The Revolution in Physics; A Non-Mathematical Survey of Quanta.

by Louis, Prince de Broglie, Ralph W. Niemeyer (Translator)

English, French (translation)

310 pages, Hardcover

First published January 13, 1970

Reviews

[Michelle · Rating 5 out of 5]

Louis de Broglie is one of the big names of early quantum mechanics - up there with Bohr, Planck, Heisenberg, Schrodinger, Dirac, Einstein. If you’ve taken a class in modern physics you probably recognize the name de Broglie from the “de Broglie wavelength,” the name for the wavelength that can be associated with any particle, when that particle (thanks to wave-particle duality) is behaving more like a wave. What you might not know is that de Broglie came up with the idea of wave-particle duality during his phd, and wrote his phd thesis about it (…overachiever) which he completed relatively later in life, at age 33, and then got a Nobel prize in physics a couple of years later, because wave-particle duality was so profound and foundational for the nascent field of quantum mechanics.

The Revolution in Physics is the English translation of a book de Broglie originally wrote in French in 1937 called “La physique nouvelle et les quanta” (New Physics and Quanta). For this American edition published in 1953, de Broglie added a few sections. I think the intended audience was the general public; the subtitle is “a non-mathematical survey of quanta,” I suppose making the genre of this book 1950's popular science. What “non-mathematical” actually means for this book though is de Broglie writes out all of the physics equations in words instead of symbolically. For example, instead of writing “F=ma” he writes “We are therefore led to characterize the material point by a coefficient of inertia, its mass: the fundamental law of the dynamics of a material point will then be that the acceleration of a material point is equal at each instant to the quotient of the force acting on it by its mass.” (26) Or instead of writing out Maxwell’s equations symbolically, he writes, “The equations of Maxwell comprise two vectorial equations, representing six equations written between the components, and two scalar equations. On one side of these equations appear the components of the fields and of the electric and magnetic inductions; on the other side, the densities of the electric charges and currents. One of the vector equations expresses the great law of induction discovered by Faraday; one of the scalar equations expresses the fact that it is impossible to isolate a magnetic pole, while the other scalar translates Gauss’ theorem of the flux of electric force.” (52)

Much of the Revolution in Physics covers topics covered in most undergrad E&M and intro quantum classes, but curated and annotated by an obvious expert, and reading it felt like listening to a mix tape of the Greatest Hits of 20th century physics. Most of the topics Louis is writing on were only a couple of decades old at the time this book was first published (and some of the most important developments in quantum physics were still yet to come - more on that later) so it was cool to be getting the story from someone who had their boots on the ground, so to speak, during the quantum revolution. I loved de Broglie explaining how various big name physicists (his buddies) deduced various famous quantum theorems and equations. Also I am a Dirac fangirl so I liked the section about how Dirac invented spinors.

The best part of reading this book, though, was the delicious dramatic irony of reading about the efforts among some physicists (including Louis) to create a deterministic interpretation or theory of quantum mechanics, but (as a reader today) knowing that this book was published in 1953 and Bell’s theorem wasn’t published until 1964. Physicists have never really liked that quantum mechanics seems to imply that the universe is nondeterministic (e.g., Einstein: “God does not play dice with the universe”). For hundreds of years, physicists found success in describing the nature of reality by making accurate mathematical rules to predict exactly where ballistic trajectories would land when launched at a given position and with a given velocity, or where the planets would fall in the sky on a specific day in a specific year - not by assuming the exact answer was unknowable. Even classical statistical mechanics, which deals with probabilities, deals with probabilities of complex systems; at the heart of classical stat mech, we still assume each constituent particle has a deterministic trajectory, it’s just that we cannot calculate these trajectories very easily when we have a system with a million particles, so we predict properties of these systems using probabilities while being assured that the underlying position and momentum of each particle is fully determined at any given moment. And even Einstein’s theory of relativity preserved determinism, though it led to its own weirdness about the true nature of space and time. (“The manner in which classical physics conceived the absolute determinism of physical phenomena rested essentially on the manner of thinking about space and time and the theory of relativity, while revising so profoundly our ideas relative to space and to time, had, however, sufficiently respected them so as not to breach classical determinism. It is not the same with the quantum theory” (102))

Today though, (as well as in the 1950s) the interpretation of quantum mechanics most popular among physicists is the Copenhagen interpretation, which posits that the true nature of reality is probabilistic and nondeterministic. This is so counter to our everyday experience of reality that it’s hard to visualize, but the most famous thought experiment which highlights the seeming paradoxical nature of the Copenhagen interpretation is Schrodinger’s cat. A cat is in a box, and prepared into a special quantum state, where it has a 50% chance of being dead and a 50% chance of being alive once the box is opened. Before the box is opened, though, the cat is somehow _neither_ dead _nor_ alive, but in a superposition of both states. Additionally, there is no way to predict, before opening the box, whether the cat will be dead or alive, even if you know everything there is to know about the box/cat setup.

