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Featured Insights Relativity using the Bondi k-Calculus - Comments

  1. Apr 10, 2017 #1

    robphy

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  2. jcsd
  3. Apr 10, 2017 #2
    Great insight.
     
  4. Apr 11, 2017 #3
    To the author, you have exposed different approaches to this body of knowledge. What approach or ways would you use and sequence say for undergraduate instruction.
     
  5. Apr 11, 2017 #4

    robphy

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    Any approach I use must use the spacetime diagram
    because I think it is difficult to represent the relativity-of-simultaneity using boxcars as "moving frames of reference".

    Any approach I use must use radar methods
    to motivate measurements and the assignment of coordinates.
    I think radar methods are more straightforward than lattices of "clocks" and "rods".
    (For inertial motions in special relativity, they are equivalent.
    However, for more general motions in special and general relativity, they may differ....
    and would require more advanced discussion to address.)

    In my opinion, the Bondi k-calculus method (with its emphasis on radar measurements) is the best starting point, especially for algebra-based physics. With the k-calculus methods, the standard textbook formulas are straightforward to derive and fall out naturally.

    A related but even less well known approach by Geroch (in his General Relativity from A to B) is also a good starting point. Geroch uses radar methods to emphasize the square-interval and give operational interpretations of the geometry of spacetime (e.g., what simultaneity means to an observer) in both Special Relativity and Galilean Relativity. My AJP article (which inspired the Insight https://www.physicsforums.com/insights/relativity-rotated-graph-paper/ ) was my attempt to combine Bondi's and Geroch's approaches.

    From here, I would go on to develop the geometry of Minkowski spacetime, while comparing and contrasting with Euclidean geometry, using the [unappreciated] geometry of Galilean spacetime (e.g., https://www.desmos.com/calculator/ti58l2sair ... play with the E-slider) ...something I call "Spacetime Trigonometry", a large ongoing project with many aspects which generates lots of posters for me at AAPT meetings. (I should really write this up soon... but it would have to be broken into a series of AJP articles.) These are examples of Cayley-Klein geometries, which includes the deSitter spacetimes.. This "unification" can help formalize the numerous analogies mentioned in the literature. In addition, I can develop vector and tensorial methods (algebraically, graphically, and geometrically) in order to make contact with traditional intermediate and advanced presentations of relativity.
     
  6. Apr 11, 2017 #5
    Please keep us posted, I will enjoy following your work.
     
  7. Apr 12, 2017 #6

    pervect

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    Thanks for posting this. A lot of times I want to refer people to Bondi's approach, as I also feel it's one of the best elementary treatments for the person new to relativity. I can and do refer interested people to his book, but it's nice to have a more accessible source.
     
  8. Apr 12, 2017 #7

    robphy

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    Thanks. I was torn between making it as elementary as possible for a beginner (which would only be a tweak on Bondi or just the equations already provided by Wikipedia) or making clarifications and connections to geometry (the logical next step).
     
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