Quantum Fluctuations and Entanglement as Illustrated by Young’s Double Slit Experiment

Figure 1, In quantum physics, a quantum fluctuation is the temporary random change in the amount of energy in any point in space. This is a simulation of those fluctuations in a very tiny space. Source: Wikipedia


In my opinion, quantum fluctuations and entanglement are the least understood elements of quantum mechanics. By examining what is happening in the double slit experiment, we can see more clearly how they work. The equations describing the interactions don’t give one any feeling for what is happening. The surprising strength of quantum entanglement is one thing that becomes clear when looking at this experiment. Another puzzle that has not yet been explained in any reasonable way is the randomness of the location of the interactions. In this paper, I hope to show that the quantum fluctuations of the Higgs field, sometimes called the quantum foam, are responsible for this randomness.

The Higgs Field

According to our present understanding of the Universe, the Higgs field permeates all of space-time. This is a scalar field that particles interact with, giving them mass. We know that this field exists because of many things. One is the experimental verification of the Higgs boson, which is the particle causing the Higgs field. Another is the brief existence of what we call virtual particles in otherwise empty space. Some of the most common virtual particles are electron-positron pairs. That is because these are lower energy particles so that the random fluctuations of the Higgs field have enough energy to produce these particles more often. These particles can be detected indirectly by various measurements including the Casimir effect. (Hendrik Casimir). These experiments prove the existence of the Higgs field in empty space.

What are the characteristics of this field? First, being a field, it has the characteristics of a wave. These waves have all possible wavelengths and all possible directions in space-time. As waves propagate, they interfere with each other resulting in a very noisy Higgs field environment in free space.

Figure 1 shows a simulation of what these quantum fluctuations look like. In quantum physics, a quantum fluctuation is the temporary random change in the amount of energy in any point in space. These are tiny random fluctuations in the value of the Higgs field which materialize into elementary particles when the energy at any point that exceeds 1.022 Mega electron volts for an electron-positron pair. These fluctuations have more effects than just the appearance of electron hole pairs. One of those effects, results in random fluctuations in the location of particle to particle interactions that happen in the double slit experiment.

Figure 2, Double-slit experiment with photons Source: David Webber in Medium
Figure 3, Photons or particles of matter (like an electron) produce a wave pattern when two slits are used. In this figure, Light from a green laser is passed through two slits 0.4mm wide and 0.1mm apart. Source: Wikipedia

Young’s Double Slit Experiment

The double slit experiment, as illustrated in Figure 2, performed by Thomas Young in 1801, is one of the most important experiments ever performed in quantum mechanics. This was before quantum mechanics was even dreamed about. It demonstrated the wave nature of photons. That was not yet well understood at that time. The experiment belongs to a general class of “double path” experiments, in which a wave is split into two separate waves that later combine into a single wave. Changes in the path lengths of both waves result in a phase shift, creating an interference pattern. Another version is the Mach–Zehnder interferometer, which splits the beam with a mirror.

In the basic version of this experiment, a coherent light source, such as a laser beam, illuminates a plate pierced by two parallel slits, and the light passing through the slits is observed on a screen behind the plate. The wave nature of light causes the light waves passing through the two slits to interfere, as shown in Figure 3, This produces bright and dark bands on the screen — a result that would not be expected if light consisted of classical particles. However, the light is always found to be absorbed at the screen at discrete points, as individual particles (not waves); the interference pattern appears via the varying density of these particle hits on the screen. Furthermore, versions of the experiment that include detectors at the slits find that each detected photon passes through one slit (as would a classical particle), and not through both slits (as would a wave). However, such experiments demonstrate that particles do not form the interference pattern if one detects which slit they pass through. These results demonstrate the principle of wave–particle duality.

Then, in 1927, Davisson and Germer demonstrated that electrons show the same behavior, which was later extended to atoms and molecules and to everyone’s surprise, we found that they were also waves. We were sure that they were particles, but this experiment showed that particles also have wavelike characteristics.

Additionally, the detection of individual discrete impacts is observed to be inherently probabilistic, which is inexplicable using classical mechanics. But, these experiments have still never been fully explained (described) by quantum mechanics either. It is merely stated that the shape of the calculated wave function describes the probability with no convincing reason.

But it is made up of individual particle/screen interactions, and the wave shape is calculated by the Schrödinger equation which gives the probabilities of the interactions. This is puzzling because other types of waves like sound waves and water waves appear to be continuous. It does not look like they are made of probabilities. Something really different is happening in the double slit experiment.

How does the particle go through both slits at once?

The double-slit experiment (and its variations) has become a classic thought experiment, for its clarity in expressing the central puzzles of quantum mechanics. Because it demonstrates the fundamental limitation of the ability of the observer to predict experimental results, Richard Feynman called it “a phenomenon which is impossible […] to explain in any classical way, and which has in it the heart of quantum mechanics. In reality, it contains the only mystery [of quantum mechanics].”

The particle, whether an electron or a photon, is really a wave. It only acts like a particle when there is an interaction. Figure 4 shows how the interference creates the intensity bands.

