To Capra, particle physics was the point where science transcended sensory experience and thus we couldn’t rely with absolute certainty on logic and common sense. Starting with the second part, common sense is a relative thing, before Galileo it was common sense that the Earth was the center of the universe, but now we know its not. The first part however is more interesting.
When this The Tao of Physics was written, there was a big problem in particle physics because the there were so thousands of particles popping up everywhere and their seamed to be no real method to the madness. So it may have very well seamed that physics was beyond logic. But soon after the Standard Model was created, a beautiful mathematical framework from which matter can be described, bring order to the chaos in particle physics. The final piece to the standard model was discovered in 2013 with the discovery of the Higgs Boson at CERN’s Large Hadron Collider.
The Standard Model is very important when it comes to putting into prospective what we dont know. Because when Newton came up with his law for gravitation, he left out any speculation on what might be causing that pull, leaving that question for the future (and quite frankly, we still dont have an understanding of what causes it). As with Newton, the Standard Model created more questions than it answered, and many of the possible answers seam to defy logic now, but eventually we will build another machine like the LHC and find the answers. Thus a new aspect of reality will become an aspect of common sense and with this new understanding, the illogical aspects of particle physics will become logical.
The reason that Capra gives for inability to rely on logic and common sense is that the realm of particle physics takes place at distances of 10^-15 meters and thus is outside of our sensory perception. To him, we only ever see the consequences of investigated phenomena, such as “the audible click of a Geiger counter, or in a dark spot on a photographic plate”. But if that is defined as beyond our sensory perception than everything see should transcend our sensory experience, because our eyes work in the same way as both of his examples. So if we take our sight as sensory perception, than why not the result of the Gieger Counter or the photographic plate or the what we observe in the Large Hadron Collider. Because all three of those work in fundamentally the same way as our sight, and we built all three off of knowledge that we gained through experiences from our sight.
Because of the nature of the Standard Model and its origins, it serves as a prime example of another aspect of The Tao of Physics. One of Capra’s main positions is that because math is so abstract, its detached from the world and is inflexible when it comes to conveying sensory experience. But while it is abstract, language is as well. Both relay on symbols to convey meaning, the only difference between normal language and mathematics then is the fact that mathematics is built purely on logic while many of the foundations for normal languages are metaphors and thus is inaccurate. But while normal language like English allows us to convey sensory experiences in ways that are easier to understand, mathematics conveys it in a more fundamental sense and this can make it hard to understand. For example, we could describe a doughnut in normal English, our you could put together all of these different mathematical equations (equation of a torus, density gradients, chemical formulas as functions of position, you could even describe the entire thing using the standard model). The only problem with this approach is that it would take up a lot of space and not only be very complex but also very hard to follow. So the English description, while less accurate, would be better.
The main point of all of this is simply this: Mathematics is a language, and when compared to other languages, it fits into what programmers would call a “low level language” or a language that has little abstraction. Because of this, it is still able to do all that languages like English could do, just in a way that is much harder to understand. And when it comes to describing nature, that fact that we can attribute all of matter to a mathematical statement that can be written on a single piece of paper, it is very hard to not look at mathematics as the language that the universe is written in.
Here is a video talking about the LHC and the standard model. FYI this was in 2008 when the LHC was being completed.