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  • Joseph Nebus 12:48 am on Thursday, 3 October, 2013 Permalink | Reply
    Tags: , quantum, quantum field theory, , ,   

    From ElKement: May The Force Field Be With You 


    I’m derelict in mentioning this but ElKement’s blog, Theory And Practice Of Trying To Combine Just Anything, has published the second part of a non-equation-based description of quantum field theory. This one, titled “May The Force Field Be With You: Primer on Quantum Mechanics and Why We Need Quantum Field Theory”, is about introducing the idea of a field, and a bit of how they can be understood in quantum mechanics terms.

    A field, in this context, means some quantity that’s got a defined value for every point in space and time that you’re studying. As ElKement notes, the temperature is probably the most familiar to people. I’d imagine that’s partly because it’s relatively easy to feel the temperature change as one goes about one’s business — after all, gravity is also a field, but almost none of us feel it appreciably change — and because weather maps make the changes of that in space and in time available in attractive pictures.

    The thing the field contains can be just about anything. The temperature would be just a plain old number, or as mathematicians would have it a “scalar”. But you can also have fields that describe stuff like the pull of gravity, which is a certain amount of pull and pointing, for us, toward the center of the earth. You can also have fields that describe, for example, how quickly and in what direction the water within a river is flowing. These strengths-and-directions are called “vectors” [1], and a field of vectors offers a lot of interesting mathematics and useful physics. You can also plunge into more exotic mathematical constructs, but you don’t have to. And you don’t need to understand any of this to read ElKement’s more robust introduction to all this.

    [1] The independent student newspaper for the New Jersey Institute of Technology is named The Vector, and has as motto “With Magnitude and Direction Since 1924”. I don’t know if other tech schools have newspapers which use a similar joke.

     
    • elkement 6:22 am on Thursday, 3 October, 2013 Permalink | Reply

      Thanks again for your kind pingback and publicity :-)
      I need to get to vectors and tensors in the next post(s) but I am still trying to figure out how to do this without mentioning those terms. Fluid dynamics is often a good starting point, e.g. to introduce, ‘derive’ or better motivate Schrödinger’s equation. On the other hand Feynman used to plunge directly into path integrals – presenting them as a rule along the lines of “This is the way nature works – live with it” – and deriving Schrödinger’s equation later.

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      • Joseph Nebus 3:20 am on Saturday, 5 October, 2013 Permalink | Reply

        I’m not quite sure how I’d do either. I think I could probably explain vectors without having to use mathematical symbolism, since the idea of stuff moving at particular speeds in directions can call on physical intuition. Tensors I don’t know how I’d try to explain in popular terms, partly because I’m not really as proficient in them as I should be. I probably need to think seriously about my own understanding of them.

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        • elkement 6:26 pm on Monday, 7 October, 2013 Permalink | Reply

          I have also always considered easier to imagine the different aspects of a vector – the abstract object and the ‘arrow’ as it lives in a specific base. But how do you really imagine the ‘abstract tensor object’ – in contrast to a ‘matrix’ (with more than 3 dimensions probably…)

          I have started to read about general relativity (… will finish after I have finally understood the Higgs…) and it took me quite a while to comprehend that you are not allowed to shift a vector in curved space as you shift the ‘arrow’. Actually it made me think about vectors in a new way…

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          • Joseph Nebus 2:46 am on Friday, 18 October, 2013 Permalink | Reply

            (I’m embarrassed that I lost this comment somehow.)

            I can sort of reconstruct the process when I think I started to get vectors as a concept, particularly in thinking of them as not tied to some particular point, or even containing information about a point, but somehow floating freely off that. If I get around to trying to explain vectors I might even be able to make all that explicit again.

            Tensors I keep feeling like I’m on the verge of having that intuitive leap to where I have some mental model for how they work but I keep finding I don’t quite do enough work with them that it gets past following the rules and into really understanding the rules.

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  • Joseph Nebus 12:25 am on Tuesday, 1 October, 2013 Permalink | Reply
    Tags: , , , , quantum,   

    September 2013’s Statistics 


    And as it’s the start of the month I have a fresh round of reviewing the statistics for readership around here. I have seen a nice increase in both views — from 367 to about 466 total views — and in visitors — from 175 to 236 — which maybe reflects the resumption of the school year (in the United States, anyway) and some more reliable posting (of original articles and of links to other people’s) on my part. (Maybe. If I’m reading this rightly I actually only posted nine new things in September, which is the same as in August. I’m surprised that WordPress’s statistics page doesn’t seem to report how many new articles there were in the month, though.) My contrarian nature forces me to note this means my views-per-reader ratio has dropped to 1.97, down from 2.10. I suppose as long as the views-per-reader statistic stays above 1.00 I’m not doing too badly.

