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Anybody know how far off relativity becomes at large velocities and small distances?

  1. Aug 1, 2008 #1
    Hi there,

    I'm wondering if anybody knows how far off relativity becomes at large velocities and small distances? Quantitativly? I just need to know a specific example at a specific velocity near c or maybe a couple along the c scale. Has anyone ran tests?

    -Devin
     
  2. jcsd
  3. Aug 2, 2008 #2

    James R

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    Re: Anybody know how far off relativity becomes at large velocities and small distanc

    This kind of thing is determined by the Lorentz factor, which is:

    [tex]\gamma = \frac{1}{\sqrt{1-(v/c)^2}}[/tex]

    This factor appears in formulae such as the time dilation and length contraction formulae of special relativity.

    The Lorentz factor at speed [itex]v = 0[/itex] has the value 1, which means no time dilation and no length contraction of an object at rest.

    At a speed of half the speed of light, for example (v = c/2), the Lorentz factor is 1.15, which means that time is dilated by 15% compared to the rest frame, and length is contracted by about 15%.

    At 90% of the speed of light (v = 0.9c), the Lorentz factor is 2.29, which means that clocks on the moving object run at a little under 1/2 the speed of clocks that are at rest, and the length of a moving object is contracted by a factor of a little over 2.

    You can try other values of v yourself to get a feel for things.
     
  4. Aug 2, 2008 #3

    George Jones

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    Re: Anybody know how far off relativity becomes at large velocities and small distanc

    Could you elaborate a bit on what you mean by
     
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