ANNA LAMARCHE

Edited by Imogen den Otter-Moore

INTRODUCTION

The quantum slit experiment is one of the most important experiments to come out of quantum physics to date. Realized in the early 1800s by Thomas Young, it helped to prove the wave-particle duality of subatomic particles such as photons and electrons. His results could later be applied to many later concepts, such as Shrodinger’s wavefunction theory which still to this day accurately describes the behaviors of subatomic particles. One of these behaviors is quantum tunneling, which is the ability of a subatomic particle to pass through or “tunnel” through an energetic barrier, a phenomenon which is not observable in classical mechanics. According to Schrodinger’s equation (Schrodinger, 1926), every subatomic particle has a probability wave that tells us the likelihood of finding that specific particle in a particular location . This means that some particles have a chance to tunnel through barriers, should there be a non-zero chance that the particle’s probability wave will continue on the other side of the barrier. In this experiment, I propose including potential barriers in the quantum double slit experiment to observe the impact these will have on its outcome. A recent series of experiments using vibrating silicone oil baths and silicone droplets have re-created phenomena observed at the quantum level (Evans, 2020, Veritasium, 2016, Couder & Fort, 2006). However in 2015, an experiment aiming to combine the silicone oil analogy with the double slit experiment proved futile (Wolchover, 2018). Using the Pilot Wave interpretation of the double slit experiment, with a single silicone droplet going through one slit while its wave went through both, caused the pattern on the plain surface to come out as two lines instead of the expected interference pattern that would indicate superposition, meaning that the silicon oil analogy was not entirely reflective of the behaviors of particles at the subatomic level. In this experiment, I will send two droplets at a time, one through each slit in an attempt to simulate superposition to see if the results differ from the original silicone oil double slit experiment, as well as add potential barriers to the slits to observe their effect on the experiment’s outcome. I will use a similar apparatus to simulate the quantum slit experiment, using plastic barriers placed at different depths under the surface of the oil to simulate potential barriers. The results of this experiment could give more insight on the behaviors of subatomic particles interacting with potential barriers and each other, and if a modification on the classical level could more accurately represent what happens on the quantum level. Should a version of this experiment be conducted later on the quantum level, its results could also provide insight on how accurately a modified silicone walker droplet analogy represents particle behavior at a quantum level.

QUESTION

This study aims to address the following research question.

How will a) adding barriers that the particles have a non-zero chance of tunneling through between the slits in the double slit experiment affect:

a.a) the pattern on the plate behind the slitted plate,
a.b) the concentration of particles in each area of the pattern and
a.c) the behaviors of the particles both before and at the second plate

and b) how closely will the results be comparable to what happens at a quantum level, due to the fact that the representation of particles itself had to be changed to make the results more accurate?

BACKGROUND INFORMATION

In the original quantum slit experiment, the results were as follows: after sending the particles towards the single-slitted surface, a single line would appear on the surface behind it, which is expected of both particles and waves. When the experiment was repeated with a double-slitted surface instead of a single-slitted one, a pattern would emerge that would be expected of interference between waves and not particles. This was due to the ability of the electrons to enter a superposition of states, where a single electron simultaneously traveled through one slit and the other at the same time. Thanks to this superposition and wave-like behavior, the electrons were theorized to have interfered with each other, creating the interference pattern that was observed. When an observer was placed at the entrance of the slits to determine which slit the electrons were going through, the interference pattern did not appear, meaning that the observation had “collapsed” the electron’s wavefunction and reduced it to a single point, which stopped it from being able to interfere with itself and create this interference pattern (figure 1).

HYPOTHESIS

It is hypothesized that the results of the experiment conducted with silicone oil droplets (or “walker” droplets) should look similar to that of the original one, if the right method is applied and the right margin for difference is allowed. In the 2015 experiment, the scientists used bouncing silicone droplets to test the pilot wave theory, sending them through the slits one at a time and observing where they would end up. The results of this experiment proved that the walker droplet analogy was not a perfect one, because it did not accurately represent what would have happened at the quantum level. But for this experiment, I propose sending one droplet through each slit at the same time, so two droplets traveling at the same speed and in the same direction through the two slits. Once they have passed the slits, the waves of the two droplets should start interacting with each other, possibly forming an interference pattern like in figure 2.

If this estimation is accurate, the two silicone oil droplets would exhibit behavior similar to the interference between the two possible paths a single particle could take when crossing the slits. This could be tested during the first part of the experimentation, which would be conducted without barriers in order to set a baseline.

