SINGLE EDGE CERTAINTY Copyright © Bill Alsept

A PARTICLE THEORY OF LIGHT

May, June, July, Oct 2014

Abstract: The nature of light has been questioned for hundreds of years. Is it a wave, particle or

both? For those unwilling to except the non conclusive concept of duality this paper offers a clear and

simple particle based solution. Contrary to scientific consensus the fringe patterns from various slit or

edge experiments can conclusively prove that photons without diffraction or interference will produce the

fringe patterns we observe. Not only can patterns be constructed with straight line geometry but the ideas

behind Single Edge Certainty will do away with the approximations, assumptions and uncertainty of the

wave theory.

This is a work in progress.

Introduction: The debate over the nature of light and matter goes back to the 17th century when

Isaac Newton and Christian Huygens offered conflicting theories. Newton proposed that light was made

of particles while Huygens's theory consisted of waves.

For 350 years these competing theories have continued to develop as new experiments confirmed new

ideas. Scientist such as Young, Planck, Einstein and many others have worked to compile the current

scientific theory that all particles have a wave nature. In other words a wave particle duality.

I never gave it much thought and until recently had never even considered the double slit experiment.

As you know there is a light source directed toward two narrow slits and a fringe pattern forms on a

distant screen. The fringe pattern is made of equally spaced bright and dark fringes and the phenomenon

has intrigued many for centuries.

Often this concept is diagramed with overlapping semicircles representing waves as in figure 1 below

Figure 1

A wave theory is explained with sets of waves overlapping to form constructive and deconstructive

interference. This got me to thinking about the wave theory in general. You can hardly find descriptions

of light that do not include analogies of water or sound when describing waves. I can understand how

water or sound forms waves because there are multiple forces involved. With water there is the initial

force pushing on a medium of water molecules. A wave crest forms as the displacement meets resistance

and gravity pushes down on the crest countering the whole effect. There wouldn't even be a wave without

gravity or any one of the other forces. As for sound waves they too have multiple forces including

momentum, pressure and density differences.

Light doesn’t have any of these countering forces. The wave theory of light doesn’t even offer an

explanation of these forces or a cause for the so called wave. The only descriptions given are Huygens

and the uncertainty principle but again nothing to explain the forces. What bothers me the most about the

wave theory of light is that most interpretations claim that only waves can explain the fringe patterns. I

believe on the contrary that light is made up of particles and it's these same experiments that will prove it.

With certainty

PHOTONS

When it comes to a particle theory of light we have the photon. Photons are very small individual

packets of energy each with a certain frequency and traveling close to 300,000 kilometers per second.

Photons oscillate electromagnetically between positive and negative amplitudes. Most importantly

photons can be counted individually as particles.

How photons oscillate is not exactly clear and could involve cycles of spinning, inflating, collapsing or

all the above. Whatever their doing they do it a lot and the term wavelength is used as a convenient unit of

measurement. In reality it's the frequency that we need to be concerned with.

A photon with a 500 nanometer wavelength actually oscillates at an extreme frequency of about 600

terahertz. That’s 600,000,000,000,000 (600 trillion) oscillations per second! In a typical slit experiment a

photon may travel one meter or 1,000,000,000 nanometers and during that short distance and time a

photon will oscillate 2,000,000 times. Now if you divide the meter (L) by the number of oscillations you

will get a very small distance of 500 nanometers. (1,000,000,000/2,000,000=500) 500λ is the distance a

photon travels during one cycle and we call it a wavelength but really it has nothing to do with waves.

Imagine a single 500nmλ photon traveling along at 300,000 kilometers per second in a straight line. As

the photon travels it oscillates through full cycles of positive and negative amplitudes every 500

nanometers. The image below represents a photon traveling left to right as it oscillates through to a

positive amplitude at 250 nanometers and then a negative amplitude after another 250 nanometers. See

figure 2

Figure 2 Photon cycle and propagation

For now it doesn’t matter how photons oscillates, just remember it’s something each photon does

locally as it travels along and has nothing to do with waves. For instance if you throw a Frisbee at 20

meters per second with a spin of 20 revolutions per second the Frisbee would complete one oscillation

per meter. It does not mean that the Frisbee has wavelength of one meter (λ1m). The term wavelength is

only used as a convenience but there are no waves involved.

