Chapter 9
My Second Experiment
"It
is the mark of an educated mind to rest satisfied with the degree of precision
which
the nature of the subject admits and not to seek exactness where only an
approximation
is possible."
Aristotle
(384 BC - 322 BC)
Where We are Going Next
My
first experiment proves, using the path of light, that the light from
lasers must
have
path momentum. I will call this "laser path momentum"
("LPM") meaning
the
light coming out of a laser (or from a target to a telescope) must have path
momentum
and the light must exit the laser at an angle.
In this
chapter and the next chapter we will look at whether the light that bounces
off of
mirrors also adds path momentum, which I will call "mirror path
momentum"
("MPM"). My second experiment, which will be discussed
in this
chapter,
concludes that MPM does not exist (i.e. MPM is false) in the
photon
theory.
The next chapter will continue this discussion using the Lunar Laser
Ranging
experiments.
Laser Path Momentum (LPM)
Because
we are going to use a little mathematics in this chapter, let us first look
at the
experiment in the last chapter and redo it using actual mathematics.
Thus,
let us assume:
1) The
speed of light is exactly 300,000 kps.
2) The
speed of the earth towards Leo is exactly 370 kps.
These
are accurate enough numbers for our purposes here. Let us assume the
experiment
is done at 50 meters (i.e. the mirror is placed 50 meters from the
laser).
Light
travels 300,000,000 meters per second. Thus, it takes 50 /
300,000,000,
or
.0000001666... seconds for light to travel 50 meters. During this time, the
earth
travels .061666... meters (.0000001666... times 370,000 meters per
second)
or 6.1666... cm towards Leo. My equipment was easily accurate enough
76
to
detect this value, furthermore, my first experiment was done at
about 100
meters,
so we could double this value.
Let us
now build a triangle, with sides a, b and c.
Side a
= .061666... m
Side b
= 50 m
Angle
A is the angle opposite Side a. While it is true that Side c is the actual
path
of the laser beam, it is not mathematically significant to this discussion and
will
be ignored.
(Note:
it may seem strange that I am using approximations for the speed of light
and
for our velocity towards Leo and that I am ignoring the actual path of the
laser
beam, but that I am using 6 or more decimals of accuracy at other times.
My
only concern is whether my equipment is capable of detecting a calculated
distance,
thus there is nothing lost in using approximations mixed in with trig
formulas.
See the quote at the beginning of this chapter.)
Since
by my first experiment, I got a "dot," then we can conclude that
Angle A is
the
angle at which the laser beam is affected by path momentum. We will now
calculate
this angle:
If we
had a right triangle, with one side of 50 m and another side of .061666... m,
then
Angle A = 0.070665 degrees. To calculate it:
Angle
A = arctan (a / b)
Angle
A = arctan (.061666... / 50)
Angle
A = 0.070665 degrees
Angle
A represents the angle at which light exits a laser beam because of path
momentum.
Now
that we know this angle we could calculate how far the earth moves in the
time
it takes light to travel 50 m. This calculation is done as follows:
side a
= (b * sin A) * sin B
side a
= (50 * sin 0.070665 degrees) * sin 89.929335 degrees
side a
= .061666... m
Obviously,
this is same number we started with because it is the number we
plugged
into Side a above (this was just a sanity check).
Note
that the angle that was calculated was designed to "get a dot." In
other
words,
since my first experiment always got a "dot," the angle of path
momentum
was
calculated so that the laser beam would hit the same spot every time.
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Let a
"path momentum unit" be a part of the experiment at
which an angle of
0.070665
is added to the laser beam. If a "path momentum unit"
was not added
at the
point the laser beam leaves the laser, because of the MTLs the laser beam
would
have missed the center of the target and I would have gotten an ellipse.
However,
because of the one "path momentum unit" added by the laser, and
because
the earth moves one "earth unit" (i.e. the distance the
earth moves
while
the laser beam is in the air - .061666... m), I got a consistent
"dot."
Generally,
as long as the number of "path momentum units" equals the number
of
"earth units," a "dot" will result for all 24 hours of the
experiment.
