Quantum mechanics doesn’t deserve its fearsome reputation.
It most certainly does.
The MWI advocacy of this sequence makes QM seem intuitive, until you start asking some hard questions (like, what’s his relativistically invariant mathematical model of world splitting for multiple spacelike-separated events?), and then it dissolves into hand-waving. If anything, it does a disservice to rationality, by making people believe, against all evidence, that you don’t need to take at least a couple of university-level QM courses to make the heads and tails of it. They guess the teacher’s password (it’s “world-splitting”, if anyone is not yet clear), and merrily go on arguing about the meaning QM, without having ever solved a practical problem.
QM, despite its mathematical foundations being fairly simple (linear algebra, complex numbers and maybe a bit of differential equations, though no more than in classical mechanics), remains highly counter-intuitive. It is full of open problems and is a topic of current research in many areas.
The only lesson “modern rationality” needs from QM is that it apparently (again, subject to some controversy) provides “true randomness”, which is handy for certain thought experiments.
what’s his relativistically invariant mathematical model of world splitting for multiple spacelike-separated events?
I don’t think Eliezer (or Everett or Deutsch) thinks “worlds” are ontologically fundamental. You just have an amplitude distribution on your Hilbert space that changes with time. This can (and does) happen in a Lorentz invariant way.
The “worlds” are a phenomenon that appear at a higher level. If you take each blob (i.e. concentrated region) and call it a “world” then they split in the same way that a large raindrop might split into two smaller ones. In particular, two quantum coin flips occurring at spacelike separated points would look like a single blob splitting into four (if we look in a frame where the flips are not simultaneous then we would see it split into two, and then each small blob would again split).
I’m not sure if this is the same as what Luke_A_Somers says in the comment sibling to this one, that comment is trying to describe how splitting looks from the inside.
I don’t think Eliezer (or Everett or Deutsch) thinks “worlds” are ontologically fundamental.
Neither is the wave function collapse, but it is much simpler a concept. The most common objection “how does it do that?” is now irrelevant, since the collapse is not “ontologically fundamental”.
The “worlds” are a phenomenon...
And now you are talking about it like it is some real thing, not an emotional crutch.
Neither is the wave function collapse, but it is much simpler a concept. The most common objection “how does it do that?” is now irrelevant, since the collapse is not “ontologically fundamental”.
How does collapse appear as a non-ontological phenomenon?
The “worlds” are a phenomenon...
And now you are talking about it like it is some real thing, not an emotional crutch.
Well it was you who brought up “worlds” in the first place! I’m happy to just talk about a wave function on all of Hilbert space evolving through time.
(EDIT: I just noticed I used “Hilbert space” wrongly in this post and the grandparent. I meant to say something like “classical configuration space”. The Hilbert space is the space of complex functions on the configuration space.
I think. QM has so many vector spaces inside each other my brain sometimes melts.)
like, what’s his relativistically invariant mathematical model of world splitting for multiple spacelike-separated events?
Why is this problematic in the least? World splitting isn’t a dynamical rule, but an interpretation of the state.
-- Decoherence—the process of world splitting—can be localized in spacetime. Not to a single event, but to a region, as it is a continuous process. Much like quantum leaps are not localized to single events of spacetime.
-- When information from a decoherent process reaches a new region, several things can happen:
a) the information impacts all local coherent processes equally, and produces no local decoherence (an incoherent long-wave radio pulse has a coherent effect on a BEC because it is sufficiently off-resonance that it doesn’t interact − 0 is equal to 0. Or, the radio pulse bounces off the wall, deflecting the cooling laser a tiny amount, but the laser beam remains coherent within itself)
b) the information has a small impact on local coherence (a photon impinging on a mirror causes the mirror to recoil, making it less coherent to the reflection of other photons)
c) the information alters the region in a way that causes it to decohere completely (a photon activates a chemical reaction)
-- So, your relativistically invariant interpretation notes the spacetime locales and degree of decoherence at each.
What problem is there? Really. QM goes and does its thing, and interpretations aren’t going to mess that up. If you have a relativistically invariant mathematical model of QM, then detecting world-splitting is the same process as you would apply to non-relativistic QM. That is, check whether there is a basis in which off-diagonal terms aren’t exponentially suppressed in time based on their energy difference scale. If there isn’t, it’s decoherent.
