An overview of the quantum realm — Quantum Superposition
This time, we have our member Krothappalli Preetam Sai to write on the nature of the quantum realm and discuss — in focus — the superposition principle.
“Our perception of regular-sized objects has impacted our intuition when it comes to the Quantum world. One of the unfathomable things about quantum mechanics is the end of determinism in the actual sense, which received a lot of criticism including that by Einstein — when he said that ‘God does not play dice’.
A lot of the features of a given system or a particle can be derived using merely the associated position and momentum. While classical mechanics facilitate these derivations, the uncertainty principle in the quantum mechanics refrains us from doing so, simultaneously. Further, while the description of a particle has point-like nature in classical mechanics, that in quantum mechanics is wavy, Ѱ. A localized “wavefunction”(fig 1) illustrates less uncertainty in the concerned domain, but also enforces a larger uncertainty in the complementary domain. Here, we see a localized one in the position domain. Correspondingly and also intuitively for the sake of pertaining to the uncertainty principle, that in the momentum domain will have a huge “variance”.
Although a significant proportion of the quantum theory was built using the wavefunction, it itself proved — on further research — to have no physical significance. While Schrodinger, who came up with his famous equation, interpreted Ѱ as the charge density of the electron, Max Born had a better interpretation, which got accepted soon in the community. He stated that the wavefunction times its complex conjugate propounds the probability of the particle to be found at those specific positions and momentums. One very peculiar feature of a “general wavefunction” is that it can exist in a superposition of different Ѱs with corresponding probability amplitudes (a,b).
’Ѱ = aѰ1 + bѰ2'
This means that the system exists in both the states simultaneously unless measured, after which, Ѱ collapses to either of Ѱ1 and Ѱ2 and ceases the superposition. In other words, the description of the particle that inscribes the possibility for it to lie in two position states collapses to either of the position — that we perceive inevitably.
Divyansh says that the “Schrodinger’s cat” is one celebrated thought experiment for illustrating the superposition principle. Being alive and dead are two possible states for the cat to be in. If the cat were to be a quantum entity, it would be dead and alive at the same time. If we were to consider being alive and dead as two properties of the cat and attribute it to a wave function of some kind, by taking the norm square of this wave function we can find the probability of finding the cat to be either dead or alive, but only on measurement, as long the cat is not observed it is both dead and alive at the same time.
These ideas give rise to a paradox called the ‘Quantum Zeno Paradox’. The Schrodinger’s (time dependant) equation is time dependant and the wave equation changes with time, but if you were to measure the particle the wave function collapses. If we were to measure a particle at a particular point in space and keep measuring it there, it arrests the time evolution and the particle stays there until one keeps measuring it. The frequent measurement of the particle arrests the time evolution of the particle.
Superposition is just one of the weird consequences of the quantum realm. It is weird only because we are not subjected to Quantum reality. The quantum reality is the fundamental nature of the universe and what we perceive in everyday situations is just an approximation of it.”
Preetam wishes to be a science communicator and we hope the best for him. Contact him here.