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.

The response function and the underlying truth

At the age of seven or eight, I recall experiencing a recurring feeling of vulnerability. Being the only child of immigrants, with all of my aunts, uncles, and grandparents overseas - most of them trapped behind the iron curtain of the powerful Soviet Union of the early 1960s - I could sense my precarious existence. The thought of being orphaned was often on my mind.

This angst lead me through various imagined scenarios. What if both my parents had died, but were surreptitiously replaced by artificial beings who were programed to react to all events exactly as would my real parents? If I hurt myself, they would hug me with facial expressions of sympathy; and, would provide the same level of emotional and material comforts as my real parents. I concluded that I would probably be just as happy. If there were no test that could betray their artificial nature, how would I know otherwise?

The scientific method works in much the same way. Controlled experiments are designed to observe the reactions of a system under various conditions to deduce its "essence." The observed behavior under the influence of an external stimulus is called a response function, and provides a window into the inner workings of everything. The characterization of my parents in terms of the sum total of all possible responses to all my possible actions defined their being. The old expression "we are what we do" is not far from saying that a full characterization of our response function defines us. We are all judged by our works - be it our compassion, diligence, intelligence, empathy, selflessness, greed, selfishness, etc.

Thermodynamics serves as an instructive example from physics. The heat capacity of a material is a response function that quantifies the change in temperature (response) per unit of heat supplied (input). Other examples are a material's compressibility; in optics, the nonlinear susceptibility; and in material structure determinations, the scattering cross-section. All of these quantities are measured by poking things and observing how they respond, from which we deduce the underlying properties.

Such simple experiments have lead to some of the deepest concepts developed by the human mind. For example, statistical mechanics seeks to explain all of thermodynamics in terms of the motions of a large number of tiny particles. Since materials responded to all experiments as predicted under the assumption of the existence of small and undetectable particles, early twentieth century scientists begrudgingly accepted the notion that for all practical purposes, materials were made of such stuff.

Whether the result of great intellect or luck, the particle picture turned out to be accurate. New experiments were designed that more directly confirmed the existence of molecules, atoms, and subatomic particles. For example, bubble chambers yield tracks of the paths of elementary particles -- from which their masses and charges can be determined. By the end of the twentieth century, the scanning tunneling microscope (STM) was developed, making it possible to not only directly image atoms and molecules, but atoms could be picked up and placed on a smooth surface at will. One early demonstration of this technique spelled out the letters IBM by intentionally arranging a group of atoms on a flat crystal surface.

This approach we call science, which views phenomena from new angles, leads to an ever more precise characterization of our world, leading us closer to what I would call the truth. The picture becomes more and more in focus as we become more clever in our prodding and poking.

Due to its complexity, studies of the human mind until modern times had been limited to measuring its response function in much the same way as I defined my parents. Breakthroughs in physics, biochemistry and new technologies now allow us to probe the brain directly with noninvasive methods. While an individual is responding to old-fashioned stimuli such as hunger, lust, satisfaction, and deep thought, the neural activity of the brain can be mapped. The STM brought us pictures of atoms while brain-scanning technology has brought us images of thought and emotion.

One can rightly argue that seeing an image of the brain while the subject is having an experience in response to stimuli does not imply that thoughts and experience reside in the complex firing of neurons. Rather, it could be merely a byproduct of thought. A definitive test would be the deliberate creation of thought, emotion, or sensation using a direct stimulus of the brain. Indeed, researchers have been able to reproduce not only simple sensations, but have been able to make subjects feel spirituality, unity with the universe, and a divine presence.

As experimental technology becomes more sophisticated, and researchers more clever, we are finding direct evidence that those qualities that define our humanness and spirituality are all the result of material processes. Ironically, my father is almost 95 years old, so I am yet to be orphaned. The fact that he is defined by his response function and I by mine does not detract from the meaning derived from human interactions. This knowledge enriches my life with the understanding of how the material world is interconnected and I value the incredible privilege of being a locus of material that has arranged itself in a way to give me consciousness and loved ones, friends and collegues with whom I can share my experiences.

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.