There are many famous physics experiments (three polarizer paradox, double slit experiment) which are suggestive of, but which do not actually prove the universe is inherently probabilistic. But because a probabilistic and nondeterministic universe is spooky and weird, physicists bent over backwards to try to preserve determinism, even in the face of mounting suggestive evidence to the contrary. At the time de Broglie was writing, people were still messing around with hidden variable theories. A hidden variable theory in quantum mechanics says that, in the case of Schrodinger’s cat, the cat was always dead (or always alive) inside the box, we just didn’t know which it was until we looked inside. Hidden variable theories preserve determinism by saying that quantum measurement results only look random because we don’t have enough information about the system we're measuring.

De Broglie himself had come up with a hidden variable theory - the pilot wave theory. In this theory, a particle constantly has a wave associated with it and the wave directs its motion in a deterministic fashion (though at the expense of locality). De Broglie also called his theory the “double solution” because he believed that Schrodinger’s equation had two solutions: a continuous wave function solution that we are all familiar with, as well as a solution containing a singularity (where the singularity could be interpreted as the localized particle). In his own book de Broglie admits the math was too hard for him to ever really prove double solutions exist, but he still thinks they might exist. The pilot wave/double solution theory is easiest to visualize for the double slit experiment.

Before de Broglie wrote the Revolution in Physics, von Neumann had already come out with a theorem supposedly proving hidden variable theorems were impossible in quantum mechanics. But de Broglie (and later many others, including John Bell) came to be critical of this theorem. My understanding of von Neumann’s proof against hidden variables in quantum mechanics is that the proof assumes that quantum mechanical expectation value of an operator is the same as the underlying true, hidden variable state of the operator, then it says but wait, the sum of the expectation value of two non-commuting operators (say, P and X) does not equal the expectation value of the sum of those operators. But these two should equal each other if the expectation value is actually equal to the true hidden variable state. In the portion his book published in 1937, de Broglie is deferential towards von Neumann’s result (“J. Von Neumann has proven that the probability laws of the new mechanics are incompatible with the existence of a hidden determinism, which makes it most improbable that determinism in atomic physics will be re-established in the future.” (217)) But in his new chapter in the American edition, de Broglie argues against von Neumann’s proof, asserting that von Neumann’s first premise, the idea that the expectation value equals the true, actual value, was false, and that von Neumann hadn’t really disproved hidden variable theories.

In the 1950s, when the American edition of de Broglie’s book was published, most physicists were skeptical of hidden variable theories, but there hadn’t yet been any definitive proof against them. Flash forward to 1964 (after this book was published), and John Bell publishes Bell’s theorem. Bell’s theorem was the final nail in the coffin for local hidden variable theories in quantum mechanics. If you’ve never worked through a proof of Bell’s theorem, I’d highly recommend it if you know the quantum basics, because it’s pretty fun and exciting. Bell’s theorem compares the correlation in spin measurements of two entangled particles, given one can change the measurement orientation axis at each detector. Say there is a set of possible orientations of the axis along which we will measure the spin of one of the particles (e.g. say 0 degrees, 1 degree, 2 degree, etc.). A local hidden variable theory would say my particle has some hidden property that physics hasn’t discovered yet, a variable called lambda which influences the measurement results. According to a local hidden variable theory, there’s a priori a mapping for each of the measurement axis orientations, where if I measure my particle with the axis of measurement 0 degrees from some global plane, I’ll get (e.g.) spin up, 1 degree, spin up, 2 degrees, spin down, etc. So one could write a mapping of the results as {M(0 degrees, lambda) = spin up, M(1 degree, lambda) = spin up, M(3 degrees, lambda) = spin down, …}. This mapping would be unknowable from the current mathematical machinery of quantum mechanics (we don’t know lambda, so the results appear random to us) but not necessarily in conflict with it. Also, this mapping would mean that despite appearing random, the results would actually be deterministic. HOWEVER, Bell’s theorem proves though that, nope, it’s impossible to make a mapping like this without also taking into account the measurement result of the other entangled particle, even though the other particle could be very far away (non-local) from the first particle when it is measured.

