Sean Carroll's description of the Many Worlds interpretation

[DaveBeal]

TL;DR

How is the Many Worlds interpretation more consistent with Schroedinger's equation than the Copenhagen interpretation?

In Sean Carroll's book The Biggest Ideas In The Universe: Quanta And Fields he gives a very brief description of Everette's Many Worlds interpretation (page 73). I think he's saying that in this interpretation, when you perform a measurement on a quantum system, the universe splits into multiple branches, one for each possible outcome of the experiment. For instance, if you were measuring the spin of an electron that was initially in a superposition, this would result in two branches, one for a spin-up result and one for a spin-down result. In each branch, the wave function of the electron now contains only the one term corresponding to the result of the measurement. So in the branch in which the electron measured spin-up, its wave function now contains only a spin-up term, and in the branch for the spin-down result, the wave function contains only the spin-down term. Do I have this correct?

Carroll seems to imply that this is somehow more consistent with the Schroedinger equation than the wave function collapse of the Copenhagen Interpretation, but I don't see why it's better. Either way, you have an instantaneous discontinuous change in the wave function which bears no resemblance to the continuous evolution described by the Schroedinger equation. Why is the Many Worlds interpretation better?

 

[PeterDonis]

Moderator's note: Thread moved to the QM interpretations subforum.

 

[PeterDonis]

Do I have this correct?

Sort of. There is only one wave function, which includes both branches; but in the wave function after the measurement, the electron is entangled with the measuring device so that in each branch, the measuring device registers the result corresponding to the electron's spin in that branch.

For example, if we measure the electron's spin in the up-down basis, the wave function before measurement would look like this:

$$
\left( \alpha \ket{\uparrow} + \beta \ket{\downarrow} \right) \ket{\text{ready}}
$$

where $\ket{\text{ready}}$ is the "ready to measure" state of the measuring device, where it hasn't yet registered a result, and $\alpha$ and $\beta$ are complex amplitudes whose squared moduli sum to $1$. And the wave function after measurement would look like this:

$$
\alpha \ket{\uparrow} \ket{\text{measured} \uparrow} + \beta \ket{\downarrow} \ket{\text{measured} \downarrow}
$$

The latter wave function is entangled between the electron and the measuring device, where the former is not.

Carroll seems to imply that this is somehow more consistent with the Schroedinger equation than the wave function collapse of the Copenhagen Interpretation

It is, because there is no collapse in the Schrodinger Equation; time evolution in that equation is always unitary. All you need is an appropriate interaction Hamiltonian to describe the measurement process and how it entangles the electron with the measuring device.

Either way, you have an instantaneous discontinuous change in the wave function

No, that's not the case with the MWI. The change between the two wave functions I described above happens over time according to unitary evolution as described by the Schrodinger Equation with an appropriate interaction Hamiltonian. There is no discontinuous change anywhere. The change just happens fast enough that our current technology can't spot it happening, we can only see the "before" and "after" states. That's what the MWI says, anyway, and whether or not you like it, it's perfectly consistent with the Schrodinger Equation.