29 May 2023

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.


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