Quantum Technology is coming: An introduction to Quantum Field theory and Technology

After Max Planck in 1900 solved the ultraviolet catastrophe (where he had to sort of invent a mathematical formula to fix a long standing problem) and used the “invented fix” to explain basic unit of energy called quanta, a new world of exploration was discovered where the Newtonian laws of physics (our physical perception of reality) is called into questions. Studies of this new world eventually gave birth to quantum mechanics, and Quantum Field Theory (QFT) as a whole. Whenever a physicist slams the word “quantum” behind any phenomenon, process or idea, what they are actually trying to say ultimately is that they know what they are talking about, but are not sure of the possible outcomes.

Contradictory! I know, right? How can they not be sure of the outcome and yet they claim that they know? This is evidently a ruse: a charade to hide their shame and embarrassment for not being able to understand and accurately describe and predict the behavior of this new “quantum world” we have discovered for over 124 years and counting. Yes, you are correct.

Over the years, physicist has acted out this charade so gracefully that when you hear of phenomenon like quantum computations, quantum de-coherence, quantum entanglement, quantum touring machine, quantum electrodynamics, quantum chromo-dynamics, and whatever else we decide to slam with the word “quantum”, you take a bow and let us speak. Then you listen to us discuss and explain using elaborated graphs and complicated equations how much we do not know about the phenomenon. It is brutal and remarkable, but yet acceptable and gaining a lot of attention and money as quantum tech seems to be the future. But when we say “quantum” what do we mean?

Everything in the universe is governed by forces, and understanding how these forces interacts with what we already know and can observe has given us control over our environment and natural process. Of the four forces that governs the universe, gravity is the most familiar; but yet the most elusive. Understanding the forces of gravity and its interaction with physical matter makes up all of Newtonian mechanics. With this we send rocket to space, keep satellites in orbits, fly around the earth on planes, and designed Inter Continental Ballistic Missiles (ICBMs) that can wipe out the world if someone chose to push the button. We have accomplished great strides indeed; but one lingering questions is, what is everything we regard as real made of?

This question has been asked by great minds for as long as historical records can show, but at the moment we have come to understand that at the smallest level possible, all things are made by fluctuation of fields and energy. This theory proposes that this field permeates throughout all of space, and its energy and interactions gives birth to subatomic particles such as electrons, quarks, protons, neutrinos, Boson, etc. These particles are unimaginably small and tiny and how they interact with each other, space and time is what is called quantum mechanics. “Quantum” given that they possess basic integer unit of energy called quanta. It is the environment where these particles play around we call the quantum world.

Simple, I suppose. Then why all the fuss about quantum this and quantum that? To use an analogy to compare the Newtonian world and the quantum world, let’s think of a coin as a particle. In the Newtonian world, if you flip a coin up in the air it would undergo the trajectory of gravitational pull, spin for a while in the air, and land with either heads or tail. This is what is called a predefined outcome. No matter who flips the coin, when it is flipped, where it is flipped, the outcome is almost predefined; like a straight line. But, in the quantum world, things are a little more interesting.

In the quantum world, if you flip a coin (observe and try to direct a quantum particle’s motion) there are almost infinite possibilities and outcomes. The coin could undergo a trajectory similar to what is expected of the Newtonian world (but this is unlikely), or it could disappear altogether, or disintegrate into a wave and/or another particle. Flipping the said coin can cause other coins which were comfortable with the coin’s original position (entanglement) to flip themselves in the skies as well, and in an uncontrolled environment, the outcome is total chaos.

Still, within this chaotic behavior of the quantum world, there is that which we know. When we physicist say we “know”, what do we mean? That is a question for another day, but at this point I would simply say that when we say we know, that means that we have devised some mathematical relations about some phenomena that are fairly consistent with experienced reality. Take note of some special words used here (italicized) as they are the only logic behind the reason why we can claim that we “know” so much about the quantum world, and yet cannot understand and predict its behavior. On the contrary, when mathematicians say they “know”, well they mean something slightly different: in their definition of “knowing” you would find words like foundations, mathematical-rigor, consistency, pedantry etc.