Ok so local hidden variable theories for quantum mechanics are out. What are we left with? In a post-Bell’s theorem world, we still have a few options but all of them are weird or unsatisfying in one way or another. If we’re very attached to locality, superdeterminism is a local hidden variable theory that assumes that when we choose the axis orientation to measure along, our choice of measurement is not independent from the particles measured (the particle influences us somehow!). This is a bit of a dead end scientifically, though. If we aren’t so attached to locality, and we’re okay with “spooky action at a distance,” we have plenty of options. The de Broglie-Bohm pilot wave interpretation (another physicist, David Bohm, has added to the theory as well) is actually still okay post Bell’s theorem because it’s a non-local hidden variable theory. However, things still get a bit weird because the orientation of the measurement apparatus has to affect the pilot wave. The de Broglie-Bohm pilot wave interpretation isn’t as nice and neat to visualize for Bell’s theorem as it is for the double slit experiment, but the benefit is we don’t have to say that reality is inherently probabilistic (like we do with the Copenhagen interpretation). Besides the de Broglie-Bohm pilot wave interpretation, we are still left with the Copenhagen interpretation, which is non-local and lacks hidden variables. And there are other interpretations, too, which are still viable (e.g. many worlds interpretation, which is technically a legit theory but is more popular among TV show writers than physicists, or the “shut up and calculate” interpretation, which is a favorite of phd advisors everywhere).

So yeah technically this book is out of date since it doesn’t include Bell’s theorem, but also, reading it is like getting a personal lecture on the history of modern physics from Louis de Broglie himself, so, I’d say it’s still worth a read. I was going to give this 4 stars because it was not always a page-turner, but I feel like Louis made a huge effort to keep this book both rich in physics content/scientifically precise but also accessible, and he was largely successful IMO, and that’s hard to do.

Misc. parts:
- “In the old physics, the simultaneous knowledge of the quantities fixing the position of the parts of a system and of the conjugate dynamic quantities permitted, at least in principle, a rigorous calculation of the state of the system at a later instant… This resulted from the form of the basic equations of the physical and mechanical theories and from the mathematical properties of these equations. This possibility of a rigorous forecasting of future phenomena starting from present phenomena, a possibility implying that the future is in some manner contained in the present and adds nothing to it, constituted what has been called the determinism of natural phenomena. But this possibility of rigorous forecasting requires the exact knowledge at the same instant of time of the variables of spatial localization and of the conjugate dynamic variables; now, it is precisely this knowledge which quantum physics considers impossible.” (17)
- The principle of least action is to particles as Fermat’s principle is to waves. (And given wave-particle duality, the two principles are equivalent!)
- “Einstein has seen in this fact proof that the existence of a gravitational field in a region of space implies the existence of a local curvature of space-time. The space-time of Special Relativity is, indeed, a continuum of four dimensions included in the category of Euclidean continua of which the plane is an example in two dimensions. But nothing prevents us from supposing that space-time is not everywhere Euclidean, that it possesses local curvatures. There does not then exist in this space, systems of rectilinear Cartesian coordinates, and the position of points in it can be determined only with the aid of coordinates analogous to those that are used in geometry for the study of curved surfaces. Observers placed in curved regions of space-time therefore necessarily use curvilinear coordinates to determine events in it, and from this follows the appearance of gravitational forces.” (96) General relativity 101.
- “Whole numbers are frequently met with, in fact, in all branches of physics where was have to be considered: in elasticity, in acoustics, in optics. They appear in the phenomena of standing waves, of interference, and of resonance. It was therefore admissible to think that the interpretation of the conditions of quantization would lead to introducing a wave aspect of the intra-atomic electrons.” (161)
- “To sum up, the fundamental postulates stated above are justified by the possibility of founding them on a coherent theory, compatible with all the experimental facts, and by the impossibility of finding another system that possesses these same qualities. In reality, all physical theories are always justified by reasons of this kind, for at the base of any physical theory lie arbitrary postulates, and it is the success of these postulates that makes their use legitimate.” (205)
- “In classical theories where probabilities enter, the elementary processes were considered to be controlled by rigorous laws, and probabilities were introduced to describe large-scale phenomena relating to an immense number of elementary phenomena. In quantum physics, on the contrary, probabilities are directly introduced to describe the course of elementary processes.” (213)
- De Broglie talks about how our everyday perceptions of macroscopic objects, of “a well-localized corpuscle, of a strictly monochromatic wave” may be “idealizations,” that they may be “overly simplified and highly rigid products of our minds” that “can never be applied exactly to reality.” And later: “We could also, in another range of ideas, examine whether all ‘idealizations’ are not that much less applicable to reality when they become more complete and, although we have little inclination to be paradoxical, we could hold, contrary to Descartes, that nothing is more misleading than a clear and distinct idea. But it is wise to stop at this dangerous point and return to physics.” (219) REALITY IS A LIE! :P

[Ricardo Vega · Rating 5 out of 5]

An excellent account from one of the protagonist of the birth and development of quantum mechanics.