I would just like to mention that “solid objects are in fact forces interacting” is massively underselling the size of the ontology shift associated with quantum mechanics to a degree that’s a bit hard to describe to someone who hasn’t studied it. It’s more like:
Fundamental physics no longer determines a single history where a particular series of things happens. It’s now the case that, even at a fundamental level, many different things all happen, and physics describes how relatively “real” each of those things are.
One consequence of this for our own universe, where entropy is increasing over time, is that the universe no longer has one history, but an exponential branching tree of histories, all of varying weights (numbers that describe how important we should consider the events in each of them). Oh, and the tree is emergent by the way, it’s not even a base component of the ontology.
The closest mathematical framework we previously had that kind-of worked this way was probability theory, and that was just meant to track our subjective uncertainties about things, not describe reality itself. But quantum mechanics doesn’t actually follow the rules of probability theory. It’s some kind of warped twisted version of probability where the probabilities are replaced with (the squared magnitudes of) complex numbers called “amplitudes”. Because complex numbers can have opposite signs, it’s possible that adding another way for something to happen can reduce the chances of it happening.
In regular probability theory (or, say, classical physics), you could describe a reversible map (like a symmetry transformation or time evolution) on a 10 state system by writing down a permutation. This initially seems like the only way it could be. You have ten possible states, and whatever you do has to be reversible, so all you can do is permute them. This could be represented with a 10x10 permutation matrix. But in quantum mechanics, such a map is not a permutation matrix, but a unitary matrix. Time evolution and symmetry transforms in QM are represented by unitary matrices, not permutations like you’d guess they should be!
Speaking of symmetry: Any non-trivial object that has all the rotational symmetry of a sphere (such as, for example, a sphere) must have infinitely many points. Except in QM, where the smallest such object has 3 points. Except that QM can tell the difference between a 360 degree rotation and doing nothing. (Not 720 degree rotations though. Those are still just like doing nothing, so at least there’s that.) As a consequence, the smallest non-trivial object that has all the rotational symmetry of a sphere actually has 2 points.
Because of the way QM works, it’s actually possible to exploit it to perform some kinds of computations faster than seems to be possible classically. This is also kind of weird.
EDIT: Made a few changes to this for clarity & accuracy based on Justin Sheek’s comment. (Thanks Justin!) List of edits:
Rewrote first sentence from “physics no longer describes what can happen” (misleading and just plain wrong) to its current form. I knew what I was trying to say here, but goofed on converting it into words. Sorry everyone.
Specified that we’re talking about fundamental physics here (since stat-mech does also involve assigning weights to various configurations).
Added paragraph break and “One consequence of this for our own universe, where entropy is increasing over time” to hopefully clarify that this part is talking about many worlds, and does not apply to every system that obeys quantum mechanics.
The bit about maps / functions was originally overstated for rhetorical reasons. This is probably not super detectable or helpful when describing a technical topic, so I’ve rewritten it to be more serious and direct.
I believe all that is written here is now something I can defend.
Oof, the amount of misinformation on QM even here on LW is staggering.
Physics no longer describes what can happen.
This is straightforwardly false. Maybe you meant to say “Physics no longer describes what definitely happens”? Still misleading, as that was already the case with statistical mechanics within the ontology of Boltzmann and Gibbs 50 years earlier.
Oh, and the tree is emergent by the way, it’s not even a base component of the ontology.
Coherent phenomena are definitely part of the base ontology of QM. The density matrix encodes the ensemble. (If by “the tree” you didn’t mean the ensemble, then your statement would make even less sense to me).
...QM will tell you that what it means to be a function has changed and you have to do it differently now.
No. QM has no bearing on “what it means to be a function”. Maybe you mean “QM encodes permutations in a surprising way”?
Except that QM can tell the difference between a 360 degree rotation and doing nothing. (Not 720 degree rotations though. Those are still just like doing nothing, so at least there’s that.)
Strictly speaking this is only sometimes true. It seems like you are alluding to the spin-statistics theorem or maybe the Aharonov-Bohm effect or Berry phase. Your quoted statement is specifically applicable only to fermionic states. It’s inapplicable to bosons or more exotic states like anyons (FQHE) or braid statistics.
Because of the way QM works, it’s actually possible to exploit it to perform some kinds of computations faster than seems to be possible classically. This is also kind of weird.
Thanks for the notes. I’ve made a few edits to my comment above based on this.
Also, for the benefit of the folks reading this: I’m not alluding to spin-statistics or Berry phase, merely the use of instead of as the group of rotational symmetries.
I would just like to mention that “solid objects are in fact forces interacting” is massively underselling the size of the ontology shift associated with quantum mechanics to a degree that’s a bit hard to describe to someone who hasn’t studied it. It’s more like:
EDIT: Made a few changes to this for clarity & accuracy based on Justin Sheek’s comment. (Thanks Justin!) List of edits:
Rewrote first sentence from “physics no longer describes what can happen” (misleading and just plain wrong) to its current form. I knew what I was trying to say here, but goofed on converting it into words. Sorry everyone.
Specified that we’re talking about fundamental physics here (since stat-mech does also involve assigning weights to various configurations).
Added paragraph break and “One consequence of this for our own universe, where entropy is increasing over time” to hopefully clarify that this part is talking about many worlds, and does not apply to every system that obeys quantum mechanics.
The bit about maps / functions was originally overstated for rhetorical reasons. This is probably not super detectable or helpful when describing a technical topic, so I’ve rewritten it to be more serious and direct.
I believe all that is written here is now something I can defend.
Oof, the amount of misinformation on QM even here on LW is staggering.
This is straightforwardly false. Maybe you meant to say “Physics no longer describes what definitely happens”? Still misleading, as that was already the case with statistical mechanics within the ontology of Boltzmann and Gibbs 50 years earlier.
Coherent phenomena are definitely part of the base ontology of QM. The density matrix encodes the ensemble. (If by “the tree” you didn’t mean the ensemble, then your statement would make even less sense to me).
No. QM has no bearing on “what it means to be a function”. Maybe you mean “QM encodes permutations in a surprising way”?
Strictly speaking this is only sometimes true. It seems like you are alluding to the spin-statistics theorem or maybe the Aharonov-Bohm effect or Berry phase. Your quoted statement is specifically applicable only to fermionic states. It’s inapplicable to bosons or more exotic states like anyons (FQHE) or braid statistics.
Indeed.
Thanks for the notes. I’ve made a few edits to my comment above based on this.
Also, for the benefit of the folks reading this: I’m not alluding to spin-statistics or Berry phase, merely the use of