Simplifying the Visualizations
Before
going on it is necessary to simplify the visualizations (assuming the
photon
theory) before things get out of hand. In the prior chapter I made 25
different
readings, over a 24 hour period, to obtain my results. In this chapter,
because
we will be dealing with a mirror, doing a simple globe experiment is not
as
practical. The good news is that we can reduce the number of markings that
we
need to study down to two.
Let us
study exactly two angles that light leaves the laser. First, we will study the
angle
when the relationship between the laser vector and our vector towards Leo
is at
its closest to perpendicular. In fact, for discussion purposes we will assume
it is
perpendicular and that Leo is to the right of the laser (i.e. to the right to a
person
standing behind the laser). Second, we will study the angle 12 hours
later,
when the laser and target have switched places relative to our path towards
Leo. I
mentioned this in the prior chapter during the globe exercise. Let us do a
simple
experiment.
Suppose
there is a long, narrow room. Now let us draw a line down the middle of
the
long axis of the room, which is half-way between the walls that form this long
axis.
In other words, this line goes down the middle of the room, along the long
axis
of the room.
Now
let us position two people that are standing face-to-face, three meters apart.
A line
drawn between these two people is perpendicular to the "line along
the
long
axis," meaning the line that goes down the middle of
the long axis of the
room.
Let the center point of the line between the two people touch the "line
along
the long axis" (i.e. the two people are equidistance from the line along
the
long
axis). Now let us put the two people at one end of the line along the long
axis,
and let us put a table or chair at the other end of the line along the long
axis
(i.e.
at the other end of the room). Let us name these people Person L and
Person
T. As Person L faces Person T, the table is to Person L's right.
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Person
L represents the laser. Person T represents the target the laser is aimed
at.
The table or chair represents Leo. The line along the long axis represents
our
path towards Leo. If Person L gently throws a ball to Person T, this will
represent
firing a laser beam at the target.
Now
let us do an experiment. Let Person L gently throw a ball such that it is
aimed
1 meter to the right of Person T (from Person L's perspective).
Note that
this
angle is in the direction of Leo, meaning it lands between Person T's original
position
and Leo. In the time it takes the ball to get to Person T, let Person T
moves
1 meter to Person' T's left (1 meter equals 1 earth unit in this crude case)
or 1
meter to Person L's right. Note that the ball hits the center of Person T. The
angle
at which Person L throws the ball represents the path momentum of laser
light
as it leaves the laser. From the perspective of Person L, the ball (i.e. the
laser
beam) leaves at an angle to his right, which is towards Leo and
in this
example
this angle represents one path momentum unit. Thus, the ball is thrown
at one
path momentum unit and Person T moves one earth unit, and the ball hits
Person
T. This represents the first measurement in my first experiment
discussed
in the prior chapter.
Now
let Person L and Person T switch places. This will represent the positions
of the
laser and target 12 hours later, meaning after 12 hours of the earth's
rotation.
Now Person L will have to throw the ball to his left (the angle
is always
towards
Leo), because the path momentum is now going to carry the laser beam
to the
left of the laser (from the perspective of the laser or Person L), in the
general
direction of Leo.
If the
reader is having problems understanding why the two people need to
switch
places, go back to the globe exercise and note that the laser (one end of
the
toothpick) and the target (the other end of the toothpick) have switched
placed
after the globe has been rotated for 12 hypothetical hours. Because of
path
momentum the laser beam will always angle away from the laser in
the
direction
of Leo, thus at the beginning the laser will angle away from
the laser to
the right
(towards Leo), and 12 hours later the laser will angle away to the left
(towards
Leo) (assuming Leo started out to the right of the laser).
In
this second case, Person T moves one earth unit to her right or one earth unit
to the
left of Person L. Because the laser beam always angles towards
Leo, the
path
momentum of the laser beam angles to the left, and the ball again hits
person
T. This represents my first experiment at the 12 hour mark.
We
have seen in two instances that Person T received the ball, in the original or
first
throw and a throw 12 hours later. We can therefore assume that if we had
done
the complete 25 throws that we would have consistently hit Person T.
