Thoughts

  Are p articles q uantized p erturbations of s ome u nderlying f ields? In classical field theory, the fields behave to minize the action – integral of the lagrangian. Does the minimal action formalism hold when the fields are quantum operators? If so, it dictakes how a field operator should evolve with time? Can the evolution of a state with time be expressed in a minimal action formalism?

  How are abstract concepts encoded, stored and recalled in a network of nodes and connections? In a simple set of n nodes, each having 2 states (on and off), the whole set can have 2^n states. The states of the whole set can represent 2^n concepts. This is much larger than the scheme of each node representing a concept, which can represent n concepts. Without external intervention, how to recall a state of the whole set, or transition from one state to another state? Will need to have connections between the nodes, which allow nodes to be activated or deactivated by other nodes.

  Iterative phase determination and information content in Fourier transformation Information content basis for iterative phase determination of Fourier transformation Consider a linear array of N complex values a(j), j = 0 to N-1. a(j) contains 2N independent real values. It’s discrete Fourier transformation is an array of N complex values Fa(2pi*j/N), j = -int(N/2) to N-int(N/2)-1. If a(j) is real, it contains only N independent real values, then Fa(j) = [Fa(-j)]’, so Fa(j) only contains N independent real values. If a(j) is real and >=0 for all j, then it contains N independent non-negative values. Then, the N real values in the Fourier transformation Fa(j) are no longer independent. In an expanded support, A(j) = a(j), for j = 0 to N-1, A(j) = 0 for j=N to 2N-1, the Fourier transformation FA( 2pi*j/(2N)), j = -N to N-1. If a(j) is real and >=0, then F A (j) = [F A (-j)]’, and |FA(j)| might be the (N+1) independent non-negati...

  Fundamental “operators” in quantum physics a + and a - They started out as the particle number operator a + a - . It is a hermitian operator: a + =((a - )’) T , For a state of n particles, <n|a + a - |n>=n. More fundamental is the operator commutation relationship a - a + -a + a - =1, for bosons. It means that if <n|a + a - |n>=n, then <n+1|a + a - |n+1>=n+1. The proof is: <n|a + a - |n>=n and a - a + -a + a - =1 means <n|a - a + |n>=n+1, meaning a + |n>= (n+1) 0.5 e iθn |n+1>, thus |n+1>=(n+1) -0.5 e -iθn a + |n>, thus <n+1|=<n|a - (n+1) -0.5 e iθn , thus <n+1|a + a - |n+1>=<n|a - (n+1) -0.5 e iθn a + a - (n+1) -0.5 e -iθn a + |n> =1/(n+1)<n|a - (a + a - )a + |n>. We specify that these operators obey (AB)C=A(BC), in other words the sequence of grouping does not matter. Then <n+1|a + a - |n+1>=<n|a - (a + a - )a + |n>/(n+1) =<n|(a - a + )(a - a...