Over the next couple of days, I’m going to share some of the essays I wrote summarizing the several books I read in Physics 361. Today’s essay is about the book “Thirty Years that Shook Physics” by the late physicist George Gamow. Here’s the book report:
In his book entitled Thirty Years That Shook Physics, George Gamow presents the story of the formation of Quantum Theory in a surprisingly human way. When reciting the History of science it is often too easy to overemphasize dry facts while underemphasizing the people, thoughts, and overall atmosphere of the time in question. Gamow has struck a gentle balance between effectively conveying the relevant concepts in logical order and providing the reader with the human connection and anecdotes that makes the book so funny and interesting to read. In Contrast, the third and fourth chapters of Peter Woit’s Not Even Wrong have only some reference to the personalities involved in the construction Quantum Theory and none of the charming personal anecdotes that define Gamow’s book. However, Woit’s explanation of Quantum Theory is refreshing in the sense that for the first time in my experience reading and learning physics, I felt that I was not being lied to in some subtle way. Woit makes the effort to convey the underlying mathematical concepts of Quantum Theory, which is enough to give the reader an honest understanding without requiring specialized knowledge of intricate details.
Quantum Mechanics is wrought with concepts so strange that it is not enough to call them unintuitive; rather, these concepts violate intuitions. One such concept is that of wave-particle duality. When thinking about such objects as electrons or atoms, it seems natural to imagine tiny particles that some very tiny men might be able to play baseball with. Likewise, when thinking about waves, one might imagine water or sound waves that come and go in an ethereal sense. It doesn’t make sense to think about a vague “wave” as having the property of mass, or a particle as having the property of wavelength. Light, which had been established to be an electromagnetic wave before the start of the twentieth century, was the first victim of the bizarre idea that objects in the world have dual nature. Planck first suggested that light comes in discrete packets of energy in order to accurately model the relationship between the intensity versus frequency of electromagnetic emission by blackbodies. However, Planck feared the philosophical conclusions of his formulation of light as packets or particles of energy. He chose rather “to believe the packages of energy arise not from the properties of the light waves themselves but rather from the internal properties of atoms which can emit and absorb radiation only in certain discrete quantities (Gamow 22).” Everyone interested in the universe must ultimately face the logical consequence of Planck’s formulation, since the existence of these “light particles”, or photons, has been confirmed by experiments like the Photoelectric Effect. In the Photoelectric Effect, the kinetic energy of electrons kicked off of metal by light depends on the frequency of the incoming light rather than intensity. This suggests that light comes in quantized packets that hit electrons with energy that is proportional to frequency. Intensity would be related to the number of these packets, thus not affecting the kinetic energy of individual electrons. This result among others shows that there is strong evidence that light has both wave and particle nature. It is hard enough to accept the dual nature of light, but even more counterintuitive is that all physical objects have the same dual nature. After Bohr derived the radius of the quantized orbits of the electrons in the hydrogen atom from Maupertuis’ principle of least action together with Planck’s constant, de Broglie saw the opportunity to apply the idea of wave-particle duality to electrons. If the electrons in hydrogen were accompanied by waves, the circumference of the orbit would have to be an integer multiple of wavelength to avoid the electron interfering with itself out of existence. Assigning electrons and other massive particles a wavelength inversely proportional to momentum means that these “particles” should theoretically show the diffraction patterns normally characteristic of waves. Sir George Thomson, G Davisson, and LH Germer observed these diffraction patterns in perfect agreement with de Broglie’s wavelength using X-Ray spectroscopy. The experimental verification of the de Broglie wavelength is perhaps more troubling than the results of the Photoelectric Effect. Understanding light as an electromagnetic wave that comes in localized packets of energy is much easier than understanding an electron as a packet of some sort of wave. The central philosophical implication of wave-particle duality seems to be that there is fundamentally no such object as a particle in the universe. The waves that describe such objects as electrons localize and behave like particles in most experimental set-ups, but the electrons themselves are not actually physical particles.
