Quantum Superposition: When You’re Not Looking, It’s Everywhere!
Newton & The Apple
Many questions can come to one’s mind within the matter of a minute; perhaps even the simplest ones grease the wheels for great scientific insights. In ancient times, many asked, “Why do objects rolling eventually slow down?” Aristotle answered such a question with, “Moving objects stop because they eventually get tired.” Here’s one, what is the difference between an apple and an electron?
There are many ways to answer this question: maybe, perhaps, we can see apples, touch them, feel them, these being things we can’t necessarily do with single electrons. One difference is that we can juggle apples, electrons are too small for us to even know if one is juggling them at first sight. Another thing is that, unlike apples, electrons are found in atoms- as fundamental constituents of everyday matter. Electrons can also be seen as what flows through wires and through circuits, in large numbers, in everyday electronic devices; electrons are also commonly seen in sparks produced by cumulonimbus clouds in thunderstorms, and in Van De Graaff generators.
These are obvious differences seen by the everyday observer: but from a modern physicist’s point of view, there is much more. Of course, apples can’t line up and produce sparks of lightning- neither can electrons be handled in the same way as apples- but can one even know where a single electron is? This might seem like a counterintuitive question with a single electron, but it might not be so with an apple. When, according to the myths, the apple fell from the tree onto Isaac Newton’s head- which, supposedly, sparked the ideas for his best works in Physics- when it bounced off and hit the ground beneath him, he was able to look to his side and state that it was “there”. He could have easily looked at it and instantaneously known where it was exactly. He could have pinpointed its position. Could the same have happened with an electron?
The first problem is that the electron is too small to see, but let’s assume that in Newton’s time, another brilliant scientist already invented a detector that was connected to a bell, and that was capable of ringing every time a single elementary particle passed through it. Or even better- a magnifying glass that could zoom in to “see” individual atoms and what make them up. Now that problem is out of the way. Let’s imagine that, this time, Newton felt an electron hit his head and peered over his side to find it. Wait! Where is it?
The ultimate problem is that, unlike with the apple- despite his ability to zoom into great depths- he can’t find the electron. Why is this so? Disappointingly, he simply can’t find it- it can be anywhere, but he physically can’t pinpoint its position in space time. His knowledge is confined. As of now, Newton can only know where it most likely can be. He can only select an area and, within the area, calculate the probabilities of the electron being in different coordinates.
Since the electron ideally has a possibility of being in any given location- since Newton doesn’t know where it is- he might as well consider the electron to be everywhere. If Newton doesn’t know where the electron is, the electron can be anywhere. Thus, it is everywhere. It is, at least, according to quantum mechanical logic.
A Superposition of States
The notion of the electron being “everywhere” is a concept greatly covered in Quantum Superposition. The electron has a superposition of states. In one frame of time, the electron can undertake multiple energy states, intrinsic spin states, and multiple location states- again, location states meaning “where it is.” In fact, Newton’s inevitable lack of knowledge on the electron’s exact location perfectly demonstrates the Quantum Uncertainty principle. The Quantum Uncertainty principle states that no one can- with the best technology- know about where it is meanwhile knowing about the momentum with which it’s propagating. Newton can’t be certain about where the electron is, but he can get closer and closer until he reaches a limit. As Newton gains more and more information about the electron’s whereabouts, he increasingly constrains himself from simultaneously gaining information about how fast it’s moving (multiplied by a factor of its mass). He can only know about one or the other- but never both. The more he knows about its position, the less he can know about its momentum.
This works as well in the other direction. The more Newton knows about how fast the electron is moving multiplied by its mass, the less he can know about the electron’s specific location. He can know more about the momentum, he’ll just be confined to know less and less about the position in spacetime. The Uncertainty principle inequality is shown below.
