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# A Suggested Experiment to Explore the Possibility that the Photon is Guided by a Semi-Classical Wave of its Own Ground State Photons

Shlomo Barak

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Shlomo Barak. A Suggested Experiment to Explore the Possibility that the Photon is Guided by a Semi-Classical Wave of its Own Ground State Photons. 2024. hal-04679178

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# A Suggested Experiment to Explore the Possibility that the Photon is Guided by a Semi-Classical Wave of its Own Ground State Photons

Shlomo Barak

Taga Innovations 16 Beit Hillel St. Tel Aviv 6701716 Israel 28 Feb 2024

Corresponding author: shlomo@tagapro.com

## Abstract

In the current paradigm we have to attribute a dualistic nature to particles - they are supposed to be both particles and waves. In this paper we suggest an experiment that if successful, can dispel the need for this attribution. This experiment can show that particles are “guided” by the semi-classical wave of their own ground state photons **-photoms** as we call them. This wave, pervades space loaded with slits, polarizers and other elements and goes through Feynman’s all possible paths **before and after** it induces the emission of a photon that follows it - emission considered to be spontaneous. Hence there is no need to attribute non-locality to our Pilot (guiding) Wave theory, in order to explain quantum phenomena.

In this paper we restrict ourselves to the case of the dualistic photon. We show theoretically that the ground states photons - the **photoms**, condense when they are in phase and disperse when in anti-phase. This feature explains the double slit experiment, both for an ensemble of photons (classical EM wave) and single photons. It dispels the need to attribute a dualistic nature to single photons that arrive at the screen one at a time, and motivates our suggested experiment.

Key Words: Photons, Electromagnetism, Geometrodynamics, Spacetime
# 1 Introduction

The reading of papers [1] and [2] is a must, otherwise the following statements will be considered an absurdity.

We contend that the photon is a confined oscillating dipole with its field. This dipole is an oscillation of the bivalent elementary charges, which in the pair-production process are converted into the stable bivalent elementary charges of the electron and positron (as it is for other particles). **The photon in our theory holds potentially all the basic features that appear in all the other elementary particles.**

We further contend that EM waves are ensembles of closely packed photons that oscillate in phase and hence are classical waves. Similarly, ensembles of closely packed ground-state photons - **photoms** as we call them -, oscillating in phase are also classical waves. As we show, **photons and photoms condense when they are in phase and disperse when in anti-phase.**

These features dispel, as we explain, the need to attribute a dualistic nature to photons.

In modern literature [3] [4] [5] the photon is considered a wavepacket, but its shape, structure and size are not discussed. We, in contrast, present models of both the Photon and Photom.

We show that:

**The Photomic semi-classical wave pervades space loaded with slits, polarizers and other elements and goes through Feynman's all possible paths before and after it induces the emission of a photon. Hence there is no need in non-locality to explain quantum phenomena.**

Particles have well defined conjugate parameters but since they are guided by a wave these parameters, when measured, are subject to the uncertainty principle.
Note that our guiding wave is neither Einstein's "Empty Wave" nor de-Broglie Bohm "Pilot Wave". It is the known ground state vibrations of space or the electromagnetic field if you want.

# 1 Our Model of the Photon

Paper [1] shows that contracted space is positive charge and dilated space is negative charge. It also shows that the electric field **E** is proportional to **u**, the Elastic Displacement Vector of the elastic space lattice. **E** is defined as **E** = -H**u**, and points in the opposite direction to **u**.

Fig. (1) shows an oscillating cylinder-like photon passing in front of us to the right, with a velocity **c** and cycle time **T**. At the moment t = 0, Fig. (1a), we see a cylinder of space with no strain and stress; each square represents a group of space cells (the following process is related to each and every space cell). At t = 1/4·T, Fig. (1b), the space in the cylinder becomes dilated below the line of propagation (the middle) and contracted above it. The displacement vector, in the figure, points upwards all the way. The electrical field vector is in the opposite direction.

At t = 1/2·T, Fig. (1c), we are facing the same situation as in Fig. (1a). At t = 3/4·T, Fig. (1d), the displacement vector reverses its direction, and the electrical field points up. At t = T, Fig. (1e), the cycle is completed.

