## Notes on Section 1, The need for a quantum theory

Paul Dirac wrote a book called “The Principles of Quantum Mechanics.” It is a very logical book with later sections depending on earlier sections. I have only read bits and pieces of this book, but now I going to embark on the challenging task of reading it chronologically while keeping a critical eye. In addition to keeping track of main ideas, I will criticize certain points if something seems off, but I doubt this will happen often since, after all, this is Dirac’s writing. Also I will ignore any questionable points that are not important to the structure of quantum theory.

The first section is called “The need for a quantum theory” so it is fairly obvious what this section will be about. From the first sentence, Dirac uses the word “dynamical system” which does imply some notion of time as well as a system which is quite generally a collection of objects that may or may not be separate from another collection of objects. Dirac also mentions the “electromagnetic field” as well as “matter.” I would like to note that a field is a mathematical concept and does not necessarily exist in a physical sense. Furthermore, matter is a word to describe “stuff.” Whether matter and space can coexist in the same “location” is a question I wonder about but I do not currently have an answer to it. I assume this is answered by general relativity. It is interesting to think about the relation between matter and space, but I digress.

Dirac also mentions the “atomic scale” which obviously implies the existence of atoms. The first sentence that stands out is “the necessity for a departure from classical mechanics is clearly shown by experimental results.” This is very different from string theory, which cannot be experimentally tested as far as we know. I am not sure what point of view I take on this topic, that is, whether experiment should guide theory or if theory should guide experiment, or both (or neither).

The first experimental problem is the stability of atoms and molecules. This, once again, assumes the existence of atoms and molecules, which is accepted in today’s scientific paradigm. Then Dirac briefly distinguishes between physical and chemical properties, which I find kind of interesting. Are physical and chemical properties two categories that fundamentally exist or are they human inventions to help us understand phenomena? In other words, could it be that physics is at the root of chemistry, or that chemistry at the root of physics? I tend to lean toward the former.

The next problem is that classical mechanics apparently cannot account for “Ritz’s Combination Law of Spectroscopy, according to which all the frequencies can be expressed as differences between certain terms, the number of terms being much less than the number of frequencies.” This certainly introduces the concept of frequency, which arises from the idea of an oscillation, which can be understood from a purely mathematical perspective I think.

Dirac then brings up a quantity from statistical mechanics called “specific heat” which can be defined in a number of ways. I will not go into the mathematical definitions here. The main point here is that “if one assumes all the spectroscopic frequencies of an atom to correspond to different degrees of freedom, one would get a specific heat for any kind of matter very much greater than the observed value.”

Another reason why classical mechanics is thought to be inaccurate is that “We have, on the one hand, the phenomena of interference and diffraction, which can be explained only on the basis of a wave theory; on the other, phenomena such as photo-electric emission and scattering by free electrons, which show that light is composed of small particles.” How do we know that the particles are fundamentally different than the waves? I suppose a particle could be a comparatively localized wave, but to my knowledge a particle and a wave are thought to be different rather than the same. Also I would like to add that I am skeptical about whether or not an electron can be truly “free.” That said, I think the wave theory for matter is a promising idea since as I mentioned above, it seems like a “particle” could be thought of as a special case of the wave. In other words, a wave seems more general than a particle.