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.)

    6 days later

    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!

    ""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.

      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.

      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,

      [math]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

      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.

      6 months later

      Hi Peter, happy to see you on FQXi and that you share your ideas, great

      Dear Peter, have you already thought to play with these koopman algebras and the entropy ?

      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.

      Dear Peter, I can understand seen that this entropy is indeed problematic and complex due to its property. I try personally to find a road for the non relativistic fields and the complexity with this dark matter encoded , I consider a different sense of rotation and the cold also , the clifford algebras and other mathematical tools for a kind of partition but it is not easy. Regards

      25 days later

      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

      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".

        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.

        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.

        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

        this quantum gravity is like I told difficult to renormalise in considering the bosonic fields, that cannot be quantified in this road, the photons encoded are not the solution apparently, we can utilise all the mathematial tools that we want and the non commutativity , we don t reach it, Connes has tried, Penrose and his twistors, the Lie E8 , the loops,the superstings or Mtheory or others, all the best thinkers have tried in fractalising the fields , they don t arrive, and verlinde also has tried with his entropical gravity, that does not solve, the problem foundamental is that the majority of thinkers have considered only these photons like primordial essence and that all comes from fields, and it is not proved , they have not renormalised it because there is a deeper secret to superimpose to unify this GR and QM simply , furthermore we need a balance for the heat and electromagnetism and to explain the anti matter also, the secret and I have reached it is to encode a deeper gravitation logic than just these photons oscillating differently, and so we change just the distances because the codes are farer and are gravitational and that this electromagnetism is just emergent. It is only simple than this, never in considering this weakest quantum force like an emergent electromagnetic force you arrive to renormalise even with all the geometrical algebras possible, the QFT is interesting but the gravitation is different than these bosons.It is necessary to reach this quantum gravitation to forget this GR and this photonic electromagnetism, the problem is easily solved when you think beyond the box.

        your photonic gravitons so oscillating differently are not the solution, and are not the answer