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Dear all,
every now and then I get this itchy feeling and start to think about quantum mechanics. Which raises, of course, some questions. These concern the measurement problem. I decided to post them in 1 single topic, so I enumerate them. If someone has some insights clarifying my confusions, I'll be very happy.
1) About decoherence: so my understanding is that decoherence is an environment-driven mechanism which erases interference-terms. If I have, say, a system which can be in two possible states ##\psi_1## and ##\psi_2##, then ##\psi_ = \psi_1+\psi_2## and the probability density becomes ##|\psi|^2 = |\psi_1|^2 + |\psi_2|^2 + 2 Re(\psi_1^* \psi_2) =|\psi|^2 = |\psi_1|^2 + |\psi_2|^2 +\text{interference}##. Am I right that decoherence states that, if our system interacts with its environment, the interferenceterm eventually dies out and that ##|\psi|^2 \rightarrow |\psi_1|^2 + |\psi_2|^2##? If so, how on Earth can some people claim that decoherence solves the measurement problem, because you still need some mechanism which eventually from this classical probability distribution picks one of the two states out? I mean, decoherence cannot induce a unitary evolution ##\psi \rightarrow \psi_i## for ##i=1,2##, right? See e.g. Tegmarks https://arxiv.org/abs/quant-ph/0101077, quoting "We argue that modern experiments and the discovery of decoherence have have shifted prevailing quantum interpretations away from wave function collapse towards unitary physics". Am I right that decoherence merely turns "quantum probability distributions (meaning, with interference terms)" into classical probability distributions (meaning, no interference terms)?
2) About the Von Neumann-Wigner interpretation: I am puzzled about this interpretation (who isn't, but bear with me). In e.g. https://arxiv.org/abs/1009.2404 it is stated that QM needs no consciousness. My question is: why not simply use the simple double slit experiment, put a detector near one of the slits, and only look at the screen? I assume we'll still see the interference pattern (right?), so doesn't this conclusively exclude the possibility that "a conscious observation near one of the slits is needed to make the interference pattern disappear"? And the same goes even more for the delayed choice experiments: because the indirect observation about the particle going through one of the slits is delayed, doesn't this show that consciousness is not a relevant factor in the whole setup but mere interaction of the measurement apparatus with the system is?
3) About the Von Neumann-Wigner interpretation: is there any way to "break out of the Von-Neumann chain of regression" without hidden variables or imposing extra dynamics on top of the Schrodinger equation? I see that people often use this Von-Neumann chain to motivate the Von Neumann-Wigner interpretation. And how do adherents of this interpretation explain cosmic events like e.g. the CMB we're receiving from events billions of years ago?
4) About the QM formalism itself (not really about the measurement problem): I do understand that the Schrödinger equation and Heisenberg relations impose that our Hilbert space is complex. But how far could one go with constructing a theory of QM on a real vector space, with writing down a real Schrödinger equation, real commutation relations from the Poisson brackets and so forth? What would be the first obstacle to encounter?
Any insights are appreciated :)
-edit If some moderator thinks these are too many questions for one topic, feel free to say so and take appropriate actions.
every now and then I get this itchy feeling and start to think about quantum mechanics. Which raises, of course, some questions. These concern the measurement problem. I decided to post them in 1 single topic, so I enumerate them. If someone has some insights clarifying my confusions, I'll be very happy.
1) About decoherence: so my understanding is that decoherence is an environment-driven mechanism which erases interference-terms. If I have, say, a system which can be in two possible states ##\psi_1## and ##\psi_2##, then ##\psi_ = \psi_1+\psi_2## and the probability density becomes ##|\psi|^2 = |\psi_1|^2 + |\psi_2|^2 + 2 Re(\psi_1^* \psi_2) =|\psi|^2 = |\psi_1|^2 + |\psi_2|^2 +\text{interference}##. Am I right that decoherence states that, if our system interacts with its environment, the interferenceterm eventually dies out and that ##|\psi|^2 \rightarrow |\psi_1|^2 + |\psi_2|^2##? If so, how on Earth can some people claim that decoherence solves the measurement problem, because you still need some mechanism which eventually from this classical probability distribution picks one of the two states out? I mean, decoherence cannot induce a unitary evolution ##\psi \rightarrow \psi_i## for ##i=1,2##, right? See e.g. Tegmarks https://arxiv.org/abs/quant-ph/0101077, quoting "We argue that modern experiments and the discovery of decoherence have have shifted prevailing quantum interpretations away from wave function collapse towards unitary physics". Am I right that decoherence merely turns "quantum probability distributions (meaning, with interference terms)" into classical probability distributions (meaning, no interference terms)?
2) About the Von Neumann-Wigner interpretation: I am puzzled about this interpretation (who isn't, but bear with me). In e.g. https://arxiv.org/abs/1009.2404 it is stated that QM needs no consciousness. My question is: why not simply use the simple double slit experiment, put a detector near one of the slits, and only look at the screen? I assume we'll still see the interference pattern (right?), so doesn't this conclusively exclude the possibility that "a conscious observation near one of the slits is needed to make the interference pattern disappear"? And the same goes even more for the delayed choice experiments: because the indirect observation about the particle going through one of the slits is delayed, doesn't this show that consciousness is not a relevant factor in the whole setup but mere interaction of the measurement apparatus with the system is?
3) About the Von Neumann-Wigner interpretation: is there any way to "break out of the Von-Neumann chain of regression" without hidden variables or imposing extra dynamics on top of the Schrodinger equation? I see that people often use this Von-Neumann chain to motivate the Von Neumann-Wigner interpretation. And how do adherents of this interpretation explain cosmic events like e.g. the CMB we're receiving from events billions of years ago?
4) About the QM formalism itself (not really about the measurement problem): I do understand that the Schrödinger equation and Heisenberg relations impose that our Hilbert space is complex. But how far could one go with constructing a theory of QM on a real vector space, with writing down a real Schrödinger equation, real commutation relations from the Poisson brackets and so forth? What would be the first obstacle to encounter?
Any insights are appreciated :)
-edit If some moderator thinks these are too many questions for one topic, feel free to say so and take appropriate actions.