Thank you for opening the discussion.

The paragraph of the essay lists the two possibilities, either modify gravity or modify the matter content, because, without additional information, both stand on equal footing next to each other.

Which one is considered "the simplest way" of modification depends on the available evidence, which simplest way is viable. It seems difficult to modify gravity in agreement with all observations we have. But, systematic investigations are ongoing which theory of gravity is consistent with a certain matter content and its dynamics.

Personally, I am agnostic about which model may turn out right, I am more curious about the evidence we can obtain to test the ideas.

I am no expert on Milky Way satellites, so I cannot comment on these measurements. As far as I can read from the ongoing debate between Kroupa et al. and others, the tensions between observations and simulations seem to be resolvable. The standard model could thus explain the properties of the Milky Way satellites.

Dear Prof. Wagner,

I loved your essay, from the inspired title to the end. Very interested example of underdetermined problem, the Smiling Gravitaitonal Lens. While there may be reasons to consider that Einstein's equations themselves were derived by imposing some arbitrary conditions, so are underdetermined by the principle of equivalence, I personally think there are little chances that they need to be modified*. Maybe just quantized, though I doubt that this will solve the "dark matter" problem. On the other hand, the Standard Model seems to me not missing anything. But I think it is clear, and your arguments are pretty convincing, that there should be some missing mass indeed. I am also convinced by the way you explained the iteration leading to the effective models. It's interesting that many different models agree, and how, in the absence of the possibility to decide among the models using the explanatory power or Occam's razor, a good choice is tho choose the most easiest to falsify one. Your essay was an adventurous journey, narrated from first-hand experience, combining inspired choices and Bayesian reasoning. Indeed, although we can only see the cat's grin, its mass is there! Thank you!

Cheers,

Cristi

_________________________

* I confess I'm attracted towards the idea of conformal gravity, but not in a way that would change Einstein's equations, something different from what's on the market.

    Dear Christi,

    thank you very much for the encouraging nice words, that's a very good summary of the message that I wanted to convey!

    I only studied physics to get to know more about Einstein's theories of gravitation, so I would also hope that they need not be modified. There is still a lot of freedom in boundary conditions and parametrisations that may save them. Furthermore, have a look at the works by Schuller and his colleagues, as I find their way of systematic investigation how much freedom the dynamics of gravity can have for a given matter content quite interesting.

    Good luck and success in the competition for your essay as well! (Going to read it soon!)

    Cheers,

    Jenny

    Dear Jenny,

    Thank you very much for the reference to Schuller and his colleagues, this is impressive and shows that there's enough freedom as you said, and the corollary I think is that there's way too much freedom in modifying gravity. Another example, in case you worry about singularities, there is enough freedom to resolve singularities and evolve through them in classical General Relativity Singular General Relativity (sorry for self-advertising my work on these issues, which is not modified GR, but a reformulation of semi-Riemannian geometry and GR in terms of quantities that remain finite even at singularities, and still have geometric and physical meaning). Thanks again for the wonderful trip you offered to us, and I wish you success with the contest and your research!

    Cheers,

    Cristi

    Hello Dr Wagner, I liked a lot your essay , I am happy that you work about this dark matter, we need to encircle this matter. I consider this matter very important in my model , I beleive that this matter is cold and permits to balance at all scales our standard model and this cosmological scale like a balance between heat and cold, entropy negentropy, matter anti matter, electromagnetism gravitation even, I consider it encoded in nuclei even and it is like this that I have reached this quantum gravitation in respecting the newtonian mechanics.

    Congrats for your works and researchs,

    best regards

      Dear Steve Dufourny,

      Thank you very much for the nice words! Yes, I also think that a very convincing and vital search for dark matter has to be performed in particle physics and it is quite puzzling that all searches so far have not lead to a significant, clear detection.

      All the best for your research as well to shed further light on the dark side of quantum gravity!

      You are welcome Dr Wagner,

      I agree , we need to have results and proofs, it is not easy to prove it and technologically it is very difficult due to fact that it does not interact with our ordinary matter. Its detection will be an exciting moment inside the sciences Community, I wait this detection.

      Thanks also for your Words.

      Best Regards

      8 days later

      Interesting account of the relationship between what's 'really' going on and what can reliably be inferred about what's going on in the context of gravitational lensing. The fact that the mass distribution of the lens is severely underdetermined reminds me of similar problems in biophysics/systems biology; there, one might be trying to infer a gene regulatory network whose behavior and parameters are severely underconstrained by experiment.

      Your central insight, (which I understood to be) that you can only reliably infer the parts of the mass distribution that you have enough data for, seems like the right takeaway. At the end of the day, if you don't have the data to support your claims, there's no way to know whether you're right or wrong. Though it seems like common sense, it's a point that's easy to forget about when working on tough scientific problems. I see people making strong claims based on bad data all the time.

      By the way, do you think this situation will ever improve? Do we just have to wait for new telescopes/observations/sources of data to constrain these lens models? Or will even those not be enough to reliably understand galaxy-scale mass distributions, without some additional (possibly hard to verify) assumptions?

