Quibbles and Bits

Quantum Theory

Quantum Theory troubles many people, even some of those who actually understand it. That would include such luminaries as one of its founders, Albert Einstein, who expressed serious concerns with what he saw as some of Quantum Theory’s fundamentally counter-intuitive precepts. This from a man who saw nothing counter-intuitive at all in General Relativity!

At its core, Quantum Theory is concerned with how the universe looks when you focus down to extremely small dimensions. What if we magnified a single atom to the size of the solar system – would there be anything to see if we looked that closely? How about if we magnified it to be the size of the entire observable universe – would things appear any differently at that scale? Viewed solely as philosophical imponderables, these are intriguing enough issues. But classical physics really does start to run out of ideas once dimensions get small enough – and many of its fundamental precepts no longer seem to hold up to a close examination. And there are plenty of experiments out there which insist on delivering perplexing results.

The first clear view that all may not be quite as it seems came with the realization that very small particles – such as electrons – can be observed to behave as either waves or particles. Particles occupy a specific point in space, and interact with each other by colliding. Waves are distributed across space, and interact by interfering with each other. The two behaviors would appear to be fundamentally exclusive. Yet if we conduct certain experiments with electrons, we find that there are times when they behave exactly as waves would – including interfering with each other. And there are other times when they behave exactly as particles would. This phenomenon has become known as wave-particle duality.

Attempting to reconcile wave-particle duality has taken physics in unexpected new directions, and has resulted in a number of concepts that not only lay people, but also physicists themselves, often find troubling and difficult to understand. It is fair to say that as our understanding deepens, so does the depth, breadth, and complexity of these many apparent paradoxes. The branch of physics that studies – and seeks to explain – these phenomena is known as Quantum Mechanics. It is a measure of the success of Quantum Mechanics that a detailed understanding of it is necessary to explain a growing number of well-established physical phenomena. For example, in the field of semiconductor lasers (devices that are used to power high-bandwidth fiber-optic communications links), microscopic structures known as quantum wells are fundamental to almost all of the designs. And quantum dots can deliver yet further advances in performance.

Quantum Mechanics says that everything is described by wave functions. For a single particle (such as an electron) in isolation, the wave function is a simple oscillating wave. The physical interpretation of this wave is that it represents the probability that the particle can be located in a specific place at a specific instant in time. That can be a troubling enough concept on its own, since the wave function extends over all space and all time. But when you go on to consider the situation where the particle is no longer in isolation, the complexity of the wave function concept can rapidly spiral out of control, because in those situations the wave function becomes a superposition of the individual wave functions of all the separate components that comprise the overall system.

This is both a good thing and a bad thing. It is a bad thing because even the simplest superpositions of wave functions can complicate the mathematics to an intractable degree. But it is also a good thing because the more wave functions you superpose on top of each other, the more likely they are to end up canceling each other out. For example, the complex wave functions describing all of the component particles which together make up a golf ball sitting on your coffee table, will tend to cancel each other out in all places other than on your coffee table. So although the wave function for the golf ball extends over all space and all time, the possibility of actually observing it anywhere other than on your coffee table, at the present time, will work out to be vanishingly small.

One of the aspects of Quantum Mechanics that many lay people have heard about is quantum tunneling. This says, in effect, that when you bounce a tennis ball off a brick wall, if you make the wall thin enough then occasionally the ball won’t bounce off it, but will magically pass through it and re-appear on the other side. Now, in the specific case of a tennis ball and a brick wall, the required thickness of the brick wall for us to actually observe this effect would be many trillions of times thinner than the thickness of an atom. So quantum tunneling doesn’t impact these sorts of aspects of our daily lives. But if instead we consider an electron, and a barrier formed by an arrangement of atoms within a solid crystal, then we can readily observe the electron tunneling through the barrier, provided the barrier is thin enough. Not only can we observe this, but we can also exploit it to make classes of electronic devices with properties that would otherwise be denied to us…flash memory is a common everyday example.