<figure><img src="image_2.png" /><figcaption>Fig. (1) The Photon's Oscillating Space Lattice</figcaption></figure>
At $t = 1/4 \cdot T$, Fig. (1b), space cells below the line of propagation (the middle) are dilated and those above it are contracted, and the electric field points downwards. At $t = 3/4 \cdot T$, Fig. (1d), the cells below are contracted and those above are dilated, and the electric field points upwards. But contracted space and dilated space are the bivalent electric charges [1]. Thus, the GDM space vibrational photon, as described, is an oscillating electric dipole with its electric field. This dipole and its field, as we show, are confined in a finite volume of space and the oscillating charges are the elementary electric charges.

## 2 The Spatial Size $r_e$ of the Photon Energy

The fine structure constant $\alpha$, where $Q$ is the **elementary charge**, is:

$$ \alpha = Q^2 / \hbar c \qquad (1) $$

From (1) we get: $\hbar c = Q^2 / \alpha \rightarrow 2\pi\hbar c/\lambda = 2\pi Q^2 / \alpha\lambda \rightarrow \hbar\omega = 2\pi Q^2 / \lambda\alpha \rightarrow$

$$ \hbar\omega = 2Q^2 / 2r_e \qquad (2) $$

where the photon energy is $\hbar\omega$ and $r_e$ is defined as:

$$ r_e = \alpha / 2\pi \cdot \lambda \qquad (3) $$

As if the energy of the photon is “concentrated” in two “spheres” of the bivalent elementary charge $Q$ with a radius $r_e$.

The factor 2 in the numerator of equation (2) accounts for the energy of contraction (one “sphere”) and that of dilation (other “sphere”). We relate to $r_e$ as the “radius” of the “cylinder”, which contains the two “spheres”.

## 3 The Oscillation of the Center of Energy of the Photon

For a spring with a constant $K$ and mass $M$:
$$y = y_0 \sin \omega t \quad v = \omega y_0 \cos \omega t \quad a = - \omega^2 y_0 \sin \omega t$$

where the axis y is perpendicular to the line of propagation.

$$U_k = 1/2 M v^2 = 1/2 M \omega^2 y_0^2 \cos^2 \omega t$$

$$U_p = 1/2 K y_0^2 = 1/2 K y_0^2 \sin^2 \omega t$$

$$U = U_k + U_p = \text{constant}$$

$$U = U_k(\max) = U_p(\max) = M \omega^2 y_0^2 = K y_0^2 \quad \omega = \sqrt{K/M} \qquad (4)$$

Since U is a constant, we are allowed to replace M, see [3], in the above equations (4), by:

$$M = U/c^2 \text{ which gives:}$$

$$U = M \omega^2 y_0^2 = U/c^2 \omega^2 y_0^2$$

Hence $y_0 \omega = c$, but $c = \lambda/(2\pi\omega)$ and the maximum amplitude of the center of energy is:

$$y_0 = \lambda/2\pi \qquad (5)$$

We denote $y_0$ as $R_e$ and relate to it as half the “cylinder height”. Note that (3) and (5) give:

$$r_e/R_e = \alpha \qquad (6)$$

This is the **same ratio**, as it is for the radii of the electron [3] (their sizes are different). From the geometry of both the electron and the photon it seems that this ratio determines the probability for the photon to interact with the electron. Hence $j = -\sqrt{\alpha} = -0.08542455$ is the probability amplitude of the QED Junction, Coupling, which is “... one of the greatest damn mysteries of physics: a magic number”; Feynman [6] in his own words.

Note that **the contraction or dilation move at the same velocity c, as the propagation does,** and hence the maximum possible half height of the disturbance is $H = c \cdot 1/4T = 1/4 \lambda$, whereas as (5) shows: $R_e = 1/2\pi\lambda$.
## 4 Photon Energy and the Planck Constant $ħ$

Using (4) and (5) we get $U = K \lambda^2 / 2\pi^2$ where K is an attribute of space similar to the K of a spring. If the “Space Spring Constant K” is a function of $\omega$ only we guess that it can be:

$$K = M\omega^2 = (U/c^2)\omega^2 = \hbar\omega^3 / c^2$$

where $ħ$, not yet identified, is a constant of proportionality.

