This is What Makes Quantum Mechanics “Weird”
You have probably heard many times that quantum mechanics is very “weird,” it definitely breaks with classical understandings of the natural world. Why is that? Here, I am going to give you the briefest rundown possible of why quantum mechanics breaks with our intuitions that even a Laymen with no background should be able grasp fairly easily.
The heart of quantum mechanics is arguably the principle of complementarity. The principle of complementarity states very simply that certain observables (properties of particles that can be observed) exist in complementarity pairs whereby if you measure one property in that complementary pair, you lose knowledge on the other property.
One of the most well-known examples of this are the property of position and momentum. Think of these like where a particle is as opposed to where it is going. These variables are complementary with one another, and thus if you measure one, you lose knowledge about the other. If you know where it is, you cannot know where it is going. If you know where it is going, you no longer know where it is.
This principle, thus, in a sense, restricts the “questions” we can “ask” about the natural world. We can probe the natural world to “ask” the properties of particles such as position and momentum, but we cannot “ask” for these properties simultaneously. Only one can be known at a given time, which goes against our intuitions in classical physics that all properties can be in principle known simultaneously.
Within the scope of classical physics, all characteristic properties of a given object can in principle be ascertained by a single experimental arrangement, although in practice various arrangements are often convenient for the study of different aspects of the phenomena. In fact, data obtained in such a way simply supplement each other and can be combined into a consistent picture of the behaviour of the object under investigation. In quantum physics, however, evidence about atomic objects obtained by different experimental arrangements exhibits a novel kind of complementary relationship. Indeed, it must be recognized that such evidence which appears contradictory when combination into a single picture is attempted, exhausts all conceivable knowledge about the object. Far from restricting our efforts to put questions to nature in the form of experiments, the notion of complementarity simply characterizes the answers we can receive by such inquiry, whenever the interaction between the measuring instruments and the objects forms an integral part of the phenomena.
— Niels Bohr, “Atomic Physics and Human Knowledge”
Why is it that, if we know one of these properties, we cease to know the other? One possibility is that when we measure the position, the particle simply ceases to have a momentum at all. The same is also true in the reverse, if we measure the particle’s position, it cases to have a momentum. If this view is correct, then particles simply do not have well-defined properties at all times, so they in a sense have no history. If a particle is detected at point A and later shows up at point B, it would not necessarily have a position in between point A and B, and so there is no history connecting the two points together, i.e. there are gaps.
If there are gaps in a particle’s history, then this inherently implies fundamental randomness as there would be nothing you could ever know explaining how the particle actually ended up at point B. These “gaps” imply a breakdown in causality and thus there can be no predetermined cause of the outcome of experiments if there genuinely are gaps.
We are so used to thinking that at every moment between the two observations the first particle must have been somewhere, it must have followed a path, whether we know it or not. And similarly the second particle must have come from somewhere, it must have been somewhere at the moment of our first observation…This habit of thought we must dismiss. We must not admit the possibility of continuous observation. Observations are to be regarded as discrete, disconnected events. Between them there are gaps which we cannot fill in…For in the times when this ideal of continuity of description was not doubted, the physicists had used it to formulate the principle of causality for the purposes of their science in a very clear and precise fashion…Obviously, if the ideal of continuous, ‘gap-less’, description breaks down, this precise formulation of the principle of causality breaks down.
— Erwin Schrodinger, “Nature and the Greeks and Science and Humanism”
Now, you might say, hold up, isn’t there a much simpler solution? Consider, for example, if the particle always has both a position and a momentum at the same time, but by measuring one of them, the observer effect perturbs the other state. For example, if the particle’s position is measured, it still has a momentum, the momentum just becomes perturbed by the very act of trying to measure the position, and thus it is only a practical limitation preventing us from knowing both simultaneously rather than one simply ceasing to exist.
To illustrate the difficulty of this position, we can take a look at the simplest experiment that demonstrates why quantum mechanics is indeed not easily reducible to classical mechanics: the Greenberger–Horne–Zeilinger experiment. This experiment begins with three entangled particles and each particle can be has one of two properties measured about them: here they will simply be referred to as property X and property Y. Since three are three particles, then there are a total of six properties which can be measured: X₁, X₂, X₃, Y₁, Y₂, and Y₃.
Each of these measurements are complementary with a third known measurement result, meaning the actual outcomes of these measurements are unknown, and thus in practice are random. However, let’s assume that the properties of three particles are only unknown because of practical limitations, of our ignorance. If that’s the case, it should be possible to assign values to all these observables simultaneously.
