This is a simple introduction to the concept of superposition, which will continue to intrigue, perplex, and captivate you throughout your life. The experiments I’m about to describe are derived from the first chapter of a book by David Albert titled “Quantum Mechanics and Experience.” I will delve into a specific set of experiments that are renowned for their unsettling nature.
These experiments involve electrons, and they have indeed been experimentally verified. In this discussion, I’ll be focusing on two properties of electrons, which we’ll refer to as “color” and “hardness.” It’s important to note that these are not their official technical names; I’ve chosen these terms to prevent any preconceived notions about what they might represent.
Experimental Setup:
Each electron can be categorized as either black or white and as either hard or soft. These attributes are binary. It’s possible to create devices to measure these properties. For instance, imagine a “color box” with three openings: one for input and two for output, one output port for black electrons and the other for white electrons to come out. The electron’s color can be determined by where it exits the box. If it comes out on the right, it’s white; if it emerges from the top, it’s black.
Similarly, we can make a “hardness box” with three openings, one for input and two for output, for hard and soft electrons as shown in the figure 1. These boxes can be built using various methods, but they all yield the same results.
Repeatability and Correlation of Color and Hardness:
One crucial aspect of these boxes is their repeatability. This means that if we send an electron through the color box and it comes out as black, if we send it through another color box, it will still come out as black as shown in the figure 3. The same goes for hardness. So, a question arises: are color and hardness related? Can we determine one from the other? Let’s say we have a white electron; does that mean we can predict its hardness?
We can answer these questions using our boxes. We take random electrons, send them through the color box, and select the ones that come out as white. Then, we send these white electrons through the hardness box and observe what comes out. What we discover is that 50% of them become hard, and 50% become soft. Similarly, if we send electrons through the hardness box and send the soft ones through the color box, 50% turn white, and 50% turn black. Similarly, If we measure the color of electrons that are all known to be soft, we’ll find that half of them will be black, and the other half will be white as shown in the figure 4. Hence, When we measure one property of electrons and then measure the other property of those electrons that share the same value for the first property, we find that the second property is randomly divided, with an equal chance for each outcome. Therefore, knowing the hardness doesn’t provide any information about the color, and vice versa. These properties are independent; measuring one doesn’t allow us to predict the other.
Indeterminism:
Let’s dive deeper into these electron properties. Knowing the results, using the following simple experiment, they will lead us to more complicated experiments. So, how many black and white electrons come out of the output port in Figure 5 when we send random electrons from the first color box.
Here’s the logic: Anything that reaches the hardness box must be white, and from previous experiments, we know that 50% of these white electrons turn out soft, and the other 50% turn out hard in the hardness box. So, we send these white and soft electrons to the second color box to check their color. Since the colors are supposed to be repeatable, our natural expectation is that they should all come out white.
But, surprisingly, 50% of them come out white, and the other 50% come out black. This is puzzling! It suggests that we can’t think of electrons like little balls with “white” and “hard” written on them because “white” and “hard” aren’t fixed properties, although once something is white, it remains white. So, what’s happening here? The same outcome occurs if we change the input electrons to black or use hard electrons; any combination yields the same results.
It seems that the presence of the hardness box somehow affects the color, and this is far from trivial. It’s suspicious. The logical conclusion is that there must be an additional property of electrons, one we haven’t measured yet, that determines whether they come out as black or white from the second color box. Researchers have searched for these properties but have never found anything that consistently determines which way the electron comes out. As far as we can tell, it’s entirely random.
This revelation is quite disturbing. It’s the first major shocker: there’s an intrinsic randomness, unpredictability, and indeterminism in the physical processes we observe in the laboratory. There’s no way to predict in advance whether an electron will come out as black or white. This experiment has thrust probability upon us.
Some might argue that the boxes we built are flawed, but no, we’ve constructed them using various materials and technologies, including electrons, neutrons, and even buckyballs (which consist of 60 carbon atoms), and the results remain the same. Surprisingly, we can’t alter the probability of getting black or white from 50%. For those who grew up believing in determinism, this can be quite painful and feel wrong. However, this is the nature of the real world, and our job is to come to terms with it.