Continuing on to the second phase of the experiment, the slitted sheet will be replaced with another slitted sheet, one with slits that are a lot shallower to mimic a potential barrier. I hypothesize that certain silicone droplets will get past these barriers while others will not, resulting in it taking longer for a pattern to emerge than it would for the original experiment. In theory, the addition of potential barriers to a quantum double-slit would collapse the wavefunction if the quantum system had too much interference. I hypothesize that since Quantum Tunneling is also an effect that takes place at the quantum level, the wavefunction should not be collapsed and the interference pattern should still be visible, though it might take longer to appear. Droplets must touch the back surface to be counted. If a droplet loses too much momentum or rejoins the oil bath before reaching the surface, it will not be counted and that run will be restarted.

MATERIALS

I have divided the materials necessary for this experiment in a few subsections. First of all, we have the baseline experimental apparatus setup section, which will be used through all phases of the experiment. This will consist of a shallow container, a speaker set to emit a sound at a specific frequency, silicone oil and a dropper tool. The next materials will vary depending on the phase of experimentation, but include thin plastic sheets cut so they protrude at different levels under the surface of the oil bath; some sheets will have two slits whereas some will only have one, and the height of the slits in the sheets will stand in for the thickness of the barriers that would be used in a quantum version of this experiment. The deeper the slit is underwater, the thinner the barrier would be in the quantum experiment. The length of the slits will be two centimeters, and the depth of the slits will only be a few millimeters. The experiment would also take place in an area with low air circulation to limit the environment’s effects on the droplet’s movements. I will also be wearing a mask so my breathing does not impact the droplet’s movements. A camera will be placed above the setup so I can record when and where the walker droplets will hit the plain surface.

PROPOSED METHODOLOGY

Part 1
Part 1 of this experiment will consist of running a simulation of the original quantum slit experiment to be able to compare the results of other phases of the experiment to this one.

I will start setting up the experiment by filling the shallow basin with silicone oil and installing the speaker so it gets the oil vibrating at 80 H (Gilet). I will then position the camera over the basin to be able to record the entire experiment. Following this, I will install the plastic sheets vertically in the basin. For section A of this part, I will be using a completely slitted sheet with a single slit to simulate the original quantum slit experiment. The back surface will remain the same for all the experiments. I will send 25 silicone droplets through the slit and record the results with the camera. I will wait for the disturbances on the surface of the oil to settle before sending new silicone droplets through to avoid any interference. Once section A is complete , I will begin section B. I will replace the slitted sheet with a double slitted sheet. Next, I will send 25 pairs of silicone droplets through the slits (both at the same time and at as equal a speed as possible) for a total of 50 droplets.

Part 2
Part 2 of the experiment will be the quantum slit experiment with potential barriers. Section A of part 2 will be very similar to section A of part 1: the back surface will remain in place, but the completely slitted section will be replaced by a partially slitted section, with a depth just a few millimeters below the surface of the oil. This will act as a potential barrier to incoming droplets: some will bounce off the barrier while some will make it across. Once again, 25 droplets will be sent towards the slit and their ending positions recorded. Section B of part 2 will consist of replacing the slitted sheet with a double slitted one. 25 pairs of silicone droplets will be sent through the slits and their positions recorded.*

*Due to the expected decrease in droplets getting across the potential barrier in part 2, I might modify the experiment to send across more droplets to get a clearer picture of the pattern that will show up on the back surface.

discussion

The original quantum experiment had a simple premise and clear cut results (as seen in Figure 1). The results from this experiment proved that subatomic particles such as electrons were both particles and waves, and that the act of observing which slit the particle would go through in the double slit part of the experiment would collapse the particle’s wave function and make the electron act as a particle, which could be observed through the two lines that appeared instead of the expected interference pattern.

Quantum tunneling occurs when a subatomic particle passes through a potential barrier due to the fact that the particle’s probability wave includes the possibility that the particle could be found on the other side of the barrier. In figure 3, we can see a particle represented by its probability wave. The probability wave of this particle is observed on the other side of the potential barrier, which is represented here by a rectangle.

There is no known way to calculate the exact location of the particles, in this case electrons, before they are observed, due to their electron-cloud nature. Even if there is a non-zero chance that the particle could tunnel through the barrier, there would be no way to know if it was going to until its location was measured. My experiment will not be able to perfectly replicate this effect, since the silicone droplet part of the droplet-wave system will act more as the particle part of the system. There are also a few ways to interpret the results filmed by the camera: I could base the final location of the “particles” (estimates of the point of wavefunction collapse) on the silicone droplet itself or on the spot where the wave first comes into contact with the back surface. Basing it on the silicone droplet might make more precise measurements, but would leave out the fact that there is a probability the “particle” could be found anywhere along the particle’s wave function. Another complication to this measurement problem is the fact that in the second part of the experiment, two droplets are used to simulate the superposition effect that would be created by a single particle. This poses another problem on top of the original droplet/wave problem: is one droplet representative of the “real” particle whereas the other is not, or are they both valid? In the case of part 2 of this experiment, it would be more logical to consider both droplets part of one whole and map the interference patterns of the waves and take the results from the probability of finding the “particle” in each spot along the back surface. For the purpose of my experiment, analyzing the data according to the wave and not the droplet would give more uniform results.

