Sunday, May 01, 2022

The multiverse, everywhere, all at once

The multiverse (in a cartoonish version of the many-words interpretation of quantum mechanics sense - see here for a more in-depth writeup) is having a really good year.  There's all the Marvel properties (Spider-Man: No Way Home; Loki, with its Time Variance Authority; and this week's debut of Doctor Strange in the Multiverse of Madness), and the absolutely wonderful film Everything, Everywhere, All at Once, which I wholeheartedly recommend.  

While it's fun to imagine alternate timelines, the actual many-worlds interpretation of quantum mechanics (MWI) is considerably more complicated than that, as outlined in the wiki link above.  The basic idea is that the apparent "collapse of the wavefunction" upon a measurement is a misleading way to think about quantum mechanics.  Prepare an electron so that its spin is aligned along the \(+x\) direction, and then measure \(s_{z}\).  The Copenhagen interpretation of quantum would say that prior to the measurement, the spin is in a superposition of \(s_{z} = +1/2\) and \(s_{z}=-1/2\), with equal amplitudes.  Once the measurement is completed, the system (discontinuously) ends up in a definite state of \(s_{z}\), either up or down.  If you started with an ensemble of identically prepared systems, you'd find up or down with 50/50 probability once you looked at the measurement results.    

The MWI assumes that all time evolution of quantum systems is (in the non-relativistic limit) governed by the Schrödinger equation, period.  There is no sudden discontinuity in the time evolution of a quantum system due to measurement.  Rather, at times after the measurement, the spin up and spin down results both occur, and there are observers who (measured spin up, and \(s_{z}\) is now +1/2) and observers who (measured spin down, and \(s_{z}\) is now -1/2).  Voila, we no longer have to think about any discontinuous time evolution of a quantum state; of course, we have the small issues that (1) the universe becomes truly enormously huge, since it would have to encompass this idea that all these different branches/terms in the universal superposition "exist", and (2) there is apparently no way to tell experimentally whether that is actually the case, or whether it is just a way to think about things that makes some people feel more comfortable.  (Note, too, that exactly how the Born rule for probabilities arises and what it means in the MWI is not simple.) 

I'm not overly fond of the cartoony version of MWI.  As mentioned in point (2), there doesn't seem to be an experimental way to distinguish MWI from many other interpretations anyway, so maybe I shouldn't care.  I like Zurek's ideas quite a bit, but I freely admit that I have not had time to sit down and think deeply about this (I'm not alone in that.).  That being said, lately I've been idly wondering if the objection of the "truly enormously huge" MWI multiverse is well-founded beyond an emotional level.  I mean, as a modern physicist, I already have come to accept (because of observational evidence) that the universe is huge, possibly infinite in spatial extent, appears to have erupted into an inflationary phase 13.6 billion years ago from an incredibly dense starting point, and contains incredibly rich structure that only represents 5% of the total mass of everything, etc.  I've also come to accept that quantum mechanics makes decidedly unintuitive predictions about reality that are borne out by experiment.  Maybe I should get over being squeamish about the MWI need for a zillion-dimensional hilbert space multiverse.  As xkcd once said, the Drake Equation should include a factor for "amount of bullshit you're willing to buy from Frank Drake".  Why should MWI's overhead be a bridge too far?  

It's certainly fun to speculate idly about roads not taken.  I recommend this thought-provoking short story by Larry Niven about this, which struck my physics imagination back when I was in high school.  Perhaps there's a branch of the multiverse where my readership is vast :-)



5 comments:

Rajendra Kshirsagar said...

Great post and links. I am going to enjoy going through them. Thanks.

Anonymous said...

If one had a big enough quantum computer, could one "solve" the measurement problem? For example, by simulating the coupling of a few qubits to a bath of qubits. I have always held the interpretation (maybe wrongly) that all time evolution for the system and environment is given by a very complex, but still unitary, Schrodinger time evolution.

Mayer Landau said...

"Perhaps there's a branch of the multiverse where my readership is vast"
A prerequisite to vast readership is responding to, or otherwise interacting with, the people who post.

Douglas Natelson said...

Anon, that's insightful and this is deeply connected to topics like "eigenstate thermalization" (how do you end up with occupations of energy eigenstates that look very thermally distributed even in the absence of some kind of bulk, classical "bath") and many-body localization (the idea that sometimes the full interacting quantum system never thermalizes within itself).

Mayer, I do my best to be responsive, but admittedly I have a lot of other responsibilities. I don't think lack of engagement on my part is the rate-limiting step here, though your mileage may vary.

DanM said...

@Mayer Landau: Phil Plait's astronomy blog is one of the most popular and widely read science blogs on the interwebs, but he has basically never interacted with the readers, even back when he allowed people to post comments.

Just sayin'.