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

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SUMMARY

The discussion clarifies the relationship between the equations E=MC² and m² = E² - p², establishing that E=MC² applies to objects at rest, while m² = E² - p² accounts for objects in motion. The variable p represents momentum, defined as mv, and is crucial for understanding kinetic energy. The validity of m² = E² - p² is affirmed, as it holds true regardless of whether mass is zero or the particle is in motion. In SI units, the equation is expressed as E² = P²c² + m²c⁴, where P denotes relativistic momentum.

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  • Knowledge of SI units and their application in physics
  • Basic grasp of mass-energy equivalence
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genome66
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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?
 
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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.
 
But the equation is valid, right?
 
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.
 
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.
 

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