Ah. So it’s not the idea that it’s weighted so much as the specific act of squaring the amplitude. “Why squaring the amplitude, why not something else?”.
I suppose the way I had been reading, I thought that the problem came from expecting a different result given the squared amplitude probability thing, not from the thing itself.
That is helpful, many thanks.
I’ve been reading the Quantum Mechanics sequence, and I have a question about Many-Worlds. My understanding of MWI and the rest of QM is pretty much limited to the LW sequence and a bit of Wikipedia, so I’m sure there will be no shortage of people here who have a better knowledge of it and can help me.
My question is this: why are the Born Probabilites a problem for MWI?
I’m sure it’s a very difficult problem, I think I just fail to understand the implications of some step along the way. FWIW, my understanding of the Born Probabilities mainly clicks here:
Firstly, I know probability is the wrong word, but I’m going to use it here, insufficiently, in the same way that it’s normally insufficiently used to talk about QM. I sure hope that’s okay because it is a pain to nail down in English.
So… If a quantum event has a 30% chance of going LEFT and a 70% chance of going right (which you could observe without entangling yourself, for example by blasting a whole bunch of photons through slits and seeing the overall density pattern without measuring individual photons) (I think), then if you entangle yourself with a single instance of it, you’ll have a 30% probability of observing LEFT and a 70% probability of observing RIGHT.
So why is this surprising? Obviously if we’re just counting observers then we would expect a 50⁄50 probability spread, but I assume the problem isn’t that naive. Obviously if the particles themselves exhibit a 30⁄70 preference, then we, being made of particles, should expect to do the same. Or… if the particles themselves can exist along a (psuedo)probability continuum, then why should we, the entagled, not expect to do the same? If those quarks are 70⁄30, then why aren’t yours? Why should MWI necessarily imply the sudden creation of exactly 2 worlds with equal weight, as opposed to just dividing experience, locally and where necessary, into a weighted continuum?
I think I’ll try this from another angle. MWI gets points for treating people/observers as particles, governed by the same laws as everything else. But are we really treating ourselves equally if we don’t assume that we too follow this 30⁄70 split? It seems like this should be the default assumption, the one requiring no extra postulates, that we divide up not into discrete worlds but along a weighted continuum. Obviously it’s easier on our typical conception of conciousness if we can just have the whole universe split neatly in two, but that feels to me like putting the weirdness where it logically belongs (on our comparatively weak understanding of concious experience).
Hope this makes at least some since to someone who can steer me in the right direction. I’d appreciate responses as to where specifically I’ve erred, as this will continue to bug me until I see where exactly I went wrong. Thanks in advance.