E=MC2 vs. m² = E² - p²: Motion vs Rest

[genome66]

Okay, so I know that E=MC², is an equation in regards to an object at rest. But I recently came across another formula: m² = E² - p²; in the description, it stated, that it was basically E=MC², in regards to an object in motion. Is this information valid?

 

[JDługosz]

Well, p is momentum, which is mv. E=MC² is for an object at rest only. It's not counting kinetic energy ½Mv², for example. For a massless particle, you don't have M at all, and the only thing you measure against is p.

 

[genome66]

But the equation is valid, right?

 

[bcrowell]

$m^2=E^2-p^2$ is generally valid, regardless of whether or not m is zero and whether or not the particle is moving. In the case of p=0, i.e., a particle at rest, you get m=E, which is simply the famous $E=mc^2$ expressed in units where c=1.

 

[Pengwuino]

Yes it is valid. Although what you see written down is in a set of units where the speed of light is set equal to 1. The equation with SI units is $$E^2 = P^2c^2 + m^2c^4$$ where $$P = \gamma mv$$ is the relativistic momentum, not just the ordinary momentum you see typically as just mv.