Quantum Superposition: A transition from determinacy of outcomes to indeterminacy, or a corollary to new ways of quantum concatenation?

After about over 100 years of dealing with quantum mechanical effects like wave-particle duality, the photoelectric effect, Compton’s scattering, pair production, superposition of quantum particles (electron, for instance) as observed in the double-slit experiment, etc., the contemporary physicists have come to take for granted what was once observed to be a mysterious behavior of natural processes – quantum mechanics. With confidence and bravado, many physicists and its affiliates can now confidently say there is nothing mysterious about quantum mechanics.

If you missed the first part of this newsletter, please read for continuity: https://www.dhirubhai.net/pulse/quantum-superposition-transition-from-determinacy-outcomes-wejeyan-havqc

“If you think you understand quantum mechanics, you don't understand quantum mechanics.” – Richard Feynmann

The statement of Richard Feynman, “…nobody understands quantum mechanics.”, is ridiculed to be an exaggeration, and as of now it seems “everybody understands quantum mechanics” is the order of the day. Did we all of a sudden became so smart and wiser? Were the pioneers of quantum mechanics amazed about the phenomena for no reason? Given that we are still unable to propose a unifying description of quantum interactions building up into classical observables and everyday understandable phenomena, has our presumption of the simplicity and regularity of quantum mechanics blinded us to some deep eternal truth about the phenomena?

In order to obtain a useful and executable understanding of quantum mechanical phenomena and processes, one has to accept completely the mysterious nature of the quantum: this mystery is not in itself, but in comparison with our regular classical understanding of the world around us. Our everyday intuition, thinking processes and consciousness is completely in tuned with classical mechanical phenomena: they are what we have to deal with and interact with every day – except for the extreme borders of relativistic speeds. Going down into the quantum worlds, our everyday understanding is thrown out of the windows, and we “experience”, so to speak, new laws that defies everything we have come to “understand” from our physical environment, and so we have to adapt to these new laws.

“No, no, you are not thinking; you are just being logical.” – Neils Bohr

It was with this dept of understanding, respect and acceptance of the unusual and mysterious nature of quantum phenomena that the pioneers of quantum mechanics were able to lay the theoretical foundations which we are building on today. And yes, as of now these quantum phenomena seem apparent after years of dealing with them, but that doesn’t make them any less mysterious than they have ever been, and would ever be. When we stop being logical and start thinking, these inherent mysteries of nature reveals themselves to us in shockingly beautiful ways.

“I object to the "Note that while the coin is still spinning in the air, the outcome is neither heads nor tail; rather it is in a state of superposition – alternating heads and tails at the same time." statement. – Patrick Van Esch

One big mistake is to try to use classical description to form the underlying foundations with which to delve into the description of quantum phenomena: this always leads to over simplification of these phenomena, which leads to further confusion. So, the spinning coin, from the previous part of this article, isn’t in a state of classical superposition – that was a mawkish analogy, strictly for the didactic purpose of simplifying the notion of superposition using a classical analogy.

“…But we did not have the faintest idea what the wavefunction ψ meant. It was a magical thing…What was this magical function?” – Isidor Isaac Rabi

For example, a classical particle is very much different from a quantum particle (maybe it shouldn’t be called a particle in the first place, as this is in itself a misnomer). A quantum particle, or better still, a quantum entity is not possible (easy) to visualize compared to classical particles which are easily localized in space and time; our knowledge about them, quantum entities, comes from indirect observations and experiments, and our most concise description of these quantum entities is that which is provided by the wave function – a magical function indeed, which combines both wave and particle properties in it.

During the early stages of the development of quantum mechanics, after Neils Bohr laid the first foundation of the description of an atom by combining and imposing classical analogies with his description of the atom, the description and terminologies he used got stuck with the physics community ever since. And this, I believe, forms one of the underlying reasons for the confusion experienced by fresh physics students about the mysteries of quantum mechanics – it creates a stubborn classical picture of everything quantum in the minds of students, and this can be dangerously misleading. So, forgive me if I try to clean up a few of the residues from Bohr’s old quantum foundations in order to properly describe and define the potentials and possibilities inherent within the phenomena of quantum superposition.

“The theory (quantum theory) produces a good deal but hardly brings us closer to the secret of the Old One. I am at all events convinced that He (God) does not play dice.” – Albert Einstein.

