By Dr. John Millam1
Part 1 of this study presented a brief overview of quantum mechanics, tracing its historical development and describing some of its more exotic features. (For a quick review, see Appendix: Overview of Quantum Mechanics.) We will now consider wave-particle duality, a subtle but powerful notion that lies at the very heart of quantum mechanics. The big questions are: what is wave-particle duality, and how do we know if it is real?
Waves Versus Particles
In classical antiquity, natural philosophers divided material objects into two mutually exclusive categories: waves and particles. This classification scheme for objects was analogous to biological classification, where at the highest-level living creatures are divided into two kingdoms: plants and animals.
To better understand the distinction between classical waves and classical particles, imagine visiting a lake on a beautiful summer day. There is no wind, so the water is as smooth as glass. Now imagine picking up a small rock and tossing it into the water. The splash causes a series of circular ripples that spread along the surface of the water (see Figure 1). The rock reflects classical particle-like behavior. The ripples, on the other hand, are classical waves.
Distinguishing Features of Classical Waves
This picture of a rock and ripples provides a simple intuitive contrast between particles and waves, but we need a more precise demarcation for scientific purposes. What properties can we use to distinguish classical waves from classical particles? Here are some defining properties of waves:
- Requires a Medium. Classical waves are simply energy propagating through a material medium. For example, sound waves are pressure waves in air. Sound waves cannot propagate in the vacuum of space because there is no matter to transmit the sound. Particles, in contrast, can travel through space because they do not require an external medium.
1 Ph.D. in Theoretical Chemistry from Rice University. Full permission is given to reproduce or distribute this document, or to rearrange/reformat it for other media, as long as credit is given, and no words are added or deleted from the text.
Figure 1: Man throwing rock into a lake.
Credit: John Millam (modified from internet).
2 - Delocalized. Waves can spread out over a region of space like ripples in water. Classical particles, in contrast, always have a well-defined position and velocity.
- Superposition. Waves permit superposition states where multiple waves can overlap, cross paths, and occupy the same space. This situation is noticeable in a noisy room where numerous conversations occur simultaneously, yet each is individually recognizable. In contrast, two particles cannot share the exact location simultaneously.
- Five Distinct Properties of Waves (see Figure 2):
1) Reflection is a change in the direction of a wave when it encounters an obstacle or a change of medium with the wave remaining in the medium from which it originated.
2) Refraction is a change in the wave’s direction as it passes from one medium to another.
3) Polarization is a property of transverse waves that specifies the orientation of the oscillations. Light is a transverse wave where photons oscillate perpendicular to the direction the wave is traveling.
4) Diffraction is a bending of waves around the corners of an obstacle or through a narrow aperture.
5) Interference is a phenomenon in which two waves combine by adding their displacements resulting in wave of greater, lower, or the same amplitude.
We can use these features to help distinguish between classical waves and classical particles.
a) b) c)
Reflection Refraction Polarization
d) e)
Diffraction Interference
Figure 2: Five key wave properties.
Credit: a) John Millam, b) Wikipedia commons, c) C. R. Nave, Georgia State University, d) John Millam, and e) MPC.
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Is Light a Wave or a Particle?
For most of history, philosophers and scientists have understood light to be a type of wave. Starting with Euclid in the 4th-3rd century BC, this view dominated until modern times. This conclusion was primarily driven by the development of optics, which relied heavily on the wave nature of light, particularly reflection and refraction. The main contrary view in classical antiquity came from Democritus (5th century BC), who viewed light as a particle. Of course, as a leader of the Greek atomists, he saw everything in terms of indestructible particles.