And yes, physicists and mathematicians, we are all together fighting a losing battle side by side against the complexity of the quantum world in an attempt to simplify it to our apparent understanding; and yet the mathematicians accuses us of not having mathematical-rigor/pedantry for the foundations of Quantum Field Theory (QFT). In other words, QFT lack a formal mathematical foundation. To understand what this means I would have to do my best to breakdown and ironically speaking, simplify QFT into parts, and maybe try to put them back together; it has taken us 100+ years to get this far, so forgive me if my attempt at squeezing all the details into one paragraph is a little untidy.

QFT can be differentiated into two broad categories; on one side we have algebraic quantum field theory (AQFT)/perturbative quantum field theory (pQFT), and on the other side functorial quantum field theory (FQFT)/non-perturbative quantum field theory. To filter out all the complications of the difference between these categories, AQFT tries to reduce quantum observable effects into infinitesimally discrete unite (in other words, we try to count these quantities, no matter how unimaginably small they are) giving us a mathematical handle to deal with them algebraically; on the other hand, FQFT is bordered by a “no-go” theorem that says that quantum observable quantities are continuous and cannot be broken into bits and pieces (discretized) but has to be taken and understood as a whole, like the Hilbert’s space. Please forgive me if we look further into Hilbert’s space some other time.

From the foundations of our understanding of the world around us, the earliest conscious human minds has used counting as a means of understanding physical phenomena and processes, and with FQFT we cannot count? How is that even possible? Understandably, AQFT has provided us with lots of theorems that has been corroborated by lots of experimental evidence, and the other side (FQFT) has made strong logically plausible and reasonable arguments that seem to check out with the big picture of things. So what is the mathematician talking about mathematical rigor and pedantry? They mean that there is no single mathematical structure that can unite the postulations of AQFT and FQFT into a consistent mathematical framework from a set-theoretical foundation.

What does all of this imply for technology? It means quantum technology is coming, yes; but there are still lots of work to be done to bring this technology with its limitless capabilities into the hands and control of the human race. One of the ways to simulate things on a computer is to first discretize its components into parts, and in doing so we can store/record and manipulate observables in the form of 0s and 1s – the bit. After AQFT has been given the ability to discretize quantum observable, another problem arises; instead of just 0s and 1s, there is another state that is neither 0s nor 1s, but in an undecided state between both. This is called a qubit (short for quantum-bit).

This qubit can collapse into either a 0 or 1 depending on our ability to control the environmental factors around the observable: they are quite difficult to predict, more so to control. For this reason all quantum computing devices are operated in near-zero temperatures in order to control the environment. We also had to invent/design a quantum Touring Machine to help simulate the possible outcomes; still it is quite difficult to put it all together.

If we decide to expand our knowledge of QFT towards cosmic scales we encounter phenomena like Dark matter, Dark energy, Black Hole, White Hole and singularities; all of these are terms we use often like we know what they are, but we actually only know how much we don’t know about them; and as we keep knowing, more obscurities arises. One thing we know and are sure about is that these phenomena, like every other thing in the universe, are made up of quantum fields as well, and their overall behavior could be summed up by QFT if we can only find the perfect fitting theory for them. That we know, and we are confident and sure about!

So quantum technology is coming: should you be worried? No. Concerned? Certainly! If and when we can find or are able to devise, in the words of mathematicians, a mathematical foundation rigorous and pedantic enough to unite all of QFT, we would have certainly a handle to manipulate and control the quantum world; it is at this point you should be concerned, maybe even worried. There has been lots of publications about the possible utilization of quantum technology; and while most of which is complete hokum, others are true and ultimately scary.

Please like, re-post and comment your thoughts, and I would be happy to respond.