this post was submitted on 19 Aug 2025
45 points (95.9% liked)
Explain Like I'm Five
18194 readers
2 users here now
Simplifying Complexity, One Answer at a Time!
Rules
- Be respectful and inclusive.
- No harassment, hate speech, or trolling.
- Engage in constructive discussions.
- Share relevant content.
- Follow guidelines and moderators' instructions.
- Use appropriate language and tone.
- Report violations.
- Foster a continuous learning environment.
founded 2 years ago
MODERATORS
you are viewing a single comment's thread
view the rest of the comments
view the rest of the comments
In classical statistical theory, manipulating a probabilistic state is equivalent to picking a single initial state with whatever probability, and then manipulating it. In quantum statistics it's provably not (at least if we're measuring particles with as much free will as we think); you need the whole thing for it to make sense. Two likely trajectories can interfere and cancel out, for example.
So, sure, a position is a vector. But we can only meaningfully talk about functions from a (measurable) set of vectors to their probability amplitude (which is like a probability, but complex). Or, in practice, the infinitesimal density of probability amplitude at that given point
The uncertainty principal is just one manifestation of that. And, like in the uncertainty principal, entanglement might not stay confined to just position if there's other parameters, so you really have to talk about functions on the whole state vector. I can't speak too much to quantum field theory, but the actual dynamics of basic quantum physics is about (very "basic") functions on those functions.