Basic question about the four fundamental forces and the relationship of energy and matter As I understand the famous “relativity formula,” it demonstrates the relationship between energy and matter.
As I am learning (on my own) about the four fundamental forces (weak and strong nuclear force, gravity, electromagnetic) I have stumbled upon something I don’t know and can’t find an answer for.
First, I would like to clarify what I understand:
Force: push or pull that can change a vector <- I will be working on this definition, a weakness in it was pointed out.
Energy: ability to do work
Note: if either of these is too simple, I am happy to be corrected.
When I point at a mass (usually matter) I can identify what it is made of (oh look a carbon based life form)...
When I refer to energy, I could be talking about gamma rays, optical light, heat, even sound (though I don’t want to include sound in this).
I understand that I should be able to convert energy to mass. At what point in converting energy to mass does gravity enter the equation?
What I mean is, is gravity a “component” of energy  I would think this because gravatic lenses act on beams of light (an energy emission?). But then would a gravatic lens act on all light (infra red, gamma rays)? Would the energy be changed by the lens in proportion to the frequency of the light? Or is this one force acting on another (gravity acting on electromagnetic) and not a force acting on non mass (energy)?
Or is there something in the process of energy conversion to mass (like a function of density) that causes what we identify as “gravity” to.... develop? Exist? Assimilate?
Or am I going about this all wrong, and the question is incorrect in some way?
Is there something you could recommend I read (I have basic college physics and pre-calc to work from)?
Understand, this isn’t for homework, and I don’t want anyone to waste their time on this with beautiful and elegant formulas, because as much as I wish I understood them, I don’t know that much yet (though reference them if you wish).
 A: General relativity tells us that mass and energy are the same thing, just measured in different units. Whatever has mass has energy and vice versa.
We are used to thinking of physical objects (matter) as having a fixed mass and a variable amount of energy, depending on how fast they are travelling. But in fact, when we add kinetic energy to an object by increasing its speed, we are increasing its mass at the same time. And when we add energy to an object by raising its temperature, we are also increasing its mass.
We are also used to thinking of radiation (photons) as having energy but no mass. But this is also incorrect. Photons have mass, which is why they are affected by gravitational fields (or, more accurately, why their paths are affected by the curvature of spacetime). This is why we have gravitational lensing and why black holes are black.
Since mass and energy are the same thing, we do not need to physically convert between them - all we do when we “convert” one to the other is to change the units in which we are measuring mass/energy. What can happen is that matter can be converted into radiation - this happens when matter and antimatter particles annihilate and produce gamma rays. It is also possible, although more difficult, to convert radiation into matter in a process called pair production.
