, the receiver will have to move about many times until
he finds a spot where the recorded time between signals (adjusted for the
lag) is greatest.

Notice that we only figured out the point where the velocity is zero
compared with an absolute frame of reference on *one* axis. Assuming that
the space around both the sender and the receiver is Euclidean, one must
redo this experiment in three directions - each perpendicular to one
another - to find out the exact location where velocity is zero compared
with an absolute frame of reference.

This method to determine where the absolute frame is requires that the space
ship with the sender must not change inertial frames of reference. Also,
this method to determine where the absolute frame is requires that the
absolute frame does not change inertial frames. If the absolute frame is
"moving about" inertial frames then the receiver will have trouble
zeroing-in on the spot where the measured time between signals is greatest.

-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
=-=-=-2) Electricity=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

Now, I am going to apply work using prescotts on an electrical circuit.
(Prescotts are discussed in the section titled "Work".) The only reason I
am including this section is because at the end we derive the correct
equation for the change in time between electron collisions.

***************************
Let's find the average drift velocity:
-------------------------
A is the cross-section of the wire (m²)
n is "free" electrons per unit volume (electrons/m³)
e is the magnitude of charge of an electron
(1.602 * 10^(-19) C/electron)
v is the average drift velocity of the electrons (m/s)
I is the current in the wire (C/s)
dq is an infinitesimal amount of charge (C)
dt is an infinitesimal amount of time (s)
dN is an infinitesimal number of electrons (electrons)
-------------------------
(1) dq = e*dN

dN = nAv*dt
(2) dt = dN/(nAv)

(1)/(2) dq/dt = e*dN/(dN/nAv)
I = enAv
v = I/(enA)

***************************
Let's find force:
-------------------------
W_j is the Work in Joules (N*m)
f is the force (N)
s is the distance (m)
V is the voltage (N*m/C)
-------------------------
W_j = F*s
dW_j = F*v*dt
dW_j/dt = F*v
V*I = F*v

V*I
F = -----
v

= VenA

-------------------------
P is pressure (Pa)
-------------------------
F
V = ---
enA

P
= --
en

So we can say that "voltage is the electromagnetic-pressure (created by an
EMF source) per density of charge."

Notice that the pressure supplied by an EMF has nothing to do with the
length of the circuit. A battery hooked to a 1-meter circuit of 1cm² wire
uses the same pressure to start a current as a similar battery hooked to a
10000-meter circuit of similar wire!

***************************
-------------------------
W_i is the Initial Work (in Prescotts) (N*s)
(the work done to start the electrical circuit)
t is a duration of time (s)
m_e is the mass of an electron (9.109 * 10^(-31) kg/electron)
-------------------------
W_i = F*t
= VenA*t

Notice that in this case "W_i" does not equal "m_e*v". This is because over
the period of time "t", which is greater than the average change in time
between electron collisions, the acceleration of the electron is hindered
when the electron loses its energy during a collision.


***************************
-------------------------
U is Initial Work (in Prescotts) per Coulomb (N*s/C)
Q is an amount of charge (C)
p is the resistivity of the wire (ohm*m)
l is the length of the wire (m)
-------------------------
U = W_i/Q
= F/I
= (VenA)/(V/R)
= enAR
= enA*(p*l/A)
= enpl

Thus, we can say that "U" is a constant for any given circuit. So, given
any circuit, a constant amount of work is done to move a coulomb along the
circuit.


***************************
-------------------------
µ is Initial Work (in Prescotts) per Coulomb*meter (N*s/(C*m))
-------------------------
µ = dU/dl
= enp

So, the rate at which work is done per unit distance depends on the
material.

***************************
-------------------------
t_c is the change in time between electron collisions (s)
-------------------------

Each electron gains "m_e*v" of energy before it makes a collision and losses
it's energy. The collision will take place in "t_c" seconds. "U" is the
amount of work to move a coulomb "l" meters along the wire. And, in "l"
meters, there will be "l/(v*t_c)" number of collisions. So,

l m_e*v
----- * ----- = U
v*t_c e

l*m_e
------- = enpl
t_c*e

m_e
t_c = ----
e²np


which is correct.

-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-
-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-

by Raheman Velji
rahemanvelji******.ca

August 11, 2005

you can also view this paper (and updated versions) at...
....http://www.angelfire.com/un/rv

or a less updated copy can be found at...
....http://www.angelfire.com/rebellion2/rahemanvelji

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