On squaring and adding a cos θ and a sin θ, a = [ a1² + a2² + 2 a1a2 cos θ ] ½, => from this equation it can be seen that when θ = 0 ,2π, 4π …. then, a = a1 + a2. The Heisenberg principle has the effect of obliterating whatever knowledge I might have of an ‘up or down’ spin if I choose to measure ‘right-ness or left-ness’. By discerning what were the fundamental rules that govern how atoms interact with each other and how they interact with light, you also have now a fundamental understanding of chemistry.

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