E=m·c² -- Total Relativistic Energy: UNIZOR.COM - Relativity 4 All - Conservation
Channel: Zor Shekhtman on UNIZOR Education
Date: 2023-10-03

UNIZOR.COM - Physics through a Looking Glass of Mathematician
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Relativistic Total Energy

Recall an expression for a kinetic energy K of an object of mass m0 moving with speed u derived in the previous lecture Relativistic Kinetic Energy of this course:
K = m0·c²/√(1−u²/c²) − m0·c²
where c is the speed of light in vacuum.

So, kinetic energy is represented as a difference between two other expressions.
Naturally, it's tempting to consider these other two expressions as representing some type of energy themselves.

Consider an equivalent to above formula
m0·c² + K = m0·c²/√(1−u²/c²)
It says that a sum of kinetic energy (K) and something else (m0·c²) equals that same something else increased by a familiar Lorentz γ-factor.
Logically speaking, that something else must be some form of energy because, when we add two physical variables, they must be of the same kind and units.

Moreover, the right side of this equation that expresses something else multiplied by Lorentz γ-factor depends on the speed of object u and becomes equal to something else when speed equals to zero.

Obvious conclusion is that something else (m0·c²) represents some form of energy that is concentrated in an object at rest in a frame of reference associated with it, while the right side of a formula is the result of increasing this rest energy by an amount of kinetic energy (K) developed by this object because of its motion.

In other words, an expression
E = m0·c²/√(1−u²/c²)
represents the total energy of a moving object that is equal to a sum of its energy at rest and kinetic energy of its motion.
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