- Quantum gravity I
- Quantum gravity II
- Relativistic quantum information
- Quantum computing
- Communication engineering
- Shannon sampling theory/data compression
- Mathematical biology
- Radar signal design for maximum information return
- The Casimir effect in layered superconductors
- Combinatorics in quantum field theory
- Further interests: Consciousness
Trying to understand what is consciousness is an interest of mine, but I have not yet published on this, except for a colloquium talk that Prof. Imants Baruss kindly invited me to present at King's College at the University of Western Ontario, on September 10, 2009. In my talk, entitled "A Physicist's View of Consciousness", I proposed the following definition for consciousness: An entity is conscious if it models its environment, including itself, to the extent that it models even its modeling. There is of course much to be discussed about this proposal. Here, let me only mention that the idea arose from the consideration of the fact that some animals species, such as apes and dolphins, apparently model their environment quite extensively, to the extent that, for example, they can recognize themselves in mirrors. It should be interesting to try to program a computer to meet my definition of consciousness. Would we ascribe it consciousness?
A related question is whether or not any entity which is consciousness in this sense also possesses free will. I gave a public lecture related to this question at a summer school organized by the German National Merit Foundation (Studienstiftung) in Ftan, Switzerland, on August 6, 2010. Since the definitions of "free" and "will" are subject to endless debate, the question I addressed in Ftan was a more well-defined one. I asked if one can ever have a really new idea, i.e., if a brain could ever have a thought that could not have been predicted even from maximally complete knowledge of the brain's state at an earlier time. My answer is yes. Part of my point was that the brain is complex and nonlinear enough to ensure that its state at one time depends on its state at an earlier time with something like exponential sensitivity. Just as the beat of a butterfly wing will influence the future weather significantly if the prediction period is chosen long enough. In the case of the weather, if you make the prediction period long enough, one would need to know not just each butterfly's wing beat. One would need to know what each elementary particle in its wing does, and ultimately with a precision that would exceed what the quantum uncertainty principle allows. The weather forecast therefore is subject to fundamentally unpredictable quantum fluctuations if you try to forecast beyond a certain length of time. And so is the brain. I have no idea how long that time period is for the brain. It depends on how chaotic it is. It may be interesting to estimate it. My point is that the time period is finite and that therefore beyond a certain time period the brain is fundamentally unpredictable. This means that, among other things, we can have new ideas that nobody could have predicted! Now if a machine is conscious according to the definition I gave above, it seems that it may still be a boring machine - namely without any truly new ideas - if it is not exponentially sensitive to initial conditions and therefore to quantum fluctuations. Remember that quantum fluctuations are the only goings-on that we know of that have no cause, i.e., that are truly new.