Most people, especially those who are not exactly related to physics find Quantum Mechanics an “out of this world” subject. Quantum Mechanics surely is a tough area of physics but people who are acquainted with physics will definitely agree that it is not more difficult that the other areas of physics. The mathematics of the “standard” Quantum Mechanics is in no way worse or even easier than perhaps electromagnetism or the laws of motion.

The way we feel something is tough or easy depends on how clearly we understand the points related to it and accordingly expand our knowledge. When students are taught new things, they are basically being helped to build upon their existing understanding. Most students do have a foundation of knowledge in different areas that can be used to give them more in-depth knowledge about those areas. For example, some basic knowledge of mathematics would come in very handy when students are being instructed on forces, motion, energy, and other related areas of physics that utilize some of the principles of mathematics. Once students have understood the basic concepts, they are then ready to move ahead into more complicated areas of the subject.

What this means is there is always a point of reference that can be considered a starting point or foundation on which new knowledge can be acquired. While this fact applies commonly to all subjects, it is not exactly so with Quantum Mechanics – exactly why non-physicists or laymen find it so tough. Most people understand only the basic tenets of physics which relates or boils down to classical mechanics.

## Physics and Quantum Mechanics

As a result, there is a complete disconnect between their understanding of physics and Quantum Mechanics. This is a totally new subject that can never be understood by using classical mechanics as a base. Even the most basic of physics terms like particle, wave, spin, energy, position, momentum, etc… acquire totally new meaning in Quantum Mechanics. Moreover there is only a fine line between the two and that too is not continuous. For example, how can we use the classical idea of a “spin” to explain a spin 1/2 particle in which one only regains the identical symmetry only upon two complete revolutions?

While the same words are used, the meanings are totally different. Under Quantum Mechanics, this spin produces a magnetic moment and has nothing to do with the classical spin concept. So it is just not possible to build an understanding of Quantum Mechanics using the classical concepts of physics.

Yet Quantum Mechanics carries almost the same mathematical formulations as classical physics. What this means is while the conceptual foundation of Quantum Mechanics is totally disconnected from traditional physics concepts, its mathematical formulation matches classical physics completely – as if there is just no discontinuity.

Effectively speaking, if you don’t really know the mathematical concepts of Quantum Mechanics, you can never truly understand the topic at all. It is the mathematical formalism that can save you from losing this subject totally. But since it is not possible for all people to be clear about the mathematical formulations part, it is not surprising that Quantum Physics is described as a form of mysticism.

Quantum Mechanics is truly defined and described by its mathematical formalism and the conceptual description is just secondary. This, however, does not mean that this subject is nothing more than “just mathematics”. Mathematics is inherent in Quantum Mechanics as in all of physics as a means to convey and clarify its ideas and principles. It is actually a form of communication, perhaps the only form of communication that can be considered accurate and unambiguous enough to describe our universe. A mathematical formulation isn’t “just math”.

The difficulty with Quantum Mechanics is you can’t subscribe to your existing understanding of physics and the universe to be able to fully grasp the various concepts of Quantum Mechanics. There is a severe discontinuity between the two and only through mathematical continuity of the description can you hope to find a smooth transition to build upon. Without this, Quantum Mechanics can never make sense.