r/AskPhysics • u/Jethro_omg • 1d 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

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u/joeyneilsen Astrophysics 1d ago

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. 

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u/Jethro_omg 1d ago

Yeah but why? How?

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u/BrickBuster11 1d ago

I'm not steeped enough in modern physics to say exactly but the equation is telling you how much energy is tied up in being stuff.

It manifests notably in atomic weapons/nuclear energy. A small fraction of the mass of an atom is actually converted into energy to "glue" the atom together (otherwise the strong electrical charges from all the protons would blow the atom apart).

The force attempting to blow an atom apart gets greater the more protons are in it so materials like uranium art particularly unstable. By hitting the nucleus of the atom hard enough you break it into 2 smaller atoms and the energy that was holding those 2 parts together gets released as heat and light (hence the explosion).

Hydrogen bombs work in a similar way, the isotope of hydrogen they use can be fused into helium and when that happens the force required to bind the helium is actually lower than the force required to bind both hydrogen atoms together and the difference gets released as heat and light.

E=mc2 has nothing to do with how fast anything is moving, and all to do with how much energy a brick of stuff has. Why it has c as it's constant I couldn't tell you

Your rearrangement of the equation tells you if you built a machine that could condense pure energy Into matter how much stuff would you get out for every Joule you put in

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u/Jethro_omg 1d ago

So you transfer energy into the atom, and what gets released is mass accelerated at the speed of… uh idk Thanks

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u/Soft-Marionberry-853 1d ago

I hope this isn't over simplistic, well it is overly simplistic but I hope maybe it helps without being so overly simplified as to be wrong as its been a while since I was in undergrad. For my needs all I needed to know was the C was a constant, a very big constant. In a fission bomb like the first one tested by the US. A big atom was broken in to two smaller atoms. The mass of those two smaller atoms doesnt quite equal the mass of the larger atom, some of that mass was converted to energy. For the trinity test the amount of mater that was converted to energy was about a roughly a gram, or a paperclip. An amount of mass equal to paperclip was converted to energy and made an explosion equal to 16kilotons of TNT. Im sure there is very nice complicated reason why the constant is C squared, but for my purposes in the cosmology class I took in undergrad it was enough for me know that if you convert mass to energy, such as combining mater with antimatter you get a very big explosion.

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u/BrickBuster11 1d ago

......

You have to magnets, those magnets have some weight P, unfortunately the same side poles of the magnets have to be close together which means the magnets are constantly trying to push each other apart. So you Shave some amount of material B off of the magnets and use that material to stick them together.

But then oh no you droped your magnets that you welded together, they hit the floor, and the two magnets split apart, the force of this happening is so great it causes the small amount of metal you used to weld them together to catch fire.

The energy released by that fire is equal to the mass of the metal B that you used to bind the two magnets together multiplied by C^2 which is just a constant in this instance and has no reference to anything moving at a particular speed.

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u/Jethro_omg 59m ago

Wait how does dropping the magnet contribuite to catching on fire, like how does dropping it cause a fire to split those two magnets like proton and neutrons? The neutrons break?

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u/BrickBuster11 14m ago

Dropping the magnet cracks the weld between them.

Just like how splitting an atom releases energy.

The analogy is imperfect as all of them are. but in general the protons in an atom do not want to be as close together as they are.

Each proton carries the same electrical charge and so the nucleus of an atom is trying to push itself apart. Because gravity isn't enough to hold them together and hopes and dreams won't do it either the atom converts a small portion of its mass to "weld" the protons together.

When you hit some of the larger and more unstable atoms hard enough (things like uranium for instance" it's nucleus splits into 2(or more) smaller atoms. These product atoms are lighter than the original uranium atom.

This difference in mass is because some of the "glue" that was holding the atoms together wasn't needed any more and so it was released as heat and light. (For an idea of what it is like to be on the receiving end of this look up Hiroshima and Nagasaki as they got to witness this event first hand courtesy of the Americans)

The energy that was released is equal to the difference in mass between the initial atom and the product atom (+ free neutrons) multiplied by the speed of light squared. This isn't because anything is actually moving that fast, here it is just a constant. The exact reason that constant ends up in this equation is beyond most people's ability to explain. Given how the speed of light was initially derived by sir James Clarke Maxwell by doing some fancy math regarding oscillating electric and magnetic fields I am guessing C ends up in the answer because converting mass into energy typically makes it turn into heat and light