The first person to seriously challenge the wave view in modern times was Isaac Newton (seventeenth century AD), who championed a corpuscular (particle-like) theory of light. Despite his fame and prestige, most of his contemporaries (e.g., Robert Hooke, Christiaan Huygens, and Augustin-Jean Fresnel) continued to refine and advance the wave viewpoint. Decisive support for the wave perspective came from Thomas Young’s double-slit experiment in 1803. When light is shown on two narrow slits and subsequently strikes a flat screen, it reveals a series of fringes (an alternating pattern of light and dark lines). These fringes could only be explained as interference patterns—a definitive wave property. (The double-slit experiment and its implications will be described in much greater detail later.) Another critical development came from James Clerk Maxwell who published a set of four equations (1861-1862) uniting electricity and magnetism into a common framework called electromagnetism. A significant consequence of his work was it described light as an electromagnetic wave.
The seemingly irrefutable conclusion that light was a wave had an unresolved problem: scientists could not explain why we can see light from distant stars through the vacuum of space. As a classical wave, it should require a medium to propagate through, but outer space lacks anything adequate to serve in this capacity. To resolve this, scientists proposed the existence of luminiferous aether, a special material pervading space capable of transmitting light waves.
Albert A. Michelson and Edward W. Morley finally tested the aethereal theory in 1887 when they attempted to measure Earth’s motion relative to the proposed medium. The Michelson-Morley experiment used a technique called interferometry to make very sensitive measurements comparing Earth’s motion along two perpendicular directions. Despite all their efforts, they failed to detect any motion of the Earth with respect to the aether, ultimately leading scientists to reject its existence. Consequently, light could not be a wave in the classical sense because it lacked a propagating medium.
The early twentieth century ushered in two new challenges to the wave nature of light. In the first case, Albert Einstein explained the photoelectric effect (1905) by treating light as a particle. In these experiments, ultraviolet light was shown on a metal surface, causing electrons to be ejected. Einstein could explain the details of these experiments if the light came in discrete particle-like “quanta” (or photons) that transferred their energy at once. In the second challenge, Arthur H. Compton demonstrated in 1923 that when light was scattered off electrons, it lost energy as if it was a particle rather than a wave. More importantly, Compton scattering established light had momentum like a particle. (Momentum is the tendency of an object to remain in motion.) These results presented a profound challenge to the traditional wave description of light.
Wave-particle Duality
These discoveries created a problem. Light has all the distinctive behaviors of a wave, yet in at least two instances it behaves as a particle. How can light behave as a wave in some circumstances and as a particle in others? Louis de Broglie resolved this by embracing both the wave and particle properties of light and weaving them into a single framework. In 1924, he laid out his theory of wave-particle duality, a radical proposal where wave and particle categories are not incompatible but are two faces of the same coin. Light could behave like a wave when passing through a glass lens but act like a particle in the photoelectric effect and in Compton scattering.
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De Broglie’s thesis required him to build a theoretical bridge between these two very distinct concepts. The principal challenge was that particles and waves were traditionally described in very different ways. Particles in Newton’s equations were primarily characterized by two quantities: momentum (p) and energy (E). In contrast, electromagnetic waves, as governed by Maxwell’s equations, were principally defined by two other quantities: wavelength (λ) and frequency (). How could he relate these two sets of quantities?
De Broglie recognized that Einstein, in his work on the photoelectric effect, had already described the relationship between energy and frequency:
E = hv, Equation 1
where E is energy, h is Planck’s constant, and ν is the frequency.
De Broglie completed this picture by introducing a relationship between momentum and wavelength:
λ = h/p, Equation 2
where λ is the wavelength, h is Planck’s constant, and p is momentum.
His work showed that light could simultaneously be described as a wave and a particle, and scientists could now interconnect these two perspectives.
But de Broglie did not stop there. He recognized the bridge he had created was a two-way street. If light waves could be treated as particles, then fundamental particles could also be treated as waves. This discovery was the stunningly logical consequence of his equations. Previously viewed as a simple point-like object, an electron could now be treated as a matter wave. Scientists initially found this hard to accept.
Because everyday objects are made of fundamental particles, they too may be treated as waves. A thrown baseball is governed by the same rules as the quantum world and therefore oscillates with a definite wavelength given by de Broglie’s formula. Even our bodies have an associated wavelength! Of course, the wavelengths of ordinary objects are so incredibly small—at least a trillion times smaller than the diameter of an atom. This means that their wave properties would be too small to be detectable. We are fortunate we do not have to contend with these wave properties in everyday life, only at the atomic scale.
