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European Journal of Applied Sciences – Vol. 11, No. 1

Publication Date: February 25, 2023

DOI:10.14738/aivp.111.14039.

Schatten, K. H. (2023). Young’s Electron Experiment Enigma. European Journal of Applied Sciences, Vol - 11(1). 666-674.

Services for Science and Education – United Kingdom

Young’s Electron Experiment Enigma

Kenneth H. Schatten

NASA/GSFC, Greenbelt, MD, 20771 USA

Now at ai-Solutions, Lanham, MD, 20706 USA

Abstract

This paper focuses on a long-standing problem in physics that originated more than

two centuries ago. In 1802 Young noticed numerous bright and dark bands formed

behind a metal sheet containing a pair of slits, when it was illuminated by

candlelight. Advances in understanding the nature of light, the bands could be

understood as “light interference patterns.” Nevertheless, in the mid-20th century,

another paradox arose when individual electrons fell upon the double slit

configuration. It was not clear how individual electrons could create the same

banded patterns. Yet the new quantum physics theory was at the peak of physics’

popularity. As a result, a special moniker was created that allowed such

idiosyncrasies: “wave-particle duality.” Under its banner, waves could act as

particles and vice-versa. This behavior failed “locality,” essentially meaning local

reality or relativity, as each electron, considered as an indivisible particle, could not

then pass through both slits simultaneously. This paper offers a modern Quantum

Field Theory (QFT) approach showing how modern Quantum Field Theory can

resolve this electron enigma.

INTRODUCTION

We begin briefly, showing what shall be the focus of this paper, in its stark beauty. It is a

numerical simulation of Young’s [1] double slit experiment by Jönsson’s [2] simulation of

electron passages. Young’s experiment began in 1802 when he noticed candlelight falling upon

two slits in a metal sheet. Rather than the expected image of the two slits projected behind the

sheet, there were a large number of banded patterns or fringes. We shall first run through some

early history of Young’s experiment, including an overview of the experimental setup.

Following this, the paper analyzes how a QFT electron would transit Young’s experiment.

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Schatten, K. H. (2023). Young’s Electron Experiment Enigma. European Journal of Applied Sciences, Vol - 11(1). 666-674.

URL: http://dx.doi.org/10.14738/aivp.111.14039

Figure 1. Graphical Abstract. Young’s[1] experiment and Clause Jönsson's [2] numerical

simulation of Young’s double-slit interference experiment with electrons. The evolution

of the electron beam intensity proceeds from the double slits on the left to the detection

screen on the right. The higher the intensity, the lighter the graphed color portrayed.

Photons, atoms and molecules follow a similar evolution in their double slit experiment.

The essentials of Young’s experimental geometry is shown in Figure 2. Young did all his early

work alone: he created the experiment, unraveling the observations, as well as identifying the

peaks and troughs associated with the paths taken by light; namely the interference patterns of

constructive and destructive interference bands! Young did all the early, heavy lifting work

himself! There was nobody he could turn to. Young considered and explained the geometry

observed, doing all the mathematical work; he stated the bands occurred when “A luminiferous

Ether pervades the Universe, rare and elastic in a high degree.” Young’s writing refers to early

views regarding light (these are pre-Maxwellian); back then it was thought light needed to be

transported. For example, waves on a clothes’ line, it needed the physical rope. There was no

thought that waves could propagate in empty space, without any substance to carry the waves;

hence the needed ether was invoked.

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Figure 2: The geometry of Young’s experiment. Rather than the expected image of the two slits,

the first slit can be regarded as preparing a columnating be of alternating “interference fringes

or bands” were observed as seen here.

In this manner, Young considered the path differences were related to these constructive and

destructive interference bands within the aether, a substance consider to fill all space. Modern

understandings of vacuum being able to transport light and other electromagnetic (EM) waves

were not around. Maxwell and colleagues created the modern views we now have. Back then,

one needed field to be transported by a substance, much as a sound wave needs air, and an

ocean wave needs water. Now we consider light to be associated with particular wavelengths

of light, without any needed aether. More recently, Young’s experiment has undergone many

variations.

