Mass-energy equivalence where's the arbitrary constant?

[hatsoff]

I'm curious about the famous formula, [tex]e=mc^2[/tex] . Since mass can be measured in any of several unit systems, shouldn't the formula read [tex]e\propto mc^2[/tex] ?

Thanks!

 

[russ_watters]

No, you just need to keep the units consistent throughout the equation.

 

[sir-pinski]

Great question! The famous formula e=mc^2 is actually derived from the more general equation E^2 = (mc^2)^2 + (pc)^2, where E is the total energy, m is the rest mass, and p is the momentum. This equation is a result of Einstein's theory of special relativity, which shows that mass and energy are interchangeable and can be converted into one another. The constant c^2 is not arbitrary, but rather a fundamental constant in the universe known as the speed of light. It is a constant that relates the units of mass and energy in the equation. Therefore, the formula e=mc^2 is not dependent on the unit system used to measure mass, as the constant c^2 remains the same. However, if using a different unit system, the value of c^2 may be different, but the relationship between mass and energy remains the same. I hope this helps clarify the concept of mass-energy equivalence and the role of the constant c^2 in the equation.