This is really interesting. I appreciate you explanation of an Operator. I have much to learn and many links to follow. This kind of post is why I’m here on SD.
Glad to send you down a Wikipedia rabbit hole 
. Operators are not exclusive to QM–they can be used in classical mechanics as well, not to mention being a concept from mathematics–but in QM they are truly fundamental. In classical mechanics, the state of the universe can be basically written down as a list of the positions and momenta of every particle. In QM, this list just does not exist. You have to apply an operator to get the classical value (a particle’s position) out of the universe’s state.
I can kinda-sorta recommend Quantum Mechanics: The Theoretical Minimum for a deeper look. It is not a pop-science intro to QM, but it is not quite a textbook either. It can get mathematically dense, but does provide a rigorous introduction to the subject. It’s probably too dense for someone without at least a course or two in college-level physics.
I did read my own wiki link:
Operators in classical mechanics[edit]
In classical mechanics, the movement of a particle (or system of particles) is completely determined by the [Lagrangian]
Looking forward to reading your link.
Right, and one should take care to note that it’s not the interaction between the measurement device and the measured object that’s responsible for any ‘change’—if we have a detector at one slit of the double slit setup, we’ll only register, and thus interact with, half the particles on average, but the interference pattern disappears completely. Even using interaction-free measurements, where the measurement device never interacts with the system measured (itself only possible in the quantum world), will yield the same ‘change’ of the system (a vivid demonstration of the possibility of measuring something without interaction is the Elitzur-Vaidman bomb tester).
I’m not sure I would phrase things like this. I think you’re talking about projection operators, specifically—they are associated with a particular value for an observable (i.e. a particular experimental outcome), and after measurement, the state will be the result of applying that operator to the state prior to measurement (and normalizing). But more generally, operators are just machines to (linearly) transform states.
This isn’t really specifically quantum mechanical, either. In the Koopman-von Neumann formalism, classical mechanics is formulated using the language of operators on Hilbert space, the main difference being the absence of an uncertainty relation.
A bit nitpicky, but that somewhat depends on the formulation of quantum mechanics. In the Bohmian approach, there absolutely is such a list. But the quantum potential will ensure that inevitable, non-local disturbances influence the values such that successive incompatible measurements invalidate prior information.
Are you the author of this book?
Right. As I noted, operators are not exclusive to QM. But they are the only way to extract an observable from the universe in QM. Although it’s possible to formulate classical mechanics in operator terms, they are not needed to extract observables. They definitely still come in handy for transforming states, though (such as time evolution operators).
As you note, it’s basically projection operators I’m talking about. The global state gets projected down to a “smaller” state, in the same way that a 3D object projected onto a 2D sheet of paper gets “smaller”. You achieve a definite outcome (a view of the 3D object from a certain direction), but you lose the original shape of the object.
That’s fair. I should have said that not only can you write down such a list in classical mechanics, but that list also gives you the complete state of the universe, which you can then use to determine all future states of the universe. Even in Bohmian mechanics, where particles have a definite position and momentum, there is still the unknown wavefunction influencing things (to be honest, I’ve never understood the point of including the classical particles once you’ve accepted that the wavefunction exists).
I am not Leonard Susskind . I’ve just enjoyed some of his other work, such as The Black Hole War. He also does various lecture series that you may find interesting (and are generally available on YouTube).
I’m still not sure if watching those made me smarter, or just made me realize how dumb I am.
I am a fan of Lenny, though.
Sean Carroll is working on a series of book in the same vein as Theoretical Minimum, but more math heavy, but he plans on teaching the necessary math as it goes along.
I’ll be interested when that comes out.