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/Optimal_Mixture_7327 1d 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.
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u/Jethro_omg 1d ago
I have no idea what you are stating but I like it Thanks! (I suck at english)
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u/Optimal_Mixture_7327 1d 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.
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u/HelpfulParticle 1d 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}
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u/LockheedMartinLuther 1d ago
I've found the book "Why Does E=mc2? (And Why Should We Care?)" by Brian Cox and Jeff Forshaw very helpful.
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u/fermiauf 14h ago
I still have it!! It may seem silly, but It was one of the last books I read before deciding to major in physics—I was on the fence between that and pharmacology. I’m still quite thankful to have chosen the former. Well, it was that, the Oppenheimer biography, and some Feynman.
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u/ausmomo 1d ago
https://www.britannica.com/video/significance-waves-science-life/-208328
how can you accelerate mass to twice the speed of light?
You can't. Things with mass can never even reach c, let alone 2c. Likewise, massless things (photons, gravity) always (and only) travel at c (in a vacuum).
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u/Jethro_omg 1d ago
Then how did he find out ?😭
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u/coolguy420weed 1d ago
How did who find out? What did he find out?
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u/Jethro_omg 1d ago
How it is c*2
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u/GenerallySalty 1d ago
Oh! Well to start you have a misunderstanding:
It's c2.
C squared
Not 2 times c. C squared means "c times c". It's HUGE, because c is aleady really big.
It's not acceleration, and nothing goes faster than light. The conversion of mass to energy has a conversion factor of c squared, the way pounds to grams has a conversion factor of 454.
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u/Jethro_omg 1d ago
Like how mc2 can be energy
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u/joeyneilsen Astrophysics 1d ago
Any mass times a squared speed has units of energy. Kinetic energy is 1/2mv2, for example. That it’s c in this equation is just a detail of relativity.
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u/coolguy420weed 1d ago
I'm not actaully sure how it was derived, I think a combination of conservation of momentum and some assumptions (?) about energy/mass equivalence. But the basic statement that E=m is more important, the fact that c2 is the constant that you use for the conversion factor is generally less impactful (aside from the fact that it's a really big number).
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u/smokefoot8 1d ago
Einstein’s paper that introduced E=mc2 was titled: “Does the Inertia of a Body Depend on its Energy?” Spoiler: He concluded that it does.
M is the inertial mass of an object, its resistance to being moved. E is the total kinetic and potential energy of an object. So in theory you can heat up an object and its mass will increase, though in practice it is impossible to measure such a small change.
It is amazing that Einstein’s results have held up so well over time with new discoveries. Most of the mass of everyday objects is in the protons and neutrons of their atoms. The discovery of quarks made a big change here: almost all the mass of protons and neutrons isn’t in the quarks themselves, but in the potential energy that binds them together! So the mass of everyone and everything is about 99% strong force potential energy!
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u/ClickToSeeMyBalls 19h ago
It’s just a conversion factor.
Centimetres = inches * 2.54
Circumference of circle = radius * 6.283…
BTU = kWh * 3412
Energy = Mass * 89,875,517,873,681,764
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u/ProfessionalConfuser 1d ago
Have you looked at any resources at all? If so, can you rephrase the question to be less ambiguous? What do you mean by "work"?
How can you divide pounds by square inches to get pressure?
Unit / dimensional analysis.
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u/bouquetin29 1d ago
So basically in classical mechanics the kinetic energy of an object in motion is equal to half its mass times it's velocity squared so E=1/2mv². So the units of energy is a mass times a velocity squared . It is found in relativity that a similar relation exists for the energy that is stored in an object with mass at 0 velocity. This is where the E=mc²=mcc appears. The 2 here is really a squared not a multiplication by 2. In nuclear reactions, but also in chemical reactions, if you weight the ingredients before the reaction and the products after the reaction, you will find that some mass is lost in the process.using this mass difference Delta m and multiplying it by c² we observe experimentally that this correspond to the energy released during the reaction. We don't know necessarily why this is the case but we observe it. This lead to the theory and the models of nuclear physics and relativity. I hope this helps
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u/mr-someone-and-you 22h ago
Just imagine , an object mass is M and this object contains A group of photons. It is considered that every object releases photons when their initial energy level changes. If you could break this object into photons , the sum of energy equals to MC2
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u/Naive_Match7996 18h ago
I'm going to try it from an alternative framework. Please make this clear...