We may not know everything about photons but we do know they electromagnetically oscillate at

different frequencies and travel in straight lines close to 300,000 kilometers per second. We also know

that photons are emitted and absorbed individually by atoms. This is all the information I need to prove

that light as a particle (individual photons) can account for the so called interference patterns. Step by step

I will show how the fringe patterns we observe can be constructed mechanically and mathematically with

straight line particle trajectories. When it comes to light there is no need for waves or diffraction.

As I was saying photons are emitted and absorbed individually, they travel in straight lines and oscillate

between positive and negative amplitudes. If a visible photon is randomly emitted toward an opaque wall

it will travel in a straight line until it impacts an atom on that wall. The photons energy will be absorbed

or the photon will be absorbed and then followed by a new photon being emitted in a new and random

direction from that spot. Figure 3 below shows examples of either.

Figure 3

If the wall has a small slit then a very small portion of the photons will miss the wall altogether and will

continue on their straight trajectories through the slit unaffected. See Fig 4 below. So far there has been

no need for waves or bending of light but now we come to the interesting part.

Figure 4 Figure 5

Sometimes a photons will impact right on the edge of a slit and something very different happens.

Again the photons are absorbed but this time when new ones are emitted they have a wider range of

emission trajectories. New photons are randomly emitted (in straight trajectories) from this new point

source and this time some of them will travel toward the other side of the wall. See figure 5 above

The sharper the edge the better this point source becomes and all photons coming from this point are

coherent. It may appear as though these photons trajectories are bending around the edge but as you can

see no waves or diffraction are required because there are two different photons involved. Next I will

piece together exactly how a particle theory of light can form the fringe patterns or the so called

interference and diffraction patterns we observe.

THE SINGLE EDGE

The most popular experiment is the double slit experiment. Obviously it’s made of two single slits but

lets take a closer look and start with the left side of the left slits and we will call it Edge 1. See figure 6

Figure 6 Figure 7

In figure 7 we have a light source and for future reference it will be 500nmλ and monochromatic. We

have a single edge which I have labeled Edge 1 and one meter (L) above the edge there is a detection

screen. From the light source photons are randomly emitted with some traveling toward the edge and

detection screen. One half of the photons will hit the wall and edge while the other half will go on to the

detection screen.

As you can see the left side of the detection screen is a shadow because the photons are blocked from

getting there. The right side is illuminated with a fringe pattern and if you look closely you will see that

the pattern is not the same as a slit fringe pattern. The spacing’s are not equal and the farther away from

the shadows edge the smaller the spacing’s are. This diminishing pattern continues until it blurs and is

typical of all single edge fringe patterns.

The fringe pattern will stay the same as long as L, λ and the angle of the screen remains square to the

closest point of the straight edge. If you move the location of the light source the shadows edge will move

but the actual fringe pattern stays in place. See figure 8 and 9 below

Figure 8 Figure 9

Single edge fringe patterns are important to any theory of light. These patterns are always there and are

the bases of all other fringe patterns. In the next few pages I will show how these patterns are constructed

with photon particles, straight lines and basic geometry. There is no bending of light or interference

needed to create them.

So getting back to the single edge as I was saying in figure 5 and 7 some photons will be absorbed

right on the edge causing new photons to be emitted from there. All the photons emitted from here are

coherent and will travel straight line trajectories in every direction. These photons will eventually impact

every single point on the detection screen that isn’t blocked.

As a photon travels from the edge to somewhere on the screen it oscillates between negative and

positive amplitudes. See Fig 3. Depending on where a photon impacts the screen it may be at a positive or

negative amplitude. In reality most photons will impact somewhere between amplitudes. See fig-10 below

Figure 10

In this experiment the distance from the edge to the detection screen (L) is 1,000,000,000nm. A 500λ

photon will oscillate between positive and negative amplitudes 2,000,000 times while traveling to the

detection screen. Whether a photon impacts in a negative or positive amplitude depends on its frequency,

the length it travels, and the phase of the amplitude cycle it was emitted at. We can then use Pythagoreans

theorem to calculate the locations of individual fringes such as (B1) the first bright spot, (D1) the first

dark spot or (B2), (D2), (B3) etc. See Fig-11

Figure 11

Fig- 11 above shows how the bright and dark Y distances are calculated but as I was saying we still

need to know at what phase of the cycle the photon was emitted. I may have found the answer to this.

