Im reading this fun and iconoclastic work by Scott Aaronson, "Quantum computing since Democritus": https://www.scottaaronson.com/democritus/
Its not really a textbook on quantum computing, for that you can go to Michael A. Nielsen & Isaac L. Chuang classic, the great lectures by john preskill http://www.theory.caltech.edu/people/preskill/ph229/, or David Mermin´s great book.
Aaronson´s book is a deep meditation on the cross references between computer science´s complexity theory, physics and philosophy. an excerpt:
"So, what is quantum mechanics? Even though it was discovered by physicists, it's not a physical theory in the same sense as electromagnetism or general relativity. In the usual "hierarchy of sciences" -- with biology at the top, then chemistry, then physics, then math -- quantum mechanics sits at a level between math and physics that I don't know a good name for. Basically, quantum mechanics is the operating system that other physical theories run on as application software (with the exception of general relativity, which hasn't yet been successfully ported to this particular OS). There's even a word for taking a physical theory and porting it to this OS: "to quantize."
But if quantum mechanics isn't physics in the usual sense -- if it's not about matter, or energy, or waves, or particles -- then what is it about? From my perspective, it's about information and probabilities and observables, and how they relate to each other.
Its not really a textbook on quantum computing, for that you can go to Michael A. Nielsen & Isaac L. Chuang classic, the great lectures by john preskill http://www.theory.caltech.edu/people/preskill/ph229/, or David Mermin´s great book.
Aaronson´s book is a deep meditation on the cross references between computer science´s complexity theory, physics and philosophy. an excerpt:
"So, what is quantum mechanics? Even though it was discovered by physicists, it's not a physical theory in the same sense as electromagnetism or general relativity. In the usual "hierarchy of sciences" -- with biology at the top, then chemistry, then physics, then math -- quantum mechanics sits at a level between math and physics that I don't know a good name for. Basically, quantum mechanics is the operating system that other physical theories run on as application software (with the exception of general relativity, which hasn't yet been successfully ported to this particular OS). There's even a word for taking a physical theory and porting it to this OS: "to quantize."
But if quantum mechanics isn't physics in the usual sense -- if it's not about matter, or energy, or waves, or particles -- then what is it about? From my perspective, it's about information and probabilities and observables, and how they relate to each other.
- Ray Laflamme: That's very much a computer-science point of view.
Scott: Yes, it is.
- Ray Laflamme: And yet, with all the structures
mathematicians studied, none of them came up with quantum mechanics
until experiment forced it on them...
Scott: Yes -- and to me, that's a perfect illustration of why experiments are relevant in the first place! More often than not, the only
reason we need experiments is that we're not smart enough. After the
experiment has been done, if we've learned anything worth knowing at
all, then hopefully we've learned why the experiment wasn't
necessary to begin with -- why it wouldn't have made sense for the world
to be any other way. But we're too dumb to figure it out ourselves!
Two other perfect examples of "obvious-in-retrospect" theories are evolution and special relativity. Admittedly, I don't know if the ancient Greeks, sitting around in their togas, could have figured out that these theories were true. But certainly -- certainly! -- they could've figured out that they were possibly true: that they're powerful principles that would've at least been on God's whiteboard when She was brainstorming the world.
In this lecture, I'm going to try to convince you -- without any recourse to experiment -- that quantum mechanics would also have been on God's whiteboard. I'm going to show you why, if you want a universe with certain very generic properties, you seem forced to one of three choices: (1) determinism, (2) classical probabilities, or (3) quantum mechanics. Even if the "mystery" of quantum mechanics can never be banished entirely, you might be surprised by just how far people could've gotten without leaving their armchairs! That they didn't get far until atomic spectra and so on forced the theory down their throats is one of the strongest arguments I know for experiments being necessary."
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