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Wording matters: why maybe physicists should reconsider using terms like 'probability' and 'uncertainty' when talking about quantum mechanics.
Elementary particles are neither waves nor (point-like) particles, nor are they both. The most general and unassuming description we have of their behaviour is formulated in terms of complementary states consisting of properties defined not in terms of specific values but as 'possibilities' (degrees of freedom). Interacting particles form a system wherein each particle's possible states are inseparably defined in such a way that the system as a whole "makes sense", and this is termed 'entanglement' between particles.
The "make sense" constraint is a restriction on quantum states to only allow those which preserve certain properties, for example:
- complementarity of states: if particles A and B are entangled and one of their properties are known to be opposites of each other, then no matter how, when or where you measure this property on any one of them, reality conspires deterministically in such a way that you will always observe the opposite result from performing the same measurement on the other,
- total energy: a composite particle that is split into subcomponents defines a system of entangled particles with all possible states giving the same total energy as the original particle,
- conservation of information: all knowledge one could ever have about an entangled system is embedded within that system in such a way that it could be theoretically retrieved at any given point along its evolution
We know, both from experiments and from our experience of the world (as a rather clearly defined reality with sharp boundaries and a seemingly linear history), that we are able to manipulate particle systems in ways that constrain their possible states to such degree that we can make definite statements about some of their properties.
How? Where did all those other possibilities go?
To answer this, one can invoke a variant of the anthropic principle known as the [anthropic bias](https://en.wikipedia.org/wiki/Anthropic_Bias_(book)). All coherent combinations of quantum states (i.e. all possible states of a system of entangled particles) define possible realities. The implications of this are controversial, but the statement can not be argued - all possibilities are clearly defined and equally valid - and each of those realities can have their own set of "observers", and each one of them could say "look, this particle is (approximately) here!". You and me could then very well be one of these.
Disambiguation: an "observer" doesn't have to be a "conscious" being; it could be an electron and it would say the same thing.. if electrons said things.
Note the way I phrased how we retrieve information about particles. There's no magic here; concepts like "consciousness" or "free will" play no part in this process as it is explained.
An "observation" is probably best understood as "the particles that make you are interacting with particles that transitively interact with the particle you're attempting to measure, entangling all of you in the process". The resulting system defines all versions of your possibly observed realities including every possible measurement result.
The outcome distribution often observed in experiments is addressed by the anthropic bias, but tl;dr is: there is often significant overlap between possible realities, and the overlap tends to follow a distribution curve such that you're simply much more likely to exist in realities where this pattern emerges.
cf:
https://en.wikipedia.org/wiki/Born_rule
https://en.wikipedia.org/wiki/Wave_function
Going back to the point raised at the beginning: I believe terms like 'probabilities' and 'uncertainties' are terribly unhelpful because they lead your thinking towards the mystical domains of "inexplicable randomness", paradoxical dualities of particles in existential crisis, spooky non-local particle conspiracies and "a consciousness observing a particle makes it behave differently", all of which seem like strawman takes, but they really aren't.
Some of the greatest physicists we've had have been known to struggle with making sense these questions because of the cultural biases they spawned into, and really, just read or watch almost any pop-science media and you'll be presented with these "paradoxes" - usually accompanied with "we just don't knoooow" because humans have such a hard time giving up on certain things that don't jive with observations (consciousness, free will, 'physical' reality, clearly defined and absolute answers etc).
I mean the resistance is natural: a human expects a direct answer to a direct question because that's life as we know it (where is the phone - it is on the couch). To then be met with vague, relatively (un)defined answers that varies along a number of degrees of freedom instead (where is the thing - it's mostly over there *gestures vaguely in all directions*) -- or even a counter question (where are you - depends.. where are *you*?) -- is understandably a hard pillow to swallow. But I think we're going to have to eat that pillow anyway.
Educators and communicators should put more emphasis on what we *know* and what the best explanations are (while applying Occam's Razor), and less on how quirky and random our models behave.
When studying physics, one is better off leaving all preconceived notions at the door. Especially pertaining to what constitutes 'time', 'space', 'real', 'defined', 'universal' or 'objective'. Better to start with established facts before getting lost in theoretical models and popular conjecture. If only that were easier.
I think a theoretical framework like [Constructor Theory](https://en.wikipedia.org/wiki/Constructor_theory) could really help.