Edited to add:
One special thing to note is that this search for a basis with non-decaying off-diagonal terms will yield the same result in all reference frames, because it already spans all momenta. Even in non-relativistic QM you had to consider bases moving at all momenta. This feature is unchanged in relativistic QM.
It most certainly does.
The MWI advocacy of this sequence makes QM seem intuitive, until you start asking some hard questions (like, what’s his relativistically invariant mathematical model of world splitting for multiple spacelike-separated events?), and then it dissolves into hand-waving. If anything, it does a disservice to rationality, by making people believe, against all evidence, that you don’t need to take at least a couple of university-level QM courses to make the heads and tails of it. They guess the teacher’s password (it’s “world-splitting”, if anyone is not yet clear), and merrily go on arguing about the meaning QM, without having ever solved a practical problem.
QM, despite its mathematical foundations being fairly simple (linear algebra, complex numbers and maybe a bit of differential equations, though no more than in classical mechanics), remains highly counter-intuitive. It is full of open problems and is a topic of current research in many areas.
The only lesson “modern rationality” needs from QM is that it apparently (again, subject to some controversy) provides “true randomness”, which is handy for certain thought experiments.
I don’t think Eliezer (or Everett or Deutsch) thinks “worlds” are ontologically fundamental. You just have an amplitude distribution on your Hilbert space that changes with time. This can (and does) happen in a Lorentz invariant way.
The “worlds” are a phenomenon that appear at a higher level. If you take each blob (i.e. concentrated region) and call it a “world” then they split in the same way that a large raindrop might split into two smaller ones. In particular, two quantum coin flips occurring at spacelike separated points would look like a single blob splitting into four (if we look in a frame where the flips are not simultaneous then we would see it split into two, and then each small blob would again split).
I’m not sure if this is the same as what Luke_A_Somers says in the comment sibling to this one, that comment is trying to describe how splitting looks from the inside.
Neither is the wave function collapse, but it is much simpler a concept. The most common objection “how does it do that?” is now irrelevant, since the collapse is not “ontologically fundamental”.
And now you are talking about it like it is some real thing, not an emotional crutch.
How does collapse appear as a non-ontological phenomenon?
Well it was you who brought up “worlds” in the first place! I’m happy to just talk about a wave function on all of Hilbert space evolving through time.
(EDIT: I just noticed I used “Hilbert space” wrongly in this post and the grandparent. I meant to say something like “classical configuration space”. The Hilbert space is the space of complex functions on the configuration space.
I think. QM has so many vector spaces inside each other my brain sometimes melts.)
Bingo.
Why is this problematic in the least? World splitting isn’t a dynamical rule, but an interpretation of the state.
-- Decoherence—the process of world splitting—can be localized in spacetime. Not to a single event, but to a region, as it is a continuous process. Much like quantum leaps are not localized to single events of spacetime.
-- When information from a decoherent process reaches a new region, several things can happen:
a) the information impacts all local coherent processes equally, and produces no local decoherence (an incoherent long-wave radio pulse has a coherent effect on a BEC because it is sufficiently off-resonance that it doesn’t interact − 0 is equal to 0. Or, the radio pulse bounces off the wall, deflecting the cooling laser a tiny amount, but the laser beam remains coherent within itself)
b) the information has a small impact on local coherence (a photon impinging on a mirror causes the mirror to recoil, making it less coherent to the reflection of other photons)
c) the information alters the region in a way that causes it to decohere completely (a photon activates a chemical reaction)
-- So, your relativistically invariant interpretation notes the spacetime locales and degree of decoherence at each.
What problem is there? Really. QM goes and does its thing, and interpretations aren’t going to mess that up. If you have a relativistically invariant mathematical model of QM, then detecting world-splitting is the same process as you would apply to non-relativistic QM. That is, check whether there is a basis in which off-diagonal terms aren’t exponentially suppressed in time based on their energy difference scale. If there isn’t, it’s decoherent.
Edited to add: One special thing to note is that this search for a basis with non-decaying off-diagonal terms will yield the same result in all reference frames, because it already spans all momenta. Even in non-relativistic QM you had to consider bases moving at all momenta. This feature is unchanged in relativistic QM.