# Inequalities and Rearranging equations

by cooev769
Tags: equations, inequalities, rearranging
 P: 106 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.
Math
Emeritus
Thanks
PF Gold
P: 39,556
 Quote by cooev769 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
Yes, -100+ 3 is equivalent to -97 which is negative.

 Rearrange to 3=3<0
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 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
"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'm not happy with this proof.
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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