Interlude 3 -Macro models of matter
Although we know that all matter is made up of atoms and molecules, for many considerations — even down to the level of cell biology the "resolution" or "pixel size" that we use to look at matter with contains very large numbers of them. It's therefore extremely useful to have continuous descriptions of matter — a description in which the discrete atomic structure of matter is ignored and we treat it using continuous, smooth functions. These two commonly used descriptions of matter — as continuous or as made up of discrete particles — are two different ways of looking at the same thing. Each description emphasizes a different aspect of the phenomenon. In biology, the interplay between these two descriptions is a major tool of modern biology. The individual molecules are sometimes essential — as when single molecules (chromosomes) control the chemistry of the entire cell. In other circumstances a continuous description can be critical — even close to a cell membrane where the motion of individual molecules and ions may be essential — but the pH of the local environment is important in determining what happens.
Neither description is wholly complete or sufficient. It depends on what we want to do. For example, we know that the temperature of a system is basically (with a proportionality constant) the average kinetic energy of the molecules of the system.
If we look at individual molecules, we see a lot of molecules traveling with different speeds — and changing their speeds each time they collide with another molecule. The idea of "temperature" is an emergent one — we only see it when we average over a large enough number of molecules. Then, despite the large and rapid variation in individual molecular speeds, the average settles down to something that is highly stable and that changes by very well-defined and quantitative laws. These laws seem to make no sense at the level of individual molecules. This is kind of like one of those "blended" images in psychology. You basically see one or the other, but it's really neither. (The transition to the collective or average view as you take more and more molecules is called emergence.)
In some biological situations,the connection between the two levels is what is essential. The continuous picture gives us a single local value for a variable such as temperature, concentration, or pH. The molecular picture reminds us that these are averages and fluctuate around the continuous value as molecules move in or out. These fluctuations produce Brownian motion, the jiggling of pollen grains floating in a fluid. Einstein's analysis of this in 1905 showed that measuring the random walk of these pollen grains could actually provide an accurate measure of Avogadro's number — effectively offering the first accurate determination of the atomic scale. Some mechanisms in biology actually depend on the fact that a "macro" variable fluctuates and does not have a well defined value.
For this middle third of the first term, we will explore the continuous view of matter: how do we describe the properties of matter that we see with our everyday lens. In the last third of the first term, we will go down to the molecular level and study how the emergence of macroscopic properties takes place.
This section of the class will study the properties of macroscopic physics systems.
Joe Redish 10/20/11
Last Modified: May 24, 2019