Beware, though; string theory may be what underlies QFT and GR, and it describes a world of stringy objects that actually do move through space
I think this contrast is wrong.[1] IIRC, strings have the same status in string theory that particles do in QFT. In QM, a wavefunction assigns a complex number to each point in configuration space, where state space has an axis for each property of each particle.[2] So, for instance, a system with 4 particles with only position and momentum will have a 12-dimensional configuration space.[3] IIRC, string theory is basically a QFT over configurations of strings (and also branes?), instead of particles. So the “strings” are just as non-classical as the “fundamental particles” in QFT are.
QFT doesn’t actually work like that—the “classical degrees of freedom” underlying its configuration space are classical fields over space, not properties of particles.
Note that Quantum Field Theory is not the same as the theory taught in “Quantum Mechanics” courses, which is as you describe.
“Quantum Mechanics” (in common parlance): quantum theory of (a fixed number of) particles, as you describe.
“Quantum Field Theory”: quantum theory of fields, which are ontologically similar to cellular automata.
“String Theory”: quantum theory of strings, and maybe branes, as you describe.*
“Quantum Mechanics” (strictly speaking): any of the above; quantum theory of anything.
You can do a change of basis in QFT and get something that looks like properties of particles (Fock space), and people do this very often, but the actual laws of physics in a QFT (the Lagrangian) can’t be expressed nicely in the particle ontology because of nonperturbative effects. This doesn’t come up often in practice—I spent most of grad school thinking QFT was agnostic about whether fields or particles are fundamental—but it’s an important thing to recognize in a discussion about whether modern physics privileges one ontology over the other.
(Note that even in the imperfect particle ontology / Fock space picture, you don’t have a finite-dimensional classical configuration space. 12 dimensions for 4 particles works great until you end up with a superposition of states with different particle numbers!)
String theory is as you describe, AFAIK, which is why I contrasted it to QFT. But maybe a real string theorist would tell me that nobody believes those strings are the fundamental degrees of freedom, just like particles aren’t the fundamental degrees of freedom in QFT.
*Note: People sometimes use “string theory” to refer to weirder things like M-theory, where nobody knows which degrees of freedom to use...
I think this contrast is wrong.[1] IIRC, strings have the same status in string theory that particles do in QFT. In QM, a wavefunction assigns a complex number to each point in configuration space, where state space has an axis for each property of each particle.[2] So, for instance, a system with 4 particles with only position and momentum will have a 12-dimensional configuration space.[3] IIRC, string theory is basically a QFT over configurations of strings (and also branes?), instead of particles. So the “strings” are just as non-classical as the “fundamental particles” in QFT are.
I don’t know much about string theory though, I could be wrong.
Oversimplifying a bit
4 particles * 3 dimensions. The reason it isn’t 24-dimensional is that position and momentum are canonical conjugates.
QFT doesn’t actually work like that—the “classical degrees of freedom” underlying its configuration space are classical fields over space, not properties of particles.
Note that Quantum Field Theory is not the same as the theory taught in “Quantum Mechanics” courses, which is as you describe.
“Quantum Mechanics” (in common parlance): quantum theory of (a fixed number of) particles, as you describe.
“Quantum Field Theory”: quantum theory of fields, which are ontologically similar to cellular automata.
“String Theory”: quantum theory of strings, and maybe branes, as you describe.*
“Quantum Mechanics” (strictly speaking): any of the above; quantum theory of anything.
You can do a change of basis in QFT and get something that looks like properties of particles (Fock space), and people do this very often, but the actual laws of physics in a QFT (the Lagrangian) can’t be expressed nicely in the particle ontology because of nonperturbative effects. This doesn’t come up often in practice—I spent most of grad school thinking QFT was agnostic about whether fields or particles are fundamental—but it’s an important thing to recognize in a discussion about whether modern physics privileges one ontology over the other.
(Note that even in the imperfect particle ontology / Fock space picture, you don’t have a finite-dimensional classical configuration space. 12 dimensions for 4 particles works great until you end up with a superposition of states with different particle numbers!)
String theory is as you describe, AFAIK, which is why I contrasted it to QFT. But maybe a real string theorist would tell me that nobody believes those strings are the fundamental degrees of freedom, just like particles aren’t the fundamental degrees of freedom in QFT.
*Note: People sometimes use “string theory” to refer to weirder things like M-theory, where nobody knows which degrees of freedom to use...