Extreme Physics

In our culture, the word "extreme" has taken on a new meaning because of its use in naming new sports that are dangerous. By "extreme physics," I mean the physics of a phenomena when one of its defining parameters is at an extrema; that is, a minimum, maximum, or point of inflection. Mathematically, an extrema of a function is defined as the point were the first derivative is zero. In many ways, extreme physics can be just as exciting as extreme sports.

It interesting to me that the underpinnings of physics are based on extremes. Surely I am not unique in thinking this way; but, I am excited by the topic because one of my projects is based on the theme of using the limits of the nonlinear-optical response to discover new things about light-matter interactions that in the end may lead to a deeper understanding.

As we have been digging deeper and deeper, new patterns are emerging. This regularity, however, is only observed at the extremes of the nonlinear-optical response. Given how all of known physics manifests itself by an extrema, it is pretty exciting to think that we may be on the verge of discovering truly new physics.

There are other projects that are going well and have potentially very exciting ramifications. For example, we are in the process of fine-tuning a new model of the self-healing process. But this is not just a model in the form of an equation that we use to fit our our data (which we are indeed doing), but the parameters represent new phenomena. If the model fits, we are potentially looking at new theory that may be generally applicable to many things. The more general the applicability of our work, the happier my mood.

I end here by lifting an excerpt from a review article we are writing for Physics Reports. It is a more detailed description of what I have written above.

The extremes of physics are characterized by unique behavior. For example, the second law of thermodynamics states that entropy cannot decrease in a closed system. The special case when entropy change is minimized (i.e. it remains unchanged) defines reversible thermodynamic processes. The maximum efficiency of a heat engine requires a reversible process. Calculations of reversible heat engine efficiencies led to the definition of entropy. While motivated by practical applications, entropy has become one of the most important fundamental concepts in physics.

Quantum mechanics is based on the fact that certain quantities cannot be simultaneously measured to arbitrary precision. To accommodate this observation, variables such as momentum and position are generalized to become operators that do not commute. The mathematical formalism naturally leads to the uncertainty principle, which states that there is a lower bound to the product of the position and momentum uncertainties. The fact that uncertainties are constrained by a lower bound is the basis of quantum mechanics, which describes a vast richness of new phenomena that is inexplicable using classical mechanics.

The principal of energy conservation originates from the more general concept of a Hamiltonian, which yields the equations of motion through a process of finding the extrema of the action. These ideas carry over into the quantum realm in the formulation of path integrals, which bring out the wave nature of matter. The absolute maximum speed limit defined by the speed of light, on the other, leads to non-absolute time, where observers in different coordinate systems view the same phenomena but from the perspective of a rotation in four-dimensional space-time. The marriage of relativity with quantum mechanics as embodied by the Dirac equation led to a natural way of accounting for the electron spin, and as a bonus unexpectedly predicted the existence of antimatter.

Clearly, the extremes are fertile soil from which the most fundamental concepts in physics grow. As we later show, the fact there there is a fundamental limit to the nonlinear-optical response of a quantum system defines an extreme that is characterized by several features. For example, while many states of a quantum system contribute to the nonlinear-optical response, at the upper bound only three states are found to contribute. This was originally postulated as a hypothesis and later confirmed to be true for many quantum systems, though it has not yet been rigorously proven. As such, it is referred to as the three-level ansatz.

We will show that systems with a nonlinear response near the fundamental limit share other properties. Why this is true is not yet understood; but, the fact that certain universal properties appear to be associated with the extremes of the nonlinear response hints at fundamental causes, perhaps grounded in new physics, which become apparent only under scaling rules that follow naturally from these limits.

Wasting time, in a good way

Today my morning started early; responding to emails at 6:30 am and an 8:00 am search committee meeting. Various other administrative tasks delayed my arrival in the lab until about 9:45am. After doing the rounds in the lab, and then signing some more paperwork in the Physics office, I made it to my desk, where I spent the rest of the morning answering emails - with a short diversion to chat with the guys fixing our sprinkler system.

After lunch, I finally got back to the task of working on Nathan's cascading paper, which incidentally, I worked on a bit last night. As I was revising text in response to the reviewer's comments, I had a stroke of genius which I imagined would make a significant impact on the world of physics.

Without going into details, cascading is a process by which two molecules cooperate by exchanging a real photon. My insight provided the means for making the exchanged photon virtual. As a consequence, this photon's energy would not need to be conserved as long as the process were fast enough not to violate the uncertainty principle. This made the problem richly beautiful; and more importantly, it meant that a large area of nonlinear optics was flawed. I couldn't resist thinking about this problem with my full attention, so I placed my long "to do" list on the back burner.

I drew Feynman diagrams of the process and immediately realized that if the virtual photon did not conserve energy, it forced the cascading process to also not conserve energy. Thus, the photon must be real and my line of reasoning flawed. I am no genius after all!

However, by taking this detour, I found myself thinking about various cases where virtual processes contribute. To cut to the chase, my understanding of nonlinear interactions took a quantum leap. It made me appreciate the clever minds of great physicists such as Feynman, whose work embodies incredibly deep reasoning.

While most detours on the road waste time and make drivers frustrated, this kind was enjoyable and fulfilling. As I sit at my desk plowing through my work, I remain permeated with a calm happiness.

Until next time...

The Physics of Limits

I spend lots of time thinking - a trance-like state where ideas flow. The feeling is similar when reading about physics, solving problems, doing calculations or randomly following the meanderings of the mind. It brings far greater pleasures than drinking or socializing, though it does not replace the need for human interactions. Exchanging ideas with others is just as fulfilling.

Undoubtedly, the naturally occurring peptide substances in the brain that act as neurotransmitters and appear in abundance while thinking are responsible for the euphoria that is associated with thought. This is augmented by the great satisfaction of new insights that are gained in the process. Strenuous physical activity releases natural endorphins that bring a similar feeling of pleasure. Perhaps these chemical triggers fuel my passion/addiction for physics and ice hockey.

One of our research areas is in fundamental limits of the nonlinear susceptibility. The limits that we calculate follow from the laws of physics. A while back, I got intrigued by the idea that the laws of physics might be derivable from a formulation in terms of limits, or more precisely, constraints. As usual, the idea is not fully original.

In a way, some of the laws of physics are already formulated in this way. For example, the entropy cannot decrease; so, there is a lower limit for the change in entropy. Then there is the upper limit of the speed of light, a crucial constraint from which special relativity follows. The uncertainty principle, which does not allow certain pairs of properties to be simultaneously measured with infinite precision, is yet another constraint. And, that fact that energy is a constant is a very stringent limit; it cannot increase or decrease.

Since physicists have been thinking about these problems for a long time, there are probably few new ideas that would provide a novel approach to physics. However, I still have this gnawing feeling that there is something interesting lurking behind this approach. For example, since the sum rules are a direct consequence of the Schrodinger equation, then perhaps under a constraint, the sum rules could be used to generate general physical principles. Such a formalizing might have unexpected consequences that could lead to the prediction of new and unexpected phenomena.

Since I have been busy with other things, I have not had time to develop this idea, and probably never will. Instead, I will occasionally tinker with paper and pencil to get my neurotransmitters flowing without delusions of success with an occasional vigorous game of hockey to add a tad of spice.