Particle Physics Made Easy

This book should be a must read for anyone that tries to understand particle physics. I've been looking for something like this for a long time. The Standard Model is explained with great skill and clarity, and with minimal use of math. This is not a mathematical book, but where minimal mathematics becomes necessary (group theory), it is introduced with the assumption that the reader knows next to nothing (which was my case) and developed to the point where, combined with physics, it makes sense. Most of the math only requires logic, not computations, and all you are required to memorize are a few rules -- conventions -- that only take a couple of lines. Beautiful.
The author limits himself to what is known and generally agreed about particle physics. The limits of the theory are also very well explained, but no significant steps into the unknown are made, which I think it is a good thing for once.
If you like Brian Greene, Michio Kaku, Lisa Randall, and others like them, do them, and yourself, a favor: read "Deep Down Things". It will open new horizons in the way you see, and appreciate, their work. These more popular authors cross into the unknown with beautiful, breathtaking constructs, but none explains the basics as Bruce Schumm does.

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A Review From a Non-Physicist


Two items set this lay physics book apart: clarity of writing and minimum of speculation. It covers only material amenable to experimentation. This rules out both string theory and multiple universes - each mentioned only briefly. Nor does it dwell on Einstein's theories of special or general relativity - the gravitational physics of the large. "Deep Down Things" is like an introductory text on quantum phenomenon and particle physics without the explicit math and with more explicit wordage.

Particle physics studies the smallest units of matter and how they interact with each other. This led to ever larger particle accelerators during the last 68 years of the 20th century. More than 150 exotic particles have been discovered - every one having differing combinations of properties that boggle the mind. An exotic particle that results from the collision of two protons may exist for only 10 to the minus 12 seconds before it decays into something else. Traveling at close to the speed of light, this is just enough time to leave a (highly sought after) 1 mm mark on a recorder, documenting the brief life of that particle. The Particle Data Group from Berkeley exists just to keep physicists updated on these particles.

For something so fleeting, why do we bother? Because this research is centerstage in explaining the Big Bang and all of cosmology. As by-products, we achieved huge gains in any industry you can name. Unless you live like a Mennonite or are on a boy scout camp-out, these technologies effect the way you live your daily life - ground floor activity on the internet itself came about because physicists desired a more immediate way to share research with each other.

The use of common sense was not a factor in the investigations of particle physics. Instead, knowledge was and is gained through particle accelerators, predictions from abstract mathematical models, and meticulous use of the scientific method by thousands of physicists. The author mentions frequently that the math works out, predicts something, disproves something, needs a cheat factor, etc. This made me want to see the math, but I'm at least a couple of college courses from there, so I guess I'll have to take his word for it. For non-physics, non-math majors, consider reading on despite lack of total understanding or you might bog down in details. As the point of view changes, concepts are restated and you'll get another stab at it. The author starts a sentence on page 187, "If you've understood, even vaguely..." and ends it with "it gets even better (or worse...) as we move on to other properties of elementary particles."

On page 351, he closes with congratulations to anyone who made it to the end - then inserts a joke about the Higgs field that only an "insider" (a physicist or one who read the book) would understand. This is a great book that I highly recommend for any physicist who wants to brush up on particle physics, any undergrad or grad student in physics, or any other scientist types who are persistent enough to want a better handle on this fascinating but difficult subject.




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It really is "Breathtaking"

This is a book about quantum mechanics, and gauge theory in particular. It's essentially non-mathematical, having just a few equations, and requires little mathematical expertise. For readers with math anxiety, or those unfamiliar with partial differential equations, the few equations in the book can be skipped without missing much, as Schumm focuses almost exclusively on providing a qualitative understanding of what's at the heart of the Standard Model of quantum mechanics.

