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 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 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 = (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.

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.

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.

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 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.

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 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 (2 / 50)

Angle A = 2.290610 degrees

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 = 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):

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.

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

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.