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Uniqueness and origin of physics theorems

  1. Oct 5, 2012 #1
    After studying some of the proofs of equations, worries arises about their uniqueness.
    1.Removal of integral
    ∫∇.Edτ = ∫(ρ/ε)dτ
    →∇.E = Q/ε

    2.Removal of (∇X)
    ∇XE = ∂B/∂t = ∂(∇XA)/∂t
    →∇X(E+∂A/∂t)=0
    →E+∂A/∂t=-∇V
    →E=-∇V-∂A/∂t

    Origin -
    Certain physics equations/theorems have no (discrete physical/mathematical) proof, or my knowledge is not board enough.
    1.F = dp/dt
    2.E = F.s
    3.Wave-particle duality
    4.c (speed of light) is ALWAYS the same for ALL observers

    Wouldn't the current theorems fail if the uniqueness fails/assumptions are not correct?
     
  2. jcsd
  3. Oct 5, 2012 #2
    you can derive gauss law using maxwell fourth eqn and continuity eqn.
    c2(∇×B)=j/ε0+∂E/∂t
    taking the divergence of it and using ∇.j=-∂ρ/∂t one gets
    ∇.E=ρ/ε0
     
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