Experimental Confirmation of Particles Behaving as Waves
How were scientists to test de Broglie’s theory of particles behaving like waves? Fortunately, electrons and other fundamental particles have wavelengths comparable to distances between atoms in solids. In 1927, G. P. Thomson, along with the parallel work of Clinton Davisson and Lester Germer, demonstrated that electrons experienced diffraction, a wave property. Thomson focused a beam of electrons onto thin metal foils and recorded the resulting electron paths on pieces of photographic film (see Figure 3a). The result was a series of concentric circles determined by the structure of the specific metal. The patterns created by electrons were directly comparable to those created by x-rays (see Figure 3b). As radical as this was, later scientists demonstrated diffraction using neutrons, neutral atoms, and even small molecules, such as buckminsterfullerene (C60).
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Does Wave-particle Duality Violate the Law of Noncontradiction?
Some have misunderstood wave-particle duality as teaching that all fundamental particles are BOTH waves and particles. This confusion leads people to ask whether this violates the law of noncontradiction.2 The answer is no. Wave-particle duality holds that they are neither classical waves nor classical particles. Instead, they are quantum entities that can behave like waves on some occasions and like particles on others, depending on the experiment being performed. They are never simultaneously waves and particles, thereby preventing a contradiction.
Wave Interference
Wave interference is the most distinctive of the wave behaviors because it cannot be explained within a classical particle framework. Demonstrating elementary particles create interference patterns therefore serves as a more substantial demonstration of wave-particle duality than diffraction.
The best model for visualizing waves and wave phenomena is simple water waves. One can perform simple demonstrations at home using a pan half-filled with water. To generate simple waves, quickly tap the surface with your finger and watch the resulting ripples. The waves undulate with alternating peaks and troughs. If we were to take a cross section of these waves, we would see that the peaks represent a positive displacement (height above the flat surface) and troughs are negative displacements (see Figure 4).
This difference in sign is important when we consider what happens when two different waves interact. Regions of overlap possessing the same sign (two peaks or two troughs) will reinforce each other (constructive interference). In contrast, those with opposite signs (a peak and a trough) will be reduced (destructive interference).
2 The law of noncontradiction, the foundational principle for all logical thinking, asserts that two contradictory statements cannot both be true at the same time in the same respect (A cannot equal A and also equal non-A). Or to put it a different way, nothing can both be and not be at the same time and in the same respect. Kenneth Richard Samples, Without a Doubt, Baker Books, Grand Rapids, MI 2004, p. 73.
a) b)
Experimental setup X-ray (left) and electron (right)
diffraction for aluminum foil
Figure 3: G. P. Thomson’s electron diffraction experiment.
Credit: Alex Montwill and Ann Breslin, The Quantum Adventure, p 128.
Figure 4: Simple wave with signs.
Credit: John Millam.
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Let us consider two special cases of combining waves of identical frequency and amplitude. In the first case, the waves are precisely aligned with the peaks of one wave corresponding to the peaks of the other. The resulting wave is twice the magnitude of the individual waves. This result is known as perfect constructive interference (see Figure 5a). In the second case, the waves are perfectly misaligned such that the peaks of one wave line up with the troughs of the other. The result is a complete cancelation. This is perfect destructive interference (see Figure 5b).
Wave Cancelation
As mentioned, when a wave encounters a different wave with the exact opposite shape, it will cancel (perfect destructive interference). This can serve many useful purposes. For example, this behavior is the basis for active noise control (noise canceling) headphones. A microphone in the headset picks up the incoming sound wave, then an internal speaker generates the opposite sound resulting in cancelation. As a result, the person wearing the headphones would not hear the incoming sound.