Another violation of ordinary intuition comes from Heisenberg’s uncertainty principle, which states that one’s uncertainty in momentum multiplied by the uncertainty in position must be greater than or equal to a number on the order of Planck’s constant. That means there is a limit to how accurately one can know the position and momentum of an object. This principle makes even less sense than the last, since one learns in introductory calculus that given the initial conditions and acceleration of a particle, one can find its precise velocity (thus momentum) as well as its precise position. For example, one should be able to say with confidence that someone sitting on the couch watching the Super Bowl has no momentum with a precisely defined center of mass. Heisenberg’s uncertainty principle dictates that this measurement cannot physically be made with perfect accuracy. However, the numerical smallness of Planck’s constant ensures that the uncertainty in both position and momentum of high-mass every-day objects can be negligible. While the uncertainty principle does not make sense in the context of Classical Physics, it is well understood with the mathematical description of Quantum Mechanics. The mathematical structure of Quantum Mechanics has two main components: The first is that at every moment in time, a vector in so-called Hilbert space describes the state of a system; and secondly, observable quantities correspond to operators on Hilbert space (Woit 32). Heisenberg’s uncertainty principle comes from the fact that the position and momentum operators on Hilbert space do not commute, so one cannot obtain well-defined values for both position and momentum simultaneously (Woit 32). Since the mathematical tools of Quantum Mechanics can be used to predict phenomena with frightening accuracy, it is reasonable to accept Heisenberg’s uncertainty principle based on its mathematical necessity alone. As Professor Tim Gay once told me, “shut up and calculate.” By that, he meant that a mathematical model of phenomena in the universe is justified insofar as it is accurate. In this sense, Heisenberg’s uncertainty principle is well justified. However, for those who like to think about the philosophical consequences of the physical laws that describe the world, calculation might not be enough. In this case, it might be useful to think about what it means to measure observable quantities. Whenever a quantity of a system is observed, the system is changed in some way. For example, when one observes the light of the stars, the photons are blocked from their rightful path by one’s retina. Notice that by this logic, the earth itself is an instrument that measures the light of stars. This is an important point, since an “observer” does not have to be a conscious human being. So, Heisenberg’s uncertainty principle can be seen as the result of the fact that any measurement disturbs a system. Quantum mechanical systems are inherently the most sensitive, so it is in this arena that one can find the minimum amount that a system can be disturbed by measurement. This means that no matter how sensitive the equipment, there is an inherent uncertainty in observed nature. This uncertainty can be formulated in different ways, but one of these ways has to do with the close relationship between uncertainty in position and uncertainty in momentum. In the limit that uncertainty is minimized, disturbing a system in order to learn more about position will result in learning less about momentum and visa-versa. This is the basis for Heisenberg’s uncertainty relation.
Quantum mechanics describes a world so far removed from the intuition born from millions of years of evolution. It is unlikely that a human mind can grasp the physical reality of the quantum world, but that doesn’t mean that one cannot try.
Max Planck: Planck postulated that the radiant energy emitted from blackbodies has to come in discrete packets called “light quanta” in order to accurately model the intensity of emission versus frequency of emission in blackbody radiation. Each quantum of light has energy proportional to its frequency. The constant of proportionality is Planck’s constant. Planck’s radical formulation paved the way for Bohr to explain the quantized orbits of the hydrogen atom.
Niels Bohr: Bohr derived the radius of the quantized orbits of the electrons in the hydrogen atom from Maupertuis’ principle of least action together with Planck’s constant. His model of the discrete orbits closely explained hydrogen’s spectral lines. In addition, Bohr founded the Royal Danish Academy of Science, fostering collaboration amongst the greatest minds in Physics of the time.
Wolfgang Pauli: Pauli is famous for his Exclusion Principle, predicting the existence of the neutrino, and the Pauli Effect. The Exclusion Principle states that only one electron can occupy a quantum state at a given time. This principle explains periodic changes of atomic volumes and ionization levels, properties of atoms and chemicals, and valencies. Pauli hypothesized that the apparent lack of conservation of energy in beta emission could be corrected if there were a small, neutrally charged particle involved in the process (later called the neutrino). The neutrino was not found until 1955 at Los Alamos. The Pauli Effect is the phenomenon that the rate of accidents and problems with physics experiments is proportional to the proximity and intelligence of nearby theoretical physicists. The Pauli Effect is well established to those who knew him, but the evidence is only anecdotal.
Louis duc de Broglie: Armed with the idea that light behaves like particles and waves, de Broglie saw that he could reformulate Bohr’s model of the hydrogen atom by assigning wavelength to the electrons with the added prediction that electrons and other massive particles should show wavelike diffraction patters. This prediction was fulfilled with X-Ray spectroscopy experiments.
Werner Heisenberg: Heisenberg used the mathematics infinite matrices to represent the physics of atoms, which was shown to be equivalent to Schrödinger’s wave mechanics. From this, he derived the Heisenberg uncertainty principle, which states that uncertainty in position multiplied by uncertainty in momentum is bounded below by Planck’s constant divided by four pi.
P.A.M. Dirac: Dirac discovered the Dirac Equation, which is an analog of Schrödinger’s equation with the added benefit of being consistent with Special Relativity. The Dirac Equation properly explained electron spin and predicted the existence of antimatter, which was later confirmed.
Enrico Fermi: Fermi was the first to develop the strict mathematical theory of beta emission. He also was a part of the extensive research that eventually led to the nuclear bomb.
Hideki Yukawa: Yukawa predicted the existence of mesons to explain the strong interactions between nucleons in atoms.