How does energy convert to matter? [duplicate]

To my understanding, matter and energy are one and the same. Shifting from $E$ to $M$ in Einstein's famous equation requires only a large negative acceleration. If $M$ really is $E/c^2$, does that make matter the solid state of energy? I've read a lot about positron-electron collisions at high energies creating larger particles, and there is obvious matter conversion in fusion and fission reactions, but I can't find anything describing the physics of the conversion from energy to matter, rather than the interactions of what is already matter.

Specifically, the thing I'm getting hung up on is the reason energy would take on a solid state in the first place. If energy is represented by waves, how does it become particles? If gravity is determined by mass, and mass is nothing more than static energy, does that make gravity a static-electromagnetic force?

• "Shifting from E to M in Einstein's famous equation requires only a large negative acceleration" - to be pedantic, this is a bit off. The conversion factor is a velocity squared, which is not an acceleration. (This comment has no bearing on the rest of the post.)
– user10851
Jun 10, 2013 at 22:45
• Possible duplicate: physics.stackexchange.com/q/47417/2451 Jun 11, 2013 at 1:04
• StE questions refered to above seem to ask in the opposite, not the same way, they ask about conversion of ass to energy. This question asks about energy to mass. Nov 7, 2022 at 10:53

Energy and matter are not the same. Matter is a type of thing, whereas energy is a property of a thing, like velocity or volume. So your premise is flawed. In particular:

• there's no such thing as "a solid state of energy" - hopefully it makes sense that a property of something does not have states
• energy is not represented by waves, though it is a property of a wave. It's also a property of a particle (which, in quantum field theory, is really just a tightly bunched wave).

Note that mass can be converted to energy, because mass actually is energy. It is one of various types of energy: kinetic energy, potential energy, mass energy, and so on. Different types of energy get converted into each other all the time.

• Ok, well then the question is, if energy and mass are the same thing, and both are properties of both moving waves and "tightly bunched" "particle" waves, what is a wave, and why are some waves static and form particles? Jun 12, 2013 at 4:57
• That's a whole different matter. Check and see what has already been asked on the site about what waves are, and also check the Wikipedia page on waves, do a Google search, etc., and if there's something not explained in those resources about what a wave is that you're confused about, feel free to post it as a new question. P.S. how much physics do you know? Jun 12, 2013 at 5:07
• I understand quite a bit (I think) about waves, and have been learning a lot recently about standing waves, but there's nothing I've seen that indicates HOW waves group densely enough together to have measurable mass, or even what kind of wave that would be. A standing wave is a wave moving though a medium of perfectly opposite velocity. The velocities "cancel out" as the waves moves through particles that are moving in the opposite direction, making the wave appear still. I've found nothing about waves that are actually still. Jun 16, 2013 at 17:33
• Actually, a standing wave is made of two waves of the same frequency moving in opposite directions. But anyway: you've probably only learned about one kind of wave so far, the kind that corresponds to massless particles. (So you know why e.g. photons can't be made to stop.) There's a different kind of wave that occurs in a "massive" medium (the mass is a property of the medium, not the wave); I'd recommend reading this, especially parts 4 and 5, to learn about that. Jun 16, 2013 at 19:38
• Thank you! That is a very helpful link, and has opened many other lines of inquiry, so I'm sure more questions are to come! Jun 18, 2013 at 1:57

The thing about energy becoming particles is not entirely true. Quantum mechanics explains that particles themselves are waves. The energy that forms mass, however, is not a part of the particles themselves. For subatomic particles such as electrons and quarks, their mass is caused by their interaction with the Higgs field. The energy itself is stored in the Higgs field, much like how electric potential energy is stored in electric fields. As for gravity, gravity is not determined by mass. General relativity explains that gravity is the curvature of spacetime caused by the presence of energy, be it in the form of mass, electric potential energy, or electromagnetic radiation. So gravity is not a static force, rather, gravity is the curvature of spacetime caused by the presence of energy.

What is conserved is energy and momentum, not mass.

For a massive particle, mass is the energy at rest (when the particle is not moving)

For instance in a 2 particles => 2 particles reaction, you will have:

$E_1 + E_2 = E_3 + E_4$

$\vec p_1 + \vec p_2 = \vec p_3 + \vec p_4$

In the case of massive particles collisions at high energies, you have to use, for each particle , the relativistic values, that is :

$$E = \frac{m c^2}{\sqrt{1 - \frac{v^2}{c^2}}}$$ $$\vec p = \frac{m \vec v}{\sqrt{1 - \frac{v^2}{c^2}}}$$

You can consider that the energy is the sum of the energy at rest, which is nothing that the mass of the particle ($mc^2$), and the kinetic energy ($K = E - mc^2$).

(For massless particles like photons, you use only $E$ and $\vec p$, of corse).

Waves is a classical point of view. In this point of view, waves can carry energy. But the correct point of view, the quantum point of view, used in Quantum Field Theories, is that there are quanta of fields, that we call "particles"

The source of the gravitation is the energy/momentum tensor, so it is not a mass, nor a mass density.