Tried watching a few videos and reading articles, dumbed down even for me, still can’t get my head around it.
Let’s assume it is a 1 kg lead weight in the vacuum of space floating at 1mph.
if its floating through space then apart from kinetic energy which sent it there, and the gravitational energy which made it, what energy is there in that object which makes it applicable to the equation. “A small amount of mass is equal to a large amount of energy” but how?
Also, why is it the speed of light squared? Surely it’d just be the speed of light. If squared that’d be a massive speed so why is it used here?
Finally how come it’s so important? Why is it still important today? Don’t want to sound reductionist but this really makes no sense to me to why it’s so famous.
There are plenty of explanations, none of which make this equation make sense. So assume I am actually 5 years old and somehow figured out how to make a reddit post, how would you explain it?
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The chair you’re sitting in is made of molecules of different things – wood, plastic, leather, whatever.
Those molecules are made of atoms.
Those atoms are made of smaller subatomic particles.
Energy – electricity, light, etc – is also made of subatomic particles.
So: at a very basic level, energy and matter are made from the same basic building blocks.
When you set a log on fire – or detonate a nuclear bomb – you are converting matter into energy. E=mc^2 is the conversion factor for how much energy you could possibly get from a certain amount of mass – or how much matter you could turn a certain amount of energy into – if you could do it at 100% maximum efficiency. Think Star Trek-style transporters and replicators.
Matter and energy are actually the same thing at a fundamental level. You can think of matter kind of like crystallized or ‘frozen’ energy. It takes a ridiculous amount of energy to fuse particles like protons and neutrons together in order to form matter. So, if you break those bonds apart, you will have that energy released.
Matter and energy can never be created or destroyed, only converted.
The formula is just giving us a mathematical framework of exactly one relates to the other. How much energy you can find per unit of mass or vice versa. It doesn’t really have anything to do with actually traveling at the speed of light. (Which should instead be called the speed of causality, but I digress…)
We can’t say “the lead weight is floating at 1mph”. Floating relative to what? Maybe the lead weight is stationary at the center of the universe and everything else is moving.
OK, what if the lead block happens to crash into another lead block made out of anti-matter? Kablooey. All mass is converted into energy at once. The formula tells how much energy you get. The squared term is needed so the units come out correctly.
E=mc^2 is what you get if you convert mass directly to energy. Take hydrogen fusion in the sun. It takes 4 H to make 1 He. If you compare the mass of 4H versus 1 He, you’d see that there is a difference of ~0.7%. That is where the sun’s energy (or nuclear fission) come from.
In conventional physics, you do not change the mass. You can change the amount of kinetic or potential energy in an object. You can remove or add mass, but the mass still exist. For example, if you burn a piece of wood in a closed system, there would be no change in mass before and after. Some of the carbon is converted into CO2, but the actual mass of all the atoms is the same. The energy you get is purely from the potential energy in the chemical bonds.
E=mc^2 is actually taking the mass and converting it to energy (or vice versa). For almost all applications, you will be able to convert 0% of mass to energy, so this term is irrelevant. It’s only when you are dealing with fission or fusion does it start to matter.
If you have the time there was a great NoVA special narrated by John Lithgow about Einstein and the history of his most famous equation. It’s called Einstein’s Big Idea. You can find on YouTube
It makes most sense if you think of it in terms of atomic bombs.
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Uranium-235 atom undergoes fission after a neutron hits it just right.
If you add up the masses of the U-235 atom and the neutron before they collide you get:
> 235.0439 Da + 1.008 Da = 236.0519 Da
If you add up the masses of the Kr-92, Ba-141, and three neutrons that result after the collision you get:
>91.9262 + 140.9144 + 3(1.008) = 235.8646 Da.
But that doesn’t add up! There is 0.1873 Da worth of mass missing!
Isn’t “Conservation of Mass” supposed to be a thing? And “Conservation of Energy” too for that matter?!
