THE QUANTUM WORLD AND THE HUMAN EXPERIENCE
At the start of the twentieth century, a group of ingenious physicists started to discover a new type of reality that did not exist according to the classical laws of physics. At a time when the Lord Kelvins of the world were saying “There is nothing new to be discovered in physics now. All that remains is more and more precise measurement." This band of misfits put forth an idea that not only raised new questions about the nature of reality but also the question of what constitutes a measurement in physics, and what happens after we measure something, in particular on the subatomic level.
The significance of quantum mechanics is not the mathematics, which is based on statistical methods of averages and basic tools of calculus like integration (which we will see in equation 1.3), it rather the ideas of Quantum Philosophy which deal with the problem of interpreting quantum mechanics and the results of the experiments that give rise to the theory.
The question that arises from studying Quantum Philosophy is: what happens when the human mind is challenged with an idea that is so elegant yet makes no intuitive sense? In the case of quantum mechanics, the ideas about the wave function collapse, which we will investigate in this article, have brought about many different interpretations of the theory, which all yield the same result, yet have widely different physical realizations.
In an effort to frame the subatomic world within the world we live in, Quantum Philosophy has created an even greater deal of disconnect between theory and reality, which we will see in the form of the Many Worlds Theory. Although Quantum Philosophy mainly deals with the physics and metaphysics of quantum mechanics, it is also much more general than that and applies to any human endeavor. More importantly, it raises the question if humans should try to make sense of everything in the context of the human experience, or accept some things about the nature of their existence as variables that are outside the scope of their intuitive understanding. In short, is there a limit to human understanding?
THE EMERGENCE OF THE QUANTUM PARTICLE
In the year 1801, Thomas Young would for the first time showcase the principle of particle- wave duality, further reinforcing the probabilistic nature of quantum mechanics. In this groundbreaking experiment, Young created a simple apparatus consisting of an electron beam gun (to shoot electrons out of), an electron detector (which could be turned on or off), a screen with two narrow slits, and yet another screen behind to be able to see where the electrons hit. If I asked you the question, what would happen if we turned on the electron gun? You would probably answer, there would be two lumps showcased on the screen, depending on which slit the electrons go to. You would not be completely wrong, in fact Young would see this in his experiment, BUT only when he would turn off the electron detector.
So if the electron detector isn’t on we would see the “classical” outcome of the experiment, where the electrons behave like discrete units of mass, known as particles. But as soon as we turn that detector on, the electrons aren’t particles anymore, they behave as waves, passing through both slits at the same time, and interfering with each other, constructively and destructively (Figure 1.1).
This pattern as you can see has many interesting features about it, namely that the center of the pattern seems to be the most intense, and it falls off as it goes to the right and to the left. Many interesting physics come out of this experiment where we treat light/electrons not as discrete particles, but as waves. But we still ask why the detector changes the outcome of the whole experiment. The truth is that this question brings up many other questions that philosophers of physics have pondered on for many years, but for now, we can answer it by saying that the particle takes a definite state.
The term we use for what happens after we observe the particle is called wave function collapse. Now we will get into what a wave function is later, but essentially, the particle is in a superposition of multiple states, with each state having a different probability of being observed, and as soon as we “look” at the particle, we force it to take on a definite state of being with that state’s corresponding probability. This is the realization of the famous statement often seen in popular physics articles about the particle being in multiple states at once. If you think this is illogical, you are right. Nothing can be in multiple states at the same time, but it can be in a mixture of those states at the same time, to showcase this more intuitively let me make a real-life statement.
The person at the crossroads (Figure 1.2) has five possible decisions to make as to where to go next. As of right now, he is in a state of indecision, and his future being is in a superposition of five different scenarios with different probabilities of realizing themselves. If we tell this person to make a decision, he will do that by picking one of the five possible outcomes, and not some OTHER outcome.
