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Schutz GR Book, Question about World line.

  1. Mar 7, 2017 #1
    This isn't homework, nor is it an exercise problem; merely a question about a diagram.

    Re: B.Schutz book "A First Course in General Relativity" 2nd Edition, (Asian print version), page 5, Figure 1.1 "A spacetime diagram in natural units".

    From section 1.4 Spacetime diagrams:
    A world line is the locus of events observed by the reference frame as a particle moves with velocity v.
    The vertical axis is t. The horizontal axis is x.
    The equation is: slope=dt/dx = 1/v where v=1 is the speed of light.
    When v=1, the slope of the world line is positive at 45 degrees. When v>1, the slope is positive but less than 45 degrees.

    Q: The World line for |v|<1 has a negative slope - goes from upper left to lower right. Can someone explain why this slope is negative and why not positive greater than 45 degrees?

    Lou.
     
  2. jcsd
  3. Mar 7, 2017 #2

    TSny

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    Welcome to PF.

    Suppose that you wish to draw a world line corresponding to |v| = .5, which is an example of |v| < 1. There are two possible values of v that satisfy |v| = .5; namely, v = +.5 and v = -.5. So, if you wanted to draw a world line that satisfies |v| = .5, you have a choice of drawing a line with a positive slope of 2 or a line with a negative slope of -2. Either line would make an angle with respect to the x-axis that has a magnitude greater than 45o. Schutz chose to draw a line corresponding to the negative value of v that satisfies |v| < 1.
     
  4. Mar 7, 2017 #3
    I understand your logic. Not very kind of Schutz to omit that small explaination
    Thanks for your help.
    I see dizzying notation coming in the next sections. I may need more help.
     
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