The third aspect of my subject is that of science as a method of finding things out. This method is based on the principle that observation is the judge of whether something is so or not. All other aspects and characteristics of science can be understood directly when we understand that observation is the ultimate and final judge of the truth of an idea. But “prove” used in this way really means “test,” in the same way that a hundred-proof alcohol is a test of the alcohol, and for people today the idea really should be translated as, “The exception tests the rule.” Or, put another way, “The exception proves that the rule is wrong.” That is the principle of science. If there is an exception to any rule, and if it can be proved by observation, that rule is wrong.
The third aspect of my subject is that of science as a method of finding things out. This method is based on the principle that observation is the judge of whether something is so or not. All other aspects and characteristics of science can be understood directly when we understand that observation is the ultimate and final judge of the truth of an idea. But “prove” used in this way really means “test,” in the same way that a hundred-proof alcohol is a test of the alcohol, and for people today the idea really should be translated as, “The exception tests the rule.” Or, put another way, “The exception proves that the rule is wrong.” That is the principle of science. If there is an exception to any rule, and if it can be proved by observation, that rule is wrong.
To remind you, this book is based on a course I taught in 2006. On the last day of class, I followed the great tradition pioneered by Richard Feynman, in which the last class should be one where you can ask the teacher anything. Feynman's rule was that you could ask about anything except politics, religion, or the final exam. In my case, there was no final exam, and I didn't even make politics or religion off-limits. This chapter collects some of the questions people asked me, together with my responses. Student: Do you often think about using computer science to limit or give us a hint about physical theories? Do you think that we'll be able to discover physical theories which give more powerful models than quantum computation? Scott: Is BQP the end of the road, or is there more to be found? That's a fantastic question, and I wish more people would think about it. I’m being a bit of a politician here and not answering directly, because obviously the answer is “I don't know.” I guess the whole idea with science is that if we don't know the answer, we don't try to sprout one out of our butt or something. We try to base our answers on something. So, everything we know is consistent with the idea that quantum computing is the end of the road. Greg Kuperberg had an analogy I really liked. He said that there are people who keep saying that we've gone from classical to quantum mechanics so what other surprises are in store? But maybe that's like first assuming the Earth is flat, and then on discovering that it's round, saying who knows, maybe it has the topology of a Klein bottle. There's a surprise in a given direction, but once you've assimilated it, there may not be any further surprise in that same direction.
It has always been the ideal of science to discover laws of nature on which we can all agree. Agreement requires evidence independent of individual judgment, i.e., objective evidence. We apply the term objective to such unbiased scientific evidence because we associate it with an external world of objects that we conceive to be the origin of our information. This external world is instinctively invented by each of us as a means of dealing with invariant patterns in his private world of experience. The invention is validated and elaborated as a consequence of the fact that it turns out to be sharable. In fact the common content of all our invented external worlds is so unambiguous and independent of individual bias that it can form the universally accepted basis for communication and action in an organized society. The consistency of the patterns of experience associated with the external world is such that we are under severe psychological compulsion to assign to this world an existence independent of our experience and a reality superior to that of any small part of our experience. Physical science is devoted to the study of the “laws” of the external physical universe, i.e., to the behaviour of the objects in it. Hence there is a strong tendency to project into the external world the information gathered by scientifically objective methods and even the theoretical concepts in terms of which the information is interpreted. Whatever is so projected is objective in a second sense of the term, i.e., assigned by us to the external world of objects.
Ed hai corragio di traitor scherzando un negozio si serio? [And you have the nerve to joke about so serious a business?] – Susanna My amiable friend Professor Mozart dropped by the other day. Now that his NSF grant has been cut way back, he has more time to think about things, and it's a pleasure to chat with him. Some of his views, though, are more than a little peculiar, as the following conversation clearly reveals. “I have to admit,” Mozart began sadly, “that particle physics over the last 40 or 50 years has been a disappointment. Who would have expected that in half a century we wouldn't learn anything really profound?” “Nothing profound?!” I exploded. “What about parity nonconservation? What about the breakdown of time-reversal symmetry?” “To be sure,” sighed Mozart, “we've learned that left can be distinguished from right and that time past is different from time future. But most ordinary people knew the difference between left and right all along, and who except the most highly trained physicists—temporarily, it now turns out—ever doubted for a moment that they could tell the future from the past? So establishing that the asymmetry is really there after all is certainly commendable. But about really serious problems we've discovered nothing—nothing whatsoever about the central puzzle.” “And just what might that puzzle be?” I urged, for he seemed in danger of succumbing to an attack of melancholia. He revived. “All particle physics has taught us about the central mystery is that quantum mechanics still works. Perfectly, as far as anybody can tell. What a letdown!” “Letdown? It's a triumph!” “Letdown!” he insisted. “Think of the previous half-century, when we went down from the macroscopic by seven or eight orders of magnitude. What delicious confusion! All the verities of the preceding two centuries, held by physicists and ordinary people alike, simply fell apart—collapsed. We had to start all over again, and we came up with something that worked just beautifully but was so strange that nobody had any idea what it meant except Bohr, and practically nobody could understand him . So naturally we kept probing further, getting to smaller and smaller length scales, waiting for the next revolution to shed some light on the meaning of the old one. But what happened? For 65 years, since 1925, we've been probing, at finer and finer levels.
When I was asked to talk about quantum beauty I was a little startled, because the beauty of quantum theory is something that practising physicists, in the course of their work, rarely think about or mention. But when I gave the idea a chance, it really caught my imagination. And that’s why I’m here. Quantum beauty really is a wonderful, true thing to talk about. I’m going to sneak up on quantum beauty by putting it in historical context. The right context, I think, is a broader question: Does the world embody beautiful ideas? That is a question that people have thought about for a long time. Its intellectual history deserves volumes and syllabi. Here, though, I want to keep things brief and entertaining, so I shall spin a simple tale of heroes. Pythagoras and Plato intuited that the world should embody beautiful ideas; Newton and Maxwell demonstrated how the world could embody beautiful ideas, in specific impressive cases. Finally, in the twentieth century in modern physics, and especially in quantum physics, we find a definitive answer: Yes! – the world does embody beautiful ideas.