This isn't your typical book on quantum mechanics, aimed at your typical armchair scientists. There's virtually no discussion about various speculative macroscopic aspects of QM, such as freewill. God doesn't come into the picture except as a non-personal synonym for "the universe." Schrödinger's cat isn't discussed. Neither is tunneling, time travel, teleportation, or Bell's inequality. This text is what I'd describe as a nuts-and-bolts qualitative look or introduction to the Standard model. I think it would be excellent reading for anyone contemplating a class in QM, before taking a quantitative and detailed course on the subject. Of course, I'd also recommend it for casual yet serious readers who want to know the basis for modern quantum theory.

The first half of the book lays the groundwork with a discussion of forces of nature, patterns, the building blocks of nature, and symmetry. I particularly liked Schumm's explanation of how symmetry relates to conserved quantities. I think he does an especially nice job of describing Lie groups and segueing the topic into the heart of this book, which is gauge theory.

The gauge principle says that objects within a system are subject to precise laws of interaction. It also says that the wave equation is invariant with respect to local changes in phase. The connection between these two notions (phase invariance and laws of interaction) provides a quantitative theory for causation, known as the gauge principle. [pp. 276-277] I commend Schumm for presenting the basic principles and arguments of gauge theory in a way that can be clearly understood at a qualitative level. Here's a summary of how he does it.

Start with the Schrödinger wave equation. Next, apply the condition that information cannot be instantaneously transmitted or transmitted with arbitrary speed over arbitrary distances. This is a principle that seems deeply ingrained in Einstein's relativity, that no object with non-zero mass energy can travel faster than the speed of light, and is the position taken by Yang and Mills in their 1954 paper in the Physical Review, where they argue the following:

"As usually conceived, however, this arbitrariness is subject to the following limitations: once one chooses [the phase of the wave function] at one space-time point, one is then not free to make any choices at other space-time points. It seems that this is not consistent with the localized filed concept that underlies the usual physical theories. In the present paper we wish to explore the possibility of requiring all interactions to be invariant under independent [choices of phase] at all space-time points. [p. 217-218]

Back to the Schrödinger wave equation, Schumm considers the case of an isolated electron (no potential). To make the wave function invariant with respect to local changes in phase, Schumm describes a trick used by Yang and Mills, in which they added a new term to the wave equation, a so-called "cheating" term, A(x). A(x) changes when the phase of the wave function changes, in just the right way so that the overall wave function is unaltered by local changes in the wave function's phase. This might seem like an obvious and trivial thing to do, but interestingly, when you do this you find that the cheating function, A(x), represents the quantum of the electromagnetic field - the photon. As Schumm explains:

"The inclusion of A(x) thus incorporates, within the field-theoretical description of the particle's behavior, the possibility that the particle emits or absorbs a photon, that is, the possibility that the particle emits or absorbs a quantum of the electromagnetic field."

This is a nifty trick. Start with the Schrödinger equation for an isolated particle, apply the relativity principle by insisting on invariance of local phase shifts, add a "cheating" factor to make phase invariant, and the "cheating factor" ends up being the quantum force mediator of the particle described by the Schrödinger equation. The nature of the cheating term depends on the symmetry of possible changes to the wave function. That's where Lie groups come in, and that's why it's so helpful the way Schumm lays the conceptual foundation with his chapter on Lie groups.

Mathematically, the symmetry of a quantum particle is described by the Lie group that describes possible changes to the particle's wave equation. If the group has only simple phase-change symmetry we end up with quantum electrodynamics, or the quantum theory of the electromagnetic force. For wave functions described by more complicated Lie groups (wave equations that have rotational symmetry in some internal symmetry space), we must add different cheating terms, as many as there are generators of the Lie group. This is the basic idea behind the gauge principle, which is at the heart of the Standard model of quantum mechanics. Of the four known forces of nature, three (electromagnetic, weak nuclear, and the strong nuclear interactions) are explainable from the well-established methods of gauge theory.

This was one of the best books I've read this year. It's long (just short of 360 pages) with lots of material between the covers. You'll want to read the Appendix and notes, and you'll most likely find yourself reading over parts of the book several times, digesting the meaning behind the words. In the end, I think you'll agree with the author's assessment that quantum mechanics - the study of "deep down things" really does reveal a breathtaking beauty of the natural world.


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