Now in the case of a particle, the realization of the particle into a single state happens because the particle is described as a linear combination of multiple state as such:
Where Ψ1(x,t) and Ψ2(x,t) are both states of the wave function with probabilities of |a²| and |b²| respectively. As soon as we observe the particle, the particle takes the state Ψ1(x,t) OR Ψ2(x,t), NOT both at the same time.
That’s it, this is the probabilistic nature of quantum mechanics, and it has started the field of Quantum Philosophy which deals with how one will interpret its realization into one state, i.e the collapse. But all this physics is dictated by a single equation called the Schrodinger's Equation, which takes the following form:
This was first postulated by Erwin Schrodinger in 1887, and has survived the test of time and experiments many times. It is THE equation that describes everything you can possibly know about a system. To stay more general in our discussion, let us skip the mathematics and tell you how the equation is utilized. Given some potential V(x,t), we are able to solve Schrodinger’s Equation for the wave function Ψ. Note that the above equation is called the wave function equation, but it is not really a wave equation as it has a second-order spatial derivative instead of the first order (∂²ψ/∂x²).
This is very confusing, because from our understanding a particle is a real thing, and when we talk about waves, we usually talk about them in the context of sound waves, seismic waves, string vibrations etc. In all these cases, there is usually something happening, for example tectonic plates shifting and resulting in a propagation throughout a medium. Examples are tectonic plates shifting and causing a propagation through the earth causing earthquakes, or vocal cords vibrating the air molecules. Well if waves are thought of as the result of physical things causing propagation through the medium, how can a particle be considered as a wave? And in that same context, how can a particle be considered a particle if it doesn’t follow the classical definition of a particle?
It turns out that the reason that we can think of a particle as a wave is simply because we can model it as such. The really unsatisfactory result is (even to physicists) that the wave function is not real. It does not exist in real life and has no intuitive physical realization, such as a pebble in the water creating propagation. We model the subatomic world like this because we know some properties about them, namely that they exhibit wave-like and particle behavior, but they are neither. So Wave Function Ψ ≠ a classical wave, and Ψ ≠ particle but exhibits both wave-like and particle-like behavior.
In any case, Schrodinger’s Equation is very useful, because after solving the wave function for one single case of a potential, we are able to measure many things about the wave function. We call the things we measure observables such as position, momentum, energy, spin etc. But since we already know that we can’t just measure the wave function without collapsing it into a definite state, these observables are made known by creating infinitely many identical systems with the same potential V(x,t), then measuring it multiple times, collecting the data on what state the particle takes, and averaging them. We call this the expectation value, and it is governed by another simple equation:
Here, the integral ∫ can be thought of as a sum over all possible outcomes, and f(x) is the observable that we are trying to measure, such as position x, or energy E. The Ψ(x) is the wave function we solved for. The reason for this very simple overview of these equations is to further show that the wave function is not a wave or a particle, and the properties of the wave function, such as position, can not be observed in the same way you observe the position of a car, and we must turn to statistical methods to do so.
THE PHILOSOPHICAL INTERPRETATION OF THE COLLAPSE
It is interesting to see that this concept of probability has created such confusion in the general public about quantum mechanics. I don’t think that the theory itself is easy to understand, but it is a lot easier to understand than a lot of other theories that the public engaged with such as String Theory. This lack of understanding is multifaceted and can be attributed partly to the ineffectiveness of popular scientists, but it is also partly due to the human brain not being able to think in terms of probability and statistical ensembles, making such arguments very difficult to internalize in our world.
As you might’ve noticed, throughout the discussion of quantum mechanics and the theory’s elegant probabilistic nature, we did not talk about what happens between the wave function collapse. This is because we looked at quantum theory within the framework of a specific interpretation called the Copenhagen Interpretation. This interpretation tells us that we have a particle that is in a mixture of states, and upon observing it we force the particle to take a definite state, but we don’t care or should care about where the particle was right before measuring it.
This is called the measurement problem, and according to Nicholas Ormrod of the University of Oxford. “One major aspect of the measurement problem is this idea … that observed events are not absolute.” [1], and as we already saw, the measurements are averages that follow Equation 1.3.