Necessarily $U = ħ\omega$ where $ħ$ becomes the known quantum constant.

Thus, a classical functionality of $K(\omega) \propto \omega^3$ leads to the basic quantum mechanical result.

## 5 The Photon's Volume

Taking the “cylinder height” as $2R_e$, gives for the maximum of the oscillatory volume:

$$V_{\text{Photon}} = \pi r_e^2 2R_e = \alpha^2 / 8\pi^2 \cdot \lambda^3 = 6.75 \cdot 10^{-7} \cdot \lambda^3 \text{cm}^3 \quad (7)$$

The shorter is $λ$, the more compact is the photon.

For $λ = 500\text{nm}$ we get: $V_{\text{Photon}} = 6.75 \cdot 10^{-7} \cdot \lambda^3 \sim 8 \cdot 10^{-20} \text{cm}^3$.

## 6 The Photon Spin

The photon spin L, for a circular polarized photon, is its linear momentum $P = U/c$ times its radius of rotation $R_e = λ/2π$, see (5), $L = PR_e = U/c \cdot λ/2π$ but $U = ħ\omega$. Hence the known result:

$$L = ħ \quad (8)$$

## 7 Photons - the Ground State Photons

QED, [5], attributes to a photon in its ground state one half of the energy, half of the momentum, and half of the spin. To distinguish a photon from a ground state photon, we name it a **Photom** (a photon at the bottom). In the GDM, however, there are two types of photoms.
**The Positive Photom - EVE:** This photom, as Fig. (2) shows, is an oscillating contraction of space (positive charge), close to the line of propagation. This oscillation is in a plane or in a rotating plane, around the line of propagation.

**The Negative Photom - ADAM:** This photom, as Fig. (3) shows, is an oscillating dilation of space (negative charge) close to the line of propagation. This oscillation is in a plane or in a rotating plane, around the line of propagation.

These photoms are the split of the photon in Fig. (1). The GDM considers them as the pair of an electron and positron of the Dirac Sea, and vacuum polarization is due to them. This way we dispel the need for a separate ground state (vacuum state) for the electromagnetic field and that for the electron and positron field (Dirac Sea).

Fig. (2) shows our cylinder-like photom passing in front of us to the right, with a velocity $c$. At the moment $t = 0$, Fig. (2a), we see a cylinder of space with no strain and stress; each square represents a group of space cells (this process is related to each and every space cell). At $t = 1/4 \cdot T$, Fig. (2b), the space in the cylinder becomes contracted above, and close to, the line of propagation (the middle). The electrical field vector points opposite to the displacement vector, shown in the figure. At $t = 1/2 \cdot T$, Fig. (2c), we face the same situation as in Fig. (2a). At $t = 3/4 \cdot T$, Fig. (2d), the displacement reverses its direction and the electrical field points down. At $t = T$, Fig. (2e), the cycle is completed.

Note that we do not know the exact shape of the photon or the photom. All we know, at this stage, is their geometric and dynamic features. This is the reason why we use terms like cylinder-like.
<figure><img src="image_3.png" /><figcaption>Fig. (2) The Positive Photom - EVE</figcaption></figure>

Figure (3) shows our cylinder-like photom passing in front of us to the right, with a velocity c.
At the moment t = 0, Fig. (3a), we see a cylinder of space with no strain and stress; each square
represents a group of space cells (this process is related to each and every space cell). At
t = 1/4·T, Fig. (3b), the space in the cylinder becomes dilated above, and close to, the line of
propagation (the middle). The electrical field vector points opposite to the displacement vector,
shown in the figure. At t = 1/2·T, Fig. (3c), we face the same situation as in, Fig. (3a). At
t = 3/4·T, Fig. (3d), the displacement reverses its direction and the electrical field points up. At
t = T, Fig. (3e), the cycle is completed.
<figure><img src="image_4.png" /><figcaption>Fig. (3) The Negative Photom - ADAM</figcaption></figure>

## 8 Spatial Density of Photons

The spatial density of an ensemble of photons of a given $\lambda$ and a bandwidth $d\lambda$, see [6], is:

$n(v) = 8\pi v^2/c^3 \cdot dv$ but $v=c/\lambda$ and $dv=c/\lambda^2 \cdot d\lambda$ hence:

$$n(\lambda)=8\pi/\lambda^4 \cdot d\lambda \qquad (9)$$

For photons of $\lambda = 500$nm and a bandwidth $d\lambda = 0.5$nm the spatial density is:

$n(\lambda) \sim 2 \cdot 10^{11}$ photons per cubic centimeter.

