## 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!

Beautiful summary of the weirdness of quantum mechanics, Richard, sometimes called the most highly confirmed theory in the history of science, as your practical examples exhibit. I personally don’t think the the wave-particle duality is in itself the hardest part of the theory to grasp. You write, “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.” Yes, but those “times” are different and easy to specify. Waves when no one is “looking,” and particles when someone “looks.” It’s this “looking” part — sometimes called the collapse of the wave function — that I think is the most problematic. You can only specify the results of quantum mechanics FROM THE PERSPECTIVE OF AN EXTERNAL OBSERVER. Thus, there is always something OUTSIDE the theory to even formulate it, and thus quantum mechanics CANNOT be a complete theory of everything. A quantum headache.

Thanks, David. A succinct description of yet another of the many problematic aspects of quantum mechanics. A quantum headache indeed! 🙂

That is probably the most strangely entangled non audio article anyone has ever written for Copper. Great, continue taking us on unexpected paths, always a pleasure to read you.

Many claims have been made about what Godel’s theorem says, and a good reference as to what it actually says and how it has been misrepresented is Torkel Franzen’s “Godel’s Theorem. An Incomplete Guide to its Use and Abuse.” The sorts of systems to which Godel’s results (improved by Rosser) can be applied are consistent “formal systems” containing sufficient arithmetic. While a particular system will be unable to prove some true statements within the system, there is nothing preventing such a proof outside the particular system. Godel’s theorem only says what it says. It’s important to keep in mind a distinction between the concept of “proof” in the vernacular sense, meaning a demonstration of truthfulness, and “proof” in the formal sense of mathematical logic, meaning derivable from other statements or axioms according to specific rules. To state that Godel’s theorem postulates that some truths are fundamentally unprovable (and here I think you mean in the vernacular sense: there are mathematical statements that are either true or false, but we’re forever prevented from knowing which is the case), when it actually proves something more specific and limited (there will be true statements independent of the axioms of any particular consistent “formal system” containing enough arithmetic) is bound to leave many readers with the impression the theorem says more than it does.

It’s usually problematic to quote Goedel. If you suitably qualify it with all the necessary if and buts, it generally becomes far too unwieldy for the context. All you write … and more … is of course totally correct.

I had a lot of problems with this when I first encountered it in the fall of 1966 in a lecture hall in college. Our professor was Dr. Hans Meissner whose father discovered the well known Meissner effect (we had the best professors in every class from beginning to end.) “Sometimze ze elektromagnetik enerchy actz like vaves unt somtimze zey akt like pahtiklez. So vee call zem vaviclez.” If that wasn’t enough to make me fall out of my chair which fortunately had steel separators on each side with arm rests and a fold down desk so I couldn’t fall out what came next would have. “Unt ven vee zink of zem as pahtiklez vee call zem fotons and zey have no mazz.” What? Something made out of nothing?

I didn’t learn about Q bits until much later. I still have problems reconciling Q bits with the Pauli exclusion principle. This principle says that every electron in an atom can be described by four unique quantum numbers (freshman chemistry.) No two electrons in the same atom can have the same four quantum numbers. But where Q bits are concerned they can have a spin number of -1/2 or +1/2. If they are in pairs like in helium atoms how can the Pauli exclusion principle be reconciled with the fact that they can have both spin numbers at the same time?

Quantum theory has led me to the conclusion that there must be more than 3 dimensions. One point of evidence is quantum entanglement. Two photons are far apart in 3 space but they interact as though they were closely bound together. How is that possible? By our current understanding they must be bound closely together in a dimension we cannot sense. Another point of evidence is quantum energy. When electrons jump from one energy state to another such as moving to a higher orbital they do not make a smooth transition. The disappear from one state and reappear at another. How is this possible? They must travel through a dimension we cannot sense.

Of all the things I ever studied, the one subject I mastered or rather devoured was Euclidean geometry. If I could turn a problem into a geometric form, that was my best chance of solving it. For the longest time I was frustrated by the fact that my three dimensional mind could only visualize 3 physical dimensions. Then in the mid 1970s I invented two different methods of visualizing things in more than three dimension. I solved the acoustics problem by turning it into a six dimensional problem I could visualize and I have a theory for this one based on a different method for visualizing it in four dimensions. I do not know if the 4th dimension is time but it might be. Perhaps one day I’ll publish a paper explaining my theory. It’s radically different from anything else I’ve seen or read about. I can probably reactivate my membership in AIP (the American Institute of Physics) by just paying my dues.

BTW, I got into trouble on another site by saying that all physicists were stark raving loonies. I roomed with one in college for 2 years. He was one of the technical experts who negotiated the START treaty. Heaven help us. Yet when he carried a pizza box to the dorm from a local pizzeria he carried it under his arm like a book and all of the cheese stuck to the top lid. I could have become one myself and wound up like the rest of them, crazy as a gooney bird but I was too drawn to electrical engineering. EEs are also often nuts. If my professors knew what I did with my life they’d be furious with me.

I would address the problem of physicist lunacy by invoking Physicist-Engineer duality. I am an engineer whenever I encounter a nutty physicist, and a physicist whenever I encounter an engineering problem I can’t solve. And in any case I am inextricably entangled with being an entrepreneur.

Your observation regarding the Pauli exclusion principle is interesting, and I don’t recall seeing it mentioned in that context. But I would suggest that Pauli only applies after the particle has “collapsed” to an observable state.

Regarding the transitioning between quantum states, I know that quantum theory allows to model the transition. I have seen people doing that in order to model the transition time, the lifetime of a state, or the cross-section of an interaction. But I have never done it myself, so don’t have an opinion on the extent to which the methods address the questions you raise.

Funny, the first time I heard that an electron could have a quantum spin number of +1/2 and -1/2 at the same time the first thing I thought of was the Pauli exclusion principle.

My entire model, theory, understanding of physics rests on one assumption and that is that photons must have some mass. I’ve got three points of evidence that leads me to this conclusion. If that is true, it leads to a contradiction that can only be reconciled by assuming at least one more dimension. An electron may look like a solid sphere in 3 space but in 4 space it is a whole ‘nother animal. The model explains a lot for which there are no other viable explanations I’ve ever heard of. Physicists put arcane names on things but they don’t explain what those things are or how and why they act the way they do, only what they will do. For example, they cannot explain the simple observation that opposite electrically charged particles attract and the same charged particles repel. They cannot explain how magnetism works. they cannot explain the reason for the relationship between magnetism and electricity.

Nearly 250 equations in the book Fano Chu Adler and Lai committed to memory including Maxwells laws in the curl and divergence forms as integral and partial differential equations. One of the questions on the final exam. They told me what would happen but not how.

If Physicists are off the deep end then electrical engineers are close to the edge. You have to be. And I’ve always said if you are an electrical engineer dealing with potentially lethal destructive power and you are not always running scared about what you might have overlooked, then you don’t know what is going on What you don’t know can kill you. As with the explosion of the space shuttle Challenger, after the smoke clears everyone’s an expert. This is the reason I do not have or want a PE license. I won’t take legal liability for the consequences of a mistake I might have made either unwittingly or because someone who was paying my salary ordered to do things his way even though I knew it was the wrong thing to do or he’d fire me. Here’s something for you to think about. The FIU bridge collapse about a year ago. One look at the dashcam video of it and I knew exactly what happened. One look at the drawings and I knew exactly why. Can you guess? It was inevitable. It was the second dumbest engineering design I ever saw. The first dumbest was the Soviet rocket that was supposed to take Cosmonauts to the moon. Five trials and five explosions. That was inevitable too.