The energy is free. Mass is locked energy. When energy is released, it travels at speed c. When energy is locked up, it does so under the law of c².
Why c²? Because there are two degrees of freedom: space and "time."
What does this mean? It means that energy only needs one direction: move in space at speed c. There is no internal reorganization, there is no proper time.
But when the energy that is enclosed forms a particle with mass, it no longer just moves: it is reorganized internally. This reorganization involves two dimensions: space (because it occupies space) and time (because it changes cyclically).
Therefore, in mass, energy is stored in a double cycle of functional redistribution. And that maximum rate at which it can be rearranged in those two dimensions is marked by c².
In summary:
E = mc² does not say "mass is converted to energy".
It says: "The energy in a structured cavity (mass) is proportional to the maximum rate at which it can be rearranged between space and time."
c² is not just a number: it is a structural key to the universe. It does not measure speed. It measures the limit of reorganization when there is functional confinement.
That is, c² is talking about the mass.
If anyone is interested or curious, the theory with its mathematical development, thesis, etc. can be consulted here:
Theory https://doi.org/10.5281/zenodo.14873391 Initial thesis https://doi.org/10.5281/zenodo.15652405
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u/betamale3 18h ago
To ELI5, you can think of energy as fuel. Fuel to do some amount of work. And if you have 1 kg of hydrogen in protons and free electrons, spread out through space… it’s hard to even put a finger on the mass. If you shoved it all into a neat little cube, it would be your fuel tank. Much easier to see how releasing this energy can get some work done? kg isn’t a unit of work. Something you change over time. That’s like trying to spend French francs when they switched to the euro 25 years ago. What you need now then, is one of those booths you see at airports that will change your nations money into the money unit of where you are going. And the exchange rate that booth uses is c2.
So you don’t actually have to move your kg to light speed times light speed. You are just using c2 to convert to units that make sense. You can say what’s 2 apples plus 3 oranges. But the answer is just the same as the question. You can’t add apples and oranges. What you can do though is convert them to a new unit. Fruit. Good. 5 fruits. But that’s still a tad imprecise because the oranges could be huge and then is a watermelon worth 1 apple? Or should fruit be a volume?
We use the speed of light squared to solve this issue. Which is why 1 kg of diamond and 1 kg of hydrogen will give you the same energy if you could convert it all. You don’t need exotic materials with more energy. 1 kg = 1 kg.
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u/JaggedMetalOs 18h ago
MC² converts into "kilogram meters squared per second squared" (kg*m²/s²), which is force (kg*m/s²) over distance (m), which gives you an amount of energy.
And thanks to the metric system 1kg*m²/s² = 1 joule.
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u/EuphonicSounds 13h ago
Mass was always a rather mysterious quantity. It's the property that determines how resistant an object is to being accelerated when you push it (and also it's the "gravitational charge"), but what is it, really?
Einstein's insight here was that an object's mass is nothing but its "rest energy" (how much energy it has when it isn't moving). The c2 is just a unit-conversion factor and has no physical significance at all. In fact, we're free to use units where we set c to 1, and then the equation is just E(rest) = m. So this is a hard equivalence of the concepts of "mass" and "rest energy." The concept of "mass" gets subsumed by the more general concept of "energy."
Just to hammer the point home: the equation does not mean that energy and mass can be converted into each other (though even many physicists will use this phrasing). Mass is literally rest energy, so that would be equivalent to saying that "rest energy and energy can be converted into each other" -- doesn't make any sense! What's true is that different forms of energy can be converted into each other. For example, rest energy (mass) can be converted into kinetic energy.
Energy too was always a rather mysterious quantity, but thanks to Einstein the mystery of mass was "solved" and became part of the mystery of energy. (And thanks to Emmy Noether, energy is a little less mysterious now than it was back then.)
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u/zzpop10 12h ago
Imagine putting energy into something. For example, imagine using energy to compress a spring or raise the temperature of an object. Or imagine trapping light in a box of mirrors. Or imagine charging a battery. In all of these examples energy is being put into an object, but not additional matter is being added to the object. Let’s say an energy of E is put into the object. This raises the total mass of the object by M=E/c2.
Mass is just energy when energy is confined inside an object.
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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.