Note that a one joule laser pulse of $\lambda = 500$nm contains $\sim 2.5 \cdot 10^{18}$ photons.

## 9 Light Velocity and Red/Blue Shift in a Gravitational Field

General Relativity shows that light velocity is slower close to a star than at a distance from it [7] [8]. As a result, a falling photon in a gravitational field gains linear momentum ($P = U/c$).

In order to retain its angular momentum ($L = P \cdot R_e$), it has to reduce its $R_e = \lambda/2\pi$, see [2], hence the blue shift. And in climbing the gravitational field, it will be red shifted.
# 10 Condensation and Dispersion

Fig. (4), shows a symbolic space lattice, which is like a 3D fisherman's net. Imagine that each vertical plane, in Fig. (4), going into the page, is a plane in which a photon or a photom are moving. If two adjacent photons or photoms of the same frequency oscillate in anti-phase side by side they stretch the lattice horizontally and move apart to ease the tension. The result is dispersion - a reduced spatial density of the photons or photoms. If, however, they oscillate in phase, they move together to ease the tension and the result is condensation - higher density. A similar situation occurs if they move one below or above the other

<figure><img src="image_5.png" /><figcaption>Fig. (4) Dispersion and Condensation</figcaption></figure>

# 11 No Dualistic Nature

In this section we dispel the need to attribute a dualistic nature to photons.

## 11.1 Interference with Classical Waves – Ensembles of Photons

Photons or photoms, of the same wavelength, when they are in phase and closely packed, move as a classical wave. Let a wave front, of such a classical wave, hit the double slit; if the photons or photoms, which are coming from the two slits and hit the screen, are in phase (on the screen) they create maxima zones on the screen, and minima if out of phase. In other words, intensity
is reduced in zones of destructive interference whereas in zones of constructive interference
intensity is enhanced. Photons and photoms entering these zones, however, are neither
annihilated nor created and the total energy is conserved. No annihilation or creation takes
place, only a spatial displacement of the particles that result in a reduction in their density
(intensity) in one zone and an increase in their density (intensity) in the other.

**11.2 Stimulated and spontaneous Emission**

Fig. (5) shows on the left an atom on a high energy level (upper line) above the lower energy level (bottom line-ground state). If a photon, with the same energy as that of the difference in the energy levels of the atom, arrives it can induce the emission of an identical photon by the atom, and its fall to the ground state. This process is termed **Stimulated Emission**.

<figure><img src="image_6.png" /><figcaption>Fig. (5) Stimulated and Spontaneous Emission</figcaption></figure>

However, the atom can also emit a photon without an inducing photon from outside. This kind
of emission is termed **Spontaneous Emission**. Some physicists, myself included, are convinced
that in this case it is a photom (ground state photon) that induces the emission. Let me remind
you that a photom is an ADAM or EVE. Below is evidence in support of my Spontaneous
Emission
idea.

Fig. (6) shows a beam of excited atoms running through a narrow tube. The rate of emission of photons from these atoms is reduced drastically compared to their rate outside the tube – more than ten times. The explanation is simple: In this tube, modes of vibrations, namely photoms, perpendicular to the tube axis and with a wavelength twice the inner diameter of the tube, cannot exist. Hence the number of photoms is drastically reduced and so is the spontaneous emission.
<figure><img src="image_7.png" /><figcaption>Fig. (6) Damping Spontaneous Emission</figcaption></figure>

In another experiment a mirror is placed close and parallel to a beam of excited atoms. This time the emission rate is doubled, since the mirror reflects incoming photons back towards the beam, thus doubling their number per unit volume.

