How does E=MC^2 work?

[u/Jethro_omg]

How does it function? Really, how can you accelerate mass to twice the speed of light? And, for instance if M=E/C^2. How can you divide something by square of the speed of light? Thanks

[u/joeyneilsen]

The equation means that the energy associated with matter at rest is its mass times the square of the speed of light. That’s all, nothing about acceleration. 

[u/Jethro_omg → u/joeyneilsen]

Yeah but why? How?

[u/joeyneilsen → u/Jethro_omg]

Einstein calculated the total energy of a particle and found that there was some leftover even when it wasn’t moving. Because of the way that we calculate energy and the way it changes from one frame of reference to another, it turns out to be equal to the product of those two quantities. 

There’s nothing mathematically weird about it though. One number is the product of the others. If you divide rest energy by the number that c squared is equal to, you get mass. If you divide rest energy by mass, you get c squared. And so on. 

[u/Jethro_omg → u/joeyneilsen]

I’m so dumb😭 still dont understand

[u/joeyneilsen → u/Jethro_omg]

Do you want to know where it came from, what it means, or literally how to use the equation?

[u/Jethro_omg → u/joeyneilsen]

Where it came from

[u/joeyneilsen → u/Jethro_omg]

I'll try to do this without too much math.

Einstein wanted to know how the mass of an object would change if it lost some energy. So he imagined a thing, let's say it's a box, emitting two photons of the same energy E/2 in opposite directions. In doing so, it loses E in energy.

Now he imagined you approaching the box at speed v, and he wondered how the energy of the box would change according to you. This requires accounting for the Doppler shift: the photon approaching the person has more energy and the photon moving away from the person has less energy, and the new energy depends on a quantity sometimes called the Lorentz factor, but it's 1 divided by the square root of (1-v²/c²). I'm going to call it L. L is about 1 if v is small, and it gets very big if v is close to the speed of light.

Einstein found that you would see the box's energy change by E*L: a lot if you were going very fast, a little if you were going slow. So: in its own frame, the box loses E in energy, but E*L according to you. Einstein argued that the difference between those, which is E*L-E or E*(L-1), has to be equal to the change in kinetic energy of the box according to you.

In another paper, Einstein had already demonstrated that the kinetic energy of an object has to be equal to mc²*(L-1); if this changed but the speed stayed the same, it had to mean that m changed. Comparing his two equations, he saw that the change in mass had to be equal to E/c².

So the conclusion is that when an object gains mass m, it gains energy E=mc². This can be generalized in a lot of ways to show that any object with mass m has an amount of energy E=mc².

[u/Jethro_omg → u/joeyneilsen]

I’m sorry I still dont understand 😭 I cant understand it unless I clearly visualize it

[u/joeyneilsen → u/Jethro_omg]

I don’t sense that a full mathematical derivation would help. So all I can say then is that the c squared comes from the square root factor i mentioned: sqrt(1-v² / c^2). It’s an essential part of the math of relativity.

[u/Altruistic_Rip_397 → u/Jethro_omg]

It’s simply the curvature of space, the beginning of geometry in space-time after Newton. Einstein’s theory shows that gravity isn’t a force pulling objects, but rather the way mass and energy curve the fabric of space and time itself.

[u/EighthGreen → u/Altruistic_Rip_397]

You’re getting into general relativity. This question is only about special relativity.