If there's a non-psychological explanation for the phenomenon you're describing, it's not quantum entanglement, it's an entirely new kind of science that we have yet to contemplate.
I think this also holds up with how ad tracking aims to hoover up all sorts of data to find correlations. There are probably a lot of non-obvious correlations in there, which causes ads to sometimes eerily seem to read minds. These same correlations may cause people to exhibit very similar thoughts without needing to invoke quantum entanglement.
From the top of my head, quantum entanglement is something:
1/ that happens at quantum level, so typically with measurable effects on a scale smaller than one atom (way smaller than one neuron);
2/ that requires specific operations on a specific group of particles (the probability that such entangled particles end up in two different brains of related people is infinitesimal);
3/ that requires many measures to confirm – and you can only do so once per group of particles (so it would not be sufficient to have two entangled particles one in each brain, you'd probably need tens of thousands).
Of course I'll now be slammed for "woo woo" unscientific thinking as is always the case on HN, when someone who "knows all" encounters someone who doesn't.
This simple observation is something physicists have hard time wrapping their head around for some reason. The reason I suspect being that it clashes with their religious beliefs about free will and whatnot.
It's weird.
> something physicists have hard time wrapping their head around for some reason
The problem is that it's fundamentally different from anything you can do in classical mechanics. And because of that, attempts to explain it in simple terms with casual language are doomed. And attempts to take shortcuts in reasoning by analogizing it to something from everyday life are doomed.
Nobel Prize in physics 2022 “for experiments with entangled photons, establishing the violation of Bell inequalities and pioneering quantum information science”
Say you have two billiard balls on a very very large table with almost no friction. One ball is stationery, the other is moving towards it and spinning along some axis. When they collide, they'll be sent along some random directions and each with some spin, and their spins are going to add up to the original spin of the moving ball (angular momentum is conserved in frictionless interactions in classical mechanics too). Now, when the ball arrive at a long distance away from each other, two experimenters which can't see the balls measure their spin. They each choose some direction and measure how much their ball spins along that direction. They repeat the experiment lots of times, keeping good track of each individual result.
When they later compare notes, they'll measure how much their respective results for each individual experiment were correlated. Since they were measuring along different axis, they didn't both see the exact same result: maybe for the ball that reached one was spinning at one revolution along the 45° axis every two seconds, and the other was spinning at half a revolution along the 1° axis every second. Ultimately, they'll find that the correlation between their experiments was about 75% (each time they measure along unrelated axis, they get no correlation, when they happen to measure along the exact same axis, they get perfect correlation, and when it's in between, it's some subset of that).
However, if we repeat the same thing with quantum particles, we actually find a higher correlation, about 85%. This can only happen if (a) measuring one particle changes the other - and we've quickly ruled out that this can happen at slower than light speeds, or (b) the particle pair don't share a definite state to begin with, but assume an appropriate state only when they are measured [or (c) the axis chosen by the experimenters in each measurement somehow depends on the spin of the particle pair].