Wednesday, 18 April 2012

Quantum foundations: what is real?

A few terms ago, I took a course called "Foundations and Interpretations of Quantum Theory". It's a physics course officially listed as an applied mathematics course although its content is more philosophy than math. The purpose of such a course is to clarify the meaning of quantum mechanics in terms of concrete physical ideas. We believe this can always be done because physics supposedly isn't just about doing some fancy mathematics. Ultimately, we would like physics to explain to us how Nature works, in terms of unambiguous laws that dictate how physical objects must behave in a variety of real-life situations.

Things are pretty simple and straightforward in Newton's version of physics, that stuff all of us learn in high school. If we wanted to, we could easily describe properties of objects like apples or tennis ball, say their current positions or speeds, and we can follow or predict how these properties will evolve if we know what forces these objects experience as they move around. It just so happens that matters become quite vague and confusing when we explore the microscopic world and study the motion of quantum objects such as atoms or electrons. 

The main issue in quantum theory is what is technically called "the measurement problem". Anybody who has studied a general chemistry course where electron clouds have been discussed or at least mentioned has actually touched upon the problem without realizing it. Roughly speaking, an electron clouds describes how the electrons of an atom are distributed around it. In the simple picture chemists like to talk about, electrons move in some orbits around the nucleus, like planets around the sun, or reside in orbitals, which in either case, as if they can be found in a specific place within the atom at any instant. However, the lessons of quantum mechanics tells us that all we really know are the regions in the atoms where the electrons are most likely to be found (see figure caption). Thus, the orbitals actually refer regions of high probability for locating the electron but we do not know where the electron exactly is within that region. 

But how do we know that the electron really is inside those orbitals? In principle, we can verify that by making a very precise measurement to spot the electron (though it would very difficult in practice) . However the unanswered question is what is the electron's exact position way before we try to measure? The mathematics of quantum theory suggests that it doesn't have one--all you can say is that it is most likely inside the orbitals and less likely outside them. (If the position can be found before measurement then we don't need to talk about probabilities or electron clouds) The implication seems to be that the measurement creates the electron's position--the electron reveals itself in a specific spot only if we force it to.      

To give another example as to the mind-boggling situations we get from quantum mechanics, let's consider radioactive decay. Radioactive materials are unstable substances whose larger parent atoms change to other smaller daughter atoms by emitting particles (called alpha, beta, or gamma depending on the atom). One who understands this decay may reasonably ask: are the particles emitted by radioactive matter formed within the atoms before they are expelled? That appears to be the logical way to think about the decay process but it is actually wrong--such a fully-formed particle can never gather enough energy to make its exit from the parent atom. We know that it does happen nonetheless because we know about quantum mechanical tunneling. However, we have no concrete physical picture of what goes on within those radioactive atoms when the decay happens. (In fact, we can't even predict the precise instant of the decay.)

All such conceptual issues and a whole lot more provide the motivation for studying quantum foundations. The basic idea is that if one can give an interpretation to quantum theory that will resolve these issues, then we can say that we truly understand quantum mechanics. However, if you bother to look at Wikipedia's article on quantum interpretations, you'll find that there are numerous candidates. The reason for this is exactly the same reason why people have endless debates on moral or ethical issues and never seem to agree: there will always be some concepts where people will attribute different meanings. For example, is it wrong to be jealous of someone else's wealth or spouse? Some will say it is not as long as you don't act upon it but others will say that it is already a sin. So in those different quantum interpretations, a few concepts are defined differently among them and they lead to very different implications. The only thing that's common to them is that they are all consistent with the standard quantum mechanics introduced by Bohr, Schrodinger, Heisenberg, and Dirac. Of course, they have to be; otherwise, it is obviously a wrong interpretation, since we know quantum theory works spectacularly in practice--it did give us our lasers, transistors, MRIs, and essentially every technology with a microchip.

But I think there is a way to get rid of the pretenders and to let the real quantum mechanical interpretation stand out. Unfortunately, it requires the answer to a very deep philosophical question: what is real? If you're wondering what that has to do with anything, well, it has to do with everything in fact! The problem of interpretation boils down to delineating which aspects of quantum theory correspond to real entities. Thus, it is crucial to first decide what constitutes a real entity. At first I was thinking in terms of negation: perhaps one can define reality in terms of what is not real. But I quickly realized that it won't work. What exactly is the defining characteristic of something that is not real? For example, unicorns are not real (I'm not even so sure about that, in fact). They are not real because they don't exist. (Don't they? Maybe there are unicorns in some hidden magic land?) But that isn't good enough because it just puts the burden on the word 'exist'. Not to mention the fact that it is actually not a precise reason since numbers like 1 and 2 can be said to exist but are not real in the physical sense we are interested in. So I'm still wondering what makes something real and if you manage to read all the way up to here, perhaps you can enlighten me on this with your own thoughts.      

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