The results of part 1, based on the point on the back surface where the silicone droplet’s wave will first come into contact, are estimated to be close to the results observed in the original quantum slit experiment. The single silicone droplet moving through a single slit is comparable to a particle moving through a single slit, and this section of the experiment should have the same outcome (Veritasium, 2016, Evans, 2020). Section two of this part should also have a similar outcome to the original quantum slit experiment despite employing different means (not using a pilot wave, but trying to recreate an indeterministic interpretation: two particles moving through two slits to approximate one particle moving through two slits at once). The waves of the droplets should interact in constructive and destructive interference and create an interference pattern (Adams, 2013).

According to the probability wave function of a subatomic particle moving through a space containing a potential barrier (such as our silicone oil droplets moving through a basin towards the underwater barriers), there are multiple ways the particle could react once it comes in contact with the barrier (taken from the quantum tunneling of particles through potential barriers):

The particle could be entirely reflected by the barrier.
The particle could be reflected inside of the barrier.
The particle could make it beyond the barrier and reach the back wall beyond.

That being said, it is fair to estimate that there will be a very small chance of all the silicone droplets getting beyond the potential barrier in both sections of part 2 of the experiment. Since this experiment is happening at such a small scale and the results can be viewed as random, there are many sources of errors. Differences in speaker frequencies could impact the silicone droplets’ bouncing or cause them to rejoin with the oil bath’s surface at a different rate than in other experiments. Air currents in the environment around the oil basin could change the direction and speed of certain droplets compared to others and impact the results. Because the drops will be made with some kind of dropping tool, they will not all be the same size and will not all be released in the same direction and at the same velocity. The visual way in which the data will be interpreted and collected makes it less reliable than in the original quantum slit experiments, where the locations of the particles along the back surface were measured more quantitatively instead of by human perspective.

CONCLUSION

In conclusion, this experiment could give more insight into the way particles interact in experiments such as the double slit experiment when adding phenomena such as quantum tunneling. Should the experiment later be realized at a quantum level, it would also help explain whether, and if, how, classical analogies such as the silicone oil walker droplet analogy can partly explain what happens in our world at the quantum level. Combining the quantum slit experiment and quantum tunneling might just give the results we think it will, or it could give us questions we’ve never thought of before. The only thing left to do now is try.

works cited

Schrödinger, E. (1926). CHAPTER 6 The Schrodinger Equation. Retrieved March 13, 2022, from https://faculty.tarleton.edu/goderya/documents/Teaching/phy334/Phy334-ch6_1.pdf
Evans, P. (2020). What can bouncing oil droplets tell us about quantum mechanics? Retrieved March 13, 2022, from https://link.springer.com/article/10.1007/s13194-020-00301-0
Veritasium. (2016, November 2). Is This What Quantum Mechanics Looks Like? [Video]. Retrieved March 13, 2022. YouTube. https://youtu.be/WIyTZDHuarQ
Couder, Y. and Fort, E. (2006) Single-Particle Diffraction and Interference at a Macroscopic Scale. Retrieved March 13, 2022, from https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.97.154101
Wolchover, Natalie. (October 11, 2018). Famous Experiment Dooms Alternative to Quantum Weirdness. Retrieved March 13, 2022, from https://www.quantamagazine.org/famous-experiment-dooms-pilot-wave-alternative-to-qu antum-weirdness-20181011/
Gilet, T. (April 2016). Figure 1. Retrieved March 13, 2022, from https://www.researchgate.net/figure/top-A-drop-of-silicone-oil-bounces-periodically-at-th e-surface-of-a-small-pool_fig2_301240830
The Quantum Tunneling of Particles through Potential Barriers. Retrieved March 13, 2022, from https://opentextbc.ca/universityphysicsv3openstax/chapter/the-quantum-tunneling-of-part icles-through-potential-barriers/
(May 3 2002). Copenhagen Interpretation of Quantum Mechanics. Retrieved March 13, 2022, from https://plato.stanford.edu/entries/qm-copenhagen/
Adams, A. (12 February 2013). Level 3: The Wave Function. Retrieved March 13, 2022 from https://ocw.mit.edu/courses/physics/8-04-quantum-physics-i-spring-2013/lecture-notes/M IT8_04S13_Lec03.pdf