Thanks to the Heisenberg’s uncertainty principle (which for the record seems classically ad hoc tailored for quantum mechanical interpretation – still a philosophical debate), there is an inherent limitation to our ability to precisely localized a quantum entity (particle) in space and time, just like we are able to do with classical particles. In other words, we cannot tell with certainty and precision exactly what a quantum entity is doing (its energy, and for how long), or where it is located (its position and momentum) in space and time; the best description we have comes in the form of probabilistic inequalities (the worst kind) – this is the foundation of quantum indeterminacy.

The simplest example of this behavior is described by the single electron of a hydrogen atom. Illustratively speaking, if the hydrogen atom can be described as localized at a particular point in space and time, and has a very massive (in comparison with the negative electron) positively charged proton at the center of the atom, then, on the other hand, its single electron is … well, we don’t know exactly where it is or what it’s doing, but we are certain it has one. Still speaking illustratively, if we map the position of the electron for every time we observe it, the next time we try to observe it again its position changes. If we do a dot mapping for a large enough number of times, and place the result of our mapping instantaneously, we find that the mapping of the electron forms a sort of dotted cloud (probability density) around the proton that can be (classically) identified.

“Stop telling God what to do with his dice” – Neils Bohr

Note that it is the cloud that can be localized, and each of the dots that makes up the cloud was the position of the electron in a past instance of measurement. Classically thinking, we are concerned about, and ask ourselves, where exactly is this electron, and how does it move around? Note that because of the result of each of our mapping (measurement by observation), we have come to think of the electron as a particle: because it expresses itself with discrete unit of energy (E = hf) each time – but it is not. It is a quantum entity that can be observed, and its position can be measured with certain a probability to be at any point within our cloud mapping at any instant in time, and this entity has both wave and particle properties at the same time. This is its natural behavior, and it is what we have come to refer to as quantum superposition. And, the mathematical function with which we describe this position/probability density cloud is called the wave function (psi).

The above illustration uses the simplest case (the hydrogen atom) to describe the superposition of an electron: but note that every quantum entity behaves in this manner, and when there are more than one quantum entity occupying the same probability cloud, they form strange and unusual patterns. Furthermore, when you try to observe the behavior and properties of these pattern, for instance, by applying a field (magnetic, electric or electromagnetic) to it, the originally strange and unusual pattern becomes more interesting and complicated. Eventually, when you find yourself trying to pin point the behavior of each quantum entity within these interesting and complicated patterns, then congratulations, you are actually doing quantum mechanics; but this doesn’t mean you “understand it”.

“Every great and deep difficulty bears in itself its own solution. It forces us to change our thinking in order to find it.” – Neils Bohr.

Understanding the logic of the supposition of a quantum entity is the first step used to design the basic unit of information used in quantum computation. The electron of a hydrogen atom can be in any of the infinite points within the probability cloud at any instance. And, although its location is uncertain at that instance, if we actually do pause everything and observe it, we would certainly find it somewhere within the cloud: this implies that the overall probability of finding the electron within the cloud is 1 (certain). Aha! That is one thing we can be certain about in the midst of uncertainties and indeterminacies. With that in mind, note that the qubit is in a superposition state of either |0> or |1>; but unlike the electron which have an infinite probability point within the density cloud, the qubit would either collapse into a 1 or a 0 point: which are conveniently the basic units of classical/Boolean information.

Unlike with the electron of the hydrogen atom, the qubit simplifies our problems to just two options – 0 or 1. But if we have a register of five (5) digit qubit (say, |10110>) in superposition, the possible options at any instance in time would be 2^5 (32). Note that things get pretty complicated pretty fast when the number of digits that forms a register is increased. If n is the number of digit qubit in superposition, then the possible option at any instance would be 2^n. Now imagine n to be infinite, like with the electron of the simplest of natural quantum superposition phenomena - the hydrogen atom. We would have to look to Ramanujan's works on infinities to make quantum computational sense of such possibilities. There are no classical analogies for this behavior, so get ready for an entirely new experience – quantum computation.

To be continued…

Please share your thoughts or some classical analogies of this entire new experience, as although they might be inaccurate, they do help with a clearer mental picture.?

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