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Inequalities and Rearranging equations 
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#1
Apr1014, 06:30 AM

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. 


#2
Apr1014, 08:39 AM

Math
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Thanks
PF Gold
P: 39,310

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. 


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