Quantum Mechanics leads physicists along a number of bizarre paths which remain far from being thoroughly mapped out. For example, there are solid theories which postulate that there is a smallest distance which can possibly exist. It is a thing called the Planck Length, and the suggestion is that space itself is constructed of discrete chunks whose dimension is the Planck Length. Furthermore, it also suggests that like space, time also comes in discrete chunks called the Planck Time. The models further suggest that the universe comprises regions of space and time, of the scale of the Planck Length and the Planck Time, which are constantly popping into and out of existence like some sort of roiling quantum foam. As yet, there are no practical implications which arise from these theories.

One of the most intriguing examples of a thoroughly bizarre property of Quantum Mechanics being used in a practical real-world system to solve a real-world problem is Quantum Cryptography. A fundamental problem with Cryptography is that you cannot tell whether someone is intercepting a private signal sent from A to B. Quantum Cryptography solves this problem through another of these strange manifestations called entanglement. Entanglement has no analogy whatsoever in classical physics. Perhaps the best way to describe entanglement is to think of it as a telepathic link between a pair of almost identical particles, in this case photons. The entangled photons can be in completely different locations, but if somebody does something to one of these photons a corresponding reaction will be instantaneously experienced by the other. Quantum Cryptography exploits this phenomenon in such a way that if a third party observes one of these photons, both the sender and the receiver will instantaneously know that this has happened. This prevents someone from eavesdropping without either sender or receiver knowing. In some implementations it also has the effect of rendering the information itself invalid. Quantum Cryptography is already in commercial use today.

Another area in which Quantum Mechanics is poised to make a dramatic impact is in Quantum Computing. In this class of device, ordinary binary bits are replaced with quantum bits, or qubits. A qubit consists of a particle which is in a superposition of two quantum states. Compared to a conventional computer bit, which can only represent one of two numbers at a time, a qubit is effectively in both of its superposed quantum states at the same time. Taking this further, four binary bits can represent one of 16 different numbers while four qubits can be in 16 different superposed states simultaneously. This scales up exponentially, so that 64 binary bits can only represent one of 18 billion billion different numbers at any one time, whereas 64 qubits can be in 18 billion billion different superposed states all at the same time. Quantum computers have the potential to operate at staggeringly fast speeds compared to even the fastest of today’s computers, which has enormous implications in many, many disciplines. Already, the taxi service in Tokyo uses a commercial quantum computer to schedule and route taxis city-wide. Intel has commenced testing a silicon-based qubit processor produced in their D1D fab. And IBM is showing their prototype Quantum Computer at this year’s CES. So this particular future might not be as far off as you might think.

Quantum Mechanics continues to open doors to unexpected avenues of exploration, the implications of which can stagger the mind. Roger Penrose is one of the most feted and decorated physicists alive today. He is described primarily as a mathematical physicist, and his thinking can be truly said to bridge the worlds of physics, mathematics, and philosophy. Penrose has proposed a theory he calls Quantum Gravity, which attempts to bridge classical and quantum physics. And he famously used the incompleteness theorem of Gödel (which basically postulates that some things can be true but are also fundamentally unprovable) to propose that human consciousness cannot be a phenomenon of classical physics, and therefore has to be a quantum process. It’s not immediately clear where you might be able to go with such a notion.

But then along came Professor Stuart Hameroff of the University of Arizona, an anesthesiologist who studies the physical basis of consciousness. His research led him to propose – controversially, it must be said – that consciousness arises from quantum states in certain neural microtubules within the brain. This got the attention of Roger Penrose, and together they developed a theory called Orchestrated Objective Reduction (known as Orch-OR), which makes use of Penrose’s theory of quantum gravity. Essentially, Orch-OR proposes that consciousness is the manifestation of processing carried out by qubits formed from superposed resonance rings within neural microtubules. And unconsciousness occurs when the superposed quantum states collapse to a classical state (i.e. no superposition) due to chemical changes in the microtubules. [That is probably the least comprehensible paragraph anyone has ever written for Copper.]

So the fact that I can write this – and that you can read it – is possibly a manifestation of Quantum Mechanical effects. How meta can you get!