Due to the Uncertainty principle, the electron, instead of being defined by a single point, or coordinate, is defined by a probability spread. This is a more technical way of referring to the selected area in which the electron can be, but, at the same time, not. Instead of being point-like, the electron is spread out. This spread of electron probability is defined by its wavefunction. Newton- with his hypothetical machinery and technology- can calculate the electron’s wavefunction and find where the electron is most likely to reside. Where the electron most likely is can be determined using measurements on where amplitude of the wave is highest. Why can’t he just look at it? Well, It’s not that simple.
In order to better grasp the concept of the problem, we need to understand what it means to look at something. In the story regarding the apple, how necessarily did Newton see the apple on the ground, what did it even mean for him to look at it? We take this for granted in our everyday lives and forget to take into account how we can even see ourselves in the mirror every morning. How did newton see the apple? This is a matter of light vs. dark. The reason why Newton was able to see the apple on the ground before he was even able to think of picking it up and taking a bite out of it was because there was light from the sun, and from other sources, hitting it. As photons from the light were hitting the apple, they were also bouncing off.
This is the reason for why we can’t see in the dark. The reason why we become visually impaired in the dark is that there are little to no photons bouncing off of objects for us to see them. This is why we use flashlights. By using a flashlight in the dark, one can throw photons at objects and thus describe their features- what they look like- based on how they throw them back. In other words, on how they reflect the light. The reason Newton was able to say that the apple on his side was red was because the apple reflected the sunlight in such a way that red photons were the ones being thrown back. In fact, the sun emits all frequencies (what we detect as colors) of light- the apple absorbed all except that of red. In our everyday lives, we use photons as particle probes.
Particle probes are thrown at pieces of matter in order for experimenters to describe the features of the pieces of matter based on how they reflect the probe particles. We use photons every day as probe particles to see; but when we use them to see smaller and smaller objects, the reflection images become fuzzier and fuzzier- thus we find the need for smaller and smaller probe particles. We see things better with smaller and smaller probe particles- they can capture finer detail. This is why electron microscopes show much more detail than normal light microscopes- electrons are much smaller than the wavelengths of visible light.
Oh, did I forget to add on that Newton’s acquaintance Edmund Halley was sitting on the other side of the tree?
“Isaac! I have an idea, let’s just use probe particles to see where the electron is! That would work wouldn’t it?”
The Observer Effect
Newton finds this idea delightful. Let’s pretend that, around his time, lasers have already been invented. Newton finds a laser of red light, he scans the area, nothing. He finds that the wavelength for red light is much too big for probing an electron, so he finds a laser emitting light of a slightly smaller wavelength- he tries yellow this time. Nothing. He finds that yellow light has too large a wavelength, so he tries green. Nothing. He tries blue. Nothing. Newton, alongside his partner Halley, with surprising patience, repeats the experiment until he gets to ultraviolet light. Still nothing. Why is this so?
Newton and Halley have run into a problem. When things move, they have energy. When using any probe particle, one throws it at matter expecting it to be thrown back. What Newton and Halley didn’t take into account was that as they were using photons to see the electron- based on how it reflected back the photons- they were giving the electron quantized impulses of energy. The process itself of using probe particles meant inevitably energizing the electron. By using probe particles, they were interacting with the electron and disturbing it.
It is quite ironic how one needs probe particles to measure the properties of a given piece of matter and that the process of measurement itself changes the states of the piece of matter being observed. The process of measurement changes the very propagation of the electron and sends it traveling into a different direction.
This is akin to a photographer’s frustration towards the constant blinking of the child that is to appear in her picture- the child is blinking because the camera’s flash is too bright. She then thinks to use a camera with flash half the intensity of the first camera. Hopefully, the child won’t blink. This turning down of the flash intensity slightly blurs out the picture, and now the photographer can’t see the child as clearly in the picture.
Newton and Halley discuss for quite a while and eventually come about why their particle probes weren’t working effectively. In fact, they notice that as they used laser lights of lower and lower wavelengths, they were probing the electron with higher and higher energies- thus increasingly disturbing the electron as they were trying to look at it. To their misfortune, this paradoxical scenario only complements the Quantum Uncertainty Principle. Along with not being able to know about the electron’s momentum and whereabouts simultaneously, they would only disturb the electron if they tried to look. By trying to see how the electron was propagating initially, they moved it.
