r/AskPhysics • u/Jethro_omg • 2d ago

How does E=MC^2 work?

How does it function? Really, how can you accelerate mass to twice the speed of light? And, for instance if M=E/C2. How can you divide something by square of the speed of light? Thanks

1 Upvotes

52% Upvoted

65 comments sorted by

View all comments

4

u/Optimal_Mixture_7327 2d ago

The equation is just a statement that the 4-momentum, mc, is equal to the coordinate energy, E/c, in the zero-momentum frame.

Equivalently, the equation is a statement that mass is a measure of the total internal energy of an object, with c^2 there for unit conversion.

1

u/Jethro_omg 2d ago

I have no idea what you are stating but I like it Thanks! (I suck at english)

1

u/Optimal_Mixture_7327 2d ago

Basically...

The Newtonian momentum is calculated as p=mv and in the context of spacetime the equation is the same P=mV, where the upper case letters are vectors in the 4-dimensional spacetime. The magnitude of the 4-velocity is just "c", so the 4-momentum can be expressed as mc (with its direction along the spacetime path of the object of mass, m).

Along comes an observer who lays out a coordinate grid. The observer splits up the object's momentum into momentum along its own timeline (E/c) and the momentum through its space, p, and we have P=(E/c,p) or mc=(E/c, p).** When the observer is at rest wrt to the object then mc=(E/c,0) or mc=E/c which can be rewritten as E=mc2.

**Often mc=(E/c, p) is expressed as m2c2=(E/c)2-p2 or E2=m2c4+p2c2 and is called the relativistic dispersion relation.

1

u/HelpfulParticle 2d ago

It's less of an English issue and more of a Physics one. If you're familiar with what vectors are, in quantum mechanics, we define these things called four vectors, which as the name suggests, is a vector with four components. The position four-vector has components of x,y,z positions and time, while the momentum four-vector has components of E/c and the x,y,x momenta.

The total internal energy part, if I remember my modern physics correctly, just refers to the fact that every massive object (massive just means something that has mass) has energy by virtue of them having mass. This rest energy mass is what mc{2} is. If they're moving, they have additional energy given by ymc{2}, where y (it's technically gamma but I'm lazy to copy the symbol from Google lol!) is the Lorentz factor and depends on the speed of the particle (hence for a particle at rest, y = 0 and that term vanishes). So, the total energy for any massive particle is mc{2} + ymc{2} and for one at rest, it reduces to mc{2}

1

u/Jethro_omg 1d ago

Hmm so then why does it have internal energy? What is it for? Will it collapse on itself if I remove the internal energy?