Of great interest here, is that modern experiments have been performed with electrons.

Surprisingly, the same interference bands are still created. This brings us to our current

understanding. Since electrons create the same patterns as light, we physicists have taken a

pragmatic approach; let us say: ‘if it is good enough for photons, it is good enough for electrons.’

We physicists allowed this by developing a moniker: “wave-particle duality.” This meant that

in quantum mechanics, particles could act like waves (namely, charged electrons could act like

electromagnetic waves), and hence the interference bands could form in a manner similar to

that of light. Particles could have associated waves, and Einstein showed that waves could

create particles, as Einstein associated with the “photoelectric effect;” for which he was

rewarded his only Nobel prize; it was a “hot topic then.” We shall choose what may be regarded

as an unpopular viewpoint; namely regarding the wave-particle moniker as highly

questionable.

Regarding Young’s experiment with electrons to consider how Quantum Field Theory’s

description of electron structure could modify our understanding of how this experiment

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Schatten, K. H. (2023). Young’s Electron Experiment Enigma. European Journal of Applied Sciences, Vol - 11(1). 666-674.

URL: http://dx.doi.org/10.14738/aivp.111.14039

worked, we chose it, not because it was simple, but because the explanation appeared “too

simple.” The explanation that electrons pass through the experiment in the same manner as

light does, seemed “too easy.” In any case, to this author, the experiment appears one of the

most paradoxical quantum experiments. Borrowing from the light paradigm, the explanation

of the electron experiment requires each electron to simultaneously pass through two separate

slits, and then these two, let us call them “halves,” need interfere with each other. This is often

called paradoxical or enigmatic. We next focus on the following roles that Young’s experiment

plays within these labeled sections:

2) Quantum Field Theory (QFT),

3) Free Electron Structure,

4) A Simple Tool: Electron Journey,

5) Summary and Conclusions,

6) Acknowledgements, and

7) References.

QUANTUM FIELD THEORY (QFT)

This paper examines an offshoot of Young’s experiment with light: the double slit interference

experiment using free electrons. We now consider this situation with a more jaundiced eye.

Namely, we do not simply rely upon the previous quantum moniker: “wave-particle duality.”

We know more about electron structure and this guides us towards another, differing more

modern approach to possibly understanding the origin of Young’s double slit banded patterns

with electrons. We shall rely on Quantum Field Theory (QFT) to guide us towards better

understanding quantum processes, namely how do free electrons transit Young’s experiment,

and yield Young’s banded structures, yet somehow remain as particles, when, for example, they

land on the film plate.

Young’s double slit interference experiment with electrons contained a troublesome theoretical

failure; namely to explain the experiment’s behaviors, it required each electron to pass through

both separated experimental slits simultaneously, as this is how light creates Young’s

interference bands! The best way to categorize the problem of assuming electrons doing this,

within the lexicon of physics, is that this paradigm comes under the category of a locality (local

reality) failure. This paper examines the passage of electrons through the experiment to

ascertain whether and how electrons are able to create the observed interference patterns

while overcoming the locality failure.

This may be framed as a question: “How do electrons create the same observed Young double

slit interference patterns as light?” This paper is an attempt to understand this, for this one

experiment: Young’s double slit experiment with electrons. Understanding this has been

hindered by the vast difference of scales involved; electrons are of size 3 x10—13 cm. This is very

small by atomic standards, and they have also been thought of, as having no size at all, namely

a “point defect” in the electric field.

FREE ELECTRON STRUCTURE

Quantum Field Theory (QFT) offers a possible route to removing the locality violation, namely

using local realism in the approach to understand the electron within Young’s experiment. In

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fairness to physicists in the past, it will be helpful to understand the structure of the electron

as this governs their motion. In QFT, the bound electron consists of an electron core plus 3

orthogonal spin matrices, with one bit of information each, controlling up or down. When free,

the electron still has the immutable electron core. To gain its freedom; however, the core is

covered with a “dressing” of EM field that allows it to escape atomic bonds, by inhibiting energy

losses associated with Bremsstrahlung (braking radiation). This electron EM field dressing is

easily shed, if matter is close by, but it requires a small fraction of the free electron’s mass to

free the dressing [3].