A more dramatic example of wave cancelation is matter-antimatter annihilation. This occurs when a particle of matter encounters its antimatter twin resulting in the pair disappearing in a flash of energy. This notion of annihilation was unthinkable within the classical particle framework. Two colliding particles should either bounce off each other or break into smaller pieces, but not disappear. The existence of antimatter, however, arises naturally within the wave framework of quantum mechanics. When Paul Dirac extended Schrödinger’s equation to satisfy special relativity in 1928, his equation predicted the existence of antimatter as a natural consequence.
Interference Patterns
Now let us consider a slightly more complicated example of wave interference. Returning to our pan of water, rhythmically tapping the water with one finger, you get a series of concentric ripples that move outward. However, if you tap using two fingers held slightly apart, you get two sets of circular wave patterns that will overlap and interfere with each other (see Figure 6).
Looking closer, we can observe both constructive and destructive interference. We find perfect constructive interference
a) b)
Figure 5: Perfect (a) constructive and (b) destructive interference.
Credit: John Millam.
Figure 6: Interference pattern between two circular wave patterns (red dashed lines mark perfect constructive interference and blue dashed lines mark perfect destructive interference).
Credit: MPC (modified with dashed lines).
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on the line midway between the two wave sources (see Figure 6, red dashed lines). Moving just above and below, we observe lines of stillness with no ripples representing perfect destructive interference (see Figure 6, blue dashed lines). Moving outward from there, we find alternating patterns of perfect constructive and destructive interference. Between these two extremes there are differing degrees of both constructive and destructive interference.
Examples of Wave Interference
Wave interference is common in the world, although we may not always recognize it. Let us briefly consider four examples (summarized from “Interference of Light Examples in Daily Life”): - Blue Morpho Butterfly. The blue color of the butterfly’s wings is mainly due to the interference of light rather than natural pigmentation. When the light falls on the surface of the wings, the blue light undergoes constructive interference, while the other colors are eliminated by destructive interference.
- Anti-reflective Coating. Anti-reflective coatings reduce the intensity of the light falling on the surface of the object using destructive interference. Useful for glasses and computer screens.
- Thin Layer of Oil on the Surface of Water. When a ray of light hits the oil, it gets reflected by the top and the bottom surface of the layer, causing light of different colors to undergo constructive as well as destructive interference. The different thicknesses of oil lead to the formation of a multi-colored visible pattern on the surface of the oil.
- Hologram. Hologram technology also makes use of the interference of light to produce a three-dimensional image of objects.
In addition, one of the main scientific applications of wave interference is interferometry. This technique allows scientists to make extremely precise measurements, accurate to atomic-scale distances. In astronomy, interferometry can be used to combine signals from multiple telescopes to achieve a spatial resolution equivalent to a much larger telescope.
The Double-Slit Experiment
The ultimate test of wave-particle duality is the double-slit experiment because it involves wave interference, the most definitive wave property. As previously described, Thomas Young developed his famous double-slit experiment in 1803. The resulting fringe patterns demonstrated wave interference and were taken as decisive proof for the wave nature of light. Let us now step through this experiment in more detail.
In the experiment, a single light source is directed at two narrow slits separated by a small distance (see Figure 7). The light emerging from each slit will
Source Slits Intensity Observed
Figure 7: The double-slit experiment using light.
Credit: John Millam (modified from University Physics, Vol 3).
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spread out due to diffraction, a wave property.3 The net effect is that the original light source has effectively been split into two separate light sources, each having precisely the same frequency and wavelength. These light waves will then overlap and interfere with each other, resulting in interference fringes (see Figure 7, “Observed”). To help visualize what is going on, this setup is closely analogous to the interference with water waves shown in Figure 6.
To understand the origin of these interference fringes, we need to analyze the distance the light must travel from each slit to a given point on the screen. The difference between the distances traveled determines how they interfere with each other. For the bright line midway between the slits, the two paths are of identical length resulting in constructive interference. The remaining bright bands correspond to path lengths differing by an integer number of the wavelengths of the light used. The dark bands are caused by destructive interference and result when the path length differs by an integer plus one-half times the wavelength.
