Firstly, thanks for taking the time to form that excellent reply (and exorcising the text formatting from my post, that must've been annoying, sorry). I think I may actually be learning something. Hopefully I'm not losing knowledge from another field to make way for new information in my brains 
It's not surprising that there is disagreement on the subject of scaling QM up to molecular levels and macro scales beyond. As I understand it, this exact subject is still one of physics' "big problems".
(b) How much is "sufficient to disturb it"? I guess the answer will be something about changing energy levels, or the Planck energy. But surely even an electron and a proton 1000 km apart are still exerting some influence on each other?
They have detectors arranged around the point of intended collision, like in my crossroads example. When they see a particle hit one of the detectors, that's when its wave function collapses and retroactively "decides" what path it took and whether or not it collided, based on the probability of it having done so. Because its wave function interacted with that of its intended collision partner, the two were entangled and so the partner's wave function also collapses at that point, even if it hasn't hit a detector yet. It's at that moment that the many paths that they could follow after exiting the emitters collapse to two single, well-defined paths, giving the appearance that the path was at every moment in their journey well-defined.
At this point you may ask, "so what counts as an observation?" I'll leave that question until the end of this post.
To me that just looks like an approximation, albiet a completely reasonable one, one that would never deviate from the reality in a million universe lifetimes, but an approximation nonetheless. But I don't know, maybe it really is a fundamental law of QM, and answers all my questions. It does pose some more questions:
Are these probabilities themselves quantised? Is there a "smallest quantum of probability," a smaller probability than which is impossible?
Is it possible to speak of a probability of exactly one for some specific attribute of a quantum? That would presumably equate to a wave function collapse, regardless of any question surrounding "infinity minus one."
Now I shall return to the question from earlier, "what counts as an observation?" Why does an interaction with a detection plate in the CERN collider count as an observation, with the power to collapse wave functions, while the collision itself does not? I address this here at the end of the post because it's more philosophical than scientific. The answer to the latter question is, neither is strictly an observation, I was just approximating, reducing to a simpler example.
The answer to the former question is, the only thing that counts as an observation is an interaction with any of the quanta within the brain which is currently reading this text. You exist in your own universe in which you are the only entity capable of collapsing wave functions. I exist in my own universe in which I am likewise. These universes happen to coincide.
Contentious? Yes. Relevant? No. Scientific? Probably not. The distinction is largely academic and may have absolutely no bearing on the science; for studying QM for real world purposes it doesn't matter. But this thread has never been about the real world.
It's not surprising that there is disagreement on the subject of scaling QM up to molecular levels and macro scales beyond. As I understand it, this exact subject is still one of physics' "big problems".
Ok, no, not equal in that sense. Just similar enough as to be indistinguishable at first glance. And I didn't say highly likely, I just said a significant probability, so something more like 1:1010 rather than 1:101000.SakSak said:
(a) Electrical charge is carried by photons, so this interaction is still just one of interfering wave functions. That's why I used gravity to make this point, because it's the only force field without a quantum force-carrier in the standard model.
(b) How much is "sufficient to disturb it"? I guess the answer will be something about changing energy levels, or the Planck energy. But surely even an electron and a proton 1000 km apart are still exerting some influence on each other?
Because they observe the results!
They have detectors arranged around the point of intended collision, like in my crossroads example. When they see a particle hit one of the detectors, that's when its wave function collapses and retroactively "decides" what path it took and whether or not it collided, based on the probability of it having done so. Because its wave function interacted with that of its intended collision partner, the two were entangled and so the partner's wave function also collapses at that point, even if it hasn't hit a detector yet. It's at that moment that the many paths that they could follow after exiting the emitters collapse to two single, well-defined paths, giving the appearance that the path was at every moment in their journey well-defined.
At this point you may ask, "so what counts as an observation?" I'll leave that question until the end of this post.
I don't dispute that.
Determinable is not the same as determinate. Determinate is closer to invariant. Sorry I don't know the "proper" terminology for this, if there is such a thing. Determinate is what a thing is only at the moment of its wave function collapse.
Ok, so your overall point seems to me to be that a wave function collapse is incurred at any moment where the probability distribution described by a wave function is distributed so as to make its probability of not being at a certain specific position "infinity minus one to one against," to use your prof's colourful misuse of mathematics.
To me that just looks like an approximation, albiet a completely reasonable one, one that would never deviate from the reality in a million universe lifetimes, but an approximation nonetheless. But I don't know, maybe it really is a fundamental law of QM, and answers all my questions. It does pose some more questions:
Are these probabilities themselves quantised? Is there a "smallest quantum of probability," a smaller probability than which is impossible?
Is it possible to speak of a probability of exactly one for some specific attribute of a quantum? That would presumably equate to a wave function collapse, regardless of any question surrounding "infinity minus one."
It seems we are in agreement.
Now I shall return to the question from earlier, "what counts as an observation?" Why does an interaction with a detection plate in the CERN collider count as an observation, with the power to collapse wave functions, while the collision itself does not? I address this here at the end of the post because it's more philosophical than scientific. The answer to the latter question is, neither is strictly an observation, I was just approximating, reducing to a simpler example.
The answer to the former question is, the only thing that counts as an observation is an interaction with any of the quanta within the brain which is currently reading this text. You exist in your own universe in which you are the only entity capable of collapsing wave functions. I exist in my own universe in which I am likewise. These universes happen to coincide.
Contentious? Yes. Relevant? No. Scientific? Probably not. The distinction is largely academic and may have absolutely no bearing on the science; for studying QM for real world purposes it doesn't matter. But this thread has never been about the real world.