In the absence of nearby matter, the dressing pervades empty or neutral space. The dressing

field can just as easily leave the electron, should it come close to a nucleus, thereby it would

lose energy and its bare core would then be recaptured. Hence, one may think of the free

electron as a type of “composite particle,” although historically, this will not happen. The

electron structure then consists of its bare charged core, as opposed to the bound electron, that

exists within atoms, and molecules. When free, the charged electron core is surrounded by a

neutral dressing EM field shell. Figure 3 (top) shows a Feynman type diagram [3] for bound

and unbound (free) electron states. The lower figure illustrates a geometric picture for the free

electron, including a spin vector. To improve our understanding of how QFT electrons will

behave in experiments, the geometric picture is more valuable than the Feynman type

representation, thus Figure 3 shows both, to understand how one converts the Feynman

picture into a geometric one.

Figure 3: (top) displays a Feynman type representation of the free electron (solid line) as the

sum of the bare charged core (dashed line) plus virtual photons that coat the core (bottom).

Equivalent geometric picture [3] includes the spin vector, . The center of the electron is

particle-like, while the outer “shell” contains electromagnetic field that can expand outwards,

even to macroscopic distances, as, for example, the divergent electric field extends outwards

until it encounters a positive opposing field. We also note that the QFT electron model allows

an order of magnitude estimate of Planck’s uncertainty principle yielding a rough estimate of

this: Δx Δpx ~ ћ.

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Schatten, K. H. (2023). Young’s Electron Experiment Enigma. European Journal of Applied Sciences, Vol - 11(1). 666-674.

URL: http://dx.doi.org/10.14738/aivp.111.14039

To obtain the double slit interference bands, using the conventional quantum view, each single

electron needs to be situated at both slits at the same time. Then these electron “twins” can

travel separate paths within the experiment to arrive at the screen/film plate and interfere with

their other twin to create interference bands associated with the phase differences due to path

length differences. Namely, a “field” can pass through Young’s two slits and interfere with itself.

It is not easy to understand, however, how a particle can do it. The particle needs to split in two,

and then must interfere with itself; classical particles simply cannot do either task. Despite this

quantum mechanical problem, quantum theorists stipulate that in QM, particles can do this,

knowing that this is problematic. Often the weirdness of particles splitting in two, and then

going along separate pathways to recombine, is considered a positive attribute of QM, as if our

failure to understand it, is a positive attribute rather than one which is questionable, and is

deserves clarification.

When we translate Young’s experiment into the 20th century, several problems emerge. The

problem, naturally, is that electrons are particles: they have a charge, a mass, and the electron

behavior is responsible for the periodic table of the elements. Let us now consider how our QFT

electrons pass through Young’s experiment, and then see where this leads us.

A SIMPLE TOOL: ELECTRON JOURNEY

The paper shall now illustrate how Quantum Field Theory (QFT) can simply analyze the passage

of free electrons journey through Young’s experiment. their path, however, will not be as

famous as Odysseus,’ king of Ithaca. After the Trojan War, he wandered for 10 years. The author

is not Homer, hence this paper shall be brief. We offer a simple way that electrons are able to

obtain interference patterns, similar to light’s. This can illustrate how electrons pass through

experiments, such as Young’s double slit device. The puzzle has been how each electron can

seemingly pass through both slits simultaneously, without each electron going through both

slits at the same time. This was how QM viewed the experiment occurring when light transited

the experiment. The interference patterns shown in Figure 4 are those calculated by Bohm and

Hiley [5] for the interference path lines. These require each electron to go through both slits, a

locality failure. For added information about the path lines, pilot waves, plus similar ideas,

viewpoints from a deterministic viewpoint, one may find them in [4-7].

