Quantum mass calculation
- 1. The purpose of this calculation is to express Newtonian force, acceleration, and mass in terms of Quantum Mechanics. c speedof light= mv p= h λ = c h f = p momentum= E Energy= ΔpΔx hbar 2 t time= c 1 μ0 ε0 = ΔEΔt hbar 2 x length= m mass= ΔE ΔpΔx Δt = Δ mv( ) Δx Δt = c Δx Δt = v= h planksconstant= ΔE Δmcc= hbar planksconstant normalized( )= v velocity= E m 1 μ0 ε0 = c= a acceleration= F force= ma= E m 1 μ0 ε0 = c 2 = μ permeability= ε permittivity= ΔE Δm μ0 ε0 = hbar 2Δt = because ΔE Δmcc= hbar 2Δt = Δt hbar μ0 ε0 2Δm = (solve for ∆t) μ0 ε0 2Δt Δm hbar Δv Δv = μ0 ε0 2Δm hbar a = 2Δm hbar F m = 2Δm 2 hbar F = NOTE: ∆t/∆v = 1/a a = F/m F 2Δm 2 hbar μ0 ε0 = therefore and a 2Δm μ0 ε0 hbar = m μ0 ε0 hbar F 2 =
- 2. As a check, lets see if F=ma... m a μ0 ε0 hbar F 2 2Δm hbar μ0 ε0 = μ0 ε0 hbar F 2 2Δm μ0 ε0 hbar 2Δm μ0 ε0 hbar = m a 2 F Δm hbar μ0 ε0 = F 2 2F Δm 2 hbar μ0 ε0 = square both sides F 2Δm 2 hbar μ0 ε0 = divide both side by "F" So what exactly is this all good for??? Suppose you have a plasma like that found in a fusion reactor... Also suppose that the relative permeability and permittivity are functions of this plasma's state at any given delta t.... t .01 0.1 25 some_function_of_plasma_1 t( ) sin 1.2t( ) t 3 t 2 t 2 2 10( ) 4 some_function_of_plasma_2 t( ) sin t( ) t 3 t 2 t 2 2 10( ) 4 εr some_function_of_plasma_1 μr some_function_of_plasma_2 0 10 20 0.1 0.05 0 0.05 0.1 εr t( ) μr t( ) t then ∆t = t2 - t1 on the graph Δt hbar μr μ0 εr ε0 2Δm =