Note that **the Photomic semi-classical wave pervades space loaded with slits, polarizers and other elements and goes through Feynman's all possible paths before it induces the emission of a photon. Hence there is no need in non-locality to explain quantum phenomena.**

Note also that **particles have well defined conjugate parameters but since they are guided by a wave these parameters, when measured, are subject to the uncertainty principle.**

## 11.3 Interference with Individual Photons

There is a body of both experimental and theoretical work that shows how the vacuum state of the electromagnetic field (photons) induces “spontaneous” emission [6]. Thus, the basic state is that of a single photon plus a single photom. When one photom, out of the many that construct a wave front of photoms. with a frequency that matches a transition in an excited atom (in the source), hits the excited atom it has a probability to induce the emission of an in-phase photon. The probability of the photon to hit a certain spot on the screen is thus the classical probability of the inducing photom to arrive at this same spot. Hence, accumulative effect of the, one at a time, photons is the interference pattern.

This dispels the need to attribute a dualistic nature to photons and solves the issue of the collapse of the “wavefunction” (although there is no such thing for a photon). Note that the width and
the height of the slits, as well as the distance between them, comply with our understanding of
the photon and photom, and the interference experiment.

In the year 2011 it was shown [9] in a “Weak-Experiment” [10] that a single photon, in the
Double Slit experiment, goes all the way from the source to the screen through only one slit.
The photon follows a trajectory known as the D. Bohm trajectory [11].

Our “mechanism” by which the photon is “guided” is also relevant to other elementary particles,
atoms, molecules, and even microscopic bodies.

12 On EM Waves

Waves we encounter in nature are, most of the time, spherical waves rather than plane waves.

However, far from a radiator, a spherical wave appears to be approximately a plane wave. Far from the radiator the electrical field of the wave **E** decreases as 1/r and hence its intensity I, which is proportional to **E**² decreases as 1/r². Thus, the classical approach complies with the quantum approach. In this case, the intensity at a far distance r depends on the number of photons that are crossing a unit area and hence the dependence on 1/r².

13 The Suggested Experiment

The Setup

Figure (7) shows a typical two-slit interference experiment with He – Ne Laser light $\lambda = 633$ nm that enters the system through the first slit on the first screen. In the second screen the two slits are 0.200 mm apart, the slit width is 0.04 mm and the third screen is 1.00 m from the slits. The third bright fringe, on the third screen, is 9.49 mm from the central fringe. It also shows to the right a Device. This Device is made of a miniature discharge glass box filled with a gas mixture
of He Ne atoms. It can also be a commercial discharge lamp. Both should be enclosed in a shielding metallic box.

In front of the box is a window (blue), less than one mm in diameter, and above it is attached a

<figure><img src="image_8.png" /><figcaption>Fig. (7) The double slit interference with our device - right</figcaption></figure>

detector and its field of view should be limited to observe the double slit This device is mounted on a carriage that can move up and down, with a micrometric mechanism, facing the plan of the third screen.

Fig. (8) shows He and Ne atoms energy levels under electrical discharge

* When an electric discharge is passed through, He-Ne gas, the electrons present in the discharge tube strike with the Helium and Neon atoms.

* Because of these collisions, Helium and Neon atoms are excited and move to the metastable states as shown in the Fig. (2) below.

* Some of the excited Helium atoms collide with unexcited Neon atoms and transfer their energy, thus, making them excited. In this way, Helium atoms induce a population inversion in Neon atoms.
* When an exited Neon atom falls from the metastable state, a photon is emitted. This emission is enabled by the presence of ground state photons – photoms – or photons with the same wavelength.

<figure><img src="image_9.png" /><figcaption>Fig. (8) He and Ne atoms energy levels under electrical discharge</figcaption></figure>

# The First Experiment

## Part 1

Place a He - Ne Laser in front of the first screen and watch the interference pattern on the third screen. Record the places m, as shown in Fig. (7) from -3 to +3.

## Part 2

Remove the laser and the third screen. Replace this screen with the Device, facing the slits.

Move slowly the device from below m= -3 to above m=+3. Record the intensity detected by the Detector. This signal is supposed to follow the intensity of the part 1 interference pattern.

# The Second Experiment

Interference effects produced by the superposition of the light beams from two independent single-mode lasers have been investigated experimentally. It is found that interference takes
place even under conditions in which the light intensities are so low, with high probability,
one photon is absorbed before the next one is emitted by one or the other laser. Since the
average number of registered photons per trial was only about 10, photon correlation
techniques were required to demonstrate the interference. The interpretation of the
experiment, and the question whether it demonstrates interference between two photons, are
discussed.

