Poynting vector power (PVP) http://en.wikipedia.org/wiki/Poynting_vector allows energy transfer from one space-time location to another. In physics, its physical dimension is defined as energy (E) per unit of time (t): PVP ~ E/t. If time is absolutely zero then power is undefined, mathematically as well as physically; and the question whether it is a vector or a scalar is meaningless and pointless. However, the variation of power is a very important aspect of all waves’ propagation.
If energy is an invariance as the zero-point energy (e) then power and time (now, again disjointed from physical space) are related by an inverse variation with e as the variational constant. This is logical if and only if power, time, and e are all scalars such that an inequality exists for the incremental changes of absolute power (DP=|PVP|) and time (Dt) and their product is always greater than or equal to e: DPDt≥e. The 2D graph is the positive branch of a hyperbola. On the other hand, the product of energy difference (DE) and time difference (Dt) is always greater than or equal to Planck’s constant of action (ħ): DEDt≥ħ. This is just an alternative expression for the uncertainty relation derived by Einstein during the heydays of quantum revolution.
Next is to ask the question what physical relation exists between these inequalities? If the first is divided by the second then DP/DE≥e/ħ and if the second is divided by the first then DE/DP≥ħ/e. Both are timeless. In the limit as DE®0 and ħ®1 then ¶P/¶E=e. In the limit DP®0 and e®1 then ¶E/¶P=ħ. The 1st suggests a continuous symmetry while the 2nd a discrete symmetry. However, expressed as products: ¶P=e¶E and ¶E=ħ¶P and by the transitive property ¶P=eħ¶P®eħ=1. This implies that the product of Planck’s constant and zero-point energy is absolute unity. It becomes dimensionless if and only if the dimension of time is equivalent to the inverse square of energy: time ~ 1/E².
__________________ Time independence: [∂E(g)]²=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: ¶a(t)·¶r(t)=c²
Re: Pvp 
Linear Mode
