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  1. #41

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    I generally prefer the less speculative aspects of quantum mechanics. For instance, how it is that so much of chemistry can be "explained" by quantum mechanics, or how electron tunneling can occur in proteins and play such an important part in the production of ATP in pretty much all of life.

    I liked Sussikind's lectures:
    http://www.youtube.com/watch?v=0Eeuqh9QfNI

    The mathematics he uses in the course is minimal, but I feel like he addresses what the main changes in intuition about the natural world that quantum theory would suggest.

    To me, the main difference between "classical" and quantum theories is in our ways of knowing and not knowing things about the world...the difference between "classical" measurement and information, and quantum measurement and information.

    In "classical" theories:
    1) We have observable variables that can be measured to pretty much arbitrary precision and accuracy.
    2) We can, in theory, measure these observable variables together to arbitrary precision if we can do it very carefully.
    3) Uncertainty is just "not knowing", and can be explained using basic probability theory.

    In quantum theories:
    1) We have observable "operators" that can result only in "proper" (eigen) values when measured.
    2) We can only measure "commuting" observables together to arbitrary precision. It is not possible to measure "non-commuting" observables together to arbitrary precision, no matter how careful we are.
    3) Uncertainty can be fundamental to what we are measuring. There are many philosophical interpretations of why this is the case. But a naive interpretation of just "not knowing" because we aren't careful enough is no longer tenable.

    Also, I don't think we need to go into idle speculation to have an interesting discussion about quantum mechanics.

    For instance:
    1) Why do we find it difficult to compress things in condensed states? (for instance, why do people call water "uncompressible", but in nuetron stars, matter can get compressed beyond this.)
    2) Why does the periodic table take the form it does?
    3) How does light interact with matter?
    4) Why do we get the results we get from the double slit experiment?
    Last edited by ygolo; 07-19-2012 at 04:00 AM.

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  2. #42
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    please explain :


    How do you prove mathematically that gauge theories with spontaneous symmetry are renormalizable

    explain the EPR "paradox" and its solution ?

    explain why quantum cloning is impossible. (it violates conservation of probability)?

    explain non-commuting variables and what they mean for the uncertainty principle?

    explain the quantum harmonic oscillator and its energy spectrum ?


  3. #43

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    The list you provided is long, and each subject can be discussed at length. I am not sure what the first question is about. The last three are the simplest, and the last two can be be found in most introductory texts in quantum mechanics (at least they are in the ones I used).

    Quote Originally Posted by Darya View Post
    explain the EPR "paradox" and its solution ?
    The Einstein-Podolsky-Rosen paradox has to do with entangled spins that are separated over large distances. The claim is that this thought experiment and Bell Test Experiments create an argument where one has to choose between non-local hidden variables and quantum mechanical counter factual definiteness.

    To be honest, this is beyond my depth. My "understanding" of these things is superficial at best. I find the GHZ experiments to be far easier to understand, and even here, I would say my "understanding" is superficial.


    Quote Originally Posted by Darya View Post
    explain why quantum cloning is impossible. (it violates conservation of probability)?
    The No-Cloning Theorem is proven by a proof by contradiction. I don't believe it can be summed up by saying it "violates conservation of probability" Then again, I find this phrase very ambiguous. Do you mean that the time evolution operator would have to produce probabilities that don't sum up to one?

    The proof can be found here:
    http://www.quantiki.org/wiki/The_no-cloning_theorem

    Quote Originally Posted by Darya View Post
    explain non-commuting variables and what they mean for the uncertainty principle?
    I think this question is essential, and can take you through a tour of introductory quantum mechanics. The proof of the generalized uncertainty principle is not long, but understanding it requires understanding operators and measurement and the formalism of quantum mechanics.
    One version can be found here:
    http://galileo.phys.virginia.edu/cla...tPrinciple.htm

    If you would like, we can discuss this further and in-depth. I feel like my understanding of this is fairly mature. But there are issues regarding Energy-Time uncertainty that I need to really think through.

    Quote Originally Posted by Darya View Post
    explain the quantum harmonic oscillator and its energy spectrum ?
    I actually find this a tiny bit tedious. The results can be used for approximations in a lot of systems, and the use of ladder operators in solving the Schrodinger Equation is an important thing to learn too. Ladder operators are reused in solving the Schrodinger Equation for Hydrogen-like systems (or any spherically symmetric system).

    Wikipedia doesn't do a great job here, but the solutions to the Shrodinger Equation is given:
    http://en.wikipedia.org/wiki/Quantum...nic_oscillator

    Again, I feel relatively comfortable going deeper into these things.

    Quote Originally Posted by Darya View Post

    Accept the past. Live for the present. Look forward to the future.
    Robot Fusion
    "As our island of knowledge grows, so does the shore of our ignorance." John Wheeler
    "[A] scientist looking at nonscientific problems is just as dumb as the next guy." Richard Feynman
    "[P]etabytes of [] data is not the same thing as understanding emergent mechanisms and structures." Jim Crutchfield

  4. #44
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    Hmm isn't quantum something like "anything can happen anywhere at any time of any place for any reason?"