The demonstration, a few years ago, that two light beams derived from two independent lasers
can give rise to observable interference fringes led to a certain amount of debate. The discussion
centered in part on the appropriate description of the state of a laser field, and on the question
whether the experiment disproved a famous statement of Dirac (1958) that ...each photon
interferes only with itself. Interference between different photons never occurs.

In this experiment, as shown in Fig. (9) we get an interference pattern of laser beams
delivered from two identical lasers. When one of the lasers is off, the pattern disappears (the
result of all relevant theories). However, if we reduce the intensity of the lasers to the extent
that statistically the time of flight to the screen is shorter than the time between sequential
deliveries of photons, we still get an interference pattern.

Suppose we adopt Dirac's argument that a photon interferes with itself, how do we get an
interference pattern in the Pfleeger and Mandel experiment, without using two slits, or some
similar device.

The guiding interference pattern, as I see it, is built by the “interference” of identical bunched
photons (waves) coming through the two lasers and the photons simply “ride” on them.
<figure><img src="image_10.png" /><figcaption>Fig. (9) Pfleeger and Mandel's Experiment</figcaption></figure>

**Part 1**

Use two He-Ne lasers and watch the interference pattern on the screen. Record the places of the maxima in the pattern.

**Part 2**

Reduce the intensity of the lasers to almost zero. Replace the screen with the Device. Move the Device, watching the lasers, from left to right. Record the intensity detected by the Detector. Its signal is supposed to follow the intensity of the Part 1 interference pattern.

**14 Summary**

Our suggested experiment can show that particles are “guided” by the semi-classical wave of their own ground state photons _-photoms_ as we call them. This wave is their **Pilot (guiding) Wave**. Thus, we dispel the need to attribute **duality** to particles.

The Photomic semi-classical wave pervades space loaded with slits, polarizers and other elements and goes through Feynman's all possible paths before and after it induces the emission of a photon. Hence there is no need in non-locality to explain quantum phenomena.
Particles have well defined conjugate parameters but since they are guided by a wave these
parameters, when measured, are subject to the uncertainty principle.

If indeed this is the case, it turns Quantum Mechanics into a **complete** realistic theory without illogical interpretations.

## Acknowledgements

We would like to thank Mr. Roger M. Kaye for his linguistic contribution and technical assistance.

## References

[1] S. Barak: On the Essence of Electric Charge, Part 1: Charge as Deformed Space
hal-01401332(Nov2016) https://hal.archives-ouvertes.fr/hal-01401332

Applied Physics Research; Vol. 11, No. 4; 2019

ISSN 1916-9639 E-ISSN 1916-9647

Published by Canadian Center of Science and Education

### Electric Charge and Its Field as Deformed Space

Shlomo Barak¹

Received: May 23, 2019 Accepted: June 14, 2019 Online Published: July 15, 2019

doi:10.5539/apr.v11n4p29

URL: http://dx.doi.org/10.5539/apr.v11n4p29

[2] S. Barak. A GeometroDynamic Model (GDM) of Reality A Realization of Einstein's Vision. (2018). https://hal.archives-ouvertes.fr/hal-hal-01435685v4

[3] R. Loudon: The Quantum Theory of Light, Oxford University Press (2000)

[4] G. Grynberg, A. Aspect and C. Fabre: Quantum Optics, Cambridge (2010)

[5] Milonni, The Quantum Vacuum (1994) Academic Press

[6] R. Feynman: QED, Princeton press (1985)
[7] S. Barak: On the Essence of Gravitation and Inertia, Part 1: Inertia and Free Fall of an Elementary Particle, hal-01404143 (2016)
https://hal.archivesouvertes.fr/hal01404143v5

[8] Ta-Pei Cheng: Relativity, Gravitation and Cosmology Oxford (2005)

[9] Steinberg et al: Science, 332(6034), 1179-1173, (2011)

[10] Y. Aharonov, et al: PRL 60, pp1351, (1988)

[11] Philippidis, Dewdney and Hiley: Il Nuovo Cimento, Vol. 52B, N1, P. 15 (1979)