In string theory, what are the small strings physically made out of?
In the standard model, what are the point particles physically made out of?
It's an axiom of the theory, not meant to be explained.
Aren't they supposed to be 'energy'?
I wouldn't bother trying to understand anything about string theory. It's a bunch of mathematical hokum.
In string theory, they are fundamental, i.e. not made of anything else. Some other theory might say that they're made of something else, but if you knew of such a theory, you would be asking a similar question about that one instead.
It should be highly stressed that what is presented in popular science accounts (Brian Greene or what have you) is a series of vague pictures and analogies intended to convey EXCITEMENT, not understanding. String theory is a deeply mathematical theory and any intuition you might have about a CGI image of a vibrating string will be completely incorrect. There are no "strings" in string theory, at least in any way that you can have an intuition about from every day life. I know very little about string theory, however, my understanding is that the central mathematical extension to the standard model is instead of taking particles to be infinitely small 0-dimensional point one instead attaches a single degree of freedom to them, this degree of freedom is the "string". It's not actually a "thing" like a real string, it's just colorful language (and CGI artists looking for a *wow* special effect with no understanding), the "string" is essentially an additional freedom of motion/physics attached to each point in the universe.
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