So, here’s something we can’t do: build a color and hardness box as in figure 6. The reason isn’t because our experiments are imprecise or because we lack the skills to build them; it goes much deeper than that. It’s not meaningful to say that electrons are both white and hard simultaneously. This concept is known as the uncertainty principle. It tells us that certain measurable properties of a system are fundamentally incompatible with each other. Incompatibility doesn’t just mean you can’t know; it means they can’t be both hard and white at the same time.
It might be tempting to think that this weirdness only applies to electrons and not to the rest of the world, but that’s absolutely wrong! Every object in the world shares these properties. Even massive objects like clusters of 60 carbon atoms (buckyballs) exhibit the same behavior. There’s a pendulum at MIT, used for detecting gravitational waves, with 20-kilogram mirrors, and it also shows these quantum mechanical effects. These are properties of everything around us.
The real miracle isn’t that electrons behave strangely; it’s that when you have 10^27 electrons, they behave predictably, like the chairs and tables. That’s the true marvel underlying all of this.
Let’s explore this further by creating a more intricate setup. We’ll position mirrors as indicated in the figure 7. These mirrors will only redirect the incident electrons and will do nothing else. Additionally, we’ll introduce another mirror to combine the electron beams into a single beam.
Frist Experiment:
We’ll send white electrons into this setup and measure their hardness using the apparatus described as shown in figure 8. So the question is: how many electrons exit through the hard aperture, and how many through the soft aperture? When you send in the white electrons, 50% come of hard and 50% come out soft from the first hardness box. The mirror does nothing to them so which should get 50% hard and 50% soft from the second hardness box.
Someone might inquire whether electrons interact with each other when we send a group of electrons together, considering their natural repulsion due to electric potential. However, it’s noteworthy that conducting the experiment by sending electrons one at a time and patiently waiting for six months, with an electron being emitted every couple of hours, still yields identical results.
Second Experiment:
In the second experiment, We plan to introduce electrons with high hardness and measure their color as in the figure 9. The initial box will consistently confirm their hardness because these hardness boxes maintain their characteristics over time. The presence of mirrors won’t affect the electrons, and when they reach the color box, the outcome is expected to be 50% black and 50% white. This expectation is based on the fact that hardness and color have been previously determined to be unrelated, as demonstrated in our earlier experiment.
Third Experiment:
Now, in the third experiment, we introduce white electrons and measure their color as they exit the apparatus as in figure 10. The question here is how many of them will emerge as white, and how many as black. When a white electron enters the hardness box, it emerges with a 50% probability of being hard and a 50% probability of being soft. Those electrons emerging as hard and also the electrons emerging as soft will maintain their hardness as they traverse the system, thanks to the mirrors that conserve this property, and eventually reach the color box.
Our previous experiments have shown that hard electrons have an equal chance of turning out black or white, both at 50%. This has been confirmed. Also, when we consider the remaining 50% of soft electrons, we expect them to also yield a 50% black and 50% white outcome. But to our astonishment, our prediction is incorrect!
In this case, all 100% of the soft electrons exit as white, with none coming out as black. This unexpected result leads us to ask a natural question: “What the hell is going on here?” Something extremely peculiar has occurred. The presence of those mirrors and the choice of two possible paths seem to have a profound influence on how electrons behave.
To further investigate this phenomenon, we move on to another experimental setup. We will introduce a small movable wall, as depicted in the figure 11, which will absorb all incident electrons. This setup will help us gain insight into how electrons navigate through the apparatus.
Fourth Experiment:
In Experiment 4, we introduce white electrons into the same apparatus and measure their color as they exit, but this time we place a barrier in the soft path. The question is, what proportion of these electrons will emerge as black and white?
