A classical physicist analyzes FTL motion.

Discussion in 'Physics & Math' started by Dinosaur, Sep 26, 2003.

  1. Dinosaur Rational Skeptic Valued Senior Member

    Messages:
    4,885
    Isaac started wondering about FTL motion. It seemed like an intriguing thot. Imagine being hit by an object you never saw coming toward you because it was outracing light itself.

    What sort of thought experiment seems proper. Anything nearby cannot really be analyzed. Suppose I imagine an object which starts one million light years away. Last week, I used a (5, 12, 13) right triangle in another analysis. I like that triangle, so here goes.

    Imagine an object moving at 4c (4 times the speed of light) along the hypotenuse of a (5, 12, 13) right triangle. As before, the 12-leg (12 light years, that is) is along the line of sight, and the 5-leg is perpendicular to the line of sight. I better draw a diagram to help me. I will use light years as the unit of distance and other units such that the speed of light is exactly one.

    What would an observer on Earth see if he had the technology to view such an object?
    • At time = 0, the object starts on its way along the hypotenuse.
    • At time = 1,000,000 million years, the observer sees the object start.
    • At time = 3.25 (13 / 4), the object arrives 13 years away along the hypotenuse and light from it starts toward Earth.
    • At time = 999,991.25 (1,000,000 - 12 + 3.25), light from the 13 light year point reaches earth.
    • Gee, the light from the 13 light year point got to Earth before the light from the starting point. That is strange, but I understand. The observer on Earth would think that the object was traveling from the 13 light year point (where he first saw it) back to the actual starting point (from which he saw light later).
    • The proper motion is about .5714c (5 / 8.75)
    If the actual proper motion was clockwise on the imaginary celestial sphere, the observed proper motion would be counterclockwise. It seems a bit strange, but then proper motion is almost never actual motion, since only a tiny fraction of the observed objects have actual motion perpendicular to the line of sight.

    There is a slight approximation in the above calculation, but it would not affect the first 5-6 decimal places due to 1,000,000 light years being so many orders of magnitude greater than 12.

    Gee, let me try that formula I derived from the analysis last week.
    • ApparentSpeed = Actualspeed*Sine(angle) / [1 - ActualSpeed*Cosine(angle) ]

      Sine = 5 / 13 and cosine = 12 / 13

      Gee that works out to about minus .5714, with the minus sign indicating that the proper motion observed would be in the direction opposite to the perpendicular component of the actual motion.
    That formula from last week is pretty good, although it looks like the denominator could be zero which is likely to be a no-no. For actual speeds greater than the speed of light, there might be other anomalies resulting from use of that formula. I better not use it for all thot experiments without doing some further analysis.
     

Share This Page