This analysis seems straightforward but let us dig a little deeper. How should we understand this when we treat light as a particle? When we considered the case of water waves, it was simple—the water waves go through both slits (see Figure 6). But surely photons of light can only go through one slit. Perhaps a photon going through one slit interferes with another going through the opposite slit. So, what would happen if only one photon went through the apparatus at a given time? When scientists tested this in 1909, they found that the interference pattern remained. That means, in some very real sense, the photon passes through both slits to interfere with itself! This is astonishing but is entirely expected based on quantum mechanics and wave-particle duality.
Double-Slit Experiment with Electrons
Thomas Young’s double-slit experiment produced interference fringes using light, but this result was not overly surprising because light had almost always been viewed as a wave. But what about particles, such as electrons? Surely, an electron can only go through one of the two slits, so we should see two bright stripes corresponding to particle behavior (see Figure 8, “Particle Pattern”). Each stripe would represent electrons coming from a single slit, and these would be completely independent of each other. But de Broglie’s work predicted electrons should produce an interference pattern, just like light (see Figure 8, “Wave Pattern”). These two possibilities serve as a diagnostic test to determine if electrons behave like a wave or a particle.
The double-slit experiment using electrons was first performed by Claus Jönsson of the University of Tübingen in 1961. A beam of electrons was fired at a pair of slits, and the resulting
3 Diffraction is a consequence of Heisenberg’s uncertainty principle. Consider light passing through a controllable width slit. As the width is reduced, the light beam will narrow until it reaches a certain size after which diffraction will cause it to widen. To understand this, consider the uncertainty relationship, xp ≥ h/4π, where x is the width of the slit. When x is small enough, the uncertainty in the momentum (p) must increase causing the wave to spread out.
Figure 8: Comparing wave and particle results for the double-slit experiment.
Credit: Robert Lea (with color modified for clarity).
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electrons were collected on a photographic film or a screen (see Figure 9). The scientists observed interference fringes, thereby demonstrating wave behavior.
As with light, this experiment was later repeated but with only a single electron passing through the device at any given time. The electrons strike the screen with pin-point hits, like particles. Of course, we never observe two half-electrons, only single electrons meaning the electron does not split into two parts to go through both slits. When performing the experiment, the resulting hits were allowed to accumulate over time. Initially, the electron impacts seem random, but eventually the interference pattern emerges (see Figure 10a-e). Something is steering the electrons toward specific areas and away from others. These observations tell us that each electron must simultaneously pass through both slits and interfere with itself.
Double-Slit Experiment with Molecules
Wave-particle duality is not limited to just elementary particles. Although technologically challenging to test, neutrons, neutral atoms, and even small molecules have been shown to display interference patterns. Currently, the largest molecule used in these experiments contains 2,000 atoms. There is no known limit on the size of particles displaying quantum behavior, although some theories predict that there must be.
One rather dramatic example of double-slit experiments with molecules comes from a team of scientists in 2012 using phthalocyanine (C32H18N8) and a derivative molecule (C48H26F24N8O8) containing 58 and 114 atoms respectively.4 The molecules were wafted through gratings in 10-nm-thick silicon nitride membranes toward a screen and visualized using fluorescence microscopy. The molecules can be seen arriving individually at the screen. Like the single-electron case, the location of the molecules seems random at first, but over time the fringe patterns become very pronounced (see Figure 11a-e). These results can also be viewed in video format (watch video).
4 T. Juffmann, A. Milic, M. Müllneritsch, et al, “Real-time single-molecule imaging of quantum interference,” Nature Nanotech 7, 297–300 (2012), arXiv:1402.1867.
Figure 10: Progressive appearance of fringes for single-electron double-slit experiment.
Credit: Wikipedia commons.
Figure 9: Double-slit experiment with electrons.
Credit: Wikipedia commons.