One can understand how free electrons can create the same interference patterns as light, by

analyzing the detailed passage of electrons as they transit the experiment. The electron’s outer

dressing shell, is comprised of electromagnetic (EM), predominantly electric field, primarily

electric. Hence in the experiment’s first chamber, the outer dressing field simply expands into

the bare vacuum, governed by the Maxwell stress tensor, consisting of tension along field lines

plus an isotropic pressure. As a result, the electric fields pass through this chamber; with a small

amount of field finds its way through the two slits. The electric field’s journey comes to an end,

when they construct a similar interference pattern as light established on the film plate. A

subsequent event follows; the electron’s core, being a sink of electric field, also has rest mass;

hence, the electron’s core follows the electric field line as Bohm and Hiley’s pilot wave travelling

in the direction towards a positive charge. Hence the electron arrives on the film plate with the

same double slit pattern that light provides! As far as “collapse of the wave function” wherein

the electron creates a dot on the film plate, rather than a spread-out interference pattern, this

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happens similar to light in that the electron core remains immutably tiny throughout the whole

experiment, and was never “spread out,” although the wave function “information” of the

electron’s location was spread out. Each electron core interacts with the film plate locally,

wherever it lands on the film plate. The spread-out quantum function, only represented the

overall probability of where the electron might be, but we know the electron itself is not

identical to where it might be!

Figure 4 illustrates the mobility physics of how QFT electrons move through the experiment.

This picture dissects the path that electrons travel in Young’s double slit experiment. The key

is that the outer electron layer is virtual photons (EM field), this layer acts just as light does; it

creates the same double slit pattern. This overcomes the problematic quantum view that the

electron needs to have its core go through both slits at the same time to create the interference

pattern. The EM field just creates the pattern, which acts then as a conduit through which the

electron’s core can follow (it is guided by this E field)! One can think of this as the object (the

electron) is the sum of its parts: core plus EM dressing. The figure shows how the QFT

interference patterns arise and can then serve as “pilot waves” shown by DeBroglie, Bohm, and

Hiley [4-6]. The Quantum Field Theory (QFT) view of free electrons having a bare core

surrounded with an electromagnetic field dressing offers a local reality (locality) explanation

for the behaviors seen when electrons are analyzed with Young’s Double Slit Interference

experiment.

Figure 4. Young’s experiment with an electron. The electric field transits into or serves as a

pilot wave. The electron enters at A. The dressing electric field expands outwards from the

bare core (portrayed) to both chambers. Not shown are the bendings of field lines perpendi- cular to the conductor walls. The electron’s outer electric field behaves as a “dressing” field. It

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Schatten, K. H. (2023). Young’s Electron Experiment Enigma. European Journal of Applied Sciences, Vol - 11(1). 666-674.

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also forms a “pilot wave” that De Broglie, Bohm and Hiley envisioned. In this view the electron’s

core can ride the E field to a specific location on the film plate. In this picture, fields behave as

fields and particles as particles. The free electron (left) has an inner particle core plus an outer

field.

The electron’s core simply follows its local electric field connection within its immediate

surroundings much as all free electrons do. The result is the electron’s core following a single

pathline to the film plate. The film then records the electron’s core arrival by creating a tiny

chemical reaction on the film plate. The electron’s dressing goes through both slits, but the

electron’s core only goes through one slit. Our view is that the electron’s core does not “spread

out,” because its core never did this; the electron’s core is considered immutable. What spread

out, was the external electric field, for although the electron is tiny, its field in a neutral

environment spreads out to wherever the conductivity and other charges are miniscule.

