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RECENT POSTS IN THIS TOPIC

**Peter Morgan**: *on* 2/26/20 at 15:25pm UTC, wrote That's not what the preview showed! Grrrrr. Aaaaannnnndddd I can't edit it....

**Peter Morgan**: *on* 2/26/20 at 15:13pm UTC, wrote I have to hope that better understanding the relationship between the...

**Peter Morgan**: *on* 2/26/20 at 14:36pm UTC, wrote The mathematics of decoherence is of course relevant in its context of...

**Stephen King**: *on* 2/26/20 at 12:36pm UTC, wrote "“Collapse” of the state is shown equivalent to a constraint on joint...

**Stephen King**: *on* 2/26/20 at 12:34pm UTC, wrote Can AlgKoopman help us think about Black holes and firewalls? If we can...

**Peter Morgan**: *on* 2/20/20 at 20:48pm UTC, wrote Note that the author link, https://authors.elsevier.com/a/1aZC%7EopqoQN9,...

**Zeeya Merali**: *on* 2/20/20 at 19:37pm UTC, wrote This is a place to discuss the article, "An algebraic approach to Koopman...

FQXi FORUM

April 5, 2020

CATEGORY:
Ultimate Reality
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TOPIC: An algebraic approach to Koopman classical mechanics [refresh]

TOPIC: An algebraic approach to Koopman classical mechanics [refresh]

This is a place to discuss the article, "An algebraic approach to Koopman classical mechanics' by Peter Morgan, a physicist at Yale. It proposes a way to unify measurements in classical physics and quantum physics. Morgan has also written an accessible description of the work in *The Quantum Daily*.

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Note that the author link, https://authors.elsevier.com/a/1aZC%7EopqoQN9, is good for free downloads only until April 2nd, so download it before then if you don't have institutional access. After that date, https://arxiv.org/abs/1901.00526 is quite close to the published version.

Any immediate reactions you may have to the pop-version on The Quantum Daily*may* be answered by the Annals of Physics article (which I've taken to calling AlgKoopman). There is a discussion of the measurement problem in Section 7.1, of the violation of Bell inequalities in Section 7.2, and of Schrödinger's cat in 7.3 (that last is somewhat whimsical, but hopefully the cat will consider it sufficiently respectful.) One strong reaction to the pop-version, from someone who has worked on the huge datasets generated by Very Long Baseline Interferometry (VLBI), was that the discussion of signal analysis is "barely coherent", so be warned that at least one expert considers me, to put it more kindly, not an expert on signal analysis, but judge for yourself. There have been 10,000+ page impressions of the pop-version, so you may have already seen some discussion of it (or, so far much less, of AlgKoopman) on Facebook.

There should be at least one more short article for The Quantum Daily, to discuss Section 7.1's mathematics, which is enough to unify "Collapse" and "No-collapse" interpretations of QM (yeah, there's inevitably some nuance to that.)

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Any immediate reactions you may have to the pop-version on The Quantum Daily

There should be at least one more short article for The Quantum Daily, to discuss Section 7.1's mathematics, which is enough to unify "Collapse" and "No-collapse" interpretations of QM (yeah, there's inevitably some nuance to that.)

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Can AlgKoopman help us think about Black holes and firewalls? If we can predict things that can be detected by instruments from basic principles.... That is Naturalness!

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I have to hope that better understanding the relationship between the classical and quantum concepts of measurement, which I think with not too much of a stretch we can call a unification of theory *frameworks*, will help us make progress on a unification of the particular quantum and classical theories, the SM of particle physics and GR. We will have to see which ideas in the various attempts at such unifications will turn out to be useful. I think black holes will surely be a good approximation in any future physics, but I think the idea of a firewall is too specifically a next level approximation that includes many assumptions for it to survive without at least some modification.

To speak to specifics, albeit in such a compressed way that it may be incomprehensible unless you've internalized at least some of my article in Physica Scripta from 2019, I point you to Eq. (12) in AlgKoopman,

[equation]rho(e^{,jlambda_1hat F_{{bf f}_1}}cdots e^{,jlambda_nhat F_{{bf f}_n}}!){=}exp!Big[-!!Bigl(sum_{i=1}^nlambda_i{bf f}_i^*,!sum_{j=1}^nlambda_j{bf f}_jBigr)/2-!!!!!!!!!!sum_{quad 1le i

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To speak to specifics, albeit in such a compressed way that it may be incomprehensible unless you've internalized at least some of my article in Physica Scripta from 2019, I point you to Eq. (12) in AlgKoopman,

[equation]rho(e^{,jlambda_1hat F_{{bf f}_1}}cdots e^{,jlambda_nhat F_{{bf f}_n}}!){=}exp!Big[-!!Bigl(sum_{i=1}^nlambda_i{bf f}_i^*,!sum_{j=1}^nlambda_j{bf f}_jBigr)/2-!!!!!!!!!!sum_{quad 1le i

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That's not what the preview showed! Grrrrr. Aaaaannnnndddd I can't edit it.

Approximately what I said after the equation that screwed up was: The inner product (f,g) that's used in Eq. (12) can be replaced by any structure for which (f_i,f_j) is a positive semi-definite matrix, which doesn't necessarily have to be sesquilinear in f_i and f_j. If we can find a manifestly diffeomorphism invariant form (f,g), with f and g appropriately structured for a candidate geometry, then we have a candidate first approximation for a quantum gravity.

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Approximately what I said after the equation that screwed up was: The inner product (f,g) that's used in Eq. (12) can be replaced by any structure for which (f_i,f_j) is a positive semi-definite matrix, which doesn't necessarily have to be sesquilinear in f_i and f_j. If we can find a manifestly diffeomorphism invariant form (f,g), with f and g appropriately structured for a candidate geometry, then we have a candidate first approximation for a quantum gravity.

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"“Collapse” of the state is shown equivalent to a constraint on joint measurements."

How does this shift as we consider quantum systems of a very large size, say planets and stars. Decoherence is a check trick.

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How does this shift as we consider quantum systems of a very large size, say planets and stars. Decoherence is a check trick.

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The mathematics of decoherence is of course relevant in its context of tensor products as a model for idealized separate systems. The SEP begins its entry on decoherence with "Interference phenomena are a well-known and crucial aspect of quantum mechanics, famously exemplified by the two-slit experiment. There are situations, however, in which interference effects are artificially or spontaneously suppressed. The theory of decoherence is precisely the study of (spontaneous) interactions between a system and its environment that lead to such suppression of interference."

I think it's important to recognize, however, that the tensor product is not a natural structure for QFT. There is no idea of distinct systems in QFT except as an approximation, certainly not for interacting fields, and even the so-called free fields have nearest neighbor interactions. Those approximations become very good when we consider planets, but also even when we consider grains of sand.

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I think it's important to recognize, however, that the tensor product is not a natural structure for QFT. There is no idea of distinct systems in QFT except as an approximation, certainly not for interacting fields, and even the so-called free fields have nearest neighbor interactions. Those approximations become very good when we consider planets, but also even when we consider grains of sand.

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