Carroll’s most recent book is Something Deeply Hidden: Quantum Worlds and the Emergence of Spacetime.
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https://www.quantamagazine.org/where-quantum-probability-comes-from-20190909/
is equal to the value of the wave function squared. The measurement problem is simply: What constitutes a “measurement”? When exactly does it occur? Why are measurements seemingly different from ordinary evolution?
Dynamical-collapse theories offer perhaps the most straightforward resolution to the measurement problem. They posit that there is a truly random component to quantum evolution, according to which every particle usually obeys the Schrödinger equation, but occasionally its wave function will spontaneously localize at some position in space.
Such collapses are so rare
that we would never observe one for a sin
particle, but in a macroscopic object made of many particles, collapses happen all the time. This prevents macroscopic objects — like the cat in Schrödinger’s infamous thought experiment — from evolving into an observable superposition. All the particles in a large system will be entangled with each other, so that when just one of them localizes in space, the rest are brought along for the ride.
Probability in such models is fundamental and objective. There is absolutely nothing about the present that precisely determines the future. Dynamical-collapse theories fit perfectly into an old-fashioned frequentist view of probability. What happens next is unknowable, and all we can say is what the long-term frequency of different outcomes will be. Laplace’s demon wouldn’t be able to exactly predict the future, even if it knew the present state of the universe exactly.
Pilot-wave theories tell a very different story. Here, nothing is truly random; the quantum state evolves deterministically, just as the classical state did for Newton. The new element is the concept of hidden variables, such as the actual positions of particles, in addition to the traditional wave function. The particles are what we actually observe, while the wave function serves merely to guide them.
In a sense, pilot-wave theories bring us back to the clockwork universe of classical mechanics, but with an important twist: When we’re not making an observation, we don’t, and can’t, know the actual values of the hidden variables. The over their possible values.