The Full Equation for Mass-energy Equivalence

[Jason Kim]

Hi.

I've seen a video by MinutePhysics that talked about the mass-energy equivalence equation,
usually known as E=mc^2.

It said that there is an extra part to it, and I didn't really understand what it meant.

(E^2)=((mc^2)^2)+((pc)^2) seems to be the full one (p being momentum)

So, any ideas?

By the way:

 

[ImaLooser]

Hi.

I've seen a video by MinutePhysics that talked about the mass-energy equivalence equation,
usually known as E=mc^2.

It said that there is an extra part to it, and I didn't really understand what it meant.

(E^2)=((mc^2)^2)+((pc)^2) seems to be the full one (p being momentum)

So, any ideas?

By the way:

Each equation uses a different definition of mass. e=mc^2 uses m="relativistic mass," which increases the faster the mass is moving relative to the observer. The second equation uses m="rest mass." The first equation was Einstein's, the second is used more these days because it is usually more convenient and less confusing.

Each equation is correct, given its definition of m.

 

[grzz]

If one starts from E = mc$^{2}$ and replaces m by $\frac{m_{0}}{\sqrt{1 - \frac{v^{2}}{c^{2}}}}$ where m$_{o}$ is the mass at rest, one gets the other version of the equivalence equation.

 

[bcrowell]

E=mc² is just the special case where p=0.

Each equation uses a different definition of mass. e=mc^2 uses m="relativistic mass," which increases the faster the mass is moving relative to the observer. The second equation uses m="rest mass." The first equation was Einstein's, the second is used more these days because it is usually more convenient and less confusing.

I don't think this interpretation works, since nobody today uses relativistic mass, but everyone uses E=mc².

 

[sardar]

I am just curious, I am not a physics student or anything.

Hello there,

I can help clarify the full equation for mass-energy equivalence for you. The equation E=mc^2 is a simplified version of the full equation (E^2)=((mc^2)^2)+((pc)^2), where p represents momentum. This full equation takes into account the total energy of an object, which includes both its rest mass energy (mc^2) and its kinetic energy (pc^2).

The addition of momentum in the full equation is important because it shows that the total energy of an object is not solely determined by its mass, but also by its velocity and momentum. This is in line with Einstein's theory of special relativity, which states that energy and mass are fundamentally related and can be converted into each other.

I hope this helps clarify the full equation for you. If you have any further questions, please don't hesitate to ask. Keep being curious and exploring the wonders of science!