The GHZ experiment is in four parts. Each part simply sets up the same initial state of particles and measures a different set of these three properties. The properties are then assigned a value 1 or -1 based on the measurement result. For example, if it is measuring electron spin, then 1 could be assigned to spin-down and -1 can be assigned to spin-up. If it is measuring qubits, then 1 can be assigned to 0 and -1 to 1, so on and so forth. All you really need to know is that there are two possible outcomes to each individual measurement on a single observable and that they are represented by either 1 or -1.
The first three parts of the GHZ experiment conduct measurements on {X₁, Y₂, Y₃}, {Y₁, X₂, Y₃}, and {Y₁, Y₂, X₃} respectively. The results of the experiments are guaranteed to follow the three equations below. These are products (multiplication). You can run the experiment as many times as you want and it is guaranteed to always satisfy these three products.
X₁Y₂Y₃=-1
Y₁X₂Y₃=-1
Y₁Y₂X₃=-1
Now, let’s take these three equations and multiply them all together. If two terms are the same then they cancel out, for example, take Y₂Y₂. If Y₂=1 then the product of two 1s is also 1. If Y₂=-1 then the product of two -1s is also 1. Hence, we can multiply all three equations together and cancel out anything that repeats.
(X₁Y₂Y₃)(Y₁X₂Y₃)(Y₁Y₂X₃)=(-1)(-1)(-1)
X₁X₂X₃Y₁Y₁Y₂Y₂Y₃Y₃=-1
X₁X₂X₃=-1
Hence, we know for certain that, if these values all are predetermined, then if we conduct a fourth experiment where we setup the same entangled triplet of particles again and measure all their X properties, then X₁X₂X₃=-1. Recall that I said the GHZ experiment is in four parts, not three, so what is the fourth part? The fourth set of measurements and the results are shown below.
X₁X₂X₃=1
In other words, we run into a contradiction with experiment. In an actual experimental setup in the real world, you do not measure what you would expect if the properties of the system all existed simulatenously. Let me just show all four equations below again all at once so we can think about more deeply what this means.
X₁Y₂Y₃=-1
Y₁X₂Y₃=-1
Y₁Y₂X₃=-1
X₁X₂X₃=1
Mathematically, it is impossible for all these to be true simultaneously. So it is just impossible for all these values to be predetermined in a way where our measurement result is simply revealing the properties of the system already there. Although, recall that I said the naive solution proposes there is an observer effect. Could this allow us to escape that conclusion?
Recall that these are four separate experiments. Even though they have the same initial conditions, there do not happen at the same time. If the results are predetermined, then you have to posit that, in order to explain these inconsistencies in results, that these equations really do not hold simultaneously because there must be something different between the four sets of experiments.
There is only one thing known to change between the four experiments: the measurement settings. In the first three experiments, two particles are having their Y property measured and one is having their X property measured, while in the fourth experiment, all particles are having their X properties measured.
If, somehow, the choice of what we measure is perturbing the system in such a way that we have to factor in our measurement settings to predict the outcome, then at first it seems like the observer effect can save us here and we can restore determinism. If somehow each particle “knew” if it was the only particle having its X property measured or if the other two particles were also having their X properties measured, then the particles could change their behavior in a way that would explain this.
However, there is a major issue with this explanation: these are three separate particles, and thus it is possible in principle to separate them. You could pick three different places on earth, each separated by thousands of miles, and in that moment you could choose to measure the three particles all at once. If the particles could “know” what other particles were doing, then it would have to know to be able to somehow communicate with those particles over vast distances, and if you measured the particles quickly enough in a similar time frame, that communication speed would need to exceed that of light.
Hence, the observer effect explanation seems to lead to a violation of the laws of physics. Nothing can communicate faster than light. So, unless you want to claim the current laws of physics are wrong, you are forced to accept that particles in some instances can genuinely do not have properties until measured.
If systems behave randomly and unpredictably, then what is even the point of quantum mechanics? Well, it turns out there is a more continuous version of the principle of complementarity known as the uncertainty principle which states that the more precisely you know the value of an observable (i.e. the more “confined” it is) the less precisely you know its complementarity pair (i.e. the more “spread out” it is). This means that it is not simply a binary “yes” or “no” as to whether or not you know the property of a system, you can model continuously how your uncertainty changes over time.
Learning the values of certain observables, in a sense, interferes with your certainty of other complementary observables, and you know what else exhibits interference properties? Waves. It turns out that you can actually model how your uncertainty of the properties of systems change over time using an abstract “probability wave.” Hence, in quantum mechanics, while you cannot predict the results of all experiments with absolute certainty, you can model the change in your uncertainty over time through a wave equation known as the Schrodinger equation, and this allows you to then derive a probability distribution of what outcomes of an experiment you are likely or unlikely to see.
That is effectively all quantum mechanics is “about.” All the philosophical questions and various interpretations stem from this premise of trying to interpret the meaning behind particles having genuinely indefinite values under certain conditions as well as the meaning of these probability waves.
