| negative time
Time appears explicitly as a conjugate variable of the uncertainty inequality given by DeDt≥h. This says that the product of change in energy with the change in time is always greater than or equal to Planck’s constant of action, h. If De=e1-e2 and Dt=t1-t2then simple algebraic expansion gives e1t1-e1t2-e2t1-e2t2. This can be separated into two linearly independent inequalities with the action evenly distributed for symmetry: e11t1-e12t2≥½h and -e21t1+e22t2≥½h then solving them for the cases of equality, the three determinants needed for finding t1 and t2 are ½h(e22-e12), ½h(e11-e21), and e11e22-e12e21. Then t1=½h(e22-e12)/(e11e22-e12e21) and t2=½h(e11-e21)/ (e11e22-e12e21). For negative time either e22<e12 or e11<e21 but not both.
For the case where e11=e22<e12=e21, then t1 and t2 reverted to being positive. However, the Fourier inversion gives the frequency domains as f1=f2=2(e11+e12)/h. For the trivial case where e11=e12 then n=f1=f2=4e/h such that the zero-point energy is given by e°=¼hn. In general, the action can be evenly distributed into n energy equipartitions such that there exists n rational factors and that r1=r2=r3=…=rn where r1+r2+r3+…+rn=1. This normalization is clearly a probabilistic requirement. Note that negative time does not necessarily imply negative energy. It can only indicate time’s directional property as a vector quantity.
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Time independence: [∂E(g)]²=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: ¶a(t)·¶r(t)=c²
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Re: negative time 
Linear Mode
