bf1.txt

Boson and Fermion
=================

假如 mass m 是容易測量的，設
{
m = m0 e^(s t) ...(1)
where m0, s = constants
s = 0 ...(2)
or
s = +/- i k ...(3), where k = real constant
}

(1):
dm/dt = m0 e^(s t) s
dm/dt = s m
d(m c^2)/dt = s m c^2
dE/dt = s E
如果 energy E 可分為 n 粒粒子 (per unit volume) 組成的, n > 0
d(n h f)/dt = s n h f
d(n f)/dt = s n f
d(n f)/(n f) = s dt
ln(n f) - ln(n0 f0) = s t
n f = n0 f0 e^(s t)
Assume f, f0, n are real, n0 = 1
n f = f0 e^(s t) ...(4)

增補資訊 conj(n f) 以組成一個世界

n f = conj(f0 e^(s t))
n f = f0 e^(-s t) ...(5)

(4) * (5)
n^2 f^2 = f0^2
n f = +/- f0 ...(6)

振動頻率，可以因觀測者移動時有 doppler effect 而有不同的觀測值。
所以相同的振動現像，可能有不同的 f 及 f0 。

n f' = +/- f0' ...(7)

set
f0' = f_ε' ~= 0 ...(*)

(7):
n f' = +/- f_ε'
{
n f' = f_ε' ...(8)
n f' = -f_ε' ...(9)
}

(6):
n f -/+ f0 = 0
n f -/+ f0 + f_ε' = f_ε' ...(10)
n f -/+ f0 - f_ε' = -f_ε' ...(11)

Case 1:
(8) & (10):
n f -/+ f0 + f_ε' = n f'
n f' = n f - f0 + f_ε' ...(12)
or
n f' = n f + f0 + f_ε' ...(13)

Case 2:
(9) & (10):
n f -/+ f0 + f_ε' = -n f'
n f' = -(n f - f0 + f_ε') ...(14)
or
n f' = -(n f + f0 + f_ε') ...(15)

Case 3:
(8) & (11):
n f -/+ f0 - f_ε' = -n f'
n f' = -(n f - f0 - f_ε') ...(16)
or
n f' = -(n f + f0 - f_ε') ...(17)

Case 4:
(9) & (11):
n f -/+ f0 - f_ε' = n f'
n f' = n f - f0 - f_ε' ...(18)
or
n f' = n f + f0 - f_ε' ...(19)

Rename f as ν, f0 as ν0
另外，再考慮正頻率 ν, ν0, ν' 等情況加上 (*) 式的效果
可以轉換座標，設定
n ν_boson = n ν' = n ν - ν0 ...(20)
n ν_fermion = n ν' = n ν + ν0 ...(21)