Archives For andersen

Every year, I read an article written in 1972 by P.W. Anderson, More is Different. This exercise provides two functions. On one hand, it is a kind of ritualistic experience through which I can reflect on the past year. On the other, it allows me to revisit the paper with an expanded knowledge base. The paper revisits an age-old discussion in science: Are less fundamental fields of research simply applied versions of their counterparts?

In 1965, V.F. Weisskopf, in an essay entitled In Defence of High Energy Physics, delineated two types of fields. One, which he called intensive, sought after fundamental laws. The other, extensive, used these fundamental laws to explain various phenomena. In other words, extensive research is simply applied intensive research. In many ways, various fields are closer in proximity to fundamental laws than others. Most of neuroscience is more fundamental than psychology, in that it is reduced to smaller scales and focuses on simpler parts of a more complex system. This psychology, however, is closer to its fundamental laws than the social sciences. Again, where psychology focuses on the workings of individual and small-group dynamics, social sciences use many of these laws to explain their work. Molecular biology is seen as more fundamental than cell biology. Chemistry is less fundamental than many-body physics, which is less fundamental than particle physics. The argument by Weisskopf seems to be in favor when discussing fields in terms of their size scale.

Changes between size scale, however, leads us to a discussion of symmetry. Anderson begins his discussion with the example of ammonia. This molecule forms a pyramid, with one nitrogen at its ‘peak’ and three hydrogrens forming the base. A problem arises, however. When discussing a nucleus, we see that there is no dipole moment, or no net direction of charge. However, the negative nitrogen and positive hydrogens form a structure that disobeys this law, or so one might think. It actually turns out that symmetry is preserved through tunneling of the nitrogen, flipping the structure and creating a net dipole moment of zero. Simply put, symmetry is preserved. Weisskopf’s argument continues to hold, even with the scale change.

However, when the molecule becomes very large, such as sugars made by living systems, this inversion no longer occurs, and the symmetry is broken. The fundamental laws applied at the level of the nucleus now no longer hold. Additionally, one can ask: Knowing only what we learned about the symmetry of a nucleus, could we then infer the behavior of ammonia, glucose, crystal lattices, or other complex structures? The fundamental laws, while still applied to the system, do not capture the behavior at this new scale. On top of that, very large systems break the symmetry entirely.

Andersen goes on to discuss a number of other possibilities. In addition to structure, he analyses time dependence, conductivity, and the transfer of information. In particular, consider the crystal that carries information in living systems: DNA. Here, we have a structure that need not be symmetric, and new laws of information transfer arise from this structure and its counterparts that would not be predicted from particle physics or many-body physics alone.  Considering the DNA example, we must then ask ourselves: Can questions in social sciences, psychology, and biology be explained by DNA alone? We are often tempted, and rightfully so, to reduce these complex systems to changes in our DNA structure. This much is true. However, can we predictably rebuild the same social psychology from such a simple code? With the addition of epigenetics, we are trying to do so, but I argue that we are not yet there. In fact, I argue that we never will be there.

The message here is that larger, more complex systems, while built upon the fundamental laws of their reduced counterparts, display unique phenomena of their own. We can continue to reduce complex systems to smaller scales. In doing so, complexities and phenomena of the larger systems are lost. Starting only with knowledge from the fundamental laws, can we predict all of the phenomena of the larger scales, without prior knowledge of those phenomena? Probably not. This is another kind of broken symmetry, where traverse fields in an intensive direction will lead one in the formulation of a fundamental laws, but traversing in the extensive direction from those fundamental laws will lead to more and more possibilities that need not be the one from where we started. As scales grow, so too does the probability of broken symmetry.

Thus, when stating that “X is just applied Y,” remember ammonia.

Relevant.