Posted on behalf of Retread
If you look back at your notes on thermodynamics, you are likely to find a blizzard of partial derivatives, state functions and total differentials. As an organic chemist, I had an intuitive understanding of the thermodynamics I needed at the molecular level (actually it’s pretty simple), but the math and the big ideas were not friends. Should you be in the same boat and wish to get the big picture, have a look at “Four Laws that Drive the Universe” by Peter Atkins. It’s 124 small pages, written extremely well and bounces back and forth between the macroscopic and the microscopic illuminating each by the other. If there is a derivative to be found, I missed it.
The book may produce in you physics envy (with apologies to Freud). On p. 45 you will find a discussion of Noether’s theorem, which states that under all the conservation laws of physics lies a symmetry. The first law (conservation of energy) is really about the symmetry of time flow — e.g., “time flows steadily, it does not bunch up and run faster then spread out and run slowly.” Chemistry just doesn’t have statements of such majesty (or strangeness).
If you liked Atkins you’ll love “Boltzmann’s Atom” by David Lindley. It concerns Boltzmann’s trials and tribulations as he developed statistical mechanics. As a neurologist I doubt that they drove him to suicide at 62 (he sounds pretty loosely wrapped throughout his life). Boltzmann’s big opponent was Ernst Mach, who didn’t see the need for atoms as an explanatory device. Mach’s view was that physics should establish laws tying observable phenomena together — e.g., the ideal gas law etc, etc… Postulating something you couldn’t see to explain something you could, was not considered science (by Mach and his followers). Pretty strange to our way of thinking today, but these were the events of just over 100 years ago.
However, vestiges of Mach’s thinking linger on in the Copenhagen interpretation of quantum mechanics. As junior chemistry majors in the 50s we had to read “The Logic of Modern Physics” written by P. W. Bridgeman in 1927. It was our introduction to quantum mechanics (as none of us had the math to tackle it). All you could hope to predict by a theory were ‘numbers on a dial’. Going deeper, by hoping for a trajectory explaining things was a no no (the nodes in atomic and molecular orbitals pretty much rule out trajectories don’t they?). The book drove us nuts at the time, as chemistry back then was firmly on the macroscopic side of the quantum mechanical divide.
Gibbs and Maxwell make their appearance in Lindley’s book, as does the culture and politics of Austria-Hungary before WWI, so there is some breathing room for the reader. One of the founders of physical chemistry, Wilhelm Ostwald, also appears. He doesn’t come off too well — he was enamored of something called energetics, which to Boltzmann (and to Lindley who is a physicist) meant that he really didn’t understand physics very well.
Atoms were finally accepted after Einstein’s work on Brownian motion in 1905 (also described). Parenthetically, there was a similar controversy ending about the same time, as to whether the brain was made of cells, and whether individual neurons existed, or whether the whole brain was a big gemish of nuclei and fibers.
Very interesting post. The discussions during the latter part of the 19th century regarding whether atoms were necessary as explanatory devices, or whether atoms could even be said to exist, was part of a philosophical discussion that continues to this day: what can we say about the reality of submicroscopic entities? Realists (and physicists tend to this persuasion, in my experience) want to say that we can in fact come to know such things as atoms, quarks, electrons,and so on,as they really are. Others want to say that while such entities may be said to exist, we can’t say that we can know them in the sense that we know tables and chairs, for example, but rather we have metaphorical ideas of them. This was more or less Boltzmann’s view. He maintained that atoms must exist, and that while we can’t see them and know just what they look like, we can make many meaningful statements about them. Even though we talk of seeing atoms, using atomic force microscopy, and other tools, we don’r really see them, except through the agency of theories and experimental artifices. We use theories such as electron tunneling, wave-particle duality and other such as the bases for understanding the observables that come from such instruments as atomic force microscopes. I had fun some years ago working my way through these ideas in writing Making Truth:Metaphor in Science, published by University of Illinois Press. My own view is that most of science is grounded in metaphorical concepts. This is especially clear in biology, but chemistry serves up many examples as well.
Dr Brown:
Thanks for your comments. Maitland Jones begins the third edition of his book “Organic Chemistry” with a quote from Neils Bohr — “When it comes to atoms, language can be used only as in poetry. The poet too, is not nearly so concerned with describing facts as with creating images.”
“Even though we talk of seeing atoms, using atomic force microscopy, and other tools, we don’r really see them, except through the agency of theories and experimental artifices.” This is of course true because of the relationship of the wavelength of electromagnetic radiation to the points it can separate (resolution). However, STED (stimulated emission depletion) microscopy gets around the wavelength/resolution limit by causing molecules in a very small volume (300 Angstrom diameter) to emit light. [ Nature vol. 440 pp. 879 – 881 ‘06 ] This could be called ’seeing’ I think.
Also Xray crystallography produces “pictures” of what we think of as atoms arranged in molecules, and more importantly the “pictures” allow us to make testable predictions based on the pictures. That seems like a pretty good form of knowledge rather than metaphor.
In your chemistry days, didn’t you shut your eyes and ‘see’ the atoms of the molecules you were interested arrranged in space? I certainly did, and my guess is that most chemists think this way.
Contrary to popular belief, X-ray crystallography does not produce pictures of molecules. Rather, they produce diffraction patterns and we generate molecular models that are consistent with these patterns. Importantly, the diffraction patterns are not sufficient to generate a picture of the molecules in the crystal because the diffraction patterns lack phase information. Crystallographers have to either guess the phase or perform experiments to help empirically determine the phase of each reflection. Sometimes crystallographers can make errors or overinterpret bad data and come up with models that are incorrect.
With regard to AFM, although it does not allow us to see atoms, (based on my understanding of the technique) it does allow us to touch and feel them (via measuring the deflection of a cantilever). That would lead to an interesting interpretation of atoms and molecules “as they really are”: tiny bumps on a surface.
Yggdrasil:
Agree — electron density maps produced by Xray crystallography aren’t ‘pictures’, but they’re pretty close, just as a topographic map is a ‘picture’ of a terrain. The electron density maps have peaks where we interpret the atoms to be, so in a sense we ‘see’ them. As I recall, a Nobel was awarded for either progress or solution of the phase problem.
There are lots of ways to apprehend an object — visualization and touching for example. AFM is an example of the latter. But the various modalities are complementary not in opposition. Heck, we can even smell some molecules.
Thanks for the comment — it’s good to know that someone is reading this stuff.