Thus,
we can reduce the number of throws (i.e. measurement points) from 25
down
to 2.
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This
simple exercise replicates the first experiment discussed in the prior
chapter.
One Mirror
Let us
suppose that we have a laser pointed at a mirror 50 m away. Let us
suppose
that the actual aim of the laser beam is exactly normal or
perpendicular
to the
mirror. Let us fire the laser at the mirror. Because of path momentum, the
angle
at which the laser beam hits the mirror will be exactly 89.929335 degrees
(i.e. 90
minus 0.070665). Thus, because this is a mirror, the light will exactly
exit
the
mirror at the same angle. In essence, the mirror creates a "reflected"
path
momentum
unit because it reflects the light at the same angle that it
receives
this
light. But this second path momentum unit is not because the mirror adds
one
path momentum unit, it is because it reflects one path momentum
unit that it
received
from somewhere else (i.e. it receives this path momentum unit from the
laser
and simply duplicates it or reflects it).
Let me
summarize this as follows. If a mirror reflects one path momentum
unit,
and
does not add one path momentum unit, then when the light gets
back to the
laser,
there are two path momentum units, one from the laser and one is a
duplicate
of the laser's path momentum unit. During the time the laser was "in
the
air," the earth moves two "earth units" (one when the light
traveled to the
mirror,
and one when it traveled back from the mirror to the laser), thus the two
path
momentum units offset the two earth units and the beam is predicted to hit
the
center of the target (i.e. a "dot" will result). The same result
would occur
twelve
hours later, even though the laser and mirror have switched places.
One Mirror - Simplified
Let us
return to our two-person example above. Suppose Person T holds a
hypothetical
mirror.
T0)
Time 0: Person L releases the ball. Both Person L and Person T are at
"origin,"
and are across from each other.
T1)
Time 1: Person L and Person T move 1 earth unit from origin between T0
and T1
and are both standing on "position earth unit 1" (i.e.
1 earth unit from
origin),
across from each other. The ball hits the mirror and the mirror angles the
ball
at the same angle that Person L threw it. The mirror aims the ball towards
position
earth unit 2.
T2)
Time 2: Person L and Person T move another earth unit between T1 and T2
(making
a total of 2 earth units that both of them have moved). Both Person L
and
Person T are standing on position earth unit 2 when the ball arrives back to
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Person
L's side. The ball lands where Person L is located because the mirror
reflected
the path momentum unit that Person L originally used.
Twelve
hours later, the reverse would happen and the ball would again hit
Person
L at T2 only in this case everything moves to the left. Thus, we predict a
dot
for the entire experiment.
(Note:
In this case the target is the laser itself, thus it would be necessary to have
the
mirror tilted slightly up (but not side-to-side) so that the beam would hit
directly
above the laser.)
Now
let's do this same example with the mirror adding one path
momentum unit.
One Mirror - Adding One Path Momentum Unit
T0)
Person L releases the ball. Both Person L and Person T are at
"origin," and
are
across from each other.
T1)
Person L and Person T move 1 earth unit from origin between T0 and T1 and
are
both standing on "position earth unit 1," across from each other. The
ball hits
the
mirror and the mirror angles the ball at the same angle that Person L threw it
plus
the mirror adds one path momentum unit. This means that at T1, the mirror
is
aiming the ball at "position earth unit 3."
T2)
Person L and Person T move another earth unit between T1 and T2 (making
a
total of 2 earth units that both of them have moved). Both Person L and
Person
T are standing on position earth unit 2 when the ball arrives back to
Person
L's side. The ball lands at position earth unit 3. Thus, the ball lands one
earth
unit to the right of where Person L is standing when the ball
arrives.
Now
let us do this experiment twelve hours later.
T0)
Person L throws the ball. Both Person L and Person T are at "origin,"
and
are
across from each other.
