Why and how can energy become matter and vice verse according to Einstein’s theories?

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I always though of energy as motion – heat is atoms vibrating and moving, sound is a wave of atoms pushing each other in a specific direction, electricity is the movement of electrons, etc. But I’ve heard that e=mc^2 means energy can become matter and matter can be energy. How can motion become physical matter?

In: Physics

Energy is not motion. Energy is the ability to do work. Motion is an example of work, or rather the effect of work, because a force, F must be applied to move a system a distance, d from rest or to change its existing motion, i.e. W = F×d.

When atoms vibrate, that is an example of kinetic energy, but particles and systems can also have potential energy.

Light is energy, and plants use that to create chemical energy, effectively creating a material that wasn’t there before. They then transport this chemical as sap, and then use it to grow.

You turn chemical energy into body heat and electrical current all day and all night.

This is possible because energy is energy not motion. If you put something on a tall shelf it has a lot of gravitation potential energy despite not moving. When it falls off the shelf it’ll be converting that potential energy into kinetic energy. When it hits the ground and shatters, some of that kinetic energy will be converted into sound energy. Energy is just something that things have whether they’re moving or not.

The most direct way that energy becomes matter is through Pair Production

If you have a photon with enough energy(usually a high energy gamma ray/cosmic ray) it can spontaneously go from being a massless photon to becoming an electron and positron. The photon had enough energy that it could be converted into these two particles, and if the electron and positron touch then they’ll annihilate each other and create a high power gamma ray.

Let’s not call it “energy” for a moment. Let’s call it That Which Is Conserved (ThWIC)

When they say “energy is the ability to do work”, they’re saying ThWIC is, well, conserved when converted into work – that is, the most friendly expenditure of energy, newtons-times-meters, indeed, your “motion”.

For you see, of all the sources they’ve found for ThWIC to be converted into your motion, they have never ever been able to cheat, and cause motion to beget other forms of ThWIC which could be harvested into motion again *without loss*. Yes, even if the sun’s rays on the panel seem to constitute a gain for us, a more complete equation featuring the sun as input does register a net loss, and God’s most complete algebra would register no loss at all, but mere rearrangement. The total of totals, which is: it’s conserved.

And matter is just energy condensed into a slow vibration. The one direction easily perceived as matter-antimatter’s annihilation into a more radiant energy. The other: if a particle accelerator’s only slightly subluminal slam of two itty bitty particles achieves 101% of the ThWIC of a big particle, sometimes that particle is just traded into existence.

You have a wrong idea of what is matter.

When people usually think of an atom (the smallest bit of matter) they think it’s a very small ball with smaller balls (electrons) gravitating around. This is false, it’s only how we represent them because our brains are used to think with “objects”.

An atom is just a bunch of energy forces interacting together. Forces that pull, forces that push, at different strength and different ranges. It’s hard to understand because it’s not something we can see or experience.