In the Many Worlds theory, what happens when there is–or instead of–collapse?
I realize that in the Many Worlds theory–as opposed to traditional theory–at a particle’s “collapse” something amazing happens. But I’ve never understood what.
What happens?
Many thanks,
Steven Esred
Well, the basic gist is that when the observer becomes entangled with the measurement apparatus, there simply is no collapse—instead, the state is interpreted as referring to one observer making one observation, and another version observing something else.
Schematically, it’s somewhat like this.
Before the measurement, we have:
(observer pre-observation) (measurement apparatus in “ready” - state) (electron spin up + electron spin down)
Then the measurement occurs, and we have:
(observer pre-observation) (measurement apparatus indicates up, electron spin up + measurement apparatus indicates down, electron spin down)
This is an entangled state between the apparatus and the electron. Now, the experimenter looks at the apparatus, and we get:
(observer sees up, measurement apparatus indicates up, electron spin up + observer sees down, measurement apparatus indicates down, electron spin down)
In Copenhagen QM, one then invokes the collapse, so that only one of the terms in the sum survives; many worlds then simply keeps the whole state as it is, and interpretes it as two ‘copies’ of the observer making distinct observations in distinct ‘worlds’.
Nothing “collapses” in this interpretation; that is kind of the point. It asserts the reality of objects being in a superposition of states. Which makes you think the pejorative name may be unfortunate: why do you need to posit many “worlds”, as opposed to one world (look around you!) containing interesting quantum states?
A related question - what has been proposed to address to the problem that Many Worlds does not seem to account for the probabilistic nature of the wavefunction?
The main proposal to address that problem is better education about how the Many Worlds interpretation works, because in fact it accounts for it just fine.
IIUC every time you physicists half-kill a cat the number of “worlds” doubles, and since you’re probably also half-killing earthworms, microbes and even molecules, the number of worlds is pretty huge by now.
But the little weirdness behind my eyes that thinks “I exist” while “I” type these words only inhabits a tiny fraction of these many worlds: in its world, that particular half-dead cat survived, but another half-dead albatross didn’t.
And a dozen half-dead septimuses in the past did survive! It makes me a believer in Quantum immortality. Given various infarctions, reckless drivings and angry gun-wielders, my survival this long without such “Immortality” working for me might defy the odds! 
I’m aware that the math works. But it’s not clear to the non-expert how to interpret the probability under Many Worlds, and the experts don’t seem to view it as a settled issue either:
I tried to read up on this a long while ago, and I didn’t understand quite a lot of it. I’m hoping one of the experts on here could explain some of it. I just found a talk online about it that I’m watching now.
I know a couple of approaches to probability in many worlds—such as the ones that developed from Everett’s original approach, decision theoretical models, self-locating uncertainty, and a couple more—and to the best of my knowledge, it’s still an active topic of research. So if there’s an easy answer to the problem of probability, it seems a lot of people missed it.