The first time I calculated the distance (Y) (measured from the shadows edge) to the 1st bright fringe

(B1). I tried adding ½ λ (250nm) to L to create a hypotenuse and then I calculated:

Y= or

Y= or

Y=707,106.82nm But turned out to be incorrect.

At first I had nothing to compare my calculation with, The only equations I could find for single edge

fringe patterns where extremely complicated. One day I came across this site about lunar occultation’s

http://spiff.rit.edu/richmond/occult/bessel/bessel.html and discovered another way to look at single edge

fringe patterns.

This was the first time I had read about occultation. By chance I happened to recognize a sequence of

numbers that were similar to the calculations I was doing for single edge fringe patterns and realized I

was on the right track. Based On what I had learned about lunar occultation I could now calculate the

diminishing spacing’s of the fringes the moon would make on the earth. The creator of this web site had

already measured these distances so I finally had something to compare with my calculations. For my

experiment all I had to do was convert (L) back to 1 meter instead of the 184,000 kilometers their

experiment had used for the distance to the moon’s edge.

Using Pythagorean Theorem and calculating backwards I converted the occultation’s measurements for

Y and L and applied to them to my experiment and then calculated for the hypotenuse. What I discovered

was that no matter what wavelength of light or distance you input (when calculating for the 1st bright

fringe B1) the hypotenuse will always be L+3/4*1/2λ or L+3/8λ. Not quite 1/2λ

This told me that these photons (maybe all photons) were emitted at the same point of their

electromagnetic cycle. This also told me that at the point of emission the photons were already part way

into their cycles or more precisely 1/8 beyond their negative amplitude. That's why 3/8λ is added to (L) so

that the first hypotenuse is the exact length needed to complete an oscillation just as it’s impacting the

screen in a positive amplitude. The distance Y from the shadows edge to the first bright fringe is

calculated as:

Y= or

Y= or

Y= or

Y=612372.46nm

See Fig 12 below

Figure 12

Note: On the calculation I have highlighted what will be the variable for calculating other fringe locations.

Only with the first bright fringe do I add 3/8λ to (L) to create the hypotenuse but after that to calculate

all the other negative and positive fringe amplitudes all we need to do is add 1/2λ to the previous

hypotenuse.

The 2nd fringe is a dark spot (D1) to calculate it I would add 1/2λ (250nm) to the previous hypotenuse

Y=

So it would now look like:

Y= or

Y= or

Y=935,414.45 nm distance to (D1)

See Fig 13 below

Figure 13

Every other bright or dark fringe can be confirmed at any Y distance no matter how far out you

calculate. As you can see there are no waves or diffraction involved. All that is needed are oscillating

photons and straight line Pythagorean geometry.

If we continue on the 3rd

fringe (B2) will again be bright and is calculated as follows:

Y= or

Y= 1172604.142nm distance to (B2)

See Fig 14 below

Figure 14 Second bright fringe B2

The 4th fringe (D2) is dark and calculated as follows:

Y= or

Y= 1541103.958nm distance to (D2) See Fig 15 below

Figure 15 Second dark fringe D2

The 5th fringe (B3) is bright and calculated as follows:

Y= or

Y= 1695583.105nm distance to (B3) See Fig 16 below

Figure 16 The third bright fringe

In the same way I calculated the first five bright and dark fringes every other fringe can be calculated.

You can infinitely calculate for the Y distance and the measurements will always be accurate no matter

how far out you go.

THE FLIP SIDE

On the shadow side of the screen the same thing is happening. It may not be bright enough to see but

the photons emitted from the sharp edge are also randomly forming the same pattern that we see on the

illuminated side. The same Pythagorean principle applies in reverse order on the shadow side. See Fig 17

Figure 17 Figure 18

So far I have diagramed these single edges using a left edge. If we use a right edge the same fringe

pattern will form in the same way but with the shadow and illuminated sides reversed. Notice that the

fringe pattern stays the same and unmoving even though the shadow switched sides. See Fig 18 above

If a sharp edge did not have this effect there would only be a shadow side and an illuminated side with

no fringe pattern at all. See Fig 19

Figure 19

Coherent photons radiate in random directions from the edge impacting the screen at every location.

