Sean Carroll

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.

And that emergent classical trajectory can indeed obey chaotic dynamics. The whole thing is very subtle. I'm not trying to undersell it. There was a whole subject for a while where people were trying to bang their heads against this question. How can there be quantum chaos? And the answer is you need to take the classical limit.

And that emergent classical trajectory can indeed obey chaotic dynamics. The whole thing is very subtle. I'm not trying to undersell it. There was a whole subject for a while where people were trying to bang their heads against this question. How can there be quantum chaos? And the answer is you need to take the classical limit.

Paul Torek says, on the memory arrow of time and the causal arrow, you said, because we have memories and records of the past, we can't change them. But I'm tempted to turn the explanation around. If you can, at time t1, select an event so you can't, at t1, have a record of the event. Sorry, I inserted a word there.

Paul Torek says, on the memory arrow of time and the causal arrow, you said, because we have memories and records of the past, we can't change them. But I'm tempted to turn the explanation around. If you can, at time t1, select an event so you can't, at t1, have a record of the event. Sorry, I inserted a word there.

If you can at time t1 select an event, you can't at time t1 have a record of the event. So it seems that either lack of influence is a precondition or else a co-condition of records. In Janan Ismail's book, How Physics Makes Us Free, she offers a united explanation of both arrows of time, influence, and records.