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I read somewhere that Einstein's formula is mostly quoted in the abbreviated version E=mc^{2} but it should actually be written E^{2}=m^{2}c^{4}. Is that true?

Asked by: Bret W.### Answer

The expression E = mc^{2}is the rest energy of an object of rest mass m. In motion, the object's total energy is a sum of its rest energy and its kinetic energy. That is

E = [(p

^{2}c

^{2}) + m

^{2}c

^{4}]

^{1/2}

where p is the object's momentum. You get this more general equation for energy using something called the momentum-energy 4-vector, which you will learn more about if you study special relativity. The 4 vector contains four components: three spatial components of momentum and one time component of momentum. E is just the magnitude of this vector. If you square both sides of the equation, you get:

E

^{2}= (p

^{2}c

^{2}) + (m

^{2}c

^{4}).

Notice that you get E

^{2}= m

^{2}c

^{4}if the object has zero momentum; that is, if the object is at rest.

Answered by: Philip Zell, Ph.D. Physics, ACT, Inc.

The 2 equations:

a. E=mc

^{2}

b. E

^{2}= m

^{2}c

^{4}

differ only if there is a physical meaning to negative mass and/or energy values. In a. a negative mass value implies a negative energy value only. In b. the same negative mass value has both negative and positive energy solutions. Also, b. allows for both positive and negative solutions for energy even if mass is positive.

Whether negative mass and energy values have any useful connection to reality is another question.

Answered by: Paul Walorski, A.B.Physics

'As long as men are free to ask what they must; free to say what they think; free to think what they will; freedom can never be lost and science can never regress. '

(

**J. Robert Oppenheimer**(

*1904-1966*)