SUMMARY AND CONCLUSIONS

We have noted that the QFT electron model allows a rough order of magnitude estimate of

Planck’s uncertainty principle yielding a rough estimate of this: Δx Δpx ~ ћ, with the first

comparable to the electron radius, and the second to the electron mass times the speed of light

speed: properties chose to be more limiting than illumination, In this paper we consider how

the Quantum Field Theory (QFT) electron is able to provide the interference pattern within

Young’s double slit experiment, while obeying the locality conservation (local reality). The

process is difficult to understand theoretically compared with light interference. Light, being a

field can engage in large-scale spatial interference patterns. Electrons, being miniscule

particles, may not be able to undergo the same scale interference patterns. Plus, the quantum

“moniker” wave-particle duality, is not really proved. It may be used solely to justify behaviors

without any clear reason, but simply to justify the workings of the experiment. Additionally, our

understanding of this analysis and then these “halves” would need to interfere with itself to

create the bands/fringes. It was clear that a real field, like the electromagnetic field, could do

this, but this seemingly created an awkward problem for a miniscule particle.

In the past, electrons were considered point particles: a defect in the electric field. With the

advent of QFT, “free electron structure” is now taken to consist of a bare core, surrounded by

virtual particles, typically one or more virtual photons. that help the electron escape its atomic

bonds. Hence we examined the behavior of this QFT electron in Young’s experiment to ascertain

how it would behave within confines of the experiment. Through this analysis, the following

events occur as the electron moves through the experiment. Although the electron itself is tiny,

its field in a vacuum, would expand to the size of the neutral atmosphere, it likely would be

embedded within. Of course, the field would be miniscule, but we are really interested in the

field lines, as this electric field is the main driving force on the electron. The electron’s external

electric field, diminishing as the inverse square formula, in the first chamber is close to a radial

monopole electric E field except near experimental plates. The E field spreads outward through

both slits into the second interior chamber, creating regions of greater than or less than average

E field strengths, depending upon the amount of constructive and destructive electric field

interference associated with the phase differences based on distance travelled. As a

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consequence, the electron can create interference bands/fringes that can lead it to the film plate

that would create a small dot on where-ever the plate it landed on.

Additionally, we would expect the electron’s core to pass somewhat delayed from its E-field, as

the core has rest mass, but the EM field would not be expected to. One may say the actual

location of the electron’s mark on the film plate is determined by a “hidden variable,” guiding

by some specific property of the electron, perhaps its spin vector, or other. This view would

then be similar to that of de Broglie, Bohm, and Hiley [4-6]. These authors may have been

prescient to deduce a mechanism that the modern Quantum Field Theory (QFT) viewpoint now

suggests!

Lastly, free electrons behaving “probabilistically” may offer an explanation to Quantum

Mechanical attributes. Additionally, interference bands may be attained with larger atomic or

molecular entities, well beyond the electrons discussed herein. QFT provides us with

opportunities, that in the future, we can gain clarity to understand the variety of quantum

paradoxes seen in atomic phenomena. They may not be as easy as this one to solve, although

this one really did need theoretical advances, that arose fairly recently compared with the

original quantum mechanics formulation.

Acknowledgements

The author appreciates valuable discussions with Sabatino Sofia and Hans Mayr. This paper is

in memory of Abner Shimony as the author owes Abner a great debt of thanks due to his

inspiration, particularly his joy in wondering about quantum puzzles.

References

[1] Young, T. (1802). The Bakerian Lecture: On the Theory of Light and Colours, Philosophical Transactions,

Royal Society of London. 92:12-48. https://royalsocietypublishing.org/doi/10.1098/rstl.1802.0004\

[2] https://physicsworld.com/a/the-double-slit-experiment/

[3] Schatten K. H. and V. Jacobs, (2019), Quantum Field Theory Model for the Einstein, Podolsky, and Rosen

Experiment, Canadian Journal of Phys., https://cdnsciencepub.com/doi/10.1139/cjp-2019-0537

[4] D. Bohm and B.J.Hiley, The Undivided Universe-Ontological Interpretation of Quantum Theory,

https://biblio.co.uk/book/undivided-universe-ontological-interpretation-quantum-theory/d/1410207159.

[5] D. Bohm, (1980), Wholeness and the Implicate Order, ISBN 0-7100-0971-2

[6] D. Bohm, (1951), Quantum Theory. Prentice Hall, Englewood Cliffs, NJ

https://bok.cc/book/2483617/2b5506.