Preprint Einstein’s Mass-Energy Equivalence is not applicable to Photon Energy
Relativistic speed refers to speed at which relativistic effects become significant to the desired accuracy of measurement of the phenomenon being observed. Relativistic effects are those discrepancies between values calculated by models considering and not considering relativity.
Mass-energy equivalence: E = mv^2, where m is relativistic mass, v is relativistic velocity, and E is relativistic energy.
c denote the speed of light. c ≠ v.
Somebodies say that E^2 = (pc)^2 + (m0c^2)^2 is applicable to the momentum pf photon. - It is wrong. Here, p = (m0v)/sqrt(1- (v/c)^2) and m0 is rest mass, But photon has neither no rest mass nor relativistic mass.
Relativistic velocity is any velocity that is "significant fraction" of light (but nevertheless, less than speed of light. What is 'significant' fraction depends on your choice . You may choose the case when gamma= (1-v^2/c^2)^(1/2) is significantly higher than 1
SO for the consideration
(note,. gamma is ratio of relativistic vs rest mass , relativistic vs 'proper' time, proper vs relativistic length etc.)
gamma=1+10^-9 when v/c=4.47*10-5; v~13400 m/s~13.4 km/s
gamma=1+10^-6 when v/c=1.4142*10^-3; v~424300 m/s~424 km/s
gamma=1+10^-3 when v/c=0.0447; v~13400 km/s
gamma=1.01 when v/c=0.14, v~42100 km/s
gamma=1.1 when v/c=0.42, v~125000 km/s
what is acceptable deviation from newtonean mechanics would vary from case-to-case i.e. the authoritative dictation of the accepting authority. GPS needs to track for one-in-a-billion or less part's deviation, we don't care if one droplet less drink falls into our cup or comes into out drinking vessel.
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