Truth is, there are many different interpretations put forth by different philosophers at different periods. A very popular interpretation that seeks to tackle the quantum measurement problem is the Many Worlds Theory revised and popularized by Hugh Everett III,
“Every quantum transition taking place in every star, in every galaxy, in every remote corner of the universe is splitting our local world on Earth into myriad copies of itself.”[2]
To simplify this broad and at first-hand nonsensical statement, the reason that our world exists in this way is because observers are ourselves wavefunctions that get entangled with other wave functions around us and force the world/wave-function to collapse to a single definite state. To explain this concept, let’s look at the graphical representation of the Many Worlds Theory in Figure 1.3, where every time Bruce makes an observation, his world splits into two copies of itself (it need not be two, it has to correspond to how many mixed states the observed system has).
The Bruce that is marked with blue has a well-defined past in time, as he can trace back to the diagram and see the Bruce that made the observation that got him here. But Bruce does not have a well-defined future as he will be split into many different Bruces, and he is unaware of any other Bruces that exist at the same time, in a different world.
In this light, the wave function doesn’t really collapse but Bruce is entangled with the wave function and is only able to see the reality that the wave function has decided to take and we simply don’t care about any of the other realities that the wave function could take because he can’t interact with the “parallel world” where Bruce might’ve observed something else. In short, we have simply rephrased the quantum measurement problem to get rid of the ambiguity of its probabilistic nature.
The Quantum Philosophy of the Many Worlds Theory gets rid of the problem of wave function collapse but introduces new ones, mainly the existence of parallel worlds. So who is to say if it is even a correct interpretation, and even if it is, who cares, as we can never really know if it IS the solution by the nature of the solution itself (not being able to detect parallel worlds).
Instead, the interpretation that I adhere to is one of my own, and it is simply the acknowledgment that none of this makes sense because it is not supposed to make sense. Quantum mechanics is inherently a mathematical model, the Schrodinger Equation (Equation 1.2) is not derived from some other physical theory but it is postulated. The wave function isn’t a physical object but a mathematical interpretation of properties of the subatomic world. When learning about quantum mechanics, we should take its axioms as they are without trying to make sense of them. We already do this in classical physics, it’s just that classical physics makes more intuitive sense to us so we never stop to think about it. The hard pill to swallow is that physics is totally and completely led by mathematics, and mathematics tells you some things about the physical systems, and in the case of the subatomic, these descriptions make no sense.
Simple as that.
Quantum Philosophy tries to frame the subatomic world into our reality by introducing more complexion into quantum mechanics. All this is because the human brain finds it impossible that the world does not work in a stern definite way, but its fate is decided by a random realization of the possibilities of the world. Opposing the great Einstein, I say that God does place dice, and He loves to keep us in the dark.
Without a doubt, the human mind is limited. It is scared that it is limited, so instead of accepting that fact, it creates fairy tales to make itself feel in control. Quantum Philosophy has become that very fairy tale in the world of physics and quantum mechanics, but this fairy tale goes back to the times of Aristotle and Plato and their metaphysical writings on the free will of humans. It is okay to create these fairy tales in our minds, but it is more important to focus on what we can understand and what we can do instead. As my wonderful professor, Scott Macdonald once said, “Shut up and calculate”.
“Whereof one cannot speak, thereof one must be silent,”.
-Ludwig Wittgenstein
[1] Ananthaswamy, Anil. “Quantum Theory’s ‘measurement Problem’ May Be a Poison Pill for Objective Reality.” Scientific American, 20 Feb. 2024, www.scientificamerican.com/article/quantum-theorys-measurement-problem-may-be-a-poison-pill-for-objective-reality/.
[2]The MIT Press Reader. “The Many-Worlds Theory, Explained.” The MIT Press Reader, 15 Apr. 2021, thereader.mitpress.mit.edu/the-many-worlds-theory/.
