Inequalities and Rearranging equations

  1. So i have an equation to calculate the impossibility of pair production during photon decay into two electrons and I'm having to do some momentum conservation, can't quite do it but a colleague of mine has suggested this which I don't particularly agree with some help would be appreciated.

    So we have some numbers which are constants and one we know is < 0 because its a square negative. He suggests using something like the simple example below which clearly doesn't work if you could suggest why that would be great.

    -100+3=-97<0

    Rearrange to

    3=3<0

    He did the same thing but with energies, where k is a constant:

    k -Ea^2/c^2 - Eb^2/c^2 - 2EaEb/c^2 = -Ei^2/c^2 < 0

    Just rearranged to:

    Ea^2/c^2 + Eb^2/c^2 + 2EaEb/c^2 -Ei^2/c^2 < 0

    Ea^2/c^2 + Eb^2/c^2 + 2EaEb/c^2 < Ei^2/c^2

    I'm not happy with this proof.
     
  2. jcsd
  3. HallsofIvy

    HallsofIvy 40,783
    Staff Emeritus
    Science Advisor

    Yes, -100+ 3 is equivalent to -97 which is negative.

    No. You don't say how you rearranged this but this incorrect. I suspect that you got "3= 3" by adding 100 to both sides of -100+ 3= -97 but the result is no longer "< 0". You would have to add 100 to each part to arrive at "3= 3< 100".

    "He" appears to have done two things to the first inequality:
    First, multiply by -1. But multiplying by a negative number reverses the inequality:
    -k+ Ea^2/c^3+ Eb^2/c^2+ 2EaEb/c^2= Ei^2/c^2> 0

    then add k to each part:
    Ea^2/c^3+ Eb^2/c^3+ 2EaEb/c^2= Ei^2/c^2+ k> k.

    I don't mean to be harsh but shouldn't two people who are working with "pair production" and "photon decay" be able to do basic, elementary school algebra?
     
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