The world of Quantum Mechanics is remarkably bizarre. Even though we and our daily life experiences are governed by classical physics, the things that make us up are not. As we probe deeper and deeper into this queer world, the things that unfold defy our intuitions on an unimaginable scale. In the world of Quantum Mechanics, on the fundamental level, there is no notion of any particle or any wave, or anything as such that you can come up with – everything is denoted by a wave function.
You can read the introductory article on Quantum Mechanics for a better understanding of the current article.
What is a Wave Function?
To understand a wave function, let’s understand quickly what a function is. If we can recollect from our memories, we studied function in our high school mathematics class. A function, in plain words, is a mathematical construct that takes some input and yields an output.
As a real-life example, consider a child throwing a ball in the playground. It will move out from his hands, be in the air for some time, and after covering some distance (depending upon how much strength was applied during the ball release), will fall upon the ground. Mathematically, it follows a curve of an upside-down parabola and is given by a function, f(x) = y = -ax^2+bx+c.
Just as the above function describes the behavior of a classic particle (the ball), a wavefunction describes the behavior of a quantum particle. So, a wave function is a mathematical description of a quantum particle that embodies the form of a wave. For the sake of simplicity, we can again go back to our childhood and take an example of a sine wave or a cosine wave.
Concept of Probability Amplitude
The standard notion of a wave function is given by the symbol psi (Ψ) and is called probability amplitude. Unlike the parabola function that describes the trajectory of the ball in the earlier case, the wavefunction doesn’t describe the quantum particle’s trajectory (let’s say an electron) but something else. Actually, a plain value of the wavefunction doesn’t infer much, it is actually the square of the wavefunction that has importance and is known by the term ‘probability density”. A probability density describes the likelihood of finding the electron in a given location.
Erwin Schrodinger came up with an equation, famously called the Schrodinger Equation, that is essentially a partial differential equation describing the dynamics of a quantum mechanical system. The solutions to this equation are the infinite probable things that the system can do.
If there are, let’s say, two solutions to the equation: “| Ψ1>” and “| Ψ2>”, then any sum of these two solutions with the arbitrary coefficients, such as “a| Ψ1> + b| Ψ2>” is also a solution. This is the concept behind a “superposition”. In essence, superpositions are systems that can be in multiple states at the same time until a measurement is made, and upon measurement, the superposition suddenly collapses into a single definite outcome.
Relevance of superposition
Building upon the above example, if we have two solutions to the Schrodinger equation that fairly resonates with realistic situations, then any superposition of them also fairly corresponds to a realistic situation. The notion of Schrodinger’s famous thought experiment stems from this viewpoint only – if the cat can be dead and the cat can be alive, then the cat can also be in a superposition of dead and alive (details of the experiment in the subsequent section).
Is superposition only applicable to quantum objects or to macroscopic things, such as humans as well?
It is quite difficult to ignore superpositions for larger objects as it is only a matter of amplification of the tiny ones to macroscopic size. This is precisely what Erwin Schrodinger tried to illustrate with a thought experiment in which one can imagine a cat placed in a box along with a vial of poison, a trigger mechanism, and a radioactive element.
If the radioactive element decays, the trigger breaks the vial of the poison, killing the cat in turn. But it is important to note that the radioactive decay follows the laws of quantum mechanics. Before the event any measurement is made, the nucleus of the radioactive element is both decayed and not decayed, and so, before anyone opens the box to measure what has actually happened to the cat, it is both dead and alive.
So, it is worth mentioning that quantum superposition holds true for a system before any measurement is made, i.e., it is observed. Once it is observed, the wave function collapses into a single state – this concept is one of the fundamental principles of quantum mechanics.
For macroscopic things like humans, it is however unlikely to be in a superposition of states as the wavefunction would be extremely complex, describing the properties of an infinitely large number of atoms. Also, macroscopic things are constantly interacting with their environment, which would cause the wave function to collapse into a single state pretty quickly.
The Many Worlds Interpretation
Quantum superposition is engraved into the fabric of reality. According to an idea, the universe can be described by a wave function, just like a quantum system. The wave function of the universe could possibly be a linear/non-linear combination of multiple states, each corresponding to a different configuration of the universe.
According to the “Many Worlds” interpretation of Quantum Mechanics, each possible measurement outcome happens in a separate universe or a parallel universe. So, there is a universe in which the cat survives and a separate universe where it dies. But this interpretation is highly speculative as there hasn’t been any experimental verification of the same.
End Note
Quantum superposition can have significant implications for the field of quantum computing and thus can have far-reaching impacts on fields such as medicine, research, and artificial intelligence. While superposition has been experimentally verified in many quantum systems, its effect on macroscopic objects is yet to be observed. If such an observation is made, it would undoubtedly be climacteric for the civilization, not only the humans but for the universe too.
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