On Monday night, I headed down to the beautiful Bell House, in the Gowanus section of Brooklyn, for the monthly Secret Science Club lecture, featuring theoretical chemist Dr Garnet Chan of Princeton University. On his website, Dr Chan describes his research focus thus:
Garnet Chan’s research lies at the interface of theoretical chemistry, condensed matter physics, and quantum information theory, and is concerned with quantum many-particle phenomena and the numerical methods to simulate them.
At the start of his lecture, which he titled "Simulation and Complexity of the Quantum World", Dr Chan gave a hilariously self-deprecating description of his work. He stated that he is a theoretical chemist, a chemist that doesn't perform chemistry experiments. He joked that he needed a kid to help him when he conducted his last experiment. Dr Chan then noted that he had looked at the descriptions of preceding talks, and that he wanted to tie some of the themes of previous lectures together, with an emphasis on the small scale. The goal of his research is simulating the quantum world, and that quantum mechanics is a complicated subject.
Dr Chan quipped that everybody tells lies about quantum mechanics, but that such lies are not indicative of low moral standards, but are simplifications because it's extremely hard to discuss quantum mechanics without bringing complex mathematics into the discussion. Physics operates from a massive scale to a tiny scale... the scale of the universe (dealing with objects in the 1026 meter range) to the quantum scale (dealing with objects in the 10-15 meter range). Theoretical chemistry involves bridging the macroscopic and the microscopic worlds, from the human scale to the scale of atoms and molecules. Dr Chan underscored the importance of the atomic theory by quoting Richard Feynman:
If, in some cataclysm, all of scientific knowledge were to be destroyed, and only one sentence passed on to the next generation of creatures, what statement would contain the most information in the fewest words? I believe it is the atomic hypothesis that all things are made of atoms — little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another. In that one sentence, you will see, there is an enormous amount of information about the world, if just a little imagination and thinking are applied.
In our daily experience, the world appears to be continuous, but matter is discrete. The nature of matter was debated until approximately a century ago, the matter finally being theoretically settled by Einstein (PDF) and verified experimentally by the observation of Brownian motion by French physicist Jean Baptiste Perrin. Perrin observed that the motion of small starch particles was not continuous, but "jagged". If matter were contiguous, such motion would be smooth. If matter were composed of discrete bits, motion within the matter would be discrete. The rapidity with which a particle will change directions is equal to the number of collisions it is involved in- the ratio of the granule to the substrate, which is Avogadro's number.
Today, clearer evidence of atoms can be obtained through the use of scanning tunneling microscopes. Dr Chan described scanning tunneling microscopes as having a tip "one atom sharp", and the magnitude of the signal obtained by the electron microscope maps out the undulation of the surface of the substance scanned. At the atomic scale, though, things are "sticky", and the difference between the human scale and the atomic scale is so pronounced that it is difficult to make observations- there's no way to "see" inside atoms. Rather than bridging these scales in the real world, the "world of the atom" has to be digitally recreated in the computer world. It is crucial that the computer simulations are completely faithful to reality. The "laws of nature" are known- aside from Planck's scale (1035 meters), the fundamental laws and particles of the universe are known. Dr Chan asked, "Is this the end of physics, or the start of something beautiful?"
Nature is made of many particles, it's not just a matter of "more of the same". Dr Chan used the analogy of a chess game to describe theoretical chemistry: we know the pieces, we know the basic interaction among the pieces, but we don't know the complexity of the game- the interaction of the known particles leads to nature's complexity.
Dr Chan then addressed the question: what is quantum mechanics? General relativity applies to the large-scale structures of the universe, while classical "Newtonian" mechanics suffice for the human scale. On the micrometer scale of atoms and molecules, Newton's predictions begin to break down. Quantum mechanics are the "theory of small", involving atoms, molecules, the strength of bonds, the color of materials, their "stickiness", their electrical properties- as an example of a subject pertinent to quantum mechanics, Dr Chan cited the adhesiveness of gecko feet.
The lecture then shifted to the topic of atoms, a subject Dr Chan called "high school redux". An atom can be illustrated as a nucleus surrounded by one or more electrons, which Dr Chan described as "a fine model, but a complete lie". The reality is that everything in quantum mechanics is "fuzzy" and indistinct- there is a fluidity to electrons, they are not discrete. These fuzzy particles move as waves do, changing shape as they go- the "billiard ball" model of a perfect rigidity localized at all times is inaccurate. Regarding the question of location, whether a particle is "here" or "there" or "both here and there", Dr Chan showed a picture of a wave and asked, "Is the wave at point A, point B, or point C?"
The measurement of the position of a particle is probabilistic, there is no definite answer. Dr Chan joked, "It's our problem, not the particle's." Measurement involves comparing referents to determine similarity- such a comparisons don't look like completely like any particular position. Measurement in quantum mechanics involves measuring fuzzy particles to localized positions probabilistically- there is no straight answer to the location of a particle. Dr Chan then displayed a lovely slide of the Schrödinger equation to show the mathematical model for measuring changes in a quantum system over time.
Simulating quantum mechanics is not easy- in the case of a single particle, one has to factor in the superposition of different local positions. When two particles are considered, they can exist in the superposition of many localized two particle configurations, with correlations between the particle positions- if one particle is "on the right", for example, the other can be considered "on the left". This correlation is known as quantum entanglement. Dr Chan described quantum entanglement as "strange". In an example using two particles, there is a 50/50 chance of either particle being "left" or "right", but if one particle is on the left, there is a 100% chance of the other particle being on the right. Does finding one particle on the left mean that the other particle is on the right? Dr Chan once again quipped, "It's our our problem, not the particles'!" We see a 50% chance that a particle is in a particular position, and we intuitively assume that it is accurate, but the position is uncertain.
When more particles are added to the mix, there is an explosion of possibilities- when two particles are involved, there are four (22) possibilities, three particles yield eight (23), one hundred particles yield 2100 possibilities. Mathematically, there are myriad possibilities- simulating quantum mechanics appears exponentially complex due to the need to describe the possible positions of multiple particles. Dr Chan then noted that it is really an illusion of complexity- certain configurations of atoms can be ruled out. Nature does not explore all quantum possibilities, the world we have has special properties, such as gravity, that limit possibilities. Nature only produces local entanglement, in order to monitor what two particles are doing simultaneously, we only need to monitor two particles in the same region of space.
Dr Chan concluded with a discussion of the material benefits that could be obtained by a thorough understanding of quantum mechanics- specifically the development of high-temp superconductors and a "materials genome project" to map out all possible materials that can be developed.
In the Q&A, the topic of spooky entanglement was brought up, and Dr Chan brought up the inability of nature to generate entanglement over long distances. Some bastard in the audience, who was going to bring up spooky entanglement, had to go to a fallback question regarding string theory, which Dr Chan indicated was not a useful model in reality, but had led to some interesting mathematical models. Funny, on the macro level, Neil Degrasse Tyson also indicated that he was unimpressed with string theory. After the lecture, the bastard, not being a bastard in real life, apologized to Dr Chan for bringing up string theory, which said "bastard" considers a bunch of hooey.
Once again, the Secret Science Club served up a great lecture. Personally, it was useful to me, because quantum mechanics is one of those topics I don't spend enough time reading up on by inclination, which means I need to force myself to read about it more. It's kinda like pushups... I do them precisely because I'm not inclined to do them.