Holographic Statistics
Suppose we take the idea that particles can never be inside a black hole event horizon as an axiom. This means we can either set the 2-particle wave function for cases where particles are too close to zero. But this does not lead to smooth functions. Another option is to reflect this part of the wave function back out to infinity. For stationary masses m_1 and m_2. Ψ (x,y) = Ψ ( (x + y)/2 + (x-y) (m_1+m_2) /|x-y|/2, (x + y)/2 - (m_1+m_2) (x-y) | x-y|/2 ) u= (x + y)/2 + (x-y) (m_1+m_2) /|x-y|/2 v= (x + y)/2 - (m_1+m_2) (x-y) | x-y|/2 L = (d/dy^2-m2^2)(d/dx^2-m1^2) Ψ (x,y) + (d/dv^2-m1^2)(d/dv^2-m^2) Ψ (u,v) ?? invariant under x->u, y->v so Ψ(0,r) = Ψ(0,m/r) ? Ψ(0,m) = Ψ(0,m) Ψ(m,0) = Ψ(m,0) Ψ(m/2,m/2) = Ψ(m/2,m/2) H=s(x,y)[ Ψ (x,y) - Ψ ( (x + y)/2 + (x-y) (m_1+m_2) /|x-y|/2, (x + y)/2 - (m_1+m_2) (x-y) | x-y|/2 ) ] dxdy