Two particles are entangled and separated by a vast distance.
At some point, I conduct a measurement on the first particle, causing me to split into two different versions of myself that have measured two different states. Now, the effect of that measurement spreads outwards from the site of the measurement, so I may affect other things based on the measurement, etc.
My problem is that if a measurement is done on the other particle, long before any message from me could possibly have got there, then that measurement and the effects it has on its local environment and the effects they have are all also dependent on my measurement.
I imagine this as a wave of universe splitting spreading out from the site of my measurement and the entangled particle despite the separation.
Now, perhaps this is a nontechnical use of the word nonlocal, but I'd describe that as a nonlocal phenomenon.
> My problem is that if a measurement is done on the other particle, long before any message from me could possibly have got there, then that measurement and the effects it has on its local environment and the effects they have are all also dependent on my measurement.
Imagine that your friend Joe writes the same word on two pieces of paper, puts them in envelopes and hands one envelope to you and mails the other envelope to Paris. At some point in time, you open up your envelope and read the word "popcorn". At some other point in time, Pierre open up his envelope and reads the same word.
The word that Pierre reads is not "dependent on your measurement". Nothing nonlocal occurred.
Sure, I used the word 'theory' incorrectly, I should have said 'explanation'.
As I understand it, hidden variables are fine if you're happy to throw away locality, which is exactly what Bohm interpretation does and exactly what we're talking about here.
Since your analogy is purportedly showing me how MWI is local, showing me that something that is significantly different (i.e. is a hidden variable explanation) is also local doesn't help a lot.
then that measurement and the effects it has on its local environment and the effects they have are all also dependent on my measurement.
I think that's your trouble there. Those are totally independent of your measurement, the waveform splits at the measurement of the other particle the exact same way, regardless of what happened to you locally.
except I can never be in a universe where it split at my measurement site in one way and it split at the other measurement site the other way. That means that I am entangled with a measurement that happens nonlocally to me and everything that it interacts with.
You're not entangled with the measurement, you're entangled with the entire wave despite the inconceivable number of measurements that happen within it. The same way my friends are still my friends despite us being in different places. I won't know instantly if they die or something, but I react differently when I hear about what happens to them than I do with ordinary people. If one of them gets into a car accident outside my light-cone and I'm more sad when I hear about it than about the car accident of a stranger, that doesn't mean that I have a non-local interaction with the car accident.
Two particles are entangled and separated by a vast distance.
At some point, I conduct a measurement on the first particle, causing me to split into two different versions of myself that have measured two different states. Now, the effect of that measurement spreads outwards from the site of the measurement, so I may affect other things based on the measurement, etc.
My problem is that if a measurement is done on the other particle, long before any message from me could possibly have got there, then that measurement and the effects it has on its local environment and the effects they have are all also dependent on my measurement.
I imagine this as a wave of universe splitting spreading out from the site of my measurement and the entangled particle despite the separation.
Now, perhaps this is a nontechnical use of the word nonlocal, but I'd describe that as a nonlocal phenomenon.