I wrote the relationship in the last post. t != E. I don't know where you got that. Here's the eq. for the E of a photon, E = f. Frequency is 1/t. Same as the Uncertainty Principle.
"delta means a rate of CHANGE of something,
Delta is simply a difference. Rate is a difference per time. Delta and rate do not mean the same thing.
" momentum means NO CHANGE of state."
No it doesn't. I gave it in the last post. p = E. Showing c explicitly gives, p = E/c. The wavelength of a massive particle is 1/p, or showing h explicitly, "h/p".
Heisenberg(1927)got it wrong in his HUP because Plank(1900)got it wrong because Simon DeLa Place(1827)got it wrong. Momentum is not a determinant of energy, it is a RESULT of balanced Wave energy equals Particle energy, or W=P. You use the term p for momentum which is easily confused with particle velocity. Planck wrote it as h=pxq where h is an area defined by p(particle velocity)and q(momentum). It creates less confusion to use capital M to denote Momentum, vs small m to denote mass. Yes, Debroglie gives MATTER WAVELENGTH as Lambda=h/mv but not h/p. mv or mc just mean Momentum, the other "hidden" v in mv is the MATTER WAVE determinant(mv^2). Think of it(W)as the ordinate in the graph and(P)is the abscissa, with the 45 degree line as the Momentum-diagonal wherein dPv is the tread and dWs is the riser in the stairway up and down the Momentum D-line, each chevron-shaped area so defined is another unit quantum(h). You still get frequency of bose photons and fermions confused, its a common mistake. It's all explained by the wave galaxy of 3 quarks at the core of fermions as the model for our milky way(spiral)galaxy. As it expands/contracts it is the inductance part of resistance/capacitance/inductance in electric circuits. You still have to overcome the mistaken idea that time and kinetic energy are 2 different things though(blessed is he who OVERCOMES)... W=P