Some hit the shadow side and some hit the already illuminated side. The positive and negative impacts of

the photons from the edge mix with the screen and form the single edge fringe patterns described above.

See Fig 10, 17 and 18

On the shadow side the oscillating photons add or subtract from the screen depending on what phase

they are in when they impact. Negative impacts subtract from the already dark and empty field so the

location remains dark. Positive impacts add a small amount to the empty field. Other than the first bright

fringes the pattern on the shadow side would not be noticed but maybe it could be detected. It would be

interesting to see if that has ever been tested before. (Maybe it has in an occultation experiment?)

On the illuminated side the oscillating photons also add or subtract to the screen depending on their

impact phase. Negative impacts subtract locally from the already illuminated side making it darker than

average at those points. Positive impacts add to the already illuminated side making it brighter than

average at those points. A unequal pattern forms of darker than average and lighter than average fringes.

The energy delivered by each photon varies from a positive amplitude to a negative amplitude with

most impacts somewhere in between. Impacts subtract or add to the local energy and this process

combined with the Pythagorean geometry described above gives us the single edge fringe pattern and its

distinct diminishing spacing’s.

As you can see there is no need for waves, diffraction, spreading or bending in anyway. There are no

other explanation that even comes close to describing and accounting for the single edge fringe pattern as

accurately as this. The math and geometry perfectly predicts the fringe locations at any point.

Based on the principle of Occam’s razor my solution to the single edge fringe pattern not only has the

least assumptions but has no assumptions. Unlike the wave theory which relies on many assumptions,

approximations, infinite wavelets and a principle called uncertainty.

SINGLE EDGE CERTAINTY

Now let’s make things more interesting and slowly bring the left and right edges closer together

keeping the screen beyond at the same distance (L). As the left and right edges move parallel to the screen

their constant (unbending) fringe patterns on the screen remain intact as they move along in the same

direction. See Fig.20 a, b, c

Figure 20 a,b,c

The single edge fringe patterns are always there even as the two edges come closer and form what we

call a slit. The two single edge fringe patterns begin to overlap and form a new pattern where the photon

impacts add up to new totals at these local points along the screen. This new pattern has equal spacing’s

as do all slit fringe patterns.

At first all that is noticed is the light going through the slit with no obvious fringe patterns. In Fig 20

this area is labeled as Illuminated. Eventually the two single edge patterns overlap enough for the new

equally spaced single slit pattern to be revealed. See Fig 21 a,b,c

Figure 21 a,b,c

Every point on the new and equally spaced fringe pattern can be accounted for with the simple math and

geometry of overlapping and combining of the two single edge patterns. Everything is still based on

straight line Pythagorean geometry. There is no diffraction or interference.

As we slowly bring the two edges even closer together the pattern on the screen appears to be spreading

but it’s not. You can still do the math of combining the two original patterns (which are still there). The

combination of adding the two overlapping patterns changes the spacing’s of the pattern. As the spacing’s

get bigger the pattern spreads out. This gives the appearance that light is diffracting around the edge. See

Fig-21 b,c above

Now at this point the “UNCERTAINTY PRINCIPLE” would tell us that because the two edges are

getting so close together the locations of the photons passing through this narrow area are becoming

more and more certain. It also says that after passing through a slit that the momentum of the photon

should become less certain for no reason at all other than to satisfy the statement “We can’t know the

location and the momentum at the same time” or something like that. What kind of reasoning is that??

As I described above the pattern can be accounted for by the overlaying (adding and subtracting) of the

two single edge patterns. The single edge patterns can be accounted for with straight line Pythagorean

geometry. Still no waves, diffraction, spreading, bending or wave interference. Why have an Uncertainty

Principle when we can have “Single Edge Certainty”

I have read that the uncertainty principle was meant for particles like electrons and not to be used for

photons. That may be so but there are a many sites that claim photons are affected this way so it is no

wonder there would be confusion about this. But why have an uncertainty principle at all. Why is it that

something needs to become more uncertain just because something else become more certain? Why have

uncertainty when it can be explained physically and mathematically with proven photon physics, simple

math and Pythagorean geometry.

