>>"The most elegant interpretation of quantum mechanics is the universe is constantly splitting."
> A joke, right?
The electronic Schrödinger equation describes fundamental properties of molecules and materials, but can only be solved analytically for the hydrogen atom. The numerically exact full configuration-interaction method is exponentially expensive in the number of electrons. Quantum Monte Carlo is a possible way out: it scales well to large molecules, can be parallelized, and its accuracy has, as yet, only been limited by the flexibility of the used wave function ansatz. Here we propose PauliNet, a deep-learning wave function ansatz that achieves nearly exact solutions of the electronic Schrödinger equation. PauliNet has a multireference Hartree-Fock solution built in as a baseline, incorporates the physics of valid wave functions, and is trained using variational quantum Monte Carlo (VMC). PauliNet outperforms comparable state-of-the-art VMC ansatzes for atoms, diatomic molecules and a strongly-correlated hydrogen chain by a margin and is yet computationally efficient. We anticipate that thanks to the favourable scaling with system size, this method may become a new leading method for highly accurate electronic-strucutre calculations on medium-sized molecular systems.
> The Schrödinger equation is just a neural network.
On Friday, March 6, 2020 at 7:51:10 PM UTC-6, Brent wrote:
On 3/6/2020 3:55 PM, Bruce Kellett wrote:
On Sat, Mar 7, 2020 at 10:17 AM John Clark <johnk...@gmail.com> wrote:
This video just went online, I thought it was excellent:
John K Clark
Impressive graphics, but the same old....same old....
Bruce
You might find this interview of Sean Carroll more interesting. He's aware of the problems with MWI and is fairly candid about it even though he likes it. Start at 54:00 to skip all the explanation of QM. https://www.youtube.com/watch?v=XjDiOu5__oA
Brent
The question on whether QM has an infinite or finite Hilbert space can be addressed with the existence of event horizons. The cosmological event horizon puts a limit. Consider a Planck scale quantum state that has been redshifted to the cosmological horizon scale. This is a ratio of around 10^{60} and from the FLRW this leads to a distance of around 1800 billion light years. Since this defines a finite region this means the Hilbert space accessible to any observer is finite, even if enormously large. Even if the global Hilbert space is infinite, observers are fundamentally local and the amount of quantum information accessible is finite. To take this further, with inflationary cosmology the cosmological event horizon on the high energy vacuum was only 10^2 or 10^3 Planck units of radius the large number of quantum states that appear accessible on the low energy physical vacuum are an enormous redundancy.
At around 1:14 Carroll gets to brass-tacks on this issue with the horn. The idea in MWI is then "everything happens that can happen," which some people find difficult. In effect even though there is a probability weight with each possible branch, an observer that witnesses a highly improbable quantum event has this sense they are on a split branch and have no post collapse information about a prior probability. MWI has the concept of a cosmic wave function, but this sense of there being only two outcomes reflects a lack of counterfactual definite reasoning tied to objective probabilities. As a result these branches occur in a certain nonlocal sense.
Is this at all demonstrable? No, counterfactual definite reasoning and the existence of a global wave are not demonstrable. There are forms of horizons, in general a form of epistemic horizon, which are a generalization of the inaccessibility of information in QM and with general relativity and event horizons. So whether there is or is not a global cosmological wave function is a metaphysical choice of an analyst. Generally ψ-ontological interpretations have a global cosmic wave function, but a subset of those with a hidden variable interpretation also have counterfactualism.
As Carroll points out there are four major types of interpretations, MWI and deBroglie-Bohm, both ψ-ontic but with and without counterfactualism, and Qubism and dynamic collapse that are ψ-epistemic. Qubism has some advantages, but it leads to odd ideas that are almost solipsism. Dynamic collapse and related idea of stochastic QM have wave functions just spontaneously collapse and the more entangled the system is the more frequent this will happen.
I have certain issues there with how to treat coherent states such as with lasers or with condensates of states. In general one can pick and choose, and these are available for those who want to think of certain problems in a certain framework. I think frankly that QM decoherence, and by extension a measurement, amounts to a sort of Gödel numbering of quantum bits by quantum bits. I see all of these interpretations of QM then as a sort of incompleteness or inconsistency that results by trying to impose a certain question or proposition on QM that is not decidable.
