Phase shift in relative frequencies due to relativistic effects invalidates relativistic covariant spacetime:

In relativity, time and space are relativistic covariant but phase shift in frequencies due to relativistic effects invalidate relativistic covariant spacetime.

Explanation

In physics and statistics, time and space are polymorphous, but in pure mathematics time and space have no physical properties. They are only mathematical parameters:

In classical physics, time and space are determinist and invariant; 

In statistical physics, time and space are probabilistic and invariant; 

In relativity, time and space are relativistic, covariant, and downgraded mere components of relativistic spacetime; 

In quantum physics, time and space are probabilistic and invariant.

However, in relativity, time and space are relativistic covariant but Phase shift in relative frequencies due to relativistic effects invalidates relativistic covariant spacetime.

Reference: Relativistic effects on phaseshift in frequencies invalidate time dilation II

My observation - "A moving particle of mass (m), spends half of its total energy in achieving electromagnetic speed":

• A particle having no rest mass (m=0), and moving at the speed of light, spends half of its total energy (E/2), in becoming a particle at rest.  
• And, a particle having mass (m=1), and at rest, spends half of its total energy (E/2), in achieving the speed of light. 
• Where, total energy of any particle equivalents it's potential energy and kinetic energy E = (E.P+E.K) = mv²; E = (E.P+E.K) = mc²; (Note: p=mv but p=Ec).

Explanation:

A moving particle has total energy (E), mass (m), speed (v) but its mechanical speed is less than the speed of light (c). 

In this case, the moving particle will have total energy (E) = {kinetic energy (E.k) + potential energy (E.p)}.

E = (E.k + E.p)....... (1).

However, according to Newtonian mechanics, the kinetic energy of a moving particle,

(E.k) = 1/2mv²........(2).

When the mechanical speed (v) of the particle attains the speed of light (c) in vacuum, the total energy of the particle becomes,

E = m(c)²/2 ............(3).

According to mass-energy equivalence, the total energy (E) of mass (m),

E = mc² ................(4).

At full speed of light, the total kinetic energy of a particle should be only (E=mc²).

However, comparing all the above equations, especially equations three (...3) and four (...4), we get the total kinetic energy of the particle (E = m(c)²/2).

That is, half of the particle's total energy (E = mc²), expended from potential energy (E.p), so that the particle acquires mechanical to electromagnetic speeds.

Soumendra Nath Thakur. May 29, 2023.