Quantum Mechanics- First Impressions!

You know when you've heard about something being extremely mysterious, mind-boggling and makes people's world turn round, but you've never had the chance of getting introduced to it? That is what Quantum Mechanics was for me, until this January. I had read people say that if you do understand Quantum Mechanics, you don't know it well enough. Such a claim makes a curious mind anxious and excited at the same time. So, without anymore build up, let me tell you about my first impression of Quantum Mechanics after one month of study.

When one is introduced to QM, it does not take one much long to realize that QM is not a theory that illustrates human incompetency during experiments, but actually, one that sheds light on the 'spooky' way in which nature works at the smallest level, namely, the quantum level. What attracts some and repels others is the fact that initially, QM challenges intuition. But if you are exposed to it for long enough and in the right way, it redefines intuition and the way you see the world. Classically, we have been taught about discrete systems with definite states and properties. So, classical mechanics talks about certainty and some might stretch the laws to even talk about determinacy. Then comes QM which talks about probabilities and uncertainties. Not only that, the Heisenberg's uncertainty principle states that uncertainty is embedded in the working of the universe. In my opinion, this leap from classical to quantum in one's intuition is the difficult part when it comes to mastering QM. 

QM owes its success to its mathematical formulation. We can mathematically calculate the outcome of an experiment without even conducting it. And when we do end up conducting the experiment, the theoretical and the experimental outcomes are in complete agreement. Whenever this happens, it lightens up the day of a physicist. Knowing this, in my opinion, one needs to realize that the best way to understand QM is to approach it mathematically and master the mathematics that makes up the theory. Once you have accomplished that mighty task, you can begin with developing the intuition for QM such that the much talked about 'spooky' action now becomes 'expected'. 

At present, I am only in the beginning stages of exploring this vast field. I started by learning about vector spaces, Dirac notation including the ket and the bra spaces, operators and their eigenvectors and eigenvalues, and their action on kets resulting in quantum states. So, you see, I really haven't done much. But the much I have done makes me excited about what is going to come and what more can be done using QM. I am curious to know how the basic principles will give rise to mysterious concepts of quantum entanglement, etc. and how and where I will be able to use my knowledge in this field.

I read about Einstein's trouble with QM and justifiably so, given the fact that QM and General Relativity don't go hand-in-hand. This is a major problem in Physics, a problem I am already interested in. It does create a sense of zeal when trying to connect a theory that works at the largest scale to one that works at the smallest. This reminds me, I am also taking a course in Theory of Relativity this semester which aims to make me proficient in Special Relativity and its consequences, and also introduce me to the formulation and aspects of General Relativity. But, talking about that is a whole other post!