      John

        Dear John,

        thanks for the nice words! Yes, you correctly understood the message that I am trying to convey. My usual slogan is "Lensing of '69 -- use data not models". You are right, that system biology is definitely another good example for under-constrained problems and a lot of results are highly based on models (judging from my experience working on quality control for a special peptide array assembly method).

        Although I am focussing on the data-driven way of science, I think, at early stages of research in a certain field, a courageous, bold assumption/model is needed to start out with. Without some concrete claim to test, it seems hard to establish a rough idea about a phenomenon and gain enough useful observational evidence, so that the data-driven approach can be set up. Maybe, system biology still needs some time to grow into this state. Luckily, in gravitational lensing, we are on the verge of being able to shift from the model-driven approach to the data-driven approach:

        For galaxy-clusters as gravitational lenses, we are expecting a multitude of multiple images (about 1000 per cluster, as estimated to be observed by the JWST) in the near future, complemented by ongoing X-ray surveys that will also deliver a lot of additional data to break degeneracies.

        For galaxies as gravitational lenses, the number of multiple images per galaxy is not expected to grow so much, but, on the other hand, the multiple images we already have, already give us a lot of information about such lenses. The lens morphology of one galaxy is much simpler than the one of an entire cluster of galaxies. For these lenses, increasing the resolution of the telescopes to resolve small-scale features in the multiple images will allow us to infer small-scale properties on sub-galaxy scale on top of the knowledge we already have e.g. about masses enclosed by the giant arc images on the scale of the entire galaxy lens.

        Best regards,

        Jenny

        4 days later

        Hi Jenny!

        This is a fantastic physical example of something that would be unknowable (an object behind a large object in space) but it actually is (thanks to gravitational lensing). I had never thought of this example before, so I enjoyed reading your essay a lot! Also, I love this point you make: "Beyond that, incorporating new evidence into the model to tighten the prediction or refute underlying assumptions is a computationally intensive endeavor." This is extremely true, and relates to the idea behind Kolmogorov complexity. Basically, it says that data created by a small computer program (or algorithm or physical law) is not complex, but things that could only be created by a very large program are very complex. Because we humans are computationally limited, we are only able to make so many observations that are energetically feasible, which forces us to be more algorithmically-minded.

        Cheers!

        Alyssa

          Dear Alyssa,

          thank you very much for the inspirations and motivating words to go on in this research direction!

          All the best for your essay as well!

          Cheers!

          Jenny

          Dear Jenny Wagner!

          Thanks for the interesting information.

          We are happy to inform you that the essay "The Cosmological Cheshire Cat Predictable and Unpredictable Dark Matter Properties" we really liked it.

          We also believe that cosmology and astrophysics ignore the problems of the methodology of science. Therefore, there are arbitrary constructions. Pavel Poluian published in Russia a monograph "Death of dark matter: philosophical principles in physical knowledge".

          We wish you successful research!

          Truly yours,

          Pavel Poluian and Dmitry Lichargin,

          Siberian Federal University.

            Dear Professor Poluian and Professor Lichargin,

            Thanks you very much for the encouraging words and the so positive ranking!

            All the best for your essay in this contest as well and let's hope that we will live to see a clear evidence for or against dark matter!

            Sincerely,

            Jenny

            Hi Jenny,

            Interesting essay. The basic concept of gravitational lensing is simple, but you nicely describe the complexity of modeling the source and lens structures to match observations. I completely agree with you that model assumptions should be driven by empirical data.

            In my essay, I argued that assumptions should be driven by the empirical data, and that we should eliminate assumptions that are consistent with empirical data but not logically implied by the data.

            In the case you describe, eliminating unnecessary assumptions that are not supported by empirical evidence and therefore do not (currently) make testable predictions, has the highly practical result of greatly reducing the computational complexity of modeling empirical observations.

            Nicely done.

            Harrison

              Dear Harrison,

              thanks a lot for the motivating words and the good synopsis of the relationships between data and model assumptions.

              I just saw that you also replied to my questions below your essay, so let's continue our discussion there.

              Best wishes,

              Jenny

              11 days later

              Hello Jenny,

              How does your essay address the question of the limits imposed by Gödel's and Turing's findings. You do address the practical computability of gravitational-lensing models; however, am I missing the theoretical connection to Gödel and Turing?

              Please let me know,

              Best,

              Luis F Patino

                Dear Luis,

                interesting question! I do not directly mention Gödel and Turing, but the theoretical uncomputabilities are tackled in Section 4: using model assumptions to obtain equations that are not under-constrained anymore, we run into inconsistencies when looking at the resulting lens reconstructions obtained by using different models. Resolving the problem, which lens reconstruction is closest to the real lens, we find that these model assumptions are often hard to support by observational evidence. Hence, I conclude that the best way to resolve the inconsistencies is to only compute the lens properties at positions where data is available. This implies that the lens contains regions in which we cannot compute its properties. Hence, the lens properties there are theoretically uncomputable and all we can get are model-based predictions based on models from which we might never know whether they apply to these cases. So, the theoretical uncomputabilities boil down to a missing-data issue.

                Best regards,

                Jenny

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