Figure 4, Numerical simulation of the double-slit experiment with electrons. Figure on the left: evolution (from left to right) of the intensity of the electron beam at the exit of the slits (left) up to the detection screen located 10cm after the slits (right). The higher the intensity is important, the more the color is light blue — Figure in the center: impacts of the electrons observed on the screen — Figure on the right: intensity of the electrons in the far field approximation (on the screen). Numerical data from Claus Jönsson’s experiment (1961). Photons, atoms and molecules follow a similar evolution. Source: Wikipedia

This pattern is the same even if only one particle at a time is passed through the slits. This proves that the particle is a wave. But it does not explain the mystery of why it shows the pattern as a frequency of interaction vs location instead of being continuous. Looking at the situation before the electron or photon passes through the slits, it is obvious that the single particle goes through both slits at the same time. It was a wave before it encountered the slits. Then when the wave encountered the slits, it is diffracted just like any other wave. Also, miraculously, all of the energy of each electron or photon passes through to the other side of the barrier. Then, that diffraction results in two wave fronts at each slit interfering with each other to produce the pattern shown in Figure 4.

Why is the location of the particle interaction random?

Figure 1 shows a simulation of how the quantum foam is constantly fluctuating. Figure 5 shows how the noise of the quantum foam is combined in superposition with the coherent particle wave. The energy of the Higgs field is random at every location in space-time. Most of the time, the Higgs field has much less energy than that required to produce an electron-positron pair. But the energy that is there is enough to alter the location of an interaction when the wave is near an atom. We have not analyzed this mathematically yet, so there are questions to be resolved to verify this picture. The picture looks good qualitatively, but we don’t know if it is correct quantitatively. But, it is still a better explanation than the current QM explanation.

Figure 5: This shows the superposition of the coherent wave of the particle with the quantum foam. Simulated by Author

How is the energy suddenly concentrated in one spot at the detector?

All particles have a wave characteristic, but when they interact with other particles(waves), they interact at the location of the second particle. Just for illustration, let’s have the traveling particle be an electron, and the interacting particle is an atom that has an electron vacancy. Let’s put that atom in or on the screen that captures the electron. So, as the electron wave approaches the atom wave, they are both in super-position to the quantum foam noise. That is altering the wave shape of both the electron and the atom. As they are distorted by the noise, there are peaks of noise that will suddenly and randomly extend the matter waves toward some random direction and thus occasionally toward a specific atom. The atom is also shooting out noisy matter waves. When they collide, an interaction happens. The location of the interaction will be more likely at the high points of the Schrodinger calculation of the wave function, and less likely at the low or zero points of the wave function. This is why the Schrodinger wave is incorrectly called a probability wave, when it is actually a matter wave.

What brings the energy together?

The wave function of the particle is very widely distributed, so it takes something very powerful to bring the energy back together again. You can see from figure 4, the wave is extremely diffuse. A single particle extends throughout a region of several centimeters. How does it get localized again?

The most powerful forces in the universe are the result of symmetry. Entangled particles are known to have links that can extend to many kilometers, and a measurement of one entangled particle can affect the connected entangled particle instantaneously. In a properly set up experiment, two electrons become entangled to have opposite spins. Then they can be geographically separated. Because the entanglement is caused by the fact that spin is a conserved quantity, “Up” spin is balanced by “down” spin for a net zero spin. When one entangled particle is measured, the opposite entangled particle behaves as if it was measured too. The universe will move heaven and earth to keep the conserved quantities balanced. We don’t know of any deeper cause for these particles behavior than the fact that they are entangled. This sometimes called a non-causal interaction.

For the double slit experiment, the energy of the electron wave is captured, and even though the electron wave is very delocalized, the whole electron is captured. The electron in free space is a coherent wave, and thus entangled with itself. This causes the whole electron wave to be attracted to the atom. There is no energy barrier to overcome. All of the energy of the electron wave now becomes part of the atom’s wave function. This is called a measurement if we are looking at it. If we are not looking at it, it happens anyway. The interacting particles do not care if we are looking at them or not.

This shows the power of entanglement. For these quantum interactions, the localized energy does not need to exceed any threshold. The total energy of the entangled wave is used to make the interaction proceed even though the localized energy is very small. It is very important to the universe to make these interactions happen. No energy is allowed to be lost, and “No entanglement is allowed to be ignored.” I think that is an important principle in the laws of Physics.

We always knew the entanglement was important. It is used in the efforts to do quantum computing. The biggest problem for quantum computing today is how to keep an entangled state of a particle long enough to do a computation. That is because our environment is full of other particles that can interact with the desired entangled particle, and destroy that entanglement, which makes quantum computing not work. Of course, when this entanglement is interfered with, the interfering particle becomes entangled with the particle used for quantum computing, thus destroying its usefulness. Even though we know entanglement is important, very little is known about it. Most of the research is devoted to trying to solve the quantum computing problem. That is very understandable, but it does nothing to fully understand entanglement.

The questions about entanglement include “spooky action at a distance” (Einstein), is dis-entanglement really instantaneous, what is the medium that carries the entanglement, does it required a 5th dimension? These, and other questions need to be answered.

I am a retired industrial physicist interested in the fundamental physics of the universe.

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