Our experiment is still set up with λ =500nm and (L)=1,000,000,000nm. When the two edges come to

within 1,000,000nm of each other the equally spaced fringe pattern can be calculated to have 500,000nm

spacing’s. Again this can be proven with straight line Pythagorean geometry from the edges. There is no

need for waves, interference or assumptions and approximations of Huygens Principle.

Now place the two edges 900,000nm apart. The math (without assumptions) will show a fringe pattern

with spacing’s of 555555nm apart. An 800,000nm slit has spacing’s of 625,000nm apart and a 700,000nm

slit has spacing’s of 714,285nm apart. A 600,000nm slit has spacing’s of 833333nm apart and when the

slit is only 500,000nm apart the fringes are equally spaced at 1,000,000nm apart.

As the slit gets smaller the overlapping of the two single edge patterns keeps forming patterns with

larger and larger spacing’s. This gives the appearance that light is spreading or diffracting but everything

can be accounted for with the straight line geometry of single edges and oscillating photons.

Why is it that principles like Heisenberg’s or Huygens are excepted so easily to explain this so called

spreading when it can be proven so easily with the geometry of the two single edge patterns being

overlaid.

A PARTICLE SIMULATOR Copyright © Bill Alsept

When I first started drawing single edge fringe patterns to scale I would actually pencil them out with a

ruler and a lot of calculating. Eventually I started diagramming them as triangle waves (even though they

are not waves). This way I could place all the positive amplitudes at one end of the chart (top) and all the

negative amplitudes at the other end (bottom) with the Y distances (spacing’s) consistently getting smaller

along the horizontal. Fig 22 below shows the difference between a real single edge fringe patterns and the

way I charted them with triangle waves.

Figure 22

++

Charting the diminishing spacing’s of a single edge pattern is not the same nor as easy as charting a

repeating sine wave pattern. And charting two edges in both directions would get even more complicated.

See Fig 23

Figure 23

Although single edge fringe patterns are produced on both sides of an edge for clarity I only charted the

right sides. This also made it easier to accurately overlay and draw two patterns with a certain separation.

See Fig 25 below

Figure 25

At first I tried many wavelengths and distances but couldn’t get an obvious pattern to form. After

setting up a laser and viewing actual fringe patterns I realized that the single edge fringes were far more

numerous than the slit fringes. I would need to calculate and draw these patterns a lot farther out to even

begin to calculate the overlap. I couldn’t draw that many so I looked for a program.

I knew that Excel could chart equally spaced patterns but could not find anything about diminishing

patterns. I soon learned enough about Excel to realize it was the perfect tool for doing this. Maybe

someone somewhere has calculated these unique patterns with a program like Excel but I couldn’t find it.

I found some examples where standing waves or constant sine wave were charted but not the diminishing

spacing’s of a single edge fringe pattern.

It turned out to be much easier than I thought and I am still surprised no one had done it before. Not

only could excel accurately chart the patterns but it could do all the calculation as I did on pages seven

through twelve above. In addition to that I could separate each edge (edge 1, 2, 3, 4 …) into separate

columns with each being calculated as far out as I wanted to go. Fig 26 and 27 show screen shots from

my simulator.

Figure 26 Single Edge Pattern

Figure 27 Single Slit Pattern (two Edges)

With my simulator I could calculate and simulate single edge fringes as well as single, double and

multiple slit fringes. This was really cool and you will see it below. You can input any wavelength,

distances or number of slits and not only compare fringe patterns but see exactly how the convolution

forms the exact patterns we observe in nature. See Fig 28 below shows my 4 slit simulator and you can

see where all 8 edges come together at 5,000,000nm.

Figure 28 Screen shot of 4 slit (8 edges) simulator showing the calculations and charting of eight edges.

This simulator is set to calculate out to 2000 points along the horizontal. It’s really amazing when you

scroll fast across a pattern and see it move. After a few days of studying these fringes you’ll begin to see

why there are differences in the many types slit patterns.

