Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

I Question about Einstein's 1905 derivation of E=mc^2

  1. Mar 14, 2016 #1
    Link: https://www.fourmilab.ch/etexts/einstein/E_mc2/www/

    The only part I'm having trouble with is how he gets the plus sign in that 1+(v/c)cos(φ) numerator for the "other" light ray (emitted in the opposite direction of the first).

    My understanding is that the φ he uses in his general Doppler equation represents the angle formed by the source/receiver line-of-sight (as seen by the source at the time of emission) and the receiver's direction of motion (as measured in the source frame). If that's right, then the plus sign in that numerator is equivalent to taking the cosine of (φ + 180°) rather than φ for the "other" light ray.

    So I'm 99% sure that it's an implied symmetry argument, but I don't know how to demonstrate its validity mathematically.

    Can anyone help me out?
     
  2. jcsd
  3. Mar 14, 2016 #2
    I think maybe I've misunderstood what the angle represents, and that this is much simpler than I suspected.
     
  4. Mar 15, 2016 #3

    stevendaryl

    User Avatar
    Staff Emeritus
    Science Advisor

    If two photons are sent in opposite directions, and one makes an angle of [itex]\varphi[/itex] with respect to the x-axis, then the other makes an angle of [itex]\varphi + 180^o[/itex] with respect to the x axis. So for the transformation of frequency, etc., for the second photon, you just replace [itex]\varphi[/itex] by [itex]\varphi + 180^o[/itex].
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Question about Einstein's 1905 derivation of E=mc^2
  1. A question about E=mc^2 (Replies: 16)

  2. Questions about E=mc^2 (Replies: 25)

  3. Derivation of E=mc^2 (Replies: 6)

Loading...