Readers that truly understand Quantum Mechanics and its progeny will not be satisfied with the version presented here. To them, the author says: “Go write your own book.”
The discipline of Quantum Mechanics is as long and broad as any field of scientific study has ever been, and to do it justice in a few chapters of a book is, quite frankly, impossible. What is presented here is a broad overview, which concentrates only on the high level ideas and some of the more understandable concepts. There is a plethora of wonderful books out there on this subject, and the readers who are not familiar with the subject matter and are curious, are encouraged to seek some out. The Odd Quantum, by Sam Treiman is a good one, so is The Trouble with Physics, by Lee Smolin, although Dr. Smolin’s book is primarily about the problems with String Theory, he is a quantum physicist at heart, and spends a good part of the book discussing the merits of his chosen field of study.
Quantum Mechanics is based on the completely tenable assumption that energy (and in fact, all known phenomena) can be divided into finite quantities that have limited and measurable values. Actually, the origins of this concept trace their roots back to Newton, who described light as being composed of ‘corpuscles’, but that was before Maxwell and Faraday had their say. Dr. Einstein named the light ‘particles’ photons and defined them to mean ‘little packets of light’. This definition has been broadened considerably since then, but the basic concept remains and is the rock foundation, the core of the Quantum movement, and that is: that all energy can be (and must be!) divided into discreet packages, quanta, and therefore, no form of energy is completely continuous. Not sunshine. Not your flashlight beam. Not (especially!) your laser pointer.
This was a complete departure from classical mechanics and field theory. As you may remember from the start of this book, physicists felt that they had pretty much worked everything out with regard to radiant energy, and the solutions that they had created were all based on utilizing massless waves as the transmitting agent.
Max and Dr. Einstein demonstrated conclusively, decisively, concretely, empirically, theoretically (and some would argue) philosophically that this was not the case. Energy has a minimum ‘dimension’, a minimum/maximum unit that we now call the quantum, and this FACT changed everything in physics. So much for Max’s professor’s prognostication.
With this information in hand, in the late1920’s and early 30’s Dr. Einstein began working with a distinguished group of European physicists who were pondering the fundamental laws of nature at the subatomic level. This group included men who have since become legendary (at least to others who study such things) and included Werner Heisenberg, Niels Bohr, Max Born, Erwin Schrodinger, Max Planck, Louis de Broglie, Wolfgang Pauli and Paul Dirac, among others.
It had been only recently discovered (around the turn of the century) that atoms were composed of two basic parts: protons, which resided in the nucleus, and electrons which seemed to inhabit the space immediately outside (they didn’t know about the neutron yet). This presented a new problem for physics.
Classical mechanical physicists modeled this relationship like a planetary system (the Rutherford model), wherein the electric attraction between the electron and the proton was counterbalanced by the centrifugal force created by the orbital velocity of the electron, which effectively kept it from crashing into the nucleus (proton). For a while.
The problem with this model (other than the fact that it is much too simplistic) is that under classical theory, the electron must lose some energy with every orbit. And even though it might be just a little bit, with no external energy input and since the charge of the proton and the electron are considered to be unwavering, the electron would eventually have to come crashing into the nucleus; rendering all mass theoretically unstable. This did not seem to match the observational data.
So it was that Niels Bohr came up with a new model for the hydrogen atom that was based the quantum theory, and the rest, as they say, is history.
Bohr based his derivation on the assumption that the electron also exists in a quantum state, and therefore, the reason that it could not fall into the proton was because, well, it just couldn’t.
There are a whole lot of theoretical calculations that support this, and it is true that the Bohr Model for Hydrogen was quickly superseded by more accurate and descriptive models (although as we shall soon see, this is where Quantum Mechanics took a BIG left turn), but the revolutionary thought here is this: matter (in this case, the electron, but this concept is now applicable to all matter) is quantized, just like light, and comes in discreet packages that can only be of a certain size, no bigger, no smaller. The electron cannot fall into the nucleus (proton) because to get small and compact enough to do that, it ceases to be an electron.
It had been determined that photons were created when an electron jumped states from a higher to a lower energy. These states, and the amount of the energy released in the jump had a definite value, based on the difference in the energy of the states and the molecular configuration. This is a perfectly logical and fundamental conclusion derived from the photoelectric effect as recorded and described by Max Planck and Dr. Einstein. Photons from particular atoms do not come in every energy level of the spectrum, they are expressed or absorbed only at specific frequencies, ones that correspond to the specific energy levels of the electron(s) of the host atom.
Therefore, an electron cannot ‘lose just a little bit’ of energy as it whirls around the nucleus, it can only lose a prescribed amount, one that corresponds to its ‘orbit’, radius and predetermined energy level. Being ‘quantized’ like that, its orbit cannot gradually decay; and therefore it cannot lose energy.
This is a very radical assumption! Classical physics is based on the observed phenomena that every system loses energy over time as it tends toward a state with higher entropy. Yet, here was logical, empirical evidence that at the atomic level, this was just not the case. Since it had been shown that the electron has only very specific energies, it cannot lose any without jumping state and releasing a photon. A photon that is an integer multiple of the base state as described by;
E = hν
As we shall soon see, this conclusion led to other, less tenable assumptions that, while providing a more comprehensive description of matter, have delved into the realm of probability and forbidden mathematics to provide a basis for the observed phenomena. But before that, we must discuss another aspect of these radical assumptions, one that has vexed the scientific community for years, and one that one would argue, continues to do so.
These last few chapters represent some of the most radical and far reaching conclusions about the nature of the physics of the universe ever written, and one could easily argue, have allowed and driven all of the developments in the field for the last century, because it is the equivalence of mass and energy and the insight that energy, and therefore mass, must have discreet energy levels that cannot be divided or violated that have allowed us to probe the subatomic world and given us lasers, photovoltaic (solar) energy, the Standard Model (which we’ll soon discuss), and someday, quantum computing.
In the next chapters we’re going to discuss some of the problems encountered with these new trains of thought and how the solutions that were proposed started to drive those trains off the tracks, starting with Dr. Erwin Schrodinger’s equations.
But the implications of these insights given to us by Dr. Planck and Dr. Einstein are enormous, and the impact of these thoughts on the field of modern physics cannot be overestimated.
Energy and mass are the same basic phenomenon, and they come only in chunks, not streams. We discovered that fact long ago when we realized that matter was in fact composed of discreet atoms, but the fact that energy is constructed basically the same way was quite a revelation.
We’ll also spend a little time discussing the Standard Model, which has been billed as the most successful model ever developed by physics, and talk just a little about General Relativity.
I’m sure that you realize that since we’ve been progressing somewhat historically, and that since we’re approaching the modern age, soon we’ll be moving on to new concepts, which is the point of this book, after all. But from my perspective, the thoughts presented in the previous chapters represent the very apex of physics theory to date, and that the subsequent efforts, including the General Theory of Relativity, are neither as revolutionary or substantive.
I know that I’ll be catching some flack for that statement.