# Inequalities and Rearranging equations

1. Apr 10, 2014

### 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

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. Apr 10, 2014

### HallsofIvy

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?