The Double Slit Experiment
An electron hits Newton on the head and falls to the ground. He looks around for the electron and isn’t able to find it; he conducts experiments using probe particles of different energies to make measurements on the electron’s location- but he just increases the possibility of not finding the electron. This observer effect compliments the Uncertainty principle, and the Uncertainty principle is partially the reason that the electron isn’t localized, but spread out and in multiple places at once. It’s just an electron, so what? Why does it matter whether the electron’s location was defined by a single coordinate, or by multiple coordinates that vary in the electron’s probability of existing? One approach to answering this question is applying the concept of the Double Slit experiment to how the electron can have a spread-out probability. How do we know in the first place that the electron is spread out- who’s to say that experimental physicists simply don’t have well enough equipment?
The Double Slit Experiment can be used to calculate the wavelength of different light frequencies, but it was initially used to show whether particles or waves constituted light. In different conditions, light acts as either particles or waves- but the Double Slit experiment is used to explain light on behalf of its wave properties. The traditional Double Slit experiment uses a light source, a thin barrier consisting of two narrow, identical, and close slits, and a strip of paper.
The idea is that the light is to pass through both slits, and then get projected onto the strip of paper mentioned in the last paragraph. Given light’s dualistic properties, as the light passes through the identical slits, it is to act in either of two ways. If light propagates as particles, the particles would travel in straight lines through each slit — in accordance to Newton’s three laws of motion- and land straight onto the strip of paper directly behind each slit. In other words, if light acted as particles, one would notice the paper displaying two identically shaped light bands. In Figure 2 and Figure 3, the strip of paper is darkened to create contrast so that it’s obvious where the photons hit.
If light propagates as waves, a new light pattern would emerge from the light after passed through the double slit barrier. As light from the source, in the form of waves, approaches and comes in contact with the double slit barrier, the light waves passing through will act differently than particles. Particles “pass straight through,” waves diffract. Instead of passing through in straight lines like the particles, the waves will spread out after passing through each slit simultaneously. Keep in mind that the waves cover both slits individually and split off to each slit opening. As the waves divert into each slit, each slit acts as a new light source, and the waves bend- spreading outward.
As the synchronized diffracted light waves propagate outward from each slit- now in pursuit of the strip of paper- they spread out to the extent such that they come in contact, overlap, and interfere. In such an interference, in some places, the light waves’ crests will meet and constructively interfere- adding up and increasing the wave amplitude. In other places, the crests will meet with the troughs and destructively interfere- canceling each other out. Essentially, some places would show darkness, and others will show light. Should light propagate as waves through a double slit barrier, a distinguishable and unique pattern consisting of light bands with dark regions in between them would emerge on the paper. According to theory, particle-like light would show only two spaced out bands; wave-like light would show the same pattern in a more repeated fashion- light-dark-light-dark-light-dark-light-dark-light.
This is what Englishman, Thomas Young, postulated in the beginning of the Eighteen- hundreds- this was his way of splitting the scientific community’s century-long debate on whether light acted as waves or particles. When he originally conducted the experiment, he found that light acted more like waves since they displayed the interference diffraction pattern. It was only until the dawn of Quantum Mechanics, a century later, that physicists began to come into a realization that it acted as both- waves and particles, given different environmental conditions. Greater than this is the realization that particles of matter acted analogously.
Around the mid-1920s, French physicist, Louis De Broglie, used a wavelength equation describing light and applied it to particles of matter. This is when he postulated that along with light, particles of matter can also propagate as particles or waves- again, given different conditions. He is greatly known for the “De Broglie wavelength,” The equation is shown below. The De Broglie Wavelength states that the wavelength of light is equal to Planck’s Constant divided by the light’s momentum.
o “λ”: Wavelength
o “h”: Planck’s Constant
o “p”: Momentum
Since particles like muons, protons, quarks- and so forth- can travel with velocities, and since they have mass, they most certainly can propagate with momenta. Since the De Broglie wavelength incorporates factors of momentum- which matter particles most certainly have while they’re moving- matter particles, too, can have wavelengths. If particles of matter have wavelengths, they most certainly have wave properties.