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This experiment adds one interesting new wrinkle to the story. The interference fringes are narrower at the top than at the bottom, rather than perfectly vertical (see Figure 11e). This effect occurs because gravity sorts the molecules according to their velocity with the fastest at the top and slowest at the bottom. A higher velocity means a smaller wavelength; hence the fringes are closer together.
Interpreting the Double-Slit Experiment Results
As explained in part 1 of this series, our understanding of quantum mechanics is incomplete. More than two dozen interpretations of quantum mechanics have been proposed to explain its inner workings. Let us consider how the three most prominent interpretations attempt to explain the double-slit experiment: - Copenhagen Interpretation. The particle’s wavefunction passes through both slits, but when measured, the particle collapses to a single location.
- Bohm’s Interpretation. The wavefunction goes through both slits, but the particle riding on the wavefunction randomly goes through one slit or the other.
- Many Worlds Interpretation. The particle splits by going through one slit in one universe and the other in a different universe. At the screen, they subsequently merge back into one reality producing an interference pattern.
Unfortunately, scientists have not been able to prove or disprove any of these models.
Summary of Double-Slit Experiments
The double-slit experiment (and its variations) has become a classic for its clarity in expressing the central puzzles of quantum mechanics, particularly wave-particle duality. Physicist Richard Feynman eloquently summarized:
“[The double-slit experiment] 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].”5
5 Richard P. Feynman; Robert B. Leighton; Matthew Sands. The Feynman Lectures on Physics, Vol. 3. Addison-Wesley, 1965, p. 1.1.
Figure 12: Sign: Quantum junction. Get in both lanes.
Credit: Uncyclopedia.
Figure 11: Double-slit experiment with phthalocyanine recorded at time a) 0 min, b) 2 min, c) 20 min, d) 40 min and e) 90 min.
Credit: Reference 4.
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The double-slit experiment’s importance is it elegantly demonstrates in a particularly intuitive way the inherent dualities in quantum mechanics: - Wave and Particle. We observe wave behavior (diffraction and interference) and particle behavior (point-like hits on the screen). Both wave and particle behavior are apparent in the experiment, although not at the same time.
- Randomness and Determinism. The particles appear to arrive randomly on the screen, yet it results in a very deterministic distribution.
- Locality and Delocalization. Particles arrive at the screen as a point (localized), yet their path to the screen involves spreading across both slits (delocalized).
To conclude, there is an excellent 2-minute animated video visually summarizing the essentials of the double-slit experiment.
“Which Path” Experiments
The lingering unresolved question is the nature of the path of the electron (or other particle) in the double-slit experiments. Does an individual electron have a well-defined path? If not, in what sense does it go through both slits? This question has stumped scientists for nearly a century. In a well-known thought experiment, Richard Feynman argued any measurement that would enable scientists to precisely determine which slit the particle traveled through should cause the interference pattern to disappear.6
This whimsical absurdity is aptly summarized by Alice the electron’s encounter with the Cheshire cat in a quantum version of Alice in Wonderland (see Figure 13).
Experimentalists, seeking a way forward, have devised new methods to glean insights into this behavior. These are termed “which path” experiments because their primary purpose is to determine the particle’s path. The following discussion and graphics are taken from KSU Physics Education Group, Visual Quantum Mechanics.7
Mach-Zehnder Interferometer
One insightful approach is based on a Mach-Zehnder interferometer (see Figure 14). For simplicity, the experiment is performed using photons, instead of electrons, but the principle is the same.
Our light source is a simple monochromatic red laser. It is directed at beam splitter 1 (a half-silvered mirror). The beam splitter is designed such that each photon has a 50% being reflected and 50% chance of passing through. The reflected photons will travel along path A while the rest travel along path B. Mirrors then deflect both beams by 90° causing them to meet at beam splitter 2 where they are merged back into a single beam. The two paths are designed to be of
6 Ibid, pp. 1.1-1.8.
7 Visual Quantum Mechanics web page: https://web.phys.ksu.edu/vqmorig/tutorials/online/wave_part/.
Figure 13: Alice the electron and the Cheshire Cat.