T1)
Person L and Person T move 1 earth unit from origin between T0 and T1 and
are
both standing on position earth unit 1, across from each other. It should be
noted
that because Person L and Person T have switched positions, that from
the
perspective of Person L, position earth unit 1 is 1 earth unit to the left
of
Person
L. In other words, everything is moving to the left from the
viewpoint of
Person
L and thus left is the natural direction of the earth units in
this case. The
mirror
angles the ball one earth unit to the left (from Person L's perspective)
because
it is reflecting the path momentum of Person L, plus it angles
the ball
one
additional earth unit to the left because it is adding a path momentum unit.
At T1,
the mirror is therefore aiming the ball at position earth unit 3.
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T2)
Person L and Person T move another earth unit between T1 and T2 (making
a
total of two earth units that both of them have moved). Both Person L and
Person
T are standing on position earth unit 2 when the ball arrives back to
Person
L's side. The ball lands at position earth unit 3, which is one earth unit to
the left
of Person L.
In the
original case the ball landed one earth unit to the right of
Person L, and 12
hours
later the ball landed one earth unit to the left of Person L.
Should we
expect
a pattern or a dot? Think about it for a moment before reading on.
The essence
of expecting a pattern is that the ball lands in exactly the same
spot, relative
to Person L's location when the ball lands, for the entire 24
hours,
on in this case, in both instances. Relative to Person L, in the first
experiment
the ball lands to his right. In the second experiment the ball
lands to
his left.
Therefore, we conclude that the ball does not land in the same
spot for
both
experiments (relative to Person L), thus we conclude we would get some
kind
of pattern. In doing these experiments we must know where the ball lands
relative
to Person L. This spot must be the same for both experiments.
Obviously,
in this case it is not.
It
will become critical later in the chapter to remember that we must keep track
of
both
the laser beam and the location of Person L. It is where the laser beam
lands,
relative to where Person L is located, that determines whether we get a
dot or
a pattern of some kind. We don't really care at this point what the pattern
looks
like, we are only concerned that we do not get a dot.
A Potential Problem
Let us
return to the example where the mirror did not add a path
momentum unit,
it
simply reflected a path momentum unit. We predicted a dot. However, there is
a
potential problem with the above analysis. What if our equipment was not set
up
correctly, and the aimed laser beam was not exactly normal to the
mirror? To
be
more specific, what if the normal vector of the mirror was not equal to the
aimed laser
beam, but rather it was equal to the actual laser beam, meaning
the
laser
beam after laser path momentum? In this case, if the mirror would
not
reflect
a path momentum unit, the mirror would reflect a 90
degree angle. In this
case
there would be two earth units, but only one path momentum unit (from the
laser).
The beam would not hit where the laser is when the beam returns.
However,
what if the mirror added one path momentum unit in this case? If
it
did,
the laser would add one path momentum unit, the laser beam would arrive at
a 90
degree angle, and the mirror would add one path momentum (this is
not a
reflected
path momentum unit, this is an added path momentum unit). Thus,
there
would be two path momentum units and two earth units, and the laser
82
beam
would hit the target. Twelve hours later, because the laser's path
momentum
unit and the mirror's path momentum unit are both in the same
direction
(towards Leo), reversing the position of the laser and target would not
change
anything, the dot would still be hit 12 hours later.
Thus,
we have a situation where if the mirror did not add a path momentum unit,
a dot
results (the case where the mirror is normal to the aimed laser
beam), and
we
have a situation where if the mirror did add a path momentum unit, a dot
results
(the case where the mirror is normal to the actual laser beam
after the
path
momentum unit angle is added). Thus, unless we had equipment accurate
enough
to guarantee the aimed laser beam was normal to the mirror, this
experiment
would tell us nothing about mirror path momentum, even if we got a
dot.
Because
the motion of our earth adds such a small angle to the laser beam, my
equipment
was not accurate enough to guarantee that the aimed laser beam
was
normal to the mirror (it is more complicated to do than it looks because you
obviously
cannot use surveyor equipment). Thus, I had to abandon
this type of
experiment
in looking for mirror path momentum.
Tilting the Mirror To One Side - No Added MPM
The
only way to resolve the problem of using a mirror that happened to be
normal
to the actual laser beam was to tilt the mirror to one side to guarantee
that
the mirror could not possibly be normal to the actual laser beam by accident.
