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RECENT POSTS IN THIS TOPIC

Jason Wolfe: on 9/15/20 at 6:28am UTC, wrote Hi Peter, My conversation always arrive somewhere useful. I come up with...

Jason Wolfe: on 9/15/20 at 5:25am UTC, wrote I agree Steve. But this forum is not the easiest place to navigate, and I...

Steve Dufourny: on 9/14/20 at 20:13pm UTC, wrote Hi, Maybe it is better to put these ideas in the blogs about the...

Jason Wolfe: on 9/14/20 at 19:51pm UTC, wrote On another topic, if there was a connection between the brain and a spirit...

Steve Dufourny: on 9/14/20 at 12:05pm UTC, wrote Hi , I beleive that I have explained what I would say to Jason, I don t...

Peter Morgan: on 9/14/20 at 11:59am UTC, wrote I hesitate to say anything here that might be oil on this fire, but the...

Steve Dufourny: on 9/14/20 at 11:00am UTC, wrote I know well in all humility what is the SR and GR and the equations...

Jason Wolfe: on 9/14/20 at 10:52am UTC, wrote Steve, Did you ever study gravitational time dilation? ...

FQXi FORUM
September 23, 2020

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

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FQXi Administrator Zeeya Merali wrote on Feb. 20, 2020 @ 19:37 GMT
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.

Peter Warwick Morgan wrote on Feb. 20, 2020 @ 20:48 GMT
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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Stephen Paul King replied on Feb. 26, 2020 @ 12:34 GMT
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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Peter Warwick Morgan replied on Feb. 26, 2020 @ 15:13 GMT
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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Peter Warwick Morgan replied on Feb. 26, 2020 @ 15:25 GMT
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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Stephen Paul King wrote on Feb. 26, 2020 @ 12:36 GMT
"“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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Peter Warwick Morgan replied on Feb. 26, 2020 @ 14:36 GMT
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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Peter Warwick Morgan wrote on Aug. 17, 2020 @ 18:10 GMT
There are now three articles on The Quantum Daily:

Unifying Classical Physics and Quantum Physics Measurement

Unifying “Collapse” and “No-Collapse” Approaches to Quantum Physics

Breaking the Hold of Bell Inequalities

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Steve Dufourny replied on Aug. 17, 2020 @ 18:32 GMT
Hi Peter, happy to see you on FQXi and that you share your ideas, great

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Steve Dufourny replied on Aug. 17, 2020 @ 20:49 GMT
Dear Peter, have you already thought to play with these koopman algebras and the entropy ?

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Peter Warwick Morgan replied on Aug. 17, 2020 @ 21:47 GMT
Dear Steve,

I generally prefer to work with the collection of probability distributions associated with a given collection of measurements, because many quantities such as entropy are undefined for nontrivial quantum or random fields. [One could perhaps work with quantities such as the relative entropy between different states, but I haven't. Entropy is problematic, in any case, I think, because it's a property of a state, not a measurement result.] I think it's really important that we work with test functions as descriptions of measurements that are performed and of how we modulate measurement results, not with what's really there (such as the entropy of the state), because many aspects of the latter are not well-defined, even though the measurement results are well-defined except at singular points.

In any case, I've started to work again on what I had been working on before AlgKoopman, the problem of renormalization, or, rather, on how to construct interacting quantum and random fields in a well-defined way. AlgKoopman came out of that research in a natural way, but it's not my principal research direction.

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Peter Warwick Morgan wrote on Sep. 12, 2020 @ 12:30 GMT
I'm pleased to announce that Annals of Physics has selected "An algebraic approach to Koopman classical mechanics" as a Highlighted Article. There is a highlight post written by Rob Lea on the Annals of Physics website.

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Steve Dufourny replied on Sep. 12, 2020 @ 12:45 GMT
Congrats Peter, Frank Delplace of Facebook also for his article about the vicosity and several others also that I know, the annals of physics are well , you are good about the Koopman alg , regards

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Jason Mark Wolfe wrote on Sep. 12, 2020 @ 18:35 GMT
The only way you know you've made progress towards quantum gravity, is if you can come up with an experiment. But congratulations on your "algebraic approch to Koopman classical mechanics".

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Peter Warwick Morgan replied on Sep. 12, 2020 @ 18:58 GMT
Thank you! I have to say that Quantum Gravity is definitely not my principal interest: I'm mostly interested in finding ways to rethink the conceptual issues in QM and in QFT, which I think AlgKoopman does in a more-or-less new way (if you read the introduction to AlgKoopman you'll see that almost everything in AlgKoopman has a precursor: Koopman, signal analysis, Wigner functions, Generalized Probability, contextuality, algebraic QM/QFT, ..., but I think they are put together in a way that I've not seen done elsewhere in the literature).

We'll hopefully know in five or ten years whether the way the ideas are put together in AlgKoopman help much or whether they just become more background noise. Still, my feeling is that anything that gives us a new way to understand the relationship between CM and QM might give someone a clue how to construct a different kind of quantum gravity, which hopefully we could test.

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Jason Mark Wolfe replied on Sep. 12, 2020 @ 19:00 GMT
I wouldn't be so adversarial if I thought you work making real progress as opposed to spinning your collective wheels. Why don't you attempt to describe quantum gravity in terms of things we can already measure?

Why don't you try to explain gravity and spacetime curvature in terms of something that already behaves similar to spacetime?

If you can't come up with an actual experiment, then you may as well be talking about unicorns and rainbows, not physics.

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Jason Mark Wolfe replied on Sep. 12, 2020 @ 19:06 GMT
Hi Peter,

You should consider the possibility that the graviton really does exist. A graviton that expands from a point, at the speed of light, with a radius r = ct, would fill all space with spacetime geometry, inertial refernece frames, and virtual photons. You could say that you captured a graviton when you create quantum entangled photons. That would be your doorway to performing an experiment.

Best wishes,

JW

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Jason Mark Wolfe wrote on Sep. 13, 2020 @ 03:53 GMT
I got the idea of expanding gravitons from the derivation of special relativity.

https://physics.stackexchange.com/questions/13498
4/time-dilation-confusion

Each inertial reference frame is created by gravitons that are expanding from a point, to a sphere with radius r = ct.

If there are gravitons being created constantly, at every point in space, and for every possible velocity, AND those gravitons are creating space and time, then the speed of light is invariant.

The spacetime interval also looks like an instantaneous condition of two gravitons expanding, with relative velocity of 0.

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