    Actually no that's wrong, it's just a nice sounding quote. Essentially this is one of those things I will never understand and have no real drive to. It annoys me because I idealise those who do want to understand such things. Those of more intelligence or at least those with an interest in what could pretentiously be dubbed 'higher pursuit's always interest me, primarily because I think people as individuals are endlessly fascinated by that which they are not.

    So im impressed by intelligence, the scientific and an understanding or interest in extremely complex theories or ideas. Because I possess none of them.

    But back to quantum, it looks interesting...well I suppose...maybe, it might possibly, definitely, certainly could be.

    I suppose this goes along with this idea ive got that you should always push yourself to try and understand or grasp something, even if you know deep down it is beyond the scope of your understanding.
    'One of (Lucas) Cranach's masterpieces, discussed by (Joseph) Koerner, is in it's self-referentiality the perfect expression of left-hemisphere emptiness and a precursor of post-modernism. There is no longer anything to point to beyond, nothing Other, so it points pointlessly to itself.' - Iain McGilChrist

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    "Suppose it didn't," said Pooh, after careful thought.
    Piglet was comforted by this.
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    i find the topic interesting, dunno really what to say about it here tho. one new interesting field of science is quantum biology, anyone interested in biology and quantum physics should really check it out
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  6. #46
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    Quote Originally Posted by AffirmitiveAnxiety View Post
    Hmm isn't quantum something like "anything can happen anywhere at any time of any place for any reason?"
    No. The key is that in the everyday world, classical mechanics still reigns supreme. It's only when you get down to the level of subatomic particles that you start to see quantum effects. For 99% of the time it has very little impact on the everyday world. Although, there are cases in molecular Biology where it has an effect, and humans have engineered numerous devices that take advantage of quantum effects.

  7. #47
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    Quote Originally Posted by rhinosaur View Post
    No. The key is that in the everyday world, classical mechanics still reigns supreme. It's only when you get down to the level of subatomic particles that you start to see quantum effects. For 99% of the time it has very little impact on the everyday world. Although, there are cases in molecular Biology where it has an effect, and humans have engineered numerous devices that take advantage of quantum effects.
    Quote Originally Posted by AffirmitiveAnxiety View Post
    Actually no that's wrong, it's just a nice sounding quote.

    Indeed!
    'One of (Lucas) Cranach's masterpieces, discussed by (Joseph) Koerner, is in it's self-referentiality the perfect expression of left-hemisphere emptiness and a precursor of post-modernism. There is no longer anything to point to beyond, nothing Other, so it points pointlessly to itself.' - Iain McGilChrist

    Suppose a tree fell down, Pooh, when we were underneath it?"
    "Suppose it didn't," said Pooh, after careful thought.
    Piglet was comforted by this.
    - A.A. Milne.

  8. #48
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    Quote Originally Posted by rhinosaur View Post
    No. The key is that in the everyday world, classical mechanics still reigns supreme. It's only when you get down to the level of subatomic particles that you start to see quantum effects. For 99% of the time it has very little impact on the everyday world. Although, there are cases in molecular Biology where it has an effect, and humans have engineered numerous devices that take advantage of quantum effects.

    Death rays?



    http://www.physik.uni-marburg.de/of/dynamics/impot.html



    If anyone's interested, i actually found an article exactly describing what I spoke of in my first post.

  9. #49
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    I can't pretend to understand quantum theory, but I'm am highly interested in the things that might come of it. Especially when it comes to computing and communication. Quantum computing strikes me as one of those killer tools for which we're not exactly sure what kinds of problems it will solve. It seems to have some of the properties of parallel processing and a huge speedup when solving NP-complete problems.

    Also one of the best results of quantum theory is giving me enought to suspend disbelief in multiple universe science fiction. Anathem rocked.

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    Quote Originally Posted by Qlip View Post
    Quantum computing strikes me as one of those killer tools for which we're not exactly sure what kinds of problems it will solve.
    basically how it would work is that you can basically store unlimited amounts of information, have a library that can store all information people put in it. but there is one fundamental problem on it, you cant search it like you search physical libraries, you cant browse the library. but what at least a while ago seemed to be the only possibility to retrieve information is to ask questions from the library, but the answers to the questions would have to be simple yes or no, either some qbit matches the search or it doesent. but they have found an smart trick to overcome this problem to some degree, which at least works in theory(everything about this is a theory, because we havent been able to build a quantum computer yet, but its still a multi million industry today and there are certain things that should be work and certain that would no way work). basically if you want to search a book from there, you write the title of the book, it gives you all the possible searches that you might be looking for(many qbits say yes to your question), and if you want to limit the amount of search results, you just start writing the start of the book, till only one qbit says yes to this "question" and fills up the rest of the book for you to read(or you could just pick one of the search results it offered).

    i think quantum technology is better for storing information, but the future of computing is on biology, which naturally has to incorporate some aspects of quantum mechanics, due to the somewhat new findings in the field of quantum biology, to make the biological computing work properly.
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