In
other words, the mirror in my second experiment was tilted so that the
returning
laser beam hit about two meters to the right of the laser
position
(looking
from behind the laser). This guarantees that the actual laser
beam does
not
accidentally hit normal to the mirror.
Let us
first calculate how much we need to tilt the mirror, to one side, in order for
the
returning beam to hit 2 meters to the right of the laser. It should be
emphasized
that the line/vector between the laser and mirror is normal to the wall
behind
the laser, meaning the entire affect of the tilt is after the
laser beam hits
the
mirror. In calculating this we will need to ignore all types of path momentum
for
the moment.
Side a
= 2 m
Side b
= 50 m
Angle
A = atan (a / b)
Angle
A = atan (2 / 50)
Angle
A = 2.290610 degrees
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This
angle assumes there is no path momentum of the laser beam. Since there
must
be LPM, we must add .070665 to the above angle to determine at what
angle
the light is actually hitting the mirror.
2.290610
+ .070665 = 2.361275
Now we
must calculate how far the reflected laser beam will miss the laser
(assuming
there is no added path momentum by the mirror):
Side a
= b * tan A
Side a
= 50 * tan 2.361275 degrees
Side a
= 2.061768 m
This
number is almost exactly equal to the 2 meter intentional miss plus the
typical
.061666... m miss caused by laser path momentum. The difference is
unmeasurable
(using my equipment).
At
this point we must calculate exactly where the laser is when the beam hits the
wall,
and exactly where the beam hits the wall.
T0)
Laser is at origin.
T1)
Laser is .061666... m from origin (towards Leo)
T2)
Laser moves another .061666... m, making a total of .123333... m
T0)
Beam is at origin
T1)
Beam is at .061666... m from origin (towards Leo) when it hits the mirror
T2)
Beam moves another 2.061768 m (see above), making a total of 2.123435
m
The
difference between where the Laser is and the Beam is is 2.000102 m. Of
course
it is to the right of the laser. This result is not surprising.
Tilting the Mirror To One Side - No Added MPM - 12 hrs. later
Now we
must go through the same exercise 12 hours later, when the laser and
the
target/mirror have switched places. This time we need to subtract the laser
path
momentum from the mirror tilt. The reason is that the mirror is still tilted to
the
right (the mirror never moves), but the path momentum is now to the left (i.e.
towards
Leo) after switching places.
2.290610
- .070665 = 2.219945
Now we
must calculate how far the reflected laser beam will miss the laser
(assuming
there is no added path momentum by the mirror):
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Side a
= b * tan A
Side a
= 50 * tan 2.219945 degrees
Side a
= 1.938238 m
This
number is almost exactly equal to the 2 meter intentional miss minus the
typical
.061666... m miss caused by laser path momentum. The difference is
unmeasurable.
At
this point we must calculate exactly where the laser is when the beam hits the
wall,
and exactly where the beam hits the wall.
T0)
Laser is at origin.
T1)
Laser is -.061666... m from origin (left of laser origin)
T2)
Laser moves another -.061666... m, making a total of -.123333... m to the
left
of the laser origin.
T0)
Beam is at origin
T1)
Beam is at -.061666... m from origin (left of beam/laser origin)
T2)
Beam moves another 1.938238 m (see above), making a total of 1.876571
m to
the right of the laser origin. This is predominantly because the
mirror is
tilted
to send the light to the right of the laser (from the perspective of the
laser).
The difference
between where the Laser is and where the Beam is is 1.999904
m. As
above, it is to the right of the laser.
The
difference between 2.000102 and 1.999904 (12 hours later) is
unmeasurable.
Thus we conclude that we would get a dot if the mirror is tilted
and
the mirror does not add path momentum. The reader should pay
close
attention
to the fact that it is where the beam hits the wall, relative to where
the
target
is (i.e. the wall behind the laser is the target in this
case), that determines
whether
a dot is received. Keeping track of where the target is is just as
important
as keeping track of where the laser beam is.
Tilting the Mirror To One Side - Added MPM
The
tilt of the mirror in this case is exactly the same (the mirror is not touched
during
the experiment, nor is the laser). But in this case we must add one path
momentum
for the reflected laser path momentum plus we must
add a second
path
momentum for the assumed (in this case) added path momentum by
the
mirror.