A reasonable prediction would be that when we send in white electrons, 50% should exit from the hard aperture and 50% from the soft aperture. However, if an electron takes the soft path, it encounters the barrier and should be prevented from proceeding. Consequently, the output should decrease by 50%. For the twist let’s maintain both paths at a length of 10 million kilometers, and I will insert the barrier after launching the electrons. Neither I nor the electrons will know at that moment whether the barrier is in place. Furthermore, the barrier is located millions of miles away from the white electron on the top path, making it impossible for the electrons on the top path to know about its existence since they have not interacted with the barrier. We do know that when we run this apparatus without the barrier, all electrons come out as 100% white. Therefore, we should expect the output to be reduced by 50%, with 100% remaining white, as the electrons cannot have knowledge of the barrier’s presence. Additionally, if they emerged as 100% white, it would imply simultaneous hardness, violating the uncertainty principle.
However, the experimental results reveal a surprising outcome: 50% of the electrons emerge as white, and the remaining 50% come out as black. Even when we place a barrier on the top path, the result remains 50% white and 50% black. This raises the perplexing question of how electrons could somehow be aware of the barrier’s presence and behave differently.
Let’s contemplate what our experiments are conveying about a single electron as it traverses this apparatus.
Now, let’s consider a single electron within the apparatus during the third experiment, with all walls removed. The question is, which path did it follow? Let’s systematically examine the possibilities:
- The Hard Path: If the electron took the hard path, we could deduce this because in our previous experiment, we placed a barrier in the soft path, and no electrons emerged from it except those that took the hard path. From this experiment, the fourth one, we know that if it had taken the hard path, it should emerge as 50% white and 50% black. Yet, in our considered apparatus, 100% of the electrons came out as white. Therefore, it cannot have taken the hard path.
- The Soft Path: Using a similar argument for the soft path, we can conclude that it did not take the soft path either. So, the answer is also “No” for this possibility.
- Both Paths: One could speculate that electrons might split into two, with one part going through each path. To test this, we could place detectors along each path and expect to observe half of an electron on one side and half on the other. However, when we conduct this experiment, we consistently observe one electron on one of the paths, indicating that it did not take both paths.
- Neither Paths: To explore this possibility, we could place barriers on both paths. If the electron did take the neither path, we would expect electron to emerge. However, this scenario is also ruled out because we do not observe any outcomes when barriers are placed on both paths.
This exhausts the range of logical possibilities, leaving us with a profound question: What exactly are electrons doing when they reside inside the apparatus? How can we describe the state of an electron within this setup? These experiments and arguments, if valid, suggest that electrons exhibit a behavior that defies conventional understanding, for which we currently lack adequate terminology in the English language.
Conclusion
Empirically, it appears that electrons possess a unique way of moving and being, a behavior distinct from what we’re accustomed to thinking about. And so do everyday objects the molecules, bacteria, or the chalk. This behavior is harder to detect in these larger objects.
As a result, we’ve introduced a new term for this novel mode of existence: “superposition.” It essentially serves as a placeholder for our inability to comprehend precisely what’s happening. The usage of this term goes as follows: an initially white electron inside this apparatus, with the walls removed, is neither hard, nor soft, nor both, nor neither. Instead, it exists in a superposition of being hard and of being soft. This challenges our ability to meaningfully attribute a specific color or hardness to the electron. It’s not due to the quality of our apparatus or our lack of knowledge; it is much deeper. Having a definite color means, not having a definite hardness; rather, it signifies being in a superposition of being hard and being soft.
Every electron ultimately emerges from a hardness box as either hard or soft. However, not every electron is exclusively hard or soft; it can also exist in a superposition of being hard and being soft. The probability of measuring it as hard or soft depends precisely on the specific superposition it is in.
To construct a more refined definition of superposition beyond a mere acknowledgment of our lack of understanding, we must turn to a new language: Quantum Mechanics. Our task, to study quantum mechanics, is to develop a deeper understanding of the concept of superposition. If this concept challenges your intuition, it should come as no surprise. We humans are not naturally equipped to grasp the intricacies of quantum effects. Our daily interactions primarily involve macroscopic objects with such substantial energies that quantum effects are practically negligible. However, when we venture into the realm of small objects and low energies, our intuition often proves inadequate.
It’s not that electrons themselves are strange; they behave in accordance with their nature. What’s truly astonishing is that when we collectively observe a multitude of electrons, they exhibit behavior that defies our common experiences. Our goal is to push beyond our everyday encounters and develop a deeper intuition regarding the phenomenon of superposition.