Experimental physicists, greatly known as Clinton Davisson and Lester Germer, put this theory on trial. Davisson and Germer conducted the Double Slit experiment, but this time, they didn’t use a beam of photons- instead, they used a beam of electrons from an electron gun. This electron beam was directed onto a Nickel Chloride crystal- the crystal consisted of structures similar to that of the double slit barrier. Alongside the crystal was a detector that collected data on how the electrons interacted with the crystal. Once the experiments were conducted, the similar constructive interference patterns, that others encountered using light, showed up when electrons were used in the same experiment. This confirmed Louis De Broglie’s hypothesis- since the electrons were found to exhibit wave properties. How could this have happened- how can separate particles of matter constitute wave patterns?
After the De Broglie wavelength, a better description of particles’ wave properties came about. Such is called a particle’s wavefunction. A particle’s wavefunction has been referred to earlier in this paper as the spread of its probability- except, it hasn’t been much expanded on that this probability spread corresponds to its wave properties. In fact, this wavefunction with variances in probability amplitudes is the matter wave. Let’s go back to photons for a brief moment.
When most experimenters conduct the Double Slit experiment, they use a laser beam with light of intensity they can see. Usually, they use multiple photons at the same time- the double slit barrier gets bombarded with photons. Interestingly, when the light intensity is lowered to the extent such that only single photons leave the laser per interval of time, the interference pattern seen with multiple waves still emerges onto the screen- ideally with detectors since the naked human isn’t capable of “seeing” single photons. Photons are being emitted individually, and thus in quantized, discrete chunks of energy. How come we’re still seeing wave patterns?
Though each individual photon is a discrete unit of energy- in other words, meaning that each is alone, that each has no other photons to interfere with, also that, this time, each is set in a condition in which they are to act as individual particles- each has its own wavefunction. When each discrete photon passes through the slit barrier, akin to the light wave, each photon wavefunction covers both slits; some of the probability leaks out of one slit, some leaks out of the other. Then, the probability from each slit diffracts and interferes with that of the other. Essentially, when only one photon is emitted at a time, due to the probability wavefunction of each single photon, the same interference pattern emerges. It is the probability that interferes with itself and accounts for the pattern. The Davisson-Germer experiment was included in this section because electrons- along with every other particle in the universe- have wavefunctions. In Quantum Mechanics, the probability spread can be looked at as an entity. It is, again, the wavefunction of said particle; the particle is spread out. This is quite counterintuitive to us humans as we are used to the world of the large where General Relativity and Newtonian Mechanics dominate. In the world of the large, probability means something completely different; rather, the flipping of a coin can be more relatable as a probability scenario. But physicists have come to the conclusion of Quantum probability due to mathematics, experimental results, and experimental data. The electrons’ corresponding wavefunctions are what were responsible for the patterns of constructive interference picked up by the detectors. These were the electron waves, these are.
Quantum Superposition is a quantum mechanical phenomenon in which particles- which were thought to be point-like by those with common sense- can be in multiple places at once. This is a consequence of the uncertainty principle. This principle tells us that we cannot exactly pinpoint where a particle is. Though, we can find where the probability amplitude in the particle’s wavefunction is highest and say that it most likely is “there.” Adding on, this wavefunction complements Wave-particle Duality in adding wave properties to particles of matter, like electrons. This has been demonstrated in the mid to late 1920s in the Davisson-Germer version of the Double Slit experiment. From classical physics to Quantum Physics, we go from thinking that individual particles can be defined by single coordinates in space-time to finding out that they are, instead, defined by multiple coordinates in space-time. Quantum logic tells us that if we don’t know where it is, it is everywhere.