LC
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On 3/7/2020 4:05 AM, Lawrence Crowell wrote:
On Friday, March 6, 2020 at 7:51:10 PM UTC-6, Brent wrote:
On 3/6/2020 3:55 PM, Bruce Kellett wrote:
On Sat, Mar 7, 2020 at 10:17 AM John Clark <johnk...@gmail.com> wrote:
This video just went online, I thought it was excellent:
John K Clark
Impressive graphics, but the same old....same old....
Bruce
You might find this interview of Sean Carroll more interesting. He's aware of the problems with MWI and is fairly candid about it even though he likes it. Start at 54:00 to skip all the explanation of QM. https://www.youtube.com/watch?v=XjDiOu5__oA
Brent
The question on whether QM has an infinite or finite Hilbert space can be addressed with the existence of event horizons. The cosmological event horizon puts a limit. Consider a Planck scale quantum state that has been redshifted to the cosmological horizon scale. This is a ratio of around 10^{60} and from the FLRW this leads to a distance of around 1800 billion light years. Since this defines a finite region this means the Hilbert space accessible to any observer is finite, even if enormously large. Even if the global Hilbert space is infinite, observers are fundamentally local and the amount of quantum information accessible is finite. To take this further, with inflationary cosmology the cosmological event horizon on the high energy vacuum was only 10^2 or 10^3 Planck units of radius the large number of quantum states that appear accessible on the low energy physical vacuum are an enormous redundancy.
At around 1:14 Carroll gets to brass-tacks on this issue with the horn. The idea in MWI is then "everything happens that can happen," which some people find difficult. In effect even though there is a probability weight with each possible branch, an observer that witnesses a highly improbable quantum event has this sense they are on a split branch and have no post collapse information about a prior probability. MWI has the concept of a cosmic wave function, but this sense of there being only two outcomes reflects a lack of counterfactual definite reasoning tied to objective probabilities. As a result these branches occur in a certain nonlocal sense.
Is this at all demonstrable? No, counterfactual definite reasoning and the existence of a global wave are not demonstrable. There are forms of horizons, in general a form of epistemic horizon, which are a generalization of the inaccessibility of information in QM and with general relativity and event horizons. So whether there is or is not a global cosmological wave function is a metaphysical choice of an analyst. Generally ψ-ontological interpretations have a global cosmic wave function, but a subset of those with a hidden variable interpretation also have counterfactualism.
As Carroll points out there are four major types of interpretations, MWI and deBroglie-Bohm, both ψ-ontic but with and without counterfactualism, and Qubism and dynamic collapse that are ψ-epistemic. Qubism has some advantages, but it leads to odd ideas that are almost solipsism. Dynamic collapse and related idea of stochastic QM have wave functions just spontaneously collapse and the more entangled the system is the more frequent this will happen.
Isn't the Transactional Interpretation a kind of dynamic collapse, in which a possibility is actualized by the absorbtion of energy or information?
Brent
--I have certain issues there with how to treat coherent states such as with lasers or with condensates of states. In general one can pick and choose, and these are available for those who want to think of certain problems in a certain framework. I think frankly that QM decoherence, and by extension a measurement, amounts to a sort of Gödel numbering of quantum bits by quantum bits. I see all of these interpretations of QM then as a sort of incompleteness or inconsistency that results by trying to impose a certain question or proposition on QM that is not decidable.
LC
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You must be a fan of Kurt Godel than? He was big time into a spinning cosmos, and yeah, a 7 sphere.
-----Original Message-----
From: Alan Grayson <agrays...@gmail.com>
To: Everything List <everyth...@googlegroups.com>
Sent: Sat, Mar 7, 2020 6:29 pm
Subject: Re: Parallel Worlds Probably Exist. Here’s Why
On Friday, March 6, 2020 at 4:17:34 PM UTC-7, John Clark wrote:This video just went online, I thought it was excellent:John K ClarkAs you know, I believe our universe is shaped like a hyper-sphere. With this in mind, perhaps the best tentative evidence for other worlds is the fact that distant galaxies are moving in unison in the direction of what is hypothesized as "The Great Attractor". But maybe what we're observing is the rotation of our universe. Rotations are caused by glancing blows, and in this case, the glancing blow might be another universe. AG
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