Below are five versions of my simulator. Ctrl + Click one version then download

for simulator to work. Copyright © Bill Alsept

Single Edge Pattern Simulator (one edge)

Single Slit Pattern Simulator (two edges)

Double Slit Pattern Simulator (four edge)

Triple Slit Pattern Simulator (six edge)

Four Slit Pattern Simulator (eight edge)

ELECTRON SLIT EXPERIMENT WITHOUT UNCERTAINTY

Many double slit experiments use electrons as a source instead of photons. Richard Feynman

popularized this experiment in his lectures. For a clear and simple description of this process see link.

http://physicsworld.com/cws/article/news/2013/mar/14/feynmans-double-slit-experiment-gets-a-

makeover

The experiment and results are nicely described but as usual the reason the electrons do what they do is

not. The results are similar to the pattern that overlapping water waves would make but as I described in

Fig-1 not quite the same. Interfering water waves form a fringe pattern with spacing’s that are not equal

but the fringe patterns formed by electrons have equal spacing’s. Still the wave theory and the uncertainty

principle are the only solution ever offered.

As I developed Single Edge Certainty I wondered about electrons and the phenomenon they displayed

when fired through a slit experiment. The electrons appear to be going through both slits and interfering

with themselves to form a pattern on the screen. Electrons unlike photons are not absorbed or emitted by

atoms. How then could they form the same fringe patterns?

Many articles make a big deal of this by turning it into some mystic impossibility of the quantum world.

I still find articles that imply that the system seems to be consciously altering the paths of the electrons

just because of our observation and perception. They never mention that the detector actually blocks or

diverts the path of the electron so that it can no longer effect the pattern. “The nature of reality being

dictated by our perception is a product of pseudoscience with no actual evidence. Experiments claiming to

support this notion have been debunked many times.” Taken from my notes of a forgotten source.

Other than self interfering or self aware electrons the general consensus seems to be that the patterns

formed by the electrons are dictated by the uncertainty principle which I’m not ready to except. The more

I thought about it the more I focused on photons and the way they interacted with electrons. I knew that

accelerated electrons emitted photons and I knew about the photoelectric effect.

If an electron is accelerated wouldn’t it emit photons as it traveled along and if fired through a slit

would the same single edge fringe patterns form from the edges as I described above? Using my

simulator I pictured an electron passing through a slit and randomly emitting photons in every direction.

Some photons going forward toward the screen and some back toward the wall and the two edges. See

Fig-29

+

Figure 29

Eventually the space between the two walls would be filled with the reflecting photons but the paths

between the edges and the amplitude points on the screen (the single edge fringe patterns) would still

form. You can clearly see where the paths and amplitudes of individual photons are concentrated or

diffused. See Fig-30

Figure 30

These concentrations form links between the edges and amplitude points. As the electron continues on

toward the screen it gets bumped left and right by the photoelectric effect of these concentrations. The

closer the electron gets to the screen the more it is corralled into the same locations of the photon pattern.

Again giving us the appearance of a so called wave pattern.

With Single Edge Certainty I have already described how photons can account for the fringe patterns

we observe. Now with the accelerated electrons, photons and the photoelectric effect we also have an

alternate solution for the electron fringe pattern. Although it does appear as if electrons are going through

some sort of wave interference or wave process in reality they are just following random paths of

probabilities as they get bumped around by the concentration and phasing at the photon paths. The

probabilities are similar to but not the same as a plinko board. See Fig-31 and 32

Figure 31 Figure 32

This is a work in progress by Bill Alsept b_alsept@yahoo.com

References Cited (in this document) Michael Richmond, “Diffraction effects during a lunar occultation”

Dept. of physics, Rochester Institute of Technology http://spiff.rit.edu/richmond/occult/bessel/bessel.html

Roger G Tobin “Wave Simulator” Fig-1a and link

Professor of physics Tuft University http://rtobin.phy.tufts.edu/Apps/interference.html

Fig-1 “Wave diagram” from “The Physics Classroom” taken from a list of images

http://www.physicsclassroom.com/class/light/Lesson-3/Young-s-Equation

Fig-31 “Image of Plinko board” http://teachingcollegemath.com/category/mathstats/

Physicworld.com http://physicsworld.com/cws/article/news/2013/mar/14/feynmans-double-slit-

experiment-gets-a-makeover