Credit: John Millam (using images from the internet).
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identical length. When correctly aligned, the photons will exclusively leave beam splitter 2 toward the screen (perfect constructive interference) and no light is found in the alternate direction due to perfect destructive interference.
This setup is analogous to double-slit experiments but with the two pathways clearly defined and spatially separated. This arrangement enables us to treat each path independently.
Experiment #1: Normal Operation
Once properly set up and activated, the light is split evenly between the two pathways and recombined to yield circular interference fringes on the screen (see Figure 15). This arrangement functions more-or-less the same as the double slit experiment, except that we get circular fringes rather than vertical ones.
Experiment #2: Single Photon Interference
The next step is to perform the experiment with only a single photon passing through at a time. One way to do this is to add grey filters in front of the laser. These filters reduce the number of photons passing through, and with enough filters, only a single photon will make it through at any given time. But even in this case, the interference pattern is still observed (see Figure 16). This result means individual photons must be interfering with themselves.
Figure 14: Mach-Zehnder Interferometer.
Credit: Footnote 7.
Figure 15: Experiment #1: Normal Operation.
Credit: Footnote 7.
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Interferometer with Polarization Filters
So far, we have merely reproduced the results of the double-slit experiment. To go beyond that, we modify our setup by adding a polarization filter along each path (see Figure 17). These filters can be independently adjusted to a vertical or horizontal orientation. These filters serve a critical role by marking the polarization state of the photons, allowing us to potentially distinguish between the two pathways.
Experiment #3: Matching Polarization Filters
For our third experiment, we will set both polarization filters to vertical. Because they are aligned in the same direction, there is no way to distinguish pathways. As expected, the interference pattern remains even for the single photon case (see Figure 18). This result is important because it establishes that the presence of the filters does not alter the results of the experiment.
Figure 16: Experiment #2: Single Photon Interference.
Credit: Footnote 7.
Figure 17: Mach-Zehnder Interferometer with Polarization Filters.
Credit: Footnote 7.
Figure 18: Experiment #3: Matching Polarization Filters.
Credit: Footnote 7.
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Experiment #4: Opposing Polarization Filters
For our fourth and last experiment, we set the polarization filters to be opposite—one vertical and one horizontal. Note, it does not matter which polarization filter is set to horizontal because only the relative orientation matters. This setup enables us to determine which path the photon takes to the screen. Unfortunately, the interference pattern disappears even though we do not actually check the final polarization state (see Figure 19). This outcome is analogous to double-slit experiments, where any attempt to distinguish which slit the particle went through causes the interference fringes to disappear.
“Which Path” Conclusion
What are we to conclude from these experiments? - To explain the differences between experiments 3 and 4, we conclude that the photon cannot be localized to path A, because it would need to “know” about the adjustment of polarization filter B (see Figure 20).
- In the same way, it cannot be localized to path B.
- The photon must, therefore, follow both paths!
This is quite a remarkable conclusion. Yet it leaves the central mystery unresolved. How does the particle “know” what is occurring along both paths? So far, no scientist has been able to unambiguously answer the question. Perhaps future experiments will be able to resolve this conundrum.
Figure 19: Experiment #4: Opposing Polarization Filters.
Credit: Footnote 7.
Figure 20: “Which Path” Conclusion.
Credit: Footnote 7.
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Appendix: Resources on Quantum Mechanics
Robert Gilmore, Alice in Quantumland: An Allegory of Quantum Physics.
Erica W. Carlson, The Great Courses: Understanding the Quantum World.
James Kakalios, The Amazing Story of Quantum Mechanics.
Alex Montwill and Ann Breslin, The Quantum Adventure: Does God Play Dice?
Brian Clegg, The Quantum Physics Bible: The Definitive Guide to 200 Years of Subatomic Science.
Banesh Hoffmann, The Strange Story of the Quantum.
Amir D. Aczel, Entanglement: The Greatest Mystery in Physics.
George Musser, Spooky Action at a Distance.