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Well, if you carefully measured the energy of all the light and heat that was generated, while measuring the speed of the Krypton and Barium atoms and those three neutrons, you can use those numbers to calculate the total energy produced by the fission reaction.
If you do multiple kinds of experiments like this in a big old particle accelerator, you eventually find that there is a relationship between the amount of energy you get from a specific fission reaction and the before-and-after mass change.
If you plot it out, you get a linear relationship where ΔE changes linearly with Δm, so ΔE/Δm equals a constant… and what is that constant equal to after all the units are worked out? c^2 .
ΔE=Δmc^2 essentially says that energy you get out of the fission comes from the mass lost during fission.
So E=mc^2 is essentially saying that you do still have conservation of energy… if you remember to account for all of the before-and-after mass energies in your accounting.
This mass-has-energy concept is what made it somewhat profound; combine that with the fact that it is so easy to remember and you get a “famous equation”.
> How come it’s so important?
If a nuclear bomb is going to convert 1000g of plutonium into 999g of uranium, you can figure out the energy released in the explosion using E = mc^2.
If you are going to use a nuclear reactor to power a spacecraft or a submarine, you need to know how much fuel you’ll need to move as far as you want to go.
> Why is it the speed of light squared?
A speed times a mass is an amount of momentum, not energy. Obviously, momentum can be converted to energy in a lot of ways, like when water turns a waterwheel or wind turns a windmill. But it’s not inherently an amount of energy in itself–a bullet and a baseball can have the same momentum but wildly different energies.
> Don’t want to sound reductionist but this really makes no sense to me to why it’s so famous.
Part of why it’s so famous is that it’s so unexpected that energy, mass, and light would have some kind of intrinsic connection between them. And not only are they connected, but they have this incredibly simple equation without any frills.
For the moment, ignore the c^2 term. Let’s look at the rest –
The main takeaway from this equation is that Energy and Mass are somehow equivalent. The c^2 is just a conversion factor showing how much mass is needed to get an unit of energy.
A very poor analogy would be that of a gas being condensed into a solid or a gas into a liquid. A large volume of gas can be condensed into a very small solid piece. Mass and energy are somewhat similar. A small amount of mass (read solid) and a large amount of energy (read gas) are basically the same thing.
What form they are in, depends on the environment and the physical constraints on the system. At low temperatures matter would prefer to be a solid/liquid. At higher temperatures, it might prefer to be a gas. Similarly, at low speeds, matter might be perceivable to us as a tangible mass, but at higher speeds, it might be perceivable to us as energy.
As for the c^2, it is just a number. As it turns out, there is a conversion factor involved i.e., a unit of mass is equivalent to ‘k’ units of energy. It just so happens that this conversion factor is a number that is the square of the maximum possible speed in vacuum ( which also happens to be the speed at which light travels in a vacuum).
Trying to keep this brief with 1 quick example.
Stuff is held together by forces, like gravity.
When you zoom in, stuff is held together by very big forces (strong nuclear force).
If you make a magic gun that takes 1 bullet of pure hydrogen (6 grams), and converts it to (helium + kinetic energy), the bullet would go about 93,000 km/s, or Mach 282,000.
The energy stored in nuclear bonds is ridiculously large compared to gravity or electromagnetism.
That is called the rest energy of matter.
Energy and matter are the same thing. If you put enough energy into one spot, it becomes matter (and an equal amount of antimatter). 1kg of mass is the same as 90000 Terajoules of energy.
In particle accelerators, when we smash particles together at high speeds, they crash into each other with so much energy that more matter and antimatter are created.
The only way to convert 100% of matter into energy is to annihilate it with an equal mass of antimatter.
During a nuclear reaction, some mass is also turned into energy. Fusing deuterium into helium, you lose a little bit of mass, but gain an equal amount of energy. When you split U-235, some mass gets turned into energy. Iron has the biggest mass discrepancy, meaning if you add or take away a proton from an iron atom, it requires you turn energy into mass.
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