Sean Carroll

when you say entangle a superposition into a classical and quantum system, that makes no sense to me. I mean, I'm sure it could make sense if I understood what you had in mind. Maybe there are some equations or something like that. But entanglement is a purely quantum thing. There's no such thing as—or, yeah, entangle a superposition. I don't even know what entangle a superposition means.

when you say entangle a superposition into a classical and quantum system, that makes no sense to me. I mean, I'm sure it could make sense if I understood what you had in mind. Maybe there are some equations or something like that. But entanglement is a purely quantum thing. There's no such thing as—or, yeah, entangle a superposition. I don't even know what entangle a superposition means.

I know what it means to entangle quantum states, and quantum states— are in superpositions from certain points of view, not in superpositions from other points of view, but classical systems are neither entangled nor in superpositions, so I really don't know what's going on. Sorry about that. I can't really be very helpful. Stephen Moradi has a priority question.

I know what it means to entangle quantum states, and quantum states— are in superpositions from certain points of view, not in superpositions from other points of view, but classical systems are neither entangled nor in superpositions, so I really don't know what's going on. Sorry about that. I can't really be very helpful. Stephen Moradi has a priority question.

I like everyone's using up their priority questions. That's good. You put some thought into what you want these to be. I've heard people say that there is no chaos in quantum processes.

I like everyone's using up their priority questions. That's good. You put some thought into what you want these to be. I've heard people say that there is no chaos in quantum processes.

Could you elucidate the difference between a three-body classical gravitational interaction with a three-body electrostatic quantum interaction, given that both are deterministic and interact via inverse square forces? This is a subtle thing, this statement that there is no chaos in quantum processes. I mean, the world is quantum and there is chaos in the world.

Could you elucidate the difference between a three-body classical gravitational interaction with a three-body electrostatic quantum interaction, given that both are deterministic and interact via inverse square forces? This is a subtle thing, this statement that there is no chaos in quantum processes. I mean, the world is quantum and there is chaos in the world.

So therefore, clearly, in some sense, there is chaos in quantum mechanics. But on the other hand, chaos is a result. Chaos is a statement about sensitive dependence on initial conditions, right? Tiny deviations in the initial conditions lead to large deviations in the final answer. How can that happen at the down and dirty level of equations?

So therefore, clearly, in some sense, there is chaos in quantum mechanics. But on the other hand, chaos is a result. Chaos is a statement about sensitive dependence on initial conditions, right? Tiny deviations in the initial conditions lead to large deviations in the final answer. How can that happen at the down and dirty level of equations?

It happens because of nonlinearities, because small deviations in the state of the system can feed back onto each other through nonlinear terms in the equations of motion. In quantum mechanics, the equation of motion is, you guessed it, the Schrodinger equation. And the Schrodinger equation is resolutely linear as a function of the wave function.

It happens because of nonlinearities, because small deviations in the state of the system can feed back onto each other through nonlinear terms in the equations of motion. In quantum mechanics, the equation of motion is, you guessed it, the Schrodinger equation. And the Schrodinger equation is resolutely linear as a function of the wave function.

There's no wave function squared terms in the Schrodinger equation. So if the question you're asking is, Is there sensitive dependence on initial conditions in the evolution of the quantum state according to the Schrodinger equation? The answer is no. There never is. It's a linear equation of motion.

There's no wave function squared terms in the Schrodinger equation. So if the question you're asking is, Is there sensitive dependence on initial conditions in the evolution of the quantum state according to the Schrodinger equation? The answer is no. There never is. It's a linear equation of motion.

But within all the different things that can pop out of the Schrodinger equation, one of the things is the classical limit. So you can have a classical limit, and it makes absolutely no difference whether we're talking about gravity or electromagnetism. They're exactly the same in this sense.

But within all the different things that can pop out of the Schrodinger equation, one of the things is the classical limit. So you can have a classical limit, and it makes absolutely no difference whether we're talking about gravity or electromagnetism. They're exactly the same in this sense.

In either case, there can be a classical limit where there is chaos, where there is nonlinear classical equations of motion that arise as the limit of quantum mechanics. How can nonlinear equations of motion arise as the limit of linear equations of motion?

In either case, there can be a classical limit where there is chaos, where there is nonlinear classical equations of motion that arise as the limit of quantum mechanics. How can nonlinear equations of motion arise as the limit of linear equations of motion?

Well, the classical limit is subtle, and it involves the combined effect of many, many different parts of the quantum mechanical wave function. So basically, you have... many, many different modes or whatever you want to call them of the wave function, either interfering constructively or destructively to give you a classical trajectory.

Well, the classical limit is subtle, and it involves the combined effect of many, many different parts of the quantum mechanical wave function. So basically, you have... many, many different modes or whatever you want to call them of the wave function, either interfering constructively or destructively to give you a classical trajectory.