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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Because of a lot of math. Its super famous and about that much misunderstood. There is no Eli5 version to fully explain how we get these results.
What it means is that Energy, mass and momentum are related. But still we would need to have a formal definition of what mass is. Otherwise E=mc² is a nothing burger.
Some some time ago asked about how light has energy while no mass. The answer is similar to what would probably give you insight to what the world’s most famous equation is about and how do we get there so might be helpful. (However its a bit beyond the realm of Eli5 but some things are just not that simple.)
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inexplainlikeimfive
>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?
There are a number of approaches to this question, but I’ll try a less common one that really helped me grasp it when I was younger:
You’ll need a concept called “Unit Analysis” (or dimensional analysis) – essentially, in order to add, subtract, or compare two things they have to be in the same units. You can’t compare a length (meters) and a mass (kg) – it just doesn’t work.
Mass is measured in kg (kilograms). Speed is measured in m/s (meters/second).
You presumably know that the formula for kinetic energy is E^k =1/2MV^2. In order for that equation to be true (and it is true) Energy must be measured in kg(m/s)^2.
Given that we can look at the units in E=MC^2 – E is in kg(m/s)^2, M is in kg, and C is in m/s.
If we weren’t squaring the speed on light, we would end up with units of kgm/s – which isn’t energy, it’s momentum.
Thus E=MC is impossible; only E=MC^2 works.
You can think of mass as an expression of energy.
If you have a bunch of energy in one place, it will express itself as a corresponding amount of mass. The energy *is* the mass.
If you give something more energy (by speeding it up, by lifting it up etc.) it will have more mass. In fact most mass comes from this. Let’s look at some examples.
A proton is made up of two “up” quarks and one “down” quark. The up quarks have a mass of ~2.2 MeV/c^(2) each and the down quark a mass of 4.7 MeV/c^(2) (don’t worry too much about the units – although they come directly from E = mc^(2)). So together we would expect a proton to have a mass of about 9.1 MeV/c^(2). But a proton has an actual mass of 938 MeV/c^(2) – over a hundred times more. All that extra mass comes from the extra energy those quarks have due to their interactions.
And this is how nuclear reactions work, giving off energy. If you take a basic nuclear fusion reaction, smashing deuterium (a proton and a neutron) into tritium (a proton and two neutrons) you get out Helium (two protons and two neutrons) and a spare neutron, and a whole bunch of energy. Which means your final products must have less mass than what you put in. “Potential” energy within the nucleuses is turned into kinetic energy, meaning the nucleuses themselves have less mass (although this gets us into some interesting follow-up questions with relativity).
This also gives us an idea of why it is important – it underpins a whole load of nuclear physics, including nuclear power.
This happens with all interactions involving energy, but outside nuclear reactions it is very rare that the change in energy involved is anything like the existing mass (thanks to that c^2 factor – even a huge amount of energy ends up being equivalent to a tiny amount of mass).
> Also, why is it the speed of light squared?
Because that’s the way the maths works out. Not a very satisfying answer, but that’s the way it is. Any explanation will ultimately come down to “that’s how the universe works.”
> if its floating through space then apart from kinetic energy which sent it there, …
Interestingly kinetic energy is also part of E = mc^(2); the full version of this equation in Special Relativity is:
> E^2 – (pc)^2 = (mc^(2))^2
where *E* is the energy of the system, *p* is it’s momentum and *m* is the mass (and *c* is this scale-factor, the local invariant speed, or local speed limit, whatever you want to call it).
If we rearrange that and do some fancy maths we get:
> E = mc^2 + 1/2 mv^2 + …
where the + … means there are a bunch of terms that are essentially 0 provided our speed, *v*, is much less than *c*.
i.e. the total energy of a system is its “mass” energy plus its “kinetic” energy. The splitting up of the energy into “mass” and “kinetic” energy works in every-day physics because of the simplification (assuming *v* much less than *c*) but things become more interesting at higher, “relativistic” speeds.
This was how Einstein came up with the equation in the first place. His paper [is deceptively short](https://www.fourmilab.ch/etexts/einstein/E_mc2/www/) (if a little technical – the labelling used in that translation doesn’t help). He basically said “let’s look at an object that sends out light, and see how much energy it loses. Then let’s look at it from a different perspective/reference frame, and see how much energy it loses now. Those must be the same.” and with a bit of algebra (and some clever thinking) he concluded that the object must lose mass, and that mass must be equal to the energy of the light emitted divided by *c^2*.
The lead weight is made up of atoms of lead. The atoms have a nucleus of protons and neutrons held together by the strong nuclear force. That is a large amount of energy holding each nucleus together.
If you were to break all those nuclei up converting your solid lead mass to just free roaming protons and neutrons (annihilating the matter completely) all that stored energy would be released and it would be huge. In fact it would be exactly equal to the square of the speed of light times the mass.
I’m not sure exactly why it’s exactly the square of the speed of light or how the speed of light comes into play here but that’s the beauty of the equation to me. Somehow these fundamental constants tie together at the most basic levels of reality.
Mass is just energy clumped together! Imagine how much energy is contained in the sun and even in the atoms on earth
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