3 ms·

My QM knowledge is quite rusty, but given what I remember, I don't understand how certain claims in this article can be correct. Hossenfelder seems to be refer

My QM knowledge is quite rusty, but given what I remember, I don't understand how certain claims in this article can be correct. Hossenfelder seems to be referring to some well-known papers on Hyperion and decoherence. For a review, see: https://arxiv.org/abs/quant-ph/0605249 https://arxiv.org/abs/quant-ph/0605249 There are lots of references there that you can follow, including a debate on whether decoherence theory is really necessary to explain what's going on. But as far as I can tell, no party in this debate ever claims the Hyperion example implies that "the chaotic motion of Hyperion tells us that we need the measurement collapse to actually be a physical process." The decoherence arguments about Hyperion do not assume this (as far as I know). Can someone please explain? Am I misunderstanding?

andi999 4y ago
Havent read the paper, but I think when she objects to 'averaging' she means the tracing out the environment; which I think is ok. Especially since all lokal measurement give the same result on the reduced density matrix.
xmcqdpt2 4y ago
No you are correct. There is at this point like 40 years of quantum chaos research. I dipped my toes into it a bit in grad school. In the eighties it was believed that chaos might be the key to understanding the quantum-classical transition. It's not a very cool area of research anymore, mainly because it hasn't really led anywhere. We know that when applying decoherence to quantum mechanical systems we recover the original classical (and potentially chaotic) equations of motion. This basically "solves" the chaos problem but doesn't actually help with measurement, because it doesn't cause collapse of the classical probabilities. This is what is referred to as "superselection". In terms of cat analogies, the quantum wavefunction is a superposition of amplitudes a|dead> + b|alive> and these amplitudes cannot be chaotic because the Schrödinger equation is linear. When the system becomes decoherent, it becomes a classical probability distribution p(alive) that evolves under potentially chaotic classical motion. However it's still probabilistic, the cat remains neither alive nor dead. We haven't "measured" anything. The confusion (and this is what Schlosshauser talks about) is that for some people (famously Ballentine) who follows the ensemble theory of quantum mechanics, there is no meadurement problem at all once we have a classical probability distribution. This view is not very popular however. So anyway the point is that the existence of classical chaos can be straightforwardly explained by decoherence without any collapse at all.
- GoblinSlayer 4y ago
  The catch is that you can know certain and impossible things without measurement by simply showing their amplitudes to be 1 and 0 respectively. In case of the cat you have state after observation |dead>|see dead> + |alive>|see alive>, then project it to basis <see definite cat| <see indefinite cat| : <see definite cat|(|dead>|see dead> + |alive>|see alive>) = 1 <see indefinite cat|(|dead>|see dead> + |alive>|see alive>) = 0

andi999 4y ago

Havent read the paper, but I think when she objects to 'averaging' she means the tracing out the environment; which I think is ok. Especially since all lokal measurement give the same result on the reduced density matrix.

xmcqdpt2 4y ago

No you are correct. There is at this point like 40 years of quantum chaos research. I dipped my toes into it a bit in grad school. In the eighties it was believed that chaos might be the key to understanding the quantum-classical transition. It's not a very cool area of research anymore, mainly because it hasn't really led anywhere. We know that when applying decoherence to quantum mechanical systems we recover the original classical (and potentially chaotic) equations of motion. This basically "solves" the chaos problem but doesn't actually help with measurement, because it doesn't cause collapse of the classical probabilities. This is what is referred to as "superselection". In terms of cat analogies, the quantum wavefunction is a superposition of amplitudes a|dead> + b|alive> and these amplitudes cannot be chaotic because the Schrödinger equation is linear. When the system becomes decoherent, it becomes a classical probability distribution p(alive) that evolves under potentially chaotic classical motion. However it's still probabilistic, the cat remains neither alive nor dead. We haven't "measured" anything. The confusion (and this is what Schlosshauser talks about) is that for some people (famously Ballentine) who follows the ensemble theory of quantum mechanics, there is no meadurement problem at all once we have a classical probability distribution. This view is not very popular however. So anyway the point is that the existence of classical chaos can be straightforwardly explained by decoherence without any collapse at all.

GoblinSlayer 4y ago
The catch is that you can know certain and impossible things without measurement by simply showing their amplitudes to be 1 and 0 respectively. In case of the cat you have state after observation |dead>|see dead> + |alive>|see alive>, then project it to basis <see definite cat| <see indefinite cat| : <see definite cat|(|dead>|see dead> + |alive>|see alive>) = 1 <see indefinite cat|(|dead>|see dead> + |alive>|see alive>) = 0