    The most popular articles the past month were:

    1. From ElKement: Space Balls, Baywatch, and the Geekiness of Classical Mechanics, which is really just pointing and slightly setting up ElKement’s start to a series on quantum field theory which you can too understand;
    2. How Many Trapezoids I Can Draw, which is a persistent favorite and makes me suspect that I’ve hit on something that teachers ask students about. If I could think of a couple other nice little how-many-of-these-things problems there are I’d post them gladly, although that might screw up some people’s homework assignments;
    3. Reading the Comics, September 11, 2012, which is another persistent favorite and I can’t imagine that it’s entirely about the date (although the similar Reading the Comics entry for September 11 of 2013 just missed being one of the top articles this month so perhaps the subject lines are just that effective a bit of click-baiting);
    4. What Is Calculus I Like?, about my own realization that I never took a Calculus I course in the conditions that most people who take it do. I’d like more answers to the question of what experiences in intro-to-calculus courses are like, since I’m assuming that I will someday teach it again and while I think I can empathize with students, I would surely do better at understanding what they don’t understand if I knew better what people in similar courses went through;
    5. Some Difficult Math Problems That You Understand, which is again pointing to another blog — here, Maths In A Minute — with a couple of mathematics problems that pretty much anyone can understand on their first reading. The problems are hard ones, each of which has challenged the mathematical community for generations, so you aren’t going to solve them; but, thinking about them and trying to solve them is probably a great exercise and likely to lead you to discovering something you didn’t know.

    I got the greatest number of readers from the United States again (271), with Canada (31) once more in second place. The United Kingdom’s climbed back into the top three (21), while August’s number-three, Denmark, dropped out of the top ten and behind both Singapore and the Philippines. I got a mass of single-reader countries this time, too: Azerbaijan, Bangladesh, Belgium, Cambodia, the Czech Republic, Indonesia, Israel, Italy, Mexico, Norway, Poland, Qatar, Spain, Sri Lanka, Switzerland, and Thailand. Bangladesh and Sri Lanka are repeats from last month, but my Estonian readership seems to have fled entirely. At least India and New Zealand still like me.

     
    • elkement 10:35 am on Tuesday, 1 October, 2013 Permalink | Reply

      It is weird that my “Austrian clicks” never show up in your statistics (?)

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      • Joseph Nebus 4:37 pm on Wednesday, 2 October, 2013 Permalink | Reply

        (I didn’t know you were from Austria. I’ve been to the country as part of a tour, but only had a couple of partial days there.) And they do show up, just … well, for the past 30 days Austria comes in tied for fourth with New Zealand. Now I’m curious who my faithful New Zealander is or are, too.

        I wouldn’t want to make the reeling off of data too overwhelming but if folks are interested in the full list of nations sending me readers it’s not hard to start reporting those. Anyone out there interested?

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  • Joseph Nebus 10:55 am on Thursday, 19 September, 2013 Permalink | Reply
    Tags: , , , quantum, ,   

    From ElKement: Space Balls, Baywatch, and the Geekiness of Classical Mechanics 


    Over on Elkement’s blog, Theory and Practice of Trying To Combine Just Anything, is the start of a new series about quantum field theory. Elke Stangl is trying a pretty impressive trick here in trying to describe a pretty advanced field without resorting to the piles of equations that maybe are needed to be precise, but, which also fill the page with piles of equations.

    The first entry is about classical mechanics, and contrasting the familiar way that it gets introduced to people —- the whole forceequalsmasstimesacceleration bit — and an alternate description, based on what’s called the Principle of Least Action. This alternate description is as good as the familiar old Newton’s Laws in describing what’s going on, but it also makes a host of powerful new mathematical tools available. So when you get into serious physics work you tend to shift over to that model; and, if you want to start talking Modern Physics, stuff like quantum mechanics, you pretty nearly have to start with that if you want to do anything.

    So, since it introduces in clear language a fascinating and important part of physics and mathematics, I’d recommend folks try reading the essay. It’s building up to an explanation of fields, as the modern physicist understands them, too, which is similarly an important topic worth being informed about.

     
    • elkement 11:03 am on Thursday, 19 September, 2013 Permalink | Reply

      Thanks a lot, Joseph – I am really honored :-) I hope I will be able to meet the expectations raised by your post :-D

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    • elkement 11:06 am on Thursday, 19 September, 2013 Permalink | Reply

      Reblogged this on Theory and Practice of Trying to Combine Just Anything and commented:
      This is self-serving, but I can’t resist reblogging Joseph Nebus’ endorsement of my posts on Quantum Field Theory. Joseph is running a great blog on mathematics, and he manages to explain math in an accessible and entertaining way. I hope I will be able to do the same to theoretical physics!

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