I think the title about says it all.
If someone asks me "What good is the Theory of General Relativity?" (or what did Einstein do that was so great, or whatever) My pat answer is, "You use GPS right? Well, GPS requires knowing the location (in time and space) of GPS satellites to an astonishing precision. The only way to obtain that precision is through an understanding of General Relativity.
Or, "What's this Bose-Einstein Condensate good for?" I will answer, that it enables extraordinarily precise measurements of the earth's gravitational field. 10 years ago, this was actively being tested as a new means of navigating submarines. (There's a lot of background as to why that's important that I go into, but presumably most readers here understand those reasons.)
So, how does one answer the question, "What good is knowing about these quark things anyway? Does any technology depend upon them?"
ps. While writing up this question, and double checking that it wasn't a duplicate, I saw this question: Why does GPS depend on relativity? which implies my assertion about GPS may be wrong. But, if nothing else, it demonstrates that the impact of General Relativity can be measured using devices/systems that are "known" to most people.
Answer
Is there any current technology that depends upon a deep understanding of quarks?
No, there isn't. There are technologies that depend in various ways upon nuclear physics and knowledge of nuclear forces. However, those technologies predate the quark model. If the quark model had never been discovered, it would have had no effect on nuclear power, nuclear weapons, MRI, radiation therapy, biological use of radioactive tracers, radioactive dating, or any other application I can think of. Every application on that list predates the quark model, at least in principle. (E.g., NMR is the only nuclear physics principle used in MRI.)
Of course, it's hard to prove a negative. I'm a nuclear physicist by training, but that's no guarantee that I'm not missing a counterexample.
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