The
reader should remember that before we tilted the mirror, assuming no MPM
was
added, we got a dot. We also got a dot if we did tilt the mirror, assuming no
MPM
was added. On the other hand, we did not get a dot if we assumed
MPM
was
added. We will come to the same conclusion if we tilt the mirror.
85
Let us
add the two path momentum units (one reflected from the laser and one
added)
to the tilt:
2.290610
+ .070665 + .070665 = 2.431940
Now we
must calculate how far the reflected laser beam will miss the laser
(assuming
there is added path momentum by the mirror):
Side a
= b * tan A
Side a
= 50 * tan 2.431940 degrees
Side a
= 2.123543 m
This
number is almost exactly equal to the 2 meter intentional miss plus double
the
typical .061666... m miss caused by laser path momentum. This is what we
expected
because the mirror is now adding path momentum in this case.
At
this point we must calculate exactly where the laser is when the beam hits the
wall,
and exactly where the beam hits the wall.
T0) Laser
is at origin.
T1)
Laser is .061666... m from origin (towards Leo)
T2)
Laser moves another .061666... m, making a total of .123333... m
T0)
Beam is at origin
T1)
Beam is at .061666... m from origin (towards Leo)
T2)
Beam moves another 2.123543 m (see above), making a total of 2.185210
m
The
difference between where the Laser is and the Beam is is 2.061876 m. This
does
not surprise us since we added one path momentum unit for the mirror.
Tilting the Mirror To One Side - Added MPM - 12 hrs. later
Now we
must go through the same exercise 12 hours later, when the laser and
the
target/mirror have switched places. This time we need to subtract the laser
path
momentum from the mirror tilt (because it is reflected) and we must subtract
the mirror
path momentum from the mirror tilt. The reason is that the mirror is
still
tilted to the right, but the reflected laser path momentum is now to the left
(i.e.
towards
Leo after switching places) and the mirror path momentum is in the
same
direction as the laser path momentum - to the left.
2.290610
- .070665 - .070665 = 2.149281
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Now we
must calculate how far the reflected laser beam will miss the laser
(assuming
there is added path momentum by the mirror):
Side a
= b * tan A
Side a
= 50 * tan 2.149281 degrees
Side a
= 1.876481 m
This
number is almost exactly equal to the 2 meter intentional miss minus the
typical
.061666... m miss caused by laser path momentum minus the path
momentum
added by the mirror.
At
this point we must calculate exactly where the laser is when the beam hits the
wall,
and exactly where the beam hits the wall.
T0)
Laser is at origin.
T1)
Laser is -.061666... m from origin (left of laser origin)
T2)
Laser moves another -.061666... m, making a total of -.123333... m to the
left
of the laser origin.
T0)
Beam is at origin
T1)
Beam is at -.061666... m from origin (left of beam/laser origin)
T2)
Beam moves another 1.876481 m (see above), making a total of 1.814815
m to
the right of the laser origin. This is predominantly because the
mirror is
tilted
to send the light to the right of the laser (from the perspective of the
laser).
The
difference between where the Laser is and the Beam is is 1.938148 m.
The
difference between 2.061876 (origin) and 1.938148 (12 hours later) is
.123728
m which is equal to 12.3728 centimeters. This is a measurable amount
with
my equipment. Thus we conclude that we would not get a dot if the
mirror
adds
path momentum. This is consistent with the result before we tilted the
mirror.
The Actual Experiment
In the
actual experiment, my laser died at the 14 hour mark, but the second 12
hours
of the experiment would have been a mirror image of the first 12 hours (i.e.
it
would have been the other half of any pattern), thus the experiment lasted long
enough
to make a determination. I got a dot for 14 hours, thus I can safely
conclude
I would have gotten a dot for 24 hours, if my laser had lasted that long.
This
means that this second experiment proves that MPM is false,
meaning a
mirror
does